A new population of planetary nebulae discovered in the Large Magellanic Cloud – III. The luminosity function

Monthly Notices of the Royal Astronomical Society, Jun 2010

Our previous identification and spectroscopic confirmation of 431 faint, new planetary nebulae (PNe) in the central 25 deg2 region of the Large Magellanic Cloud (LMC) permit us to now examine the shape of the LMC planetary nebula luminosity function (PNLF) through an unprecedented 10 mag range. The majority of our newly discovered and previously known PNe were observed using the 2dF, multi-object fibre spectroscopy system on the 3.9-m Anglo-Australian Telescope and the FLAMES multi-object spectrograph on the 8-m Very Large Telescope. We present reliable [O iii] 5007 Å and Hβ flux estimates based on calibrations to well-established PN fluxes from previous surveys and spectroscopic standard stars. The bright cut-off (M*) of the PNLF is found by fitting a cumulative function to the bright end of the PNLF over a 3.4 mag range. This cut-off is used to estimate a new distance modulus of 18.46 to the LMC, in close agreement with previous PNLF studies and the best estimates by other indicators. The bright-end cut-off is robust to small samples of bright PNe since significantly increased PN samples do not change this fiducial. We then fit a truncated exponential curve directly to the bright end of the function over a 6 mag range and test the curve's ability to indicate the position of M*. Because of the significant increase in the number of LMC PNe, the shape of the PNLF is now examined in greater detail than has previously been possible. Newly discovered features include a small increase in the number of PNe over the brightest 4 mag followed by a steep rise over 2 mag, a peak at 6 mag below the bright cut-off and an almost linear drop-off to the faint end. Dips at the bright end of the PNLF are examined in relation to the overall shape of the PNLF and the exponential increase in the number of PNe. Through cumulative functions, the new LMC PNLF is compared to those from the Small Magellanic Cloud and a new deep local Galactic sample revealing the effects of incompleteness. The new [O iii] 5007 Å LMC PNLF is then compared to our new Hβ LMC PNLF using calibrated and measured fluxes for the same objects, revealing the effects of metallicity on the [O iii] 5007 Å line.

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A new population of planetary nebulae discovered in the Large Magellanic Cloud – III. The luminosity function

Warren A. Reid 1 Quentin A. Parker 0 1 0 Anglo-Australian Observatory , PO Box 296, Epping, NSW 1710 , Australia 1 Department of Physics, Macquarie University , Sydney, NSW 2109 , Australia A B S T R A C T Our previous identification and spectroscopic confirmation of 431 faint, new planetary nebulae (PNe) in the central 25 deg2 region of the Large Magellanic Cloud (LMC) permit us to now examine the shape of the LMC planetary nebula luminosity function (PNLF) through an unprecedented 10 mag range. The majority of our newly discovered and previously known PNe were observed using the 2dF, multi-object fibre spectroscopy system on the 3.9-m AngloAustralian Telescope and the FLAMES multi-object spectrograph on the 8-m Very Large Telescope. We present reliable [O III] 5007 and H flux estimates based on calibrations to well-established PN fluxes from previous surveys and spectroscopic standard stars. The bright cut-off (M) of the PNLF is found by fitting a cumulative function to the bright end of the PNLF over a 3.4 mag range. This cut-off is used to estimate a new distance modulus of 18.46 to the LMC, in close agreement with previous PNLF studies and the best estimates by other indicators. The bright-end cut-off is robust to small samples of bright PNe since significantly increased PN samples do not change this fiducial. We then fit a truncated exponential curve directly to the bright end of the function over a 6 mag range and test the curve's ability to indicate the position of M. Because of the significant increase in the number of LMC PNe, the shape of the PNLF is now examined in greater detail than has previously been possible. Newly discovered features include a small increase in the number of PNe over the brightest 4 mag followed by a steep rise over 2 mag, a peak at 6 mag below the bright cut-off and an almost linear drop-off to the faint end. Dips at the bright end of the PNLF are examined in relation to the overall shape of the PNLF and the exponential increase in the number of PNe. Through cumulative functions, the new LMC PNLF is compared to those from the Small Magellanic Cloud and a new deep local Galactic sample revealing the effects of incompleteness. The new [O III] 5007 LMC PNLF is then compared to our new H LMC PNLF using calibrated and measured fluxes for the same objects, revealing the effects of metallicity on the [O III] 5007 line. 1 I N T R O D U C T I O N The planetary nebula luminosity function (PNLF) describes the number density of planetary nebulae (PNe) within a given system over any given luminosity range based on a prominent emission line such as [O III]. Its most frequent use is as an extragalactic distance indicator where it is the only standard candle that can be applied to all the large galaxies in the Local Supercluster (Jacoby 1980; E-mail: , (QAP) Ciardullo et al. 1989; Ciardullo & Jacoby 1992; Ciardullo 2006). In this role, the distance estimate relies on the shape created by the binning of [O III] 5007 fluxes at the bright end of the PNLF, which appears to be essentially invariant across all galaxies tested thus far, regardless of their morphological type or metallicity (Mendez et al. 1993; Ciardullo et al. 2004). There is a consistent [O III] 5007 high luminosity cut-off beyond which no PNe are observed. The bright cut-off point is identified by fitting an exponential curve to the bright end of the PNLF and is believed to be invariant for all PN systems in all galaxies (Stanghellini 1995; Ciardullo 2006). The concept of using PNe as a cosmological distance indicator was first suggested in the 1960s (Henize & Westerlund 1963; Hodge 1966). It was slow to gain acceptance because individual PNe are not standard candles, distances to local Galactic PNe were very difficult to estimate and extragalactic PNe were severely under-sampled. The first study using an [O III] 5007 emission-line-based PNLF as a distance indicator was performed in 1990 by Jacoby, Ciardullo & Ford (1990a). Today, with large numbers of PNe being discovered in external galaxies (Kniazev et al. 2005; Ciardullo 2006; Jacoby 2006) it is recognized as one of the most important and resilient distance indicators in extragalactic astronomy (Ciardullo 2006). The PNLF method has been proven to be an accurate standard candle (Ciardullo et al. 1989; Jacoby 1989; Jacoby et al. 1990a; Jacoby, Walker & Ciardullo 1990b) and appears to be extremely insensitive to parent stellar population (Ciardullo & Jacoby 1992). The PNLF has other uses apart from distance determination. Establishing the consistent shape of the function provides a basis for estimating the number of PNe in any galaxy, given only the number of PNe in the brightest 3 or 4 mag. A PNLF which comprises a near complete sample of PNe across a galaxy can be used to estimate the luminosity-to-mass and dynamical age relations (Mendez et al. 1993). It has also been suggested as a valuable tool for studies of the initial-to-final mass relation and related mass loss processes in stars of early-type galaxies (Mendez et al. 1993). Finally, the PNLF provides a unique probe into a galaxys chemical and dynamical evolution. The mass and metallicity of the progenitor star largely determine the maximum [O III] line luminosity of the PN (Dopita, Jacoby & Vassiliadis 1992). This makes the shape of the [O III] PNLF an important diagnostic for galactic chemical evolution. The first luminosity function for PNe in the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) was constructed by Jacoby (1980). The advantage of using PNe in these local, external galaxies to create a luminosity function was clear since the distance to all the PNe was essentially equal, faint PNe could still be identified and each galactic system could be studied in its entirety. The majority of bright PNe in each galaxy had already been identified, so the bright end of the PNLF was able to be modelled and successfully used as a distance indicator. However, with a faint cutoff only 6 mag below the brightest, the overall shape of the PNLF, especially at the faint end, was still unknown. The overall shape of the PNLF has previously been difficult to determine for any galaxy due to sample incompleteness at the faint end. With 431 medium to faint PNe together with 162 previously identified PNe now uncovered within the central 25 deg2 of the LMC (Reid & Parker 2006b, hereafter RPb), we can now update the LMC PNLF and provide measured estimates to compare with previous theoretical simulations and other observed PNLFs. The Reid & Parker (RP) PNe were discovered using an Anglo-Australian Observatory (AAO)/United Kingdom Schmidt Telescope (UKST) H (+ effectively [N II]) 40-field mini-survey of the entire LMC, SMC and surrounding regions. The details are provided in Reid & Parker (2006a, hereafter RPa) and will not be repeated here. For details regarding the overall H survey, see Parker et al. (2005) and for the candidate selection technique and follow-up spectroscopic object confirmations, see RPb. The new RP sample will enable both the shape and structure of the LMC PNLF to be analysed in detail for the first time over a much wider 10 mag range. The distance has always been estimated using an empirical (or theoretical) luminosity function and fitting this curve to the data using a statistically robust technique such as 2 or the maximum likelihood method to give the appropriate bright-end position. The bright-end intersection of this curve with the magnitude plane gives the position of M (the brightest possible PN in the system) and the distance modulus. In this work, we use a cumulative function to determine the position of M. We also fit the truncated exponential curve directly to the very complete bright end of the PNLF over a 6 mag range to test its ability to depict PN evolution and indicate distance. Our ability to identify PNe to magnitudes as faint as 25 in [O III], 10 mag below M, gives us confidence that we are largely complete at the bright end of the PNLF. It also largely does away with the need to simulate and extrapolate the PNLF to account for unobserved, faint PNe with (M M) > 5. A brief description of the PN spectra used in this study is provided in Section 2 along with the data reduction procedure. The new method of flux calibration for fibre spectra together with the dereddening procedure is outlined in Section 3. In Section 4 we present the new [O III] PNLF for the LMC using 574 bright to faint PNe and compare the shape to the previous best LMC PNLF from Jacoby et al. (1990a), and the empirical predictions of Ciardullo et al. (1989) and Mendez et al. (1993). In Section 5 the PNLF is constructed using the H line, a good predictor of central star temperature, and compared to our new determination of the traditional [O III] 5007 based PNLF. 2 2 D F A N D F L A M E S O B S E RVAT I O N S 2.1 Brief description A five night observing run on the Anglo-Australian Telescope (AAT) using 2dF (Lewis et al. 2002) was undertaken in 2004 December to spectroscopically confirm LMC emission candidates as PNe and to eliminate contaminants such as H II regions and emission-line stars. 2dF was an ideal choice of instrument for the spectroscopic follow-up of large numbers of candidate emission objects due to its unique ability to simultaneously observe 400 targets (including objects, fiducial stars and sky positions) with 2 arcsec fibres over a wide 2 diameter field area. The large corrector lens incorporates an atmospheric dispersion compensator (ADC), which is essential for wide wavelength coverage using small diameter fibres. The observations provided 4000 spectra. Individual exposure times were mostly 1200 s using the 300B grating with a central wavelength of 5852 and a wavelength range of 36008000 at a dispersion of 4.30 pixel1. These low-resolution observations, at 9.0 full width at half-maximum (FWHM), were used as the primary means of object classification and provided the bright [O III] 5007 fluxes for this study. All fields were then re-observed using the 1200R grating for kinematic studies (RPb) and improved resolution of the [S II] 6716, 6731 lines for determination of electron densities. The 2dF raw data were processed using the AAO 2dF data reduction system, 2DFDR.1 This software can probe the multifibre spectra creating the necessary calibration groups (e.g. BIAS, DARK, FLAT, ARC, etc.). As a calibration exposure is reduced, it is inserted into the appropriate group. The software was instructed to perform a subtraction of background-scattered light prior to the extraction. The background is determined by fitting a function through the dead or unused fibres in the image. A bias frame was obtained for each observed field. The mean of the bias frame has the bias strip removed. This strip is subtracted from the data and the bias strip is trimmed from the data frame. A variance array is then derived from the data with values determined 1 http://www.aao.gov.au/AAO/2df/software.html#2dfdr from photon statistics and readout noise. The resulting frame was then used throughout the reduction process. The data reduction system performs a wavelength calibration using the information from the spectrograph optical model. This is then refined using data from the arc lamp exposure. The lines in the arc lamp exposure are matched against a line list. A cubic fit for each fibre is then performed to the predicted and measured wavelengths of all lines which are non-blended, not too wide and not too weak. This fit is then used to further refine the wavelengths. To perform the sky subtraction, the data are first corrected for the relative fibre throughput, based on a throughput map derived from the dedicated sky fibres. The relative intensities of the skylines in the object data frame are used to determine the relative fibre throughput. This method saves time, as no offsetsky observations are required. The median sky spectrum was calculated from the median of all the sky spectra normalized by their mean flux. Each of these spectra is continuum subtracted, using a boxcar median smoothing with a 201 pixel box to define the continuum. A robust leastsquares fit of the counts was performed in the differential or continuum-subtracted data fibres versus the counts in the differential or continuum-subtracted median sky. Assuming that the sky was the dominant source of emission, the slope of this fit gives the fibre throughput. The robust fit is especially important when dealing with faint objects. The sky fibre spectra in the data were then combined and subtracted from each fibre. Cosmic rays were rejected automatically during the process of combining two or more observations. Our data include spectroscopic observations of a sub-sample of 21 PNe in dense regions of the LMC main bar, undertaken using the multi-object fibre spectroscopic system FLAMES (Pasquini et al. 2002), on the Very Large Telescope (VLT) Unit Telescope 2 (UT2) over three nights in 2004 December. Gratings LR2 and LR3 allowed us to cover the most important optical diagnostic lines for PNe in the blue including [O III] 4363 , He II 4686 , H, and [O III] 4959 and 5007 . Grating LR6 covered the H, [N II] 6548 and 6583 lines as well as the [S II] 6716 and 6731 lines for electron densities. Details are provided in RPa and RPb but we will produce a separate paper examining all 420 objects [including PNe, H II regions and WolfRayet (WR) stars] observed using FLAMES. The VLT FLAMES spectra were reduced using IRAF tasks IMRED, SPECRED and CCDRED for multispec files. Cosmic rays were rejected when combining frames. Using the weighted intensity of the continuum, the IRAF SCOMBINE task was then used to combine the three different wavelength portions of the spectrum into one spectral image. 2.2 Continuing object follow-up Every PN in the LMC sample, both previously known and new, has been re-analysed in order to identify and exclude interlopers which may affect the PNLF. This is particularly important at the bright end for distance determination. H and off-band red images were examined alongside high- and low-resolution optical spectra. In addition, we have searched the SAGE (Meixner et al. 2006), Spitzer maps and overlaid false colours at 3.6, 4.5, 5.8 and 8 m to assist verification. Finally, with mosaic radio maps of combined LMC data from the Australia Telescope Compact Array and Parkes we were able to re-classify three ultra-bright true PNe as contaminants due to their strong radio fluxes of >3 mJy (see Filipovic et al. 2009). This is despite optical spectra which would otherwise strongly indicate a PN. These compact emission objects are now classified as H II regions. For a full list of re-classified objects, see Table 1. In order to provide independent checks of our 2dF data and create the most accurate LMC PN sample possible, we have undertaken a deep multiwavelength study of PN candidates selected from our original discovery list that exhibited unusual characteristics and/or were deemed suspicious. In particular, due to the possibility of minor positioning errors, we have made 78 long-slit observations of previous possible and likely PNe candidates in the RP sample using the Mount Stromlo and Siding Spring Observatories (MSSSO) 2.3-m telescope in order to firm up their status. Using the double-beam spectrograph (DBS) on this telescope, the visible range (32009000 ) is split by a dichroic at around 6000 and fed into two spectrographs, with red and blue optimized detectors. We used the 300B and 316R gratings to obtain a resolution of 4 for each arm of the DBS. Reduction and extraction of 2.3-m spectra were performed using the standard IRAF tasks IMRED, SPECRED, CCDRED and FIGAROs task BCLEAN. One-dimensional spectra were created and the background sky was subtracted. Final flux calibration used the standard stars, LTT7987, LTT9239, LTT2415 and LTT9491. Results are given in Table 1, where eight likely and 12 possible PNe have been re-classified. 3 F L U X C A L I B R AT I O N A N D D E - R E D D E N I N G O F T H E 2 D F F I B R E S P E C T R A Decent flux calibration of the 2dF LMC PN spectra was required in order to combine PN spectra from different 2dF fields and to make meaningful comparisons between fibre spectroscopy and long-slit observations of individual objects. A reliable flux calibration permits quick conversion to magnitudes for luminosity studies. It also permits a study of other nebula characteristics such as excitation class, temperature, density and mass. Since the majority of the spectra were gained by multifibre spectroscopy, it was necessary to verify the reliability of the measured line intensities. A comparison of the same objects observed in two or more overlapping 2dF field-plate exposures revealed variations in line strengths of up to 35 per cent from field to field, clearly rendering the standard reduced spectra unsuitable for combination in their raw state. A further comparison was made between combined 2dF line intensities and published fluxes from the Magellanic Cloud Planetary Nebulae spectral catalogue (MCPN hereafter; Stanghellini et al. 2002).2 The results, using all 65 MCPN which correspond to the RP sample, are shown in Fig. 1. General agreement is evident through an essentially loglinear relation but the scatter is too wide (1 dex) to provide a reliable flux calibration. The variations in the [O III] 5007 line intensities shown are mainly due to the different relative strengths in the [O III] 5007 line from one 2dF field exposure to another in the raw, reddened spectra. A flux calibration of the spectra was required but to achieve this, a reliable method had to be found. Previously, this has proved quite difficult to do with fibre-based spectra (e.g. Mortlock, Madgwick & Lahav 2001; Georgakakis et al. 2004). Below, an effective new method is described, which, in its careful application, is shown to be able to produce reliable flux calibration for the 2dF spectra. 3.1 Flux calibration technique Altogether, 18 overlapping 2dF field-plate exposures were taken in order to cover the entire central 25 deg2 survey region of the LMC. A 2 Magellanic Cloud planetary nebula data are available from http://archive. stsci.edu/hst/mcpn 05 40 28.18 05 40 45.26 05 37 17.35 05 37 14.33 05 37 31.73 05 37 06.38 05 30 26.20 05 28 18.80 05 26 13.74 05 28 08.09 05 24 38.82 05 24 25.18 05 30 54.58 05 30 33.09 05 22 49.80 05 19 56.77 05 20 16.84 05 19 06.88 05 21 29.65 05 21 22.00 05 00 32.23 04 54 24.49 05 03 51.47 04 54 33.78 05 04 47.34 05 19 18.44 70 56 07.1 70 28 06.7 70 07 49.3 66 26 54.61 71 10 48.8 69 47 17.3 70 15 01.5 69 28 15.3 69 25 45.1 69 10 21.9 69 04 13.7 69 39 06.3 68 34 22.4 66 57 41.5 66 40 55.5 70 39 03.6 68 45 10.1 68 21 34.4 67 51 06.6 67 47 28.6 70 00 49.0 69 29 42.5 68 57 23.7 69 20 35.7 66 40 30.3 69 47 17.2 IR comparison of line intensities from overlapping areas revealed that each field plate/observational set-up resulted in its own individual spectrum intensity scale. In addition, the 400 spectra from each field were fed to two identical spectrographs. Although they were well matched, small instrumental differences were noticeable. Overall, the combined use of two different field plates, each sending spectra to two different spectrographs and CCD cameras, resulted in the observed deviations seen when comparing previously published fluxes with line intensities for the same objects from multiple 2dF fields (Fig. 1). Experiments were undertaken in order to find the most reliable method of flux calibration using the observed line intensities. The best results were obtained by individually calibrating each spectral line on each field plate from each CCD camera to raw MCPN fluxes gained from Hubble Space Telescope (HST) exposures. The known PNe included and observed on each field plate were used as flux calibrators for each individual measured field. In order to extend the reliability of the [O III] 5007 flux calibration to >19 mag, the [O III] 4959 and H 4861 lines (Shaw et al. 2006) were included in the calibration. All three lines are close enough in the optical spectrum to produce reliable flux ratios. The individual H and [O III] 4959, 5007 2dF line intensities for known PNe observed for each CCD and each field-plate exposure were graphed against the individual published fluxes for the same lines (e.g. Fig. 2). The same method was applied to our multifibre spectra from VLT FLAMES. All 2dF and FLAMES fields purposefully contained sufficient PNe with well-calibrated fluxes to enable this process. The agreement of flux-calibrated PNe from each spectrograph/fieldplate combination was considered strong enough (within 0.2 dex; see Fig. 2) to allow its application to all the H and [O III] 4959, 5007 emission lines for other PNe observed in the same field. In each case, a line of best fit was derived and the underlying linear equation extracted. This equation became the calibrator for each emission line in each uncalibrated PN from the CCD and individual 2dF field-plate exposure used. The equation was applied to each spectrum with a detectable line intensity in that field. Fluxes for LMC PNe from other catalogues (Meatheringham et al. 1988; Jacoby et al. 1990a; Leisy et al., private communication) were also included in order to build up the number of calibrators per field. Where only a de-reddened flux value was published, a relative reddening was applied in order to make a better correlation. Where two or more published fluxes were found for the same PN, stronger comparisons could be made. Each independent survey showed a mean agreement to within 0.2 dex, slightly increasing as the magnitude grew fainter. A comparison between calibrated [O III] 5007 fluxes from 2dF and published fluxes from the MCPN (Jacoby et al. 1990a; Leisy et al., private communication) is shown in Fig. 3. The agreement ( < 0.2 dex) is very good across all surveys, especially since they represent space versus ground-based observations in some cases with a variety of detectors and measurement methods. It also shows that the 2dF-calibrated fluxes remain within the < 0.2 dex agreement. The mean slope of the fit (2dF/MCPN) is 1.01, where 1 would represent a perfect match. The median is exactly 1 and the standard deviation = 0.12 dex. A spread in published line fluxes for the same PN is common but helps us to establish the uncertainties. Since the MCPN catalogue contained the largest number of PNe and the raw fluxes were as measured (not de-reddened) these were given preference where irregularities became obvious. The MCPN set also includes some ground-based fluxes from ELCAT (Kaler, Shaw & Browning 1997) available at http://stsdas.stsci.edu/elcat/ where the spectra are uncorrected for extinction. The intention was to provide self-consistent fluxes for all the 2dF observations. A calibrated quality and consistency check was then performed where fluxes for several PNe observed on more than one field-plate exposure (due to the overlaps in 2dF pointings across the survey) were compared for consistency once the new flux calibration had been applied to each field. Fig. 4 shows an excellent match in the high as well as the low flux regimes, proving that reliable and consistent fluxes can in fact be achieved this way. The equation to convert line intensities to fluxes in each field was then applied to the 2dF and FLAMES [O III] 5007 line intensities for each corresponding field. Further line-to-flux calibration equations were then derived for other spectral lines such as H which, together with H, controls the de-reddening. A similar procedure was then carried out for each of the spectral lines to provide their individual flux calibration. 3.2 Reliability of the line intensities and fluxes At the distance of the LMC, most PNe are compact and pointlike in ground-based observations allowing most of the flux to fall within the 2 arcsec diameter 2dF fibre. This is despite the larger reported angular diameters, which suffer from point spread function growth as a function of source intensity and include the very faint surrounding haloes. The extended outer haloes typically represent about 1000th of the flux of the inner PN (Corradi et al. 2003). Clearly, the central region of LMC PNe contains the majority of the light. There are 70 PNe out of our sample of 589 with inner shell diameters which exceed 2 arcsec by more than 1 arcsec. These are among the brightest LMC PNe and, despite the anticipated loss of light by 2dF spectroscopy, are still able to be accurately flux calibrated. For example, the loss of light from bright PNe is evidenced by the bright turnover in Fig. 1. However, individual spectrograph calibration, which includes the brightest PNe in each field (Fig. 2), is able to largely correct for the assumed loss of light at the highest magnitude level. It does this by calibrating the increasing brightness received by the fibre directly to a well-established flux level. This level will vary for each spectrograph/plate observation. For this reason, calibration of 2dF spectra to a single standard star would produce erroneously low fluxes for bright and extended LMC objects. In the same way, if a long-slit is too narrow, flux levels will be underestimated (Jacoby & Kaler 1993). This may be the cause of some small deviations in previously published fluxes for LMC PNe. Flux ratios of doublet or close lines from the central shell of the PN, such as the [S II] ratio used for the estimation of nebula densities, are largely consistent across the nebula and do not require flux calibration. The [S II] 6716, 6731 lines were measured from the high-resolution 1200R spectra. All other lines, into the blue, were measured from the 300B spectra. 3.2.1 Error estimations The line intensities measured from 2dF 300B and 1200R spectra have two main sources of error. The first is due to an uncertainty in where to place the continuum level for line intensity measurement. Since the author performed all the line measurements, they were all performed in the same manner, at the same base positions for any line, relative to the continuum and/or noise. Repeated measurements, however, indicated that an increased error estimate should apply to lines with a signal-to-noise ratio (S/N) of 5 or less. The error estimate increases from 10 per cent at S/N = 5 to 40 per cent at S/N = 3. About 5 per cent of H intensities are low enough that the increased measurement error should be applied. This is never applied to the [O III] 5007 line used for the PNLF in this study. These lines mostly have intensities of >4 H and have repeat error estimates no greater than 3 per cent for the faintest PNe. This system, however, provides a general error estimate for the line measurements in all 631 PNe. Secondly, there are difficulties in placing exact errors on the individual lines, due to the inherent variations in detector response with wavelength. Luckily, this is the same for all objects on any given field-plate exposure and can therefore be estimated from the response curve. The exposure times are also exactly the same across any given field and most of the exposures for the different fields are also of the same duration. With a small error included for these two variables, the remaining difficulty is the different absolute fluxes which cause a variation in the S/N. One fortunate aspect of having a relatively large number of PNe re-observed on different 2dF fields is that a comparison between two or more observations of the same object is possible. A comparison of line intensity ratios for the same PN, observed on two or more fields (Fig. 4), gives an agreement to within 0.2 dex with = 0.15 using a sample of 81 repeated PNe. This discrepancy includes ratios between strong lines and between strong to weak lines. In addition to the estimates for spectral line errors, the flux calibration adds an extra level of error. With a very good calibration of the 300B spectra to the MCPN fluxes (Fig. 2), the average difference to the published fluxes following calibration is 0.18 dex with = 0.5. These published fluxes will themselves have both measurement and systematic errors, and these have been estimated at 0.2 dex through direct comparison. An allowance is made for these errors to increase with decreasing flux. This estimated increase is based on the standard deviation in the calibrated fluxes increasing to 0.3, = 0.2 dex. With ground-based spectroscopy, atmospheric dispersion can produce an extended object on the slit where blue light is separated from red light, also received by the detector (Filippenko 1982). This effect can cause a systematic difference when comparing standard stars observed at a lower airmass. It can also produce larger images in the blue than in the red due to more blue light being captured by the fibre. The increase is estimated as (1/)0.2 (Fried 1966; Boyd 1978). To overcome this problem, 2dF has an ADC which largely compensates for this. With our flux calibration technique, however, lines from different regions of the optical spectrum are individually calibrated to HST-based fluxes, largely circumventing problems of atmospheric dispersion and the differential airmass of standard stars. A correction for extinction is applied using the Balmer decrement, where the fixed ratio of 1:2.86 applies between H and H in the absence of extinction. This corrected ratio is discussed in detail in the following subsection. In addition to the photometric and flux calibration errors, an error estimate for the inclination of the LMC to the line of sight may be included. This could be as much as 0.04 mag (Jacoby et al. 1990) based on a 1 depth uncertainty. One further problem can cause errors in flux estimations for LMC PNe. The LMC is filled with faint stars and diffuse emission of varying intensities. For individual slit spectroscopy, it can be extremely difficult to find a region of blank sky along the slit. In the case of 2dF fibre spectroscopy, we dedicated 40 fibres to specially selected sky positions. These positions represented average values of background sky in each field observed. The H map provided the most appropriate positions. For each field, the 2DFDR reduction program sampled and averaged these regions before applying the sky subtraction to the objects. The resulting error estimates for [O III] 5007 as a function of line measurement and flux calibration are based on results from Figs 3 and 4. Line measurement errors increase from 2 to 10 per cent and flux calibration errors increase from 6 to 20 per cent. The line measurement error also includes an estimated error based on a function of the discrepancy between repeated, field-to-field and line ratio measurements. 3.3 Corrections for extinction and reddening Extinction of light from distant objects is mainly the result of interstellar dust. The light is both scattered and absorbed, which increases the interstellar extinction towards shorter wavelengths. The amount of extinction will differ for each object and needs to be corrected to gain true fluxes. In the optical regime, the H/H ratio was used to determine the extinction constant c(H) (i.e. the logarithmic extinction at H for each nebula). These hydrogen transitions are the strongest and easiest to accurately measure in the nebula spectrum and therefore provide a better estimate than other H lines. The observed H/H ratio, when compared to the recombination value of 2.86 (Aller 1984), gives a logarithmic extinction at H of This estimation is based on the relationship between observed and intrinsic intensities: Iobs(H) = Iint(H) Iint(H) 10c(H)[f (H)f (H)], where [f (H) f (H)] = 0.34 from the standard interstellar extinction curve given in Osterbrock (1989) and c(H) is the logarithmic extinction of H. The intrinsic ratio is mildly dependent on temperature: for Te between 2500 and 20 000 K, the ratio varies from 3.30 to 2.76 (Osterbrock & Ferland 2006). The value of c and I() for all other lines was then used to correct for interstellar extinction using the galactic extinction law Icor(H) = Iobs(H) from Whitford (1958) in the form of Miller & Mathews (1972): Icor() = Iobs()10c[1+f ()]. Reworking this equation for the H line, all other lines could be corrected for reddening using Application of the Balmer decrement ratio of 2.86 between the H and H lines is able to correct the spectrum in terms of the required ratios; however, the degree of c is dependent on flux calibration for each of these lines and any internal inconsistencies. For fibre-based observations, the uncertainty in c(H) is extremely difficult to estimate as there may be small inconsistencies between fibres resulting from light transmission and position of the fibre on the plate. These will have an effect on the reddening-corrected fluxes. Calibration of both the red and blue sides of the spectra each show a maximum uncertainty of 0.2 dex. This is consistent with the uncertainty found comparing published fluxes, indicating that internal inconsistencies are low. The reddening law of Howarth (1983) where E(B V ) = 0.689c was also employed. It then follows that A5007 = 3.5 E(B V ) and A4861 = 3.63 E(B V ). When estimating the errors, flux calibration is given predominant consideration together with the wide spectral range between the H and H lines. This is estimated for H using the same method of 2dF flux calibration described above where the H spectral line in each nebula was individually compared to published H fluxes for the same objects. The estimated uncertainty in c(H) as a result of combined maximum errors in line measurement and flux calibration estimations is <7 per cent. The optical image of every PN was inspected for the presence of diffuse H II across its immediate field. This was used as a means of testing the environment of PNe with high values of c(H) in the range from 1.4 to 2.0. The available 8 m Spitzer SAGE image (Meixner et al. 2006) was also examined for areas where infrared emission extended across individual PNe. This was added confirmation that foreground dust could play a significant role in flux determination for some LMC PNe. The intensity of the ambient emission in H was then measured in counts, where, for a measure below 3 , the noise begins to have a significant effect on the observed PN flux. Velocity measurements (RPb) for PNe and the velocity for the H I disc in the vicinity of each PN were then examined to estimate whether the PN was foreground, within or background to the bulk of observed emission. From the list of 292 newly discovered true PNe, 11 were found in areas of relatively strong H II emission. Of these, only two were identified as lying beyond the visible emission. Of the newly discovered PNe, all four likely PNe in areas of strong, dense H II emission (>3 the noise) exist within or beyond the H I disc. All of these PNe have values of c(H) > 0.8. Due to the suspected low metallicity of many of the new, faint PNe in the RP LMC sample, as well as the generally low metallicity of all PNe in the LMC compared to the Galaxy (Leisy & Dennefeld 1996), we also consider the effect of collisional excitation on the H line (Stasi n`ska 2002) and the effect it may have on the extinction calculation. Because PNe are excited by power-law photoionization or shock-heating from the central star, collisional excitation and self-absorption can affect the intrinsic Balmer decrement. This can be caused by high Te resulting in the H/H ratio no longer holding the canonical recombination value of 2.86 (Osterbrock & Ferland 2006). It is possible that this scenario applies to some PNe in the LMC. Since the de-reddening procedure involves H, there may be some overestimation of the extinction c(H). It has been shown that this error, which is independent of extinction, can be large when the lines have far separated wavelengths (Stasin`ska 2002). In low metallicity nebulae, there may be a range of evolutionary sequences where H/H is significantly larger than the accepted recombination value. The resulting error has been estimated to be as high as 10 per cent. Since there is no precise means to estimate the amount of correction required, care was taken to identify faint, low-mass PNe with high Te and extremely high H/H > 10 ratios which may have been affected by power-law photoionization or shock-heating (see fig. 2 in Stasin`ska 2002). In the LMC sample, six PNe with c(H) > 0.8 and Te > 25 000 K have been identified. They are marked as footnote b in Column 3 of Tables A1 and A2. Where inconsistencies (such as ultra-low N/O abundances) are found in one of these PNe (RP1584), the cause can be traced to collisional excitation or self-absorption affecting c(H). The derived values for c(H) are shown in the histogram of Fig. 5. Despite low extinction towards the LMC PNe, we still find a few PNe with values of c reaching as high as 1.6. Most of the brighter previously known LMC PNe generally occupy the lower range from 0 to 0.6; however, some fainter Jacoby (1980) PNe in dusty, nebulous areas have c(H) values up to 1.0. Results for bright LMC PNe agree with values derived using fluxes in the MCPN catalogue. The majority of these PNe have c(H) between 0 and 0.6 but also range as high as 1.6. For all the RP PNe, there is a peak at 0.4 with the largest proportion of PNe occupying the range of 0.30.5. The mean extinction of 0.4 corresponds to E(B V) = 0.31 mag, which is considerably higher than the line-of-sight reddening of 0.0740.11 for stars in the LMC (Caldwell & Coulson 1986). It is also higher than a value of 0.2 found for LMC PNe by Herrmann & Ciardullo (2009) using a pre-RP catalogue sample to produce a basic skeleton of our Fig. 5 plot. They cover less than half the magnitude range with lower sampling and base the Balmer decrement on estimated H values. None the less, their sample of the bright end also shows evidence of an increase in extinction beginning at 3 mag below the brightest. Somewhat higher values of c(H) in the RP sample are to be expected due to their faint magnitudes and often dusty environments. It does suggest that average internal dust reddening may be as great as 0.5 mag. Most of the dust is expected to consist of carbon-rich and dredged-up material, the quantity of which will have dependence on the mass and metallicity of the central star (Dopita et al. 1992). PNe at the bright end mainly occupy the medium excitation range (Reid & Parker 2006c) with central stars ranging in temperature from 80 000 to 126 000 K making them very efficient at converting central star luminosity to luminosity in the nebula. Necessary corrections for c(H) were applied to the whole LMC sample on an individual object basis. The derived values of c(H) for each previously known and newly discovered PN are given in Tables A1 and A2, respectively. When deriving the distance to an extragalactic source using the PNLF, we use the raw [O III] 5007 fluxes corrected only for foreground reddening. This is because none of the measured PNLFs and simulations to date has included the effects of circumstellar dust. Most surveys have been based on the [O III] 5007 line. The H line, required to derive c, is extremely difficult to measure from individual objects in external galaxies. Circumstellar dust therefore plays a large part in determining the observed brightness of the PNLFs bright end. In order to make the correct comparison, our PNLF for distance determination has only been corrected for foreground reddening. The contribution of Galactic dust was removed assuming a foreground reddening value of E(B V ) = 0.074 (Caldwell & Coulson 1986). 4 T H E N E W P N L F F O R T H E L M C The PNLF is a plot of the total number of PNe in a defined volume at a particular magnitude at a given point of time. Since the [O III] 5007 line is generally the brightest line optically emitted by the nebula, it has traditionally been used to plot the PNLF. The raw fluxes are listed in Tables A1 and A2 for the 164 previously known and 432 newly discovered PNe, respectively. The [O III] 5007 fluxes for the observed PN sample, corrected only for foreground reddening, have been transformed to the magnitude system using the relation provided by Jacoby (1989): m5007 = 2.5 log F5007 13.74. Using the magnitudes, the luminosity function can be displayed through several methods. In principle, we can get an approximation to the luminosity function (l) by plotting the number of PNe found within any number of equally spaced luminosity bins. Using this method, all previously known and new RP PNe within the central 25 deg2 of the LMC have been plotted into one of 54 bins, each 0.2 mag wide. This luminosity function, based on the foreground de-reddened flux of the [O III] 5007 emission line, in magnitudes, is shown as a histogram in Fig. 6. The magnitude assigned to each bin represents the magnitude at the central position of each bin. Poisson error bars have been included. In the first PNLF derived for the Magellanic Clouds, Jacoby (1980) using a sample of 41 PNe demonstrated the theoretical exponential function of Henize & Westerlund (1963), whereby a PN is treated as a uniformly expanding homogeneous sphere ionized by a non-evolving central star. It follows therefore that the number of PNe in each luminosity bin is proportional to the time those PNe spend at that luminosity (Jacoby 1980; Ciardullo et al. 1989, 2004). This may be represented by an exponential curve (Henize & Westerlund 1963) with a sharp truncation designed to accommodate the bright end (Ciardullo et al. 1989). The resulting curve is described by N (M) e0.307M {1 e3(MM)} In this equation, the key parameter M is the absolute magnitude of the brightest possible PN. The limit to the high luminosity of the [O III] 5007 line is mainly due to the initial mass of the progenitor star and its evolution to a white dwarf (WD) as a function of time in the ranges of 311 Gyr (Jacoby 1989; Mendez et al. 1993; Stanghellini 1995; Jacoby 1997; Richer, McCall & Arimoto 1997). This PNLF model has been demonstrated as an excellent standard candle when compared to other distance indicators (Ciardullo 2006). It has been shown that there is a weak correlation between the luminosity of M and the metallicity of a galaxy (Ciardullo & Jacoby 1992; Dopita et al. 1992; Richer 1993; Ciardullo et al. 2002, 2005). This trend has been modelled by Dopita et al. (1992), showing that M is bright for solar oxygen abundances but fades where metallicity increases or decreases away from solar. The correction for M is given by where solar metallicity is assumed to be 12 + log(O/H) = 8.87 (Grevesse, Noels & Sauval 1996) (see Ciardullo et al. 2002 for additional details). The metallicity of the LMC has been determined from the emission lines of H II regions. A mean value of (12 + log[O/H]) 8.45 0.11 from LMC H II regions was found by averaging mean values from Dufour, Shields & Talbot (1982), Dennefeld (1989), Monk, Barlow & Clegg (1988) and Ferrarese et al. (2000). With this value, using the metallicity dependence of Dopita et al. (1992) we find a metal dependence (M ) of 0.1 mag. In the LMC, the estimated metallicity is low compared to the Galaxy. The low oxygen abundance in LMC PNe, whether inherent or through depletion, also raises the electron temperature thereby increasing the rate of collisional excitations per ion. Since oxygen is a coolant, a decrease in oxygen abundance only decreases the [O III] 5007 flux by roughly the square root of the difference in abundance (Jacoby 1989). The central star at the core of a PN affects the luminosity the opposite way to low metallicity. Low metallicity in the progenitor star produces a more massive radius with greater UV flux (Lattanzio 1986). This energy compensates for the decreased emissivity of the nebula. The total [O III] 5007 flux then becomes somewhat independent of metallicity. In order to reveal the effects of dust, internal to the LMC and the environment of each individual PN, we include another PNLF (see Fig. 7) where the same objects have been corrected for what we will refer to as internal extinction using the Balmer decrement. Both functions have been plotted on the same scale in order to clearly demonstrate the offset caused by extinction. A comparison of the foreground de-reddened (Fig. 6) and internally de-reddened (Fig. 7) plots shows a highly consistent shape in the function. Unfortunately, with most external galaxies, it is almost impossible to correct each observed PN for the effects of internal extinction. Remarkably, however, Fig. 7 implies that if the foreground de-reddened PNLF is simply shifted by applying 1 mag of extinction to each object, the internally de-reddened PNLF is recovered, so that the shapes of the observed and de-reddened PNLFs are essentially identical. This result is rather surprising since although individual object extinctions vary between 0 < c(H) < 1.3 (02 mag), from a global perspective, the PNLF responds as though each PN has c(H) = 0.4. The magnitude range and shape of the plot (Fig. 7), corrected for internal extinction, have only shifted 1 mag brighter than those corrected for line-of-sight reddening. It implies that the one-dimensional PNLF of external galaxies can be modelled by simply applying a mean offset. In order to observe the effects of internal dust extinction within the LMC PNe, the foreground de-reddened [O III] 5007 magnitudes are plotted against extinction in Fig. 8. PNe in the brightest 4 mag have low to medium extinction (0 to 0.6) while PNe with medium to high extinction (>0.6) are only found >4 mag below the brightest. These highly reddened faint PNe probably have intrinsically fainter cores which have evolved over a longer time-scale. It is therefore possible that the dust properties of these objects may be rather different to those of the higher core mass objects. Most of the PNe, across the full magnitude range, are located in the low to medium extinction range. This suggests that, regardless of the diminishing intrinsic luminosity as a consequence of age, a large proportion of these PNe with high-mass cores have evolved fairly rapidly and their surrounding circumstellar envelope, which provides the extinction, has remained of similar opacity. This is not to say that there has not been evolution within each nebula such as decreasing electron density against changes in mass. Although the trends shown in Fig. 8 are strong, there are selection effects which may come into play. A further study including electron densities, masses and dynamical ages will be required in order to reveal these effects and understand the role played by circumstellar dust. 4.1 New PNLF-based distance estimate to the LMC The standard means of determining the distance to a galaxy using the PNLF has been previously confined to the brightest 1 or 2 mag. We now extend this range to the brightest 3.4 mag. With a good estimate of completeness to this magnitude depth, we avoid including the effects of any possible dip in the function, 4 mag below the brightest. To estimate the distance, we use the 2 method to fit a model PNLF to the observed PNLF corrected for foreground reddening (Fig. 9). The bright cut-off absolute magnitude (M) has been estimated as M = 4.44 0.05 (Ciardullo et al. 1989, 2002; Jacoby et al. 1992). We adopt this value because it reflects the theoretical dependence of M on metallicity (Dopita et al. 1992) and in order to make a direct comparison to previous LMC PNLF distance estimates using this value. This gives us a distance modulus of 18.46 0.2 for the LMC where the magnitude errors are used as systematic uncertainties for the distance modulus. The error estimate allows for errors in line measurement and calibration, a 1 error in the fit, uncertainties in the distance calibrator galaxy, M31, and the shape model of the PNLF. The previous best PNLF for the LMC using real LMC PNe for a distance estimate is shown as fig. 4 in Jacoby et al. (1990b). This figure includes the model exponential curve of Ciardullo et al. (1989). Fig. 6 shows that we have only added one extra PNe to the bright end of the function. This being the case, it is not surprising that the distance modulus does not deviate greatly from the distance modulus of 18.44 previously determined by Jacoby et al. (1990b). Speculation has arisen as to whether the shape of the PNLF itself can be used for distance determinations (e.g. Mendez & Soffner 1997). Only a deep and complete survey can answer this question. Although it is extremely difficult to place an exact limiting magnitude on our survey data, we are confident that we are complete to 7 mag below the brightest. We are therefore in a good position to test if the truncated exponential curve (Ciardullo et al. 1989) is a good predictor of the PNLF shape and can be used as a distance indicator. In order to test this, we fit the theoretical truncated exponential from Ciardullo et al. (1989) to the brightest 6 mag of the PNLF using the LevenbergMarquardt fit method to achieve the best-fitting position. To check how well the observed PNLF follows the theoretical exponential curve (equation 6) we ran the KolmogorovSmirnov (KS), AndersonDarling and 2 tests since all three work very well with binned data. Three assumed distributions were tested in order to find the best fit. The results represent values of the 0.2 mag binning, and no poor fitting data points have been smoothed or excluded. The KS test, based on the largest vertical difference between the theoretical and empirical cumulative distribution functions, found a statistic of D = 0.11 down the brightest 6 mag assuming an exponential distribution. The threshold value of the significance level (P-value) of 0.677 between the observed and theoretical functions means that the null hypothesis (H0) that the observed distribution does not match the theoretical distribution must be accepted with a 95 per cent confidence limit. The major departure from the theoretical curve occurs 1.5 mag below the brightest PN and lasts for 1.5 mag. This may be referred to as a dip in the observed function and will be discussed in Section 4.2. Despite peaks and troughs in the observed function, if one were to estimate PN populations simply by integrating equa Table 2. Summary of the goodness-of-fit tests between the observed and empirical PNLFs. Extinction Foreground Foreground Foreground Internal Internal Internal Distribution Exponential Normal Johnson SB Exponential Normal Johnson SB AndersonDarling tion (6) over 6 mag one would overestimate the population by only 3 per cent. The same objects, after correction for internal extinction, are plotted in linear space (Fig. 10) in order to fit and test the truncated exponential curve while examining the bright end with increased detail. Error bars represent Poisson statistics. The same truncated exponential curve again has a mean bin-to-bin agreement of 87 53 per cent against the observed data over 6 mag. The goodness-offit tests between the observed and empirical PNLFs are summarized in Table 2. Clearly, the exponential increase in the number of PNe to be found with decreasing magnitude, first suggested by Henize & Westerlund (1963), is equally invalid once internal extinction is removed. The close statistical results are also further proof of the identical shape of the observed and internally corrected PNLFs, discussed in Section 4. An up-to-date compendium of distance estimates to the LMC is shown in Table 3. These results represent a variety of calibration objects, methods and extinction estimates. The PNLF method has been shown to be a very robust method (Ciardullo et al. 2005) across all galaxies tested. Our confirmed distance estimate of 18.46 0.20 is in very good agreement with Cepheid and RR Lyrae distances derived from optical observations. It is also in close agreement with the previous PNLF distance estimate of 18.44 0.18 as found aLMC short distances. Distance modulus by Jacoby et al. (1990a) where the underlying universal luminosity function is used as a probability distribution function. The estimated distance was given by the abscissa of graphed maximum likelihood solutions. It is extremely encouraging that a direct fit to the bright end of the PNLF using our considerable new data over the first 6 mag has produced a result in keeping with the previous LMC PNLF work using far fewer PNe. This important result shows that the bright-end cut-off fit is robust to far less complete PN samples obtained for a galaxy and that its use as a standard candle is not compromised by modest sampling of the bright end of the PNLF. The 1990 International Astronomical Union LMC distance consensus of 50 kpc was presented by Mould (1990). Using an absolute magnitude of 4.44 for M in the LMC, the brightest PN would need to have an apparent magnitude of 14.05 to equal the 50 kpc distance. An increase in the value of M would move the PNLFbased distance towards higher distance estimates. Our new PNLF distance indicator places the LMC at precisely 49.2 0.2 kpc, very close to 48.7 2.32 kpc, which is the mean distance and mean error found from all the distance results shown in Table 3. 4.2 The shape of the PNLF Since the PN population in the LMC is now one of the most complete, observed samples at fixed distance available, modelling of the PNLF can be undertaken using this population. Although this study has extended the luminosity range to far fainter limits than previously achievable, and is therefore more complete, there still exists the possibility that the most luminous PNe are over-represented due to all surveys being flux-limited. The large number of PNe now available from the RP sample has a strong effect on the shape of the PNLF fainter than 5 absolute magnitudes below the brightest. When examining the overall shape of the LMC PNLF, it is important to remember that the sample includes PNe that are both optically thick and optically thin, hydrogen burners and helium burners, Type I and Type II PNe (Peimbert 1978), and young, middle-aged and old with different evolutionary characteristics and morphologies (Dopita et al. 1992; Vassiliadis & Wood 1994). It is beyond the scope of this paper to undertake evolutionary modelling of the PNe at this stage; however, the shape of the PNLF can now be examined in detail. Unless specified, we use the PNLF, corrected for internal extinction when discussing the shape of the PNLF and any evolutionary models. The peak number of PNe occurs at a magnitude of 19, which is half a magnitude fainter than half the magnitude range of the sample. The distribution on both sides of the peak is rather different. The bright end is relatively flat for the initial 3.5 mag before a steep and almost constant rise to the peak. The faint end drops off far more gradually with only three detections in the faintest bin. The rapid rise at the bright end, from 17.5 mag (4 mag below the brightest), is a new major feature. It has not been seen before in an observed sample of PNe in any galaxy but was previously predicted due to the mean age of 38 Gyr for stars in the LMC (Stryker & Butcher 1981; Frogel & Blanco 1983; Hyland 1991). This places the largest number of PNe close to a luminosity of log(L/L ) 3.653.75 in keeping with previous predictions (Dopita et al. 1992). This rise in the function coincides with the faint end of a sudden dip or inflection point found in some extragalactic studies (Ciardullo 2006). Importantly, we do not see a strong dip (also known as the Jacoby dip) hinted at in the earlier but far more incomplete LMC PNLF (see Figs 6 and 7). Although there is a small decrease in the number of PNe between magnitudes of 16.4 and 17.2, it is not a strong feature. Rather, the function is relatively flat until 17.2 mag. The dip in the number of PNe occasionally seen at 3.54 mag below the bright cut-off (e.g. Jacoby & De Marco 2002) has been attributed to the decline in luminosity of the central star as it starts descending the WD cooling track (e.g. Frew 2008). Alternatively, it may indicate that the PN evolutionary phase can occur at different luminosity levels for stars of different progenitor masses where 4 mag below the brightest is representative of the largest group. It may also be evidence for the bimodal luminosity function expected from post-asymptotic giant branch (AGB) stars (Vassiliadis & Wood 1994). Interestingly, the PNe populations sampled in star-forming galaxies exhibit a broad dip at 1.52 mag below the brightest. Both PNLFs (Figs 6 and 7) corrected for foreground and internal extinction, respectively, show some convincing evidence for the existence of this dip. This is characteristic of galaxies and models in which the evolution of [O III] 5007 in PNe is governed by the rapid evolution of a high-mass core. By graphing the PNLF into 0.4 mag bins as a smoothed frequency distribution (Fig. 11), it becomes easier to identify any possible evolutionary dips in the shape of the PNLF. By including the truncated exponential curve, we have a clearer impression of the dip between 15 and 16 mag. Overall, however, we see a relatively flat distribution over the brightest 34 mag followed by a steep rise in the function. It agrees very well with the theoretically simulated PNLF created by Mendez et al. (2008), where there is a sudden rise at the bright end followed by a very gradual decline for 4 mag and a steep rise over 2 mag to a peak in the function. The reason for the function remaining relatively flat for 4 mag may be related to the bright LMC PNe being a combination of H-burning and He-burning central stars with a small proportion of low-mass H-burners. Fig. 7 in Mendez et al. (2008) shows that the function steadily rises with no dip if the simulation includes too many central stars with masses as low as 0.55 M . It conversely dips too low if there are too many high-mass central stars. The relatively steady distribution over the brightest 4 mag of the LMC PNLF found through this study adds weight to the probability that central star mass plays a major role in shaping the bright end, especially if we accept that the steep rise of 4 mag represents the point at which the central star starts its descent down the WD cooling track (see Sch onberner et al. 2007). The number of PNe identified in our deep H survey begins to decline at magnitudes m5007 > 19. Is this due to incompleteness or is there a real turnover close to this point in the function? The decline begins rather steeply over the next 4 mag but clearly becomes increasingly incomplete in the faintest 2 mag of the survey (23 25 mag). If the theoretical and empirical PNLFs (Ciardullo et al. 1989; Jacoby 1989) were employed beyond the peak magnitude of 19 as found in this work, they would predict the presence of a large number of PNe by a magnitude of 25. Are they there? Is there sufficient mass in the LMC to permit the co-existence of tens of thousands of faint PNe at this end of the function? It would be very surprising if we have missed detecting hundreds of PNe more than 5 mag brighter than our detection limit. Our PNe were selected using a deep H filter (see RPa) which includes the [N II] 6548 and 6583 lines. Deep PN surveys of the LMC have already been conducted using [O III] filters with enormous success (RPa). Our survey using H and [N II] has allowed us to discover a large number of PNe with extremely low [O III] levels. Where [O III] is low in abundance, [N II] is normally enhanced (RPa; RPb), permitting us to uncover a large population of PNe that would be very difficult to discover in an [O III] survey. Even so, it is always possible that a deeper [O III] survey and new extraction techniques may uncover more PNe. The only really hard constraint on the number of PNe to be found in the LMC comes from stellar evolutionary theory. The number of PNe should not be greater than the product of the stellar evolutionary flux (2E11 stars yr1 L1) times the LMC bolometric luminosity times the PN lifetime. Our previous work (RPb) estimates the existence of 956 141 PNe in the LMC, in close agreement with an earlier estimation of 996 by Jacoby (1980). The derived luminosity-specific number of PNe () in the LMC according to Buzzoni, Arnaboldi & Corradi (2006) is given as log = 6.57 0.04, representing 1040 60 PNe. We therefore suggest that a turnover is likely to occur at some mid-point in the function. At this stage, we can safely say that equation (6) represents the bright end of the PNLF with a range of 6 mag. After this initial 6 mag and the peak in the PNLF, there is likely to be a flattening or even a decline in the number of PNe to be found. Only further deep surveys will be able to solve this issue conclusively. 4.3 Luminosity implied time If we accept that the number of PNe in each luminosity bin is generally proportional to the time those PNe spend at that luminosity (Jacoby 1980; Ciardullo et al. 1989, 2004), then we may conclude that PNe evolve away from the brightest 3 mag at a proportionally fast pace. The time spent at each luminosity bin is plotted in Fig. 12 where each luminosity bin is 1 mag wide. This histogram ignores the possible incompleteness of the faint end. It is also insensitive to any intrinsic variation and birth-to-death luminosity range for a given PN as progenitors range between 1 and 8 M . Many PNe may have low-luminosity cores and therefore join the luminosity function at fainter magnitudes. A simulated increase of the faintest 2 mag would further decrease the percentages at the bright end. All this plot can effectively show is the number of PNe that may be found per luminosity bin at a single instant of time. Each bin has been scaled as a percentage of the number of PNe in the whole sample. Fig. 16 shows that the percentage of PNe in the brightest 4 mag accounts for only 14.6 per cent of all LMC PNe within the deep sample. In other words, 40 per cent of the magnitude range contains only 14.6 per cent of the PNe. It has been suggested that this drop in number density brighter than 18 mag is due to the negative slope of the initial mass function (IMF), especially affecting young stellar populations (Shaw 1989) and the rapidly accelerating rate of evolution across the HertzsprungRussell diagram with increasing luminosity, particularly evident on the hydrogen-burning tracks (Dopita et al. 1992). Simulations conducted by Mendez et al. (1993) suggest that these PNe at the bright end are also predominantly optically thin. 4.4 The cumulative PNLF and comparisons with other galaxies In order to compare the depth of our derived PNLF with previous LMC PNLF models and PNLF in other galaxies, we create a cumulative distribution of the function. We present the cumulative function as a percentage of PNe found at each magnitude and compare this to model cumulative functions. This approach helps to reveal the positions at which incompleteness begins to set in. It also shows the way in which incompleteness affects the overall shape of the cumulative function. The cumulative LMC PNLF for [O III] 5007 is shown in Fig. 13 where it is compared with the cumulative PNLFs calculated in the same way for the SMC, using data from Jacoby (2006) and for local PNe using the new highly complete local Galactic volume catalogue of Frew (private communication) which includes PNe out to 3 kpc. These objects are included in the MASH catalogues of Parker et al. (2006) and Miszalski et al. (2008). Although each PNLF is affected by incompleteness, compared to the LMC, the local and SMC samples have a larger percentage of PNe in the brightest 6 mag range (41 per cent for the LMC, compared to 54 per cent for the SMC and 55 per cent for the local PNLFs). The shape of the bright end of the PNLF is therefore very sensitive to the relative number of PNe included at the very brightest magnitude. It is also sensitive to the peak number density, the flux limit of the survey and the decreasing number of PNe at the faint end. The large increase in the number of LMC PNe between 4 and 7 mag below the brightest causes the LMC PNLF to rise away from the predicted exponential curve. With an identical magnitude range, the local PNLF shows a more constant rise. The SMC PNLF, with its smaller magnitude range, shows a small dip between 4 and 5 mag below the brightest, after which it also rises steeply. The steepest section of each cumulative function represents a rise to the peak in number density. This feature is easiest to see in the LMC PNLF; however, its presence also in the SMC and between 6 and 7.5 mag ranges in the local PNLF suggests that it may be common to PN evolution in most galaxies. The final 3 mag of the LMC PNLF show a gradual turnover towards the faint drop-off. A stronger turnover is also seen in the local sample, affecting the final 2 mag, with only 8 per cent of PNe found in this range, prior to the faint drop-off. These turnovers are the result of incompleteness at the faint end, where we would expect the number of PNe to either rise or remain stable beyond the peak density (6 mag below the brightest). We do not discount the possibility that a certain drop in number density towards the faint end may be a real feature suggesting that most PNe spend the majority of their life cycle between 4 and 7 mag below the brightest. The SMC PNLF only shows a turnover (drop in number density) in the final magnitude of its faint end. This short turnover would normally indicate that the SMC PNLF is more complete up to its final magnitude drop-off than the other two PNLFs. The SMC faint turnover, however, also coincides with the drop-off from the peak number density in the LMC PNLF. The LMC contains a further 228 PNe fainter than this magnitude. Therefore, the faint end of the SMC PNLF is actually less complete than the other two and we predict more PNe be found >4 mag below the brightest and 3 mag deeper than currently available. Using equation (6), Mendez et al. (1993) have obtained the cumulative PNLF for any magnitude M fainter than the cut-off by integrating N(M) between M and M using the following formula: The dotted lines in Fig. 13 represent this predicted cumulative PNLF from equation (8), adjusted to fit the magnitude range of PNe in the SMC and LMC. Comparing this predicted curve to the SMC PNLF suggests that there is a lack of PNe in the range of 46 mag below the brightest. This is affecting the overall shape of this PNLF and creating the upward hump from 1 to 4 mag below the brightest. The cumulative curve from equation (8), when fitted to the LMC, agrees very well at the brightest 4 mag. After this, it does not follow the strong peak in the function but continues at a steady exponential rate. A larger number of PNe at the faintest 3 mag would effectively bring the LMC PNLF closer to the predicted curve. The local PNLF also shares a 10 mag range in [O III] and so shares the same predicted curve as our LMC PNLF, but traces out a path much further to the bright end and away from the simulated PNLF. This position for the local PNLF, when compared to the LMC PNLF, suggests that either there should be a great many more faint PNe (>6 mag below the brightest) to be found within the local 3 kpc radii range or the local PNLF is affected by selection effects since it is only sampling a relatively small region of our Galaxy. While the formula of Ciardullo et al. (1989) results in a constantly increasing PNLF towards fainter magnitudes, the simulated PNLF of Mendez & Soffner (1997) produces two rises and declines. The first decline is between [O III] 5007 magnitudes of 3.5 and 2.5 (fig. 4 in Mendez et al. 1997). It then rises again from magnitudes fainter than 2.3 until it reaches a peak at 0.2. From this point, it begins a steady decline. This simulation, however, was re-worked to allow for PNe on cooling tracks by including a random distribution of the absorbing factor between 0.1 and 1. With this adjustment, the simulation fits the formula of Ciardullo et al. (1989) very well (see fig. 5 in Mendez et al. 1997). This was a prediction, where severe incompleteness hampered any true test with observations. The simulation of Mendez et al. (1997, fig. 5), after a correction to allow absorbing factors to tend to 0, shows a peak in the function at 6 mag and a faint-end decline from that point. This is exactly what is seen in the LMC PNLF using the RP sample (Fig. 13). This in turn strengthens the case for a strong rise in the function from 4 mag below the brightest. This rise is the result of an evolutionary change where a young, high-mass and luminous PN reaches a peak in its photoionization potential. It then shifts towards the WD cooling track with increasingly lower density-to-mass ratios. The sudden rise in number density shows that this change occurs rapidly. The extension of the PNLF to fainter magnitudes describes complete population effects as predicted by the Shklovski model (1981) and permits us to observe what effect the faint PN population may reveal for successful PNLF modelling. It is hoped that this will in turn help to further refine PNLF simulations. 5 T H E P O T E N T I A L O F T H E L M C H P N L F The PNLF is essentially based on the evolution of the central ionizing star (Jacoby 1989). In particular, the H intensity is a measure of the central stars ionizing luminosity (Osterbrock 1989) and can also indicate the heating of the nebula as long as it is optically thick. This would indicate that a hydrogen emission line would also be a natural choice for a PNLF (Sch onberner et al. 2007). Since the evolution of the central stars luminosity gives rise to the PNLF, there should be a correlation between the relative strengths of the integrated [O III] 5007 and H fluxes. The H line is also less influenced by the metallicity of the parent galaxy, which could make it an ideal choice for distance determination. A PNLF was constructed using H in order to discover the bright cut-off and shape of the function. A comparison with the [O III] 5007 PNLF should then reveal broad influences of the LMCs low metallicity. The H flux by comparison is typically more than five times fainter than [O III] 5007 in most PNe, making it much more difficult to spectroscopically measure in external galaxies. This is why H is not generally used for distance determination. H has a bright cut-off at about 2.4 mag fainter than that of [O III] 5007 . For optically thick PNe, the H flux should be a reliable indicator of stellar luminosity. The maximum conversion efficiency from stellar luminosity to luminosity in the H line only varies by a factor of 2, even though a maximum of just under 1 per cent of stellar luminosity is converted into H photons (Dopita et al. 1992). Dopita et al. (1992) have found the variation in this conversion efficiency to be even less. In order to convert our H fluxes, expressed in erg cm2 s1, to magnitudes, we use the definition given by Jacoby (1989): mf = 2.5 log f 13.74, where f represents the flux to be roughly converted to the broad V-band magnitude. The close interval between the [O III] 5007 and H lines allows use of the same definition to convert fluxes from erg cm2 s1 to magnitudes for both lines. This technique, previously adopted by Mendez et al. (1993), allows us to make a direct comparison between [O III] 5007 and H magnitudes on the same scale. The luminosity function for the H line is shown in Fig. 14 for foreground de-reddened objects where the brightest PN is found at an apparent magnitude of m4861 = 16.8 In Fig. 15 the PNLF is shown following correction for internal extinction where the brightest PN is found at an apparent magnitude of 16.2. In Fig. 16, we show the H PNLF as a log plot with the truncated exponential curve of Ciardullo et al. (1989) added for comparison. The curve has been placed at the best fit to the bright end, using the LevenbergMarquardt fit method. Using the bright intersection of the curve with the x-axis, a value of M4861 = 16.8 0.21 was found. This corresponds to an absolute magnitude of 1.68 0.21 for M4861. Statistically, the goodness-of-fit tests to the theoretical exponential curve give F = 1.31, a KS statistic of 0.13 and 2 statistic of 2.85 providing 95 per cent confidence limits that the observed PNLF is unlikely to be drawn from the empirical one. At present, there are little data on extragalactic H fluxes available with which to compare these results. Stanghellini (1995) constructed an H PNLF for the Magellanic Clouds based on the fluxes of Richer (private communication) together with a simulation of 1000 optically thick PNe using Salpeters IMF and Weidemanns initial mass final mass relation, with Mmax = 0.7 M (Weidemann 1987). These data produced very encouraging comparisons; however, variations in the mass truncation produced significantly different results. Using Mmax = 0.7 M , the peak in the distribution occurred only 1 mag below the brightest PN. Increasing Mmax to 1.4 M shifted the peak 2.2 mag fainter, but the entire distribution only covered a 4 mag range. Only the bright end is plotted in linear space in Fig. 17 using the same data corrected for internal extinction. Analogous to the [O III] 5007 function, the brightest PN in the H function also increases by 0.8 mag after correction. Assuming an exponential growth in the function, and comparing the empirical PNLF of Ciardullo et al. (1989), the KS statistic is 0.122 and the 2 statistic is 5.0. This indicates that the observed PNLF is unlikely to be drawn from the extrapolated one at the 90 per cent confidence level. Improved simulations of the empirical PNLF were presented for both the [O III] 5007 and H lines by Mendez & Soffner (1997). By varying the estimated fraction of stellar ionizing luminosity absorbed by the nebula, better known as the absorbing factor , and using available evolutionary tracks to produce a good representation of varying Teff , mass and log L for 3000 10-yr intervals between 0 and 30 000 yr, they produced good representations to the standard predictions of Ciardullo (1995). Their fig. 6 simulation of the H PNLF shows a peak in the distribution at precisely the same position of M = 3.8 found in this study using real LMC PNe. This remarkable match to model predictions proves that not all PNe on cooling tracks can have = 1, since that would create a strong hump at the peak and make fainter PNe extremely hard to find. The values of most likely vary between 0.1 and 1 between ages of 1 and 30 000 yr. 5.1 PNe with low central star temperatures It is important to note that we have found three PNe (SMP numbers 64, 31, 55) with very high H fluxes belonging to excitation class 1, the lowest category (Reid & Parker 2009). In RPb, SMP64 and SMP31 were classified as possible PNe belonging to a class known as very low excitation (VLE) PNe. They have central stars with Teff so low (31 20038 500 K) that the [O III] 5007 is extremely low by comparison to H (details in RPb). A further four PNe (SMP67, 77, 76 and MG62) also have [O III] 5007/H flux ratios of 3, low excitation classes from 2 to 3 and Teff between 46 500 and 64 200 K. The presence of VLE PNe has previously been reported by Mendez et al. (1993) and can be seen in fig. 4(a) of Dopita et al. (1992) for several Magellanic Cloud PNe. In order for the H luminosity to remain constantly high in these PNe, the number of ionizing photons from the central star must increase by a factor of 2.5 as the temperature increases from Teff 30 000 to 70 000 K. If these nebulae were optically thick, we would expect a proportional increase in the H luminosity with increasing central star temperature. To keep these nebulae constantly bright on the horizontal portion of the post-AGB evolutionary tracks, Mendez et al. (1993) suggest that they must be optically thin in the H Lyman continuum. The fraction of stellar ionizing luminosity absorbed by the nebula, defined as the absorbing factor (Mendez, Kudritzki & Herrero 1992), may also play a defining role here. Another possibility is that many of these central stars are burning He rather than H. This might account for a decrease in luminosity as Teff increases. Comparisons have been previously drawn between the [O III] 5007 and H + [N II] line ratios in a given population of extragalactic PNe (e.g. Ciardullo et al. 2002, 2004). The H, being the brightest line in the Balmer series, is the easiest hydrogen line to measure in extragalactic PNe. Unfortunately, due to filter responses, it usually includes the adjacent [N II] 6548 + 6583 lines. The LMC is close enough that the H line is easy to measure using our spectroscopic observations. Since it is cleanly separated and yet relatively close to the [O III] 5007 line in the optical spectrum, the ratios will be less affected by errors in flux calibration and extinction estimates. The shape of the H PNLF has strong similarities to that of [O III] (Fig. 6), but there are some differences. Once again, there is a peak to the distribution; however, it is not as strongly marked as its counterpart in [O III]. With the H peak occurring at a magnitude of 22.4 mag (absolute magnitude of 2.6), 5 mag below the brightest, 48 per cent or 287 PNe have fluxes occurring at the bright end. This may be compared with the [O III] function where the peak occurs at a magnitude of 20.4 (absolute magnitude of 0.4); however, only 242 or 41 per cent of PNe are found at the bright end of the peak. This is despite the [O III] peak occurring 5.2 mag below the brightest, which is relatively 0.2 mag fainter than the peak in H. In general terms, across a broad range of evolution, this suggests that the H flux increases and fades at a steadier rate than the [O III] flux. The [O III] flux appears to be highly sensitive to evolutionary spikes and dips, whereas the H flux is more sensitive to the opacity of the nebula. It also suggests that the central star evolves over the dynamic lifetime of a PN as it ionizes the uniformly expanding shells (Henize & Westerlund 1963), affecting temperature, luminosity and excitation of the nebula. These parameters will be closely examined in a further paper in this series. All the previously known and new PNe in this survey are included in Fig. 18 where the [O III] 5007 magnitudes are plotted against the H magnitudes, both de-reddened and corrected for extinction. The correction between the line fluxes is generally very small. Even for a huge reddening of E(B V ) = 1.0, the differential reddening between [O III] 5007 and H is less than 0.06 dex (Schild 1977). Fig. 18 shows that the [O III] 5007 line intensities span 10 mag. The H line intensities on the other hand only span 8.5 mag. The faint dotted line in Fig. 18 represents the H function, moved to the best-fitting position with the [O III] 5007 function. Statistically, on a bin-to-bin basis, there is an agreement of 82 per cent between them. This, however, should be viewed only in terms of the overall shape of the PNLF since [O III] 5007/H in individual PNe may vary by as much as 2.5 mag. With this in place, it becomes apparent that [O III] 5007 fluxes extend approximately 1 mag brighter than the bright end of the H function. Assuming an exponential distribution, the KS statistic is 0.10 and the 2 statistic is 9.72 indicating a 92 per cent probability that the two functions do not correspond. None the less, we cannot statistically exclude the possibility that the two samples are essentially of the same shape. At the bright end, the H PNLF like that of [O III] 5007 starts to climb almost immediately without any strongly defined dips but a series of peaks and troughs. This may indicate that the central stars progression on to the WD cooling track has little immediate impact on stellar luminosity. Although the stellar temperature begins to fall, causing a dip in the [O III] 5007 line, the H flux is maintained longer, probably due to the higher ionization potential of H. Although the transition probability (3 to 1) between the [O III] 5007 and 4959 lines (Osterbrock & Ferland 2006) remains constant, our measurements of PNe in the LMC show that the H flux varies widely by comparison to these lines. Combined [O III] 5007 + 4959 fluxes lie between 62 and 0.9 the strength of H PN fluxes in the LMC survey sample. Fig. 19 directly compares the measured fluxes. A fitted trend line shows a steady regression towards the line of equality with fainter magnitudes. PNe at the brightest 4 mag have consistently high 5007/4861 ratios. The marked lack of low 5007/4861 ratios in this region suggests that these PNe are young, optically thick, medium to high excitation PNe with central stars which have not yet reached the WD cooling track. PNe with low [O III] fluxes, 0.9 to two times H, are found in both faint, highly evolved PNe and within magnitude ranges fainter than 18. Other diagnostics such as high [N II] 6583/H together with morphology, when available from HST images, help to distinguish these candidates as possible VLE PNe. The mean ratio ([O III] 5007, 4959/H) across the entire central 25 deg2 survey region is 8.93 7.31. By far, the majority (94 per cent) of [O III] 5007 + 4959 fluxes are below 20 H fluxes. The H bright cut-off occurs 2.4 mag fainter than the equivalent position for [O III] 5007 . Fig. 19 shows that PNe with the brightest H fluxes also have strong [O III] 5007 fluxes. In fact, sampling the brightest 50 H fluxes, the average [O III] 5007 flux is 8.9 times H. These include mostly medium and some high excitation PNe with central star temperatures between Teff = 31 800 and 136 000 K. The H PNLF shows the same rather flat distribution seen across the initial 2 brightest magnitudes of the [O III] 5007 PNLF. The initial peak in the H distribution is only 1.8 mag fainter than the equivalent position for [O III] 5007 . Similarly, the faintest PNe in each wavelength are generally 1.8 mag in separation. Both of these PNLF estimates agree closely with the average magnitude difference of 1.7 0.9 by directly comparing 591 LMC PNe. By comparison, if we average the magnitude difference between [O III] 5007 and H for the brightest 30 PNe in H, the result is a much higher 2.3 0.6 mag difference. The flat distribution at the bright end of the [O III] 5007 PNLF is therefore the result of a bright extension, peculiar to the bright end of the [O III] 5007 PNLF. This extension is an average of 0.6 mag greater than the average difference for the remaining 95 per cent of PNe. These results, despite the evolutionary effects, indicate that the temperature of the central star is the most dominant contributor to the PNLF (e.g. Jacoby 1989), giving rise to both the H and [O III] 5007 luminosity. The raw cumulative luminosity functions derived from the [O III] and H magnitudes are shown in Fig. 20. In each case, the bright end of the functions is fitted with a straight line, indicating the upper luminosity cut-off. This line traditionally represents the observational basis for distance estimates once corrections for reddening and luminosity efficiency of the [O III] or H line photons are made. The graphs clearly show, however, that most PNe follow the steeper slope which represents the greatest growth, peak and fall in the function. The number of PNe on this line is equal in [O III] 5007 and H (7075 per cent for both). The stronger peak in the [O III] 5007 function results in the oscillation seen either side of the arrow, to the right and left of the central line. Tables A1 and A2 provide a compendium of H and [O III] 5007 raw flux estimates for previously known and newly discovered RP PNe, respectively, in the LMC. The tables also include the measured values of c(H) and the estimated errors. Table A2 includes the PN object probability where T represents true, L represents likely and P represents possible. It is anticipated that once the RP survey is extended to the outer LMC, a similar shape for the PNLF to that newly obtained for the central 25 deg2 would be found. The increase in total numbers should create a much tighter fit to the exponential curve, providing a very accurate distance estimate. The combination of previously known and newly discovered PNe in this study currently provides the most accurate estimate for the shape of the LMC PNLF obtained thus far. 6 C O N C L U S I O N Due to the depth of the UKST multistacked H survey, the subsequently uncovered large RP PN sample is able to show the influence of population effects on the shape of the PNLF for the first time. We present details of a new technique for the flux calibration of fibrebased spectra. Using this technique, we provide carefully calibrated [O III] 5007 and H flux estimates from 2dF and FLAMES spectra together with fluxes from calibrated long-slit spectra for 584 LMC PNe. These fluxes are converted to magnitudes and used to construct a PNLF in [O III] and in H. The PNe are separated into previously known and newly discovered PNe where a significant increase in the number of LMC PNe below an apparent magnitude of 18.6 in [O III] 5007 is possible, thanks to this work. The [O III] 5007 PNLF is used to directly estimate the distance to the LMC. By fitting an exponential curve to the bright end of the function over a 6 mag range, an m value of 14.02 is found. Applying the accepted M value of 4.44, we find a distance modulus of 18.46 for the LMC. This is in excellent agreement with the best recent calibrations (see Table 2). The bright-end cut-off is found to be robust to small samples of bright PNe since our significantly increased PN samples have no effect on this fiducial. We find a peak in the [O III] 5007 PNLF which is 6 mag below the brightest. This peak was previously predicted but not seen in a real sample until now. The steep rise to the peak in the function over a 2 mag range was also not seen before but was also predicted due to the position of the WD cooling track and a mixture of H- and He-burning stars in the LMC. Not withstanding incompleteness, the faint end of the PNLF can now be examined for the first time. Over a 4 mag range, we find a linear drop-off in the number of PNe per magnitude bin. A comparison of the foreground de-reddened [O III] 5007 PNLF with the same [O III] 5007 PNLF after correction for internal extinction reveals almost no change in the overall shape of the PNLF. If the observed PNLF is shifted by applying 1 mag of extinction to each object, then the de-reddened PNLF can be almost exactly recovered. This remarkable finding means that although the PN extinction ranges from 0 < c(H) < 1.3, from a global prospective, the PNLF acts as if each one has c(H) = 0.4. This will clearly make it easier to model the PNLF in distant galaxies, as it implies that, for a one-dimensional analysis, there is only a mean offset to be applied. We have constructed the first LMC PNLF in H using 591 measured PN spectra. We find a value of 16.8 for the m4861 bright cut-off. This leads to an estimate of M = 1.68 for H-based PNLF distance estimates. A clear relation is found between the shape of the [O III] 5007 and the H PNLF with a mean difference of 2.8 mag at the bright cut-off decreasing to 1.8 mag by the peak of the distributions or 6 mag below m5007. The new LMC PNLF is compared to a new PNLF constructed using local Galactic PNe to 3 kpc and the newest sample from the SMC. The magnitude range is almost exactly the same for both the LMC and local surveys. A small dip of 3 and 4 mag below the brightest is evident in the local and LMC surveys, respectively. The rollover at the faint end of the PNLF is generally interpreted as a sign of incompleteness in the survey, where the rollover occurs across the faintest 1 or 2 mag. Using 584 PNe in the RP sample from this survey, the rollover occurs over 1.5 mag, causing the shape of the faint end to inversely reflect the shape of the PNLF at the bright end. This would indicate that the peak distribution found in this work is close to the true peak distribution for LMC PNe. This occurs at an absolute magnitude of 0.8. By comparison, the peak distribution of local Galactic PNe occurs at an absolute magnitude of 2, 1.2 mag fainter than that found for the LMC. Once we complete our survey by including the outer LMC, we expect that the estimated extra 80 PNe at the bright end of the function will fill out much of the exponential curve. It should thereby clarify the position of the rise, 4 mag below the brightest, and the position of any dip if it exists. The extra objects are not expected to alter the distance modulus of 18.46, similar to the result found by Jacoby (1989). Final results will largely depend on individual luminosities up to 6 mag below m. AC K N OW L E D G M E N T S The authors wish to thank the AAO board for observing time on the AAT and UKST. The authors also thank the European Southern Observatory for observing time on the VLT and Australian National University along with their telescope time allocation committees for supporting our programme of follow-up spectroscopy. We thank Martin Cohen for making SAGE data available and assisting in the follow-up analysis of LMC PNe. We also thank Robin Ciardullo for very helpful comments and suggestions while carefully reviewing the paper. WAR thanks Macquarie University, Sydney, for travel grants. R E F E R E N C E S Table A1. A compendium of H and [O III] 5007 raw flux estimates for LMC PNe. RP Common Ref. nomenclature Table A1 continued RP Common Ref. nomenclature Table A1 continued RP Common Ref. nomenclature Table A2. A compendium of H and [O III] 5007 raw flux estimates for RP PNe in the LMC. 1.46E15 7.29E17 2.60E15 1.30E16 7.11E15 3.56E16 9.66E16 8.21E16 3.39E15 1.69E16 5.12E15 2.56E16 1.06E14 5.32E16 2.64E13 1.32E14 5.42E15 2.71E16 1.74E15 8.69E17 3.79E16 3.79E17 5.30E15 2.65E16 3.28E16 3.28E17 7.68E15 3.84E16 1.43E15 7.16E17 7.24E16 7.24E17 6.03E15 3.02E16 1.29E15 6.46E17 2.32E15 1.16E16 2.08E15 1.04E16 2.04E15 1.02E16 3.45E15 1.73E16 2.23E15 1.12E16 5.08E15 2.54E16 4.74E15 2.37E16 3.03E14 1.51E15 7.47E15 3.74E16 1.31E15 6.55E17 3.60E16 3.60E17 3.26E15 1.63E16 7.19E15 3.60E16 4.82E15 2.41E16 6.77E15 3.38E16 4.62E15 2.31E16 4.36E15 2.18E16 1.13E15 5.65E17 2.55E15 1.28E16 6.09E16 6.09E17 3.67E15 1.84E16 4.95E15 2.47E16 3.73E15 1.87E16 1.40E15 6.98E17 6.36E15 3.18E16 1.50E15 7.49E17 1.99E15 9.93E17 2.31E15 1.15E16 2.11E15 1.05E16 1.70E15 8.52E17 2.57E15 1.28E16 4.12E15 2.06E16 2.83E15 1.42E16 1.83E15 9.17E17 2.17E15 1.08E16 5.91E15 2.96E16 9.00E15 4.50E16 1.73E14 8.66E16 2.27E14 1.14E15 2.78E15 1.39E16 1.12E14 5.58E16 2.52E15 1.26E16 2.32E14 1.16E15 1.39E14 6.96E16 7.76E15 3.88E16 1.72E14 8.58E16 5.60E15 2.80E16 2.07E14 1.04E15 3.52E13 1.76E14a 2.28E14 1.14E15 1.01E14 5.04E16 3.32E15 1.66E16 3.05E14 1.53E15a 2.28E15 1.14E16 1.64E14 8.20E16 6.20E15 3.10E16 9.28E16 9.28E17 1.11E14 5.54E16 3.52E15 1.76E16 1.57E14 7.84E16 7.02E15 3.51E16 2.27E15 1.13E16 4.26E14 2.13E15 7.00E15 3.50E16 2.06E14 1.03E15 1.26E14 6.28E16 8.84E14 4.42E15a 1.73E14 8.67E16 4.29E15 2.15E16 1.57E15 1.34E15 7.80E15 3.90E16 1.74E14 8.72E16 7.93E15 3.97E16 2.24E14 1.12E15 7.49E15 3.75E16 2.50E14 1.25E15 8.83E15 4.42E16 2.84E15 1.42E16 3.59E15 1.79E16 1.21E14 6.05E16 8.55E15 4.28E16 1.47E14 7.34E16a 3.96E15 1.98E16 2.31E14 1.16E15 1.61E15 8.04E17 2.26E15 1.13E16 2.27E14 1.13E15 3.30E15 1.65E16 3.98E15 1.99E16 9.78E15 4.89E16 8.13E15 4.07E16a 1.75E14 8.75E16 1.71E14 8.53E16 3.37E15 1.68E16 7.20E15 3.60E16 1.49E14 7.45E16 4.65E14 2.32E15 3.65E14 1.82E15 7.84E15 3.92E16 2.74E14 1.37E15 Table A2 continued 1.24E14 6.19E16 1.15E14 5.74E16 1.02E14 5.08E16 8.60E15 4.30E16 3.82E14 1.91E15 8.71E15 4.36E16 9.85E15 4.92E16 2.50E14 1.25E15 1.43E14 7.15E16 4.16E15 2.08E16 9.39E15 4.70E16 7.73E15 3.86E16 3.32E14 1.66E15 9.27E15 4.64E16 1.16E14 5.80E16 1.36E14 6.80E16 7.81E14 3.90E15 3.39E14 1.69E15 1.80E15 9.02E17 3.31E15 1.66E16 1.01E14 5.07E16 1.25E15 6.25E17 4.85E15 2.42E16 7.70E16 7.70E17 9.12E15 4.56E16 7.22E15 3.61E16 9.22E15 4.61E16 4.39E15 2.19E16 4.44E16 4.44E17 1.02E15 5.12E17 4.03E15 2.01E16 8.30E16 8.30E17 1.65E16 1.65E17 1.16E15 5.79E17 9.86E16 8.38E16 1.04E15 5.20E17 1.00E15 5.02E17 6.53E16 6.53E17 1.71E15 8.57E17 8.81E16 8.81E17 2.21E14 1.10E15 1.61E14 8.05E16 1.46E14 7.28E16 1.33E15 6.65E17 1.96E14 9.78E16 1.47E15 7.37E17 9.67E16 8.22E16 1.74E15 8.68E17 2.22E15 1.11E16 2.14E16 2.14E17 1.59E15 7.96E17 9.74E15 4.87E16 9.75E15 4.88E16 9.75E15 4.88E16 2.56E14 1.28E15 1.79E15 8.96E17 1.42E15 7.10E17 1.21E15 6.07E17 5.07E15 2.54E16 1.08E15 5.40E17 4.01E14 2.00E15 4.75E14 2.38E15 2.72E14 1.36E15 2.93E14 1.46E15 3.07E14 1.54E15 3.96E14 1.98E15 1.80E14 8.98E16 4.98E14 2.49E15 1.22E14 6.12E16 5.11E15 2.56E16 1.80E14 9.01E16 1.20E14 5.98E16 3.04E14 1.52E15 1.42E14 7.08E16 1.19E14 5.96E16 4.39E14 2.20E15 8.69E14 4.35E15 7.75E14 3.87E15 3.00E15 1.50E16 6.40E15 3.20E16 1.25E14 6.23E16 1.60E15 7.99E17 1.95E14 9.73E16 1.79E15 8.95E17a 2.51E14 1.26E15 2.57E14 1.29E15 2.76E14 1.38E15 9.02E15 4.51E16 2.05E15 1.03E16 2.28E15 1.14E16 2.24E14 1.12E15 5.02E15 2.51E16 1.66E15 8.29E17 2.00E15 1.00E16 2.93E15 1.46E16 4.91E15 2.46E16a 1.13E15 9.61E16a 1.90E15 9.48E17 8.07E15 4.03E16 8.64E16 8.64E17 8.00E14 4.00E15 4.16E14 2.08E15 6.26E14 3.13E15a 9.60E15 4.80E16 6.69E14 3.34E15 2.33E14 1.16E15 2.29E15 1.15E16 3.82E15 1.91E16 5.87E15 2.94E16a 1.08E15 9.16E16 1.21E14 6.05E16 5.30E14 2.65E15 6.42E14 3.21E15a 6.42E14 3.21E15 6.65E14 3.32E15 1.35E14 6.76E16 3.52E15 1.76E16a 3.96E15 1.98E16 1.38E14 6.89E16 3.45E15 1.72E16 Table A2 continued 1.11E14 5.56E16 1.18E14 5.91E16 1.99E15 9.93E17 2.94E15 1.47E16 1.40E15 7.00E17 9.97E16 8.48E16 1.76E15 8.80E17 7.90E15 3.95E16 9.88E15 4.94E16 1.85E14 9.27E16 1.74E15 8.68E17 4.44E15 2.22E16 1.46E15 7.31E17 1.61E16 1.61E17 2.01E14 1.00E15 1.53E15 7.64E17 1.47E15 7.36E17 1.12E15 5.58E17 2.37E15 1.18E16 4.75E15 2.38E16 6.56E16 6.56E17 2.31E15 1.16E16 1.56E13 7.82E15 1.41E14 7.03E16 1.08E15 5.41E17 1.47E15 7.35E17 2.87E15 1.43E16 7.45E15 3.73E16 1.25E14 6.27E16 5.32E15 2.66E16 6.06E16 6.06E17 5.32E15 2.66E16 3.02E15 1.51E16 5.45E15 2.72E16 1.12E15 5.62E17 4.74E15 2.37E16 1.85E15 9.24E17 4.73E15 2.37E16 3.77E15 1.88E16 1.34E14 6.69E16 1.44E15 7.21E17 4.97E15 2.49E16 2.74E15 1.37E16 1.53E15 7.63E17 3.24E15 1.62E16 5.33E16 5.33E17 1.10E14 5.49E16 3.10E15 1.55E16 2.62E15 1.31E16 5.76E16 5.76E17 7.87E15 3.93E16 9.51E15 4.75E16 3.19E15 1.59E16 1.79E14 8.95E16 8.46E14 4.23E15 1.02E14 5.09E16 3.00E15 1.50E16 3.93E14 1.96E15 5.06E15 2.53E16 4.09E15 2.04E16 2.13E14 1.06E15 1.15E13 5.73E15 5.92E14 2.96E15 2.68E15 1.34E16 1.77E14 8.85E16 6.28E15 3.14E16a 1.96E14 9.79E16 6.29E15 3.14E16 1.20E14 5.98E16 2.81E14 1.40E15 3.66E14 1.83E15 1.62E13 8.09E15 6.90E15 3.45E16 1.85E14 9.26E16 4.27E15 2.14E16 6.84E16 6.84E17 6.09E14 3.05E15 1.56E15 9.88E16 2.71E15 1.36E16 4.20E15 2.10E16 2.38E15 1.19E16 3.85E14 1.93E15 1.53E15 1.30E15 6.46E15 3.23E16 6.18E14 3.09E15 6.33E14 3.16E15 1.24E14 6.18E16 3.50E15 1.75E16 1.22E14 6.11E16 1.37E14 6.87E16 4.50E14 2.25E15a 1.67E14 8.34E16a 1.76E15 8.79E17 4.13E15 2.06E16 3.43E14 1.72E15 3.38E14 1.69E15 1.29E14 6.43E16a 3.31E14 1.66E15 3.85E15 1.92E16 3.16E14 1.58E15a 3.24E15 1.62E16 1.64E14 8.19E16 5.73E15 2.87E16 3.50E14 1.75E15 4.78E15 2.39E16 4.23E15 2.11E16a 4.06E14 2.03E15 6.01E15 3.00E16 7.01E14 3.50E15 3.82E15 1.91E16 3.10E14 1.55E15 4.12E15 2.06E16 2.85E14 1.42E15 3.38E14 1.69E15 1.12E14 5.62E16 5.19E14 2.59E15 1.31E13 6.55E15 4.83E14 2.41E15a 1.96E14 9.79E16 5.68E14 2.84E15 2.77E14 1.38E15 1.20E14 5.99E16 2.96E14 1.48E15 Table A2 continued 2.91E15 1.45E16 7.46E15 3.73E16 3.61E14 1.81E15 2.27E15 1.13E16 7.63E15 3.81E16 3.40E15 1.70E16 3.64E15 1.82E16 5.53E15 2.76E16 8.48E16 8.48E17 9.23E15 4.61E16 1.24E14 6.22E16 8.85E16 8.85E17 1.42E14 7.09E16 4.58E15 2.29E16 2.22E15 1.11E16 2.20E15 1.10E16 2.09E14 1.04E15 1.19E14 5.93E16 1.64E15 8.21E17 3.33E14 1.67E15 1.61E14 8.03E16 2.63E16 2.63E17 1.12E14 5.60E16 2.35E14 1.18E15 1.34E15 6.70E17 1.15E14 5.75E16 1.31E14 6.53E16 1.80E14 9.00E16 1.38E15 6.89E17 8.10E15 4.05E16 1.04E15 5.22E17 3.14E15 1.57E16 3.96E16 3.96E17 5.12E16 5.12E17 5.79E15 2.89E16 1.09E14 5.47E16 2.00E14 1.00E15 2.05E13 1.03E14 9.96E14 4.98E15 3.24E15 1.62E16 1.57E14 7.86E16 2.48E15 1.24E16 1.82E15 9.09E17 4.44E15 2.22E16 2.30E15 1.15E16 1.97E15 9.86E17 2.96E16 2.96E17 3.53E16 3.53E17 5.79E15 2.89E16 4.69E15 2.35E16 1.30E15 6.48E17 6.98E16 6.98E17 3.39E14 1.69E15 2.58E13 1.29E14 3.26E15 1.63E16 3.06E15 1.53E16 2.75E15 1.37E16 2.80E15 1.40E16 3.51E16 3.51E17 4.44E17 6.67E18 3.90E15 1.95E16 5.92E16 5.92E17 1.51E14 7.54E16 1.24E14 6.19E16 2.75E14 1.38E15 3.13E14 1.56E15 5.52E14 2.76E15 1.16E14 5.82E16 9.39E15 4.69E16 5.98E14 2.99E15 1.02E15 8.67E16 3.02E14 1.51E15 1.83E14 9.16E16 3.28E15 1.64E16 2.12E14 1.06E15 1.40E14 7.01E16 1.84E14 9.21E16 1.87E14 9.35E16 3.54E14 1.77E15 5.86E14 2.93E15 6.50E15 3.25E16 1.49E13 7.45E15 1.02E13 5.11E15 1.36E15 1.16E15 5.33E14 2.67E15 7.77E14 3.89E15 1.84E15 9.18E17 1.03E14 5.17E16 3.34E14 1.67E15 9.28E14 4.64E15 3.61E15 1.81E16 3.19E14 1.59E15 3.92E16 3.92E17 5.56E15 2.78E16 1.18E15 1.01E15 1.00E15 8.51E16 2.56E14 1.28E15 1.19E14 5.97E16 8.47E14 4.24E15 9.10E13 4.55E14 5.83E14 2.91E15 2.84E14 1.42E15 5.25E14 2.62E15 4.46E15 2.23E16 4.10E15 2.05E16 1.60E14 8.01E16 6.72E15 3.36E16 1.52E14 7.61E16 1.45E15 1.23E15a 1.45E15 1.24E15 1.67E14 8.37E16a 1.16E14 5.80E16a 4.27E15 2.14E16 2.73E15 1.37E16 6.90E14 3.45E15a 8.94E15 4.47E16a 2.23E14 1.12E15 4.11E14 2.06E15 1.14E14 5.70E16 1.94E14 9.72E16 1.45E15 1.23E15 4.89E16 4.89E17 3.60E14 1.80E15a 7.84E15 3.92E16 Table A2 continued Table A2 continued 9.76E15 4.88E16 1.17E15 5.85E17 3.41E16 3.41E17 1.17E14 5.83E16 3.88E15 7.63E17 7.22E15 3.61E16 1.59E15 7.94E17 3.62E15 1.81E16 5.86E16 5.86E17 1.26E15 6.30E17 1.27E15 6.36E17 7.70E15 3.85E16 3.00E15 1.50E16 4.54E15 2.27E16 3.19E14 7.64E16 1.19E14 2.11E16 1.39E14 1.06E16 2.81E16 8.48E17 5.77E16 5.77E17 9.76E15 1.62E16 9.28E16 7.89E16 2.79E15 1.39E16 2.07E14 4.35E16 7.11E17 1.07E17 7.76E16 7.76E17 6.23E15 3.11E16 2.67E15 1.33E16 1.90E15 9.50E17 3.92E15 1.96E16 9.46E16 8.04E16 2.91E15 1.45E16 3.14E15 1.57E16 6.20E15 3.10E16 3.24E15 1.62E16 1.22E14 6.09E16 1.83E15 9.13E17 3.05E15 1.52E16 3.01E15 1.50E16 1.50E15 7.50E17 8.65E16 8.65E17 9.99E16 8.49E16 1.03E15 5.14E17 3.41E16 3.41E17 1.02E15 5.10E17 2.12E15 1.06E16 4.31E15 2.15E16 6.86E15 3.43E16 1.50E14 7.49E16 1.27E15 6.35E17 9.79E15 4.89E16 1.96E14 9.82E16 2.18E15 1.09E16 7.24E16 7.24E17 1.66E15 8.29E17 5.09E15 2.54E16 1.10E14 5.50E16 1.14E14 5.68E16 4.93E15 2.47E16 4.84E15 2.42E16 7.93E15 3.97E16 1.41E13 7.07E15 1.99E14 9.93E16 1.84E15 9.19E17 3.38E15 1.69E16 9.36E14 4.68E15 4.00E15 1.30E15 4.40E14 2.20E15 4.07E15 2.03E16 2.73E14 1.37E15 2.85E15 1.43E16 1.17E14 5.84E16a 1.19E14 5.93E16 4.68E14 2.34E15 9.72E15 4.86E16 3.25E14 1.63E15 1.81E13 7.44E15 4.15E14 1.08E15 8.43E14 1.04E15 2.95E15 3.17E16a 7.76E15 3.88E16 2.45E14 5.42E16 1.14E14 5.72E16 1.14E14 5.72E16 2.78E14 6.39E16 3.26E16 3.26E17 4.04E15 2.02E16 2.99E14 1.50E15 5.89E15 2.94E16 2.19E14 1.09E15 2.12E14 1.06E15 1.33E15 1.13E15 1.72E14 8.62E16 2.53E14 1.27E15 4.78E14 2.39E15 5.90E15 2.95E16 1.26E13 6.32E15 1.23E14 6.13E16 3.71E14 1.85E15 9.06E15 4.53E16 9.82E15 4.91E16 5.44E15 2.72E16 5.69E15 2.84E16 5.76E15 2.88E16 1.77E15 8.86E17 2.02E15 1.01E16 1.45E14 7.25E16 1.31E14 6.55E16 2.08E14 1.04E15 4.24E14 2.12E15 3.00E15 1.50E16 2.75E14 1.37E15 7.06E14 3.53E15 7.48E15 3.74E16 3.02E15 1.51E16 1.81E14 9.07E16 4.25E14 2.12E15 4.66E14 2.33E15 2.11E14 1.05E15 2.93E14 1.46E15 1.30E14 6.52E16 6.31E14 3.16E15 1.82E13 9.08E15 1.44E15 7.20E17 2.24E15 1.12E16 1.21E15 6.07E17 4.21E15 2.10E16 3.38E15 1.69E16 1.08E15 5.42E17 9.18E16 7.81E16 3.56E15 1.78E16 1.28E15 6.40E17 5.36E15 2.68E16 6.36E15 3.18E16 2.55E15 1.28E16 1.58E15 7.90E17 3.99E15 1.99E16 2.26E15 1.13E16 3.88E15 1.94E16 8.08E16 8.08E17 2.76E14 1.38E15 6.31E16 6.31E17 6.30E16 6.30E17 7.67E16 7.67E17 1.81E14 9.03E16 2.95E15 1.47E16 1.60E16 1.60E17 3.89E15 1.94E16 8.42E15 4.21E16 1.25E14 6.27E16 2.23E14 1.11E15 1.11E15 5.57E17 2.39E15 1.20E16 3.49E15 1.75E16 1.63E15 8.16E17 7.41E15 3.70E16 6.71E15 3.36E16 8.78E15 4.39E16 8.66E15 4.33E16 5.98E15 8.53E17 3.37E15 1.69E16 4.96E15 6.67E17 5.62E15 2.81E16 2.14E15 1.07E16 6.95E16 6.95E17 9.27E16 7.88E16 4.39E15 2.19E16 9.42E16 8.01E16 1.24E14 6.20E16 1.74E15 8.72E17 5.18E15 2.59E16 1.86E15 9.30E17 7.12E16 7.12E17 1.50E15 7.48E17 1.93E15 9.65E17 1.04E15 5.21E17 5.19E15 2.60E16 5.87E16 5.87E17 8.48E16 8.48E17 2.95E15 1.47E16 5.11E16 5.11E17 3.03E15 1.51E16 1.34E15 6.69E17 5.73E15 2.86E16 8.34E15 4.17E16 1.56E14 7.78E16 5.74E15 2.87E16 1.60E14 8.01E16 2.65E14 1.33E15 3.19E15 1.60E16 2.24E15 1.12E16 3.60E14 1.80E15 1.48E14 7.42E16 1.13E14 5.63E16a 4.37E14 2.18E15 2.77E14 1.39E15 5.86E15 2.93E16 2.44E14 1.22E15 9.24E15 4.62E16 1.27E14 6.33E16 4.46E15 2.23E16 3.46E14 1.73E15 2.17E15 1.09E16 5.52E15 2.76E16 5.34E15 2.67E16 9.16E15 1.58E16 2.32E14 1.16E15 1.31E15 1.11E15 2.14E14 1.07E15 8.23E14 4.12E15 8.01E14 4.00E15 8.59E14 4.29E15 2.10E15 1.05E16 1.14E14 5.69E16 1.04E14 5.22E16 8.21E15 4.11E16 7.02E14 3.51E15 8.20E15 4.10E16 1.18E14 5.92E16 1.31E14 6.57E16 1.53E14 2.91E16 7.62E15 3.81E16 1.50E14 2.84E16 4.41E14 2.20E15 1.12E14 5.58E16a 1.26E15 1.07E15 5.78E15 2.89E16 3.24E14 1.62E15 2.49E15 1.25E16 5.08E14 2.54E15 1.44E14 7.22E16 4.09E14 2.04E15 1.46E14 7.29E16 3.57E15 1.78E16 5.24E15 2.62E16 1.92E15 9.62E17 1.56E15 1.33E15 3.25E14 1.63E15 9.08E16 9.08E17 1.44E14 7.20E16 2.07E14 1.04E15 3.47E15 1.73E16 2.05E14 1.03E15 1.35E14 6.74E16 1.91E14 9.53E16 Table A2 continued 1.85E15 9.25E17 1.30E15 6.50E17 5.66E15 2.83E16 6.06E16 6.06E17 4.58E15 2.29E16 4.04E15 2.02E16 9.26E16 7.87E16 8.82E16 8.82E17 7.37E16 7.37E17 5.66E15 2.83E16 4.31E15 2.16E16 3.74E15 1.87E16 5.88E15 2.94E16 1.06E14 5.29E16 3.16E15 1.58E16 1.52E15 7.62E17 1.88E15 9.38E17 1.67E15 8.35E17 3.39E15 1.69E16 8.59E16 8.59E17 9.21E16 7.83E16 2.02E15 1.01E16 9.77E15 4.88E16 8.40E16 8.40E17 5.70E15 2.85E16 1.57E14 7.87E16 3.71E15 1.86E16 7.34E16 7.34E17 1.35E14 6.74E16 4.20E15 2.10E16 1.25E14 6.25E16 2.22E15 1.11E16 6.07E15 3.04E16 1.68E15 8.42E17 8.13E15 4.06E16 5.60E15 2.80E16 4.69E15 2.35E16 2.38E15 1.19E16 3.26E16 3.26E17 5.20E15 2.60E16 1.10E14 5.52E16 8.78E16 8.78E17 5.08E15 2.54E16 2.14E15 1.07E16 4.82E15 2.41E16 3.72E16 3.72E17 4.96E14 2.48E15 1.32E14 6.59E16 8.28E15 4.14E16 6.85E15 3.42E16 1.80E14 9.00E16 1.95E15 9.77E17 2.99E14 1.49E15 2.70E14 1.35E15 7.58E16 7.58E17 2.04E14 1.02E15 3.08E15 1.54E16 2.39E14 1.20E15 1.45E14 7.26E16 1.26E14 6.31E16 1.46E14 7.31E16 2.09E14 1.04E15 2.29E15 1.14E16 5.37E15 2.69E16 7.51E15 3.76E16 4.68E15 2.34E16 8.74E15 4.37E16a 1.59E15 1.35E15 7.10E15 3.55E16 1.86E14 9.28E16 2.57E14 1.28E15 5.68E15 2.84E16 3.44E14 1.72E15 4.59E14 2.29E15 1.46E14 7.32E16 3.52E15 1.76E16 2.24E14 1.12E15 5.91E14 2.96E15 1.01E13 5.03E15a 4.20E15 2.10E16 3.01E14 1.50E15 1.25E14 6.26E16 1.80E14 8.98E16 5.32E14 2.66E15 1.75E14 8.74E16 1.92E14 9.60E16 1.10E15 9.36E16 1.53E14 7.66E16 5.18E14 2.59E15 4.82E15 2.41E16 2.04E14 1.02E15 4.44E14 2.22E15 1.34E14 6.68E16 1.17E15 9.93E16 2.00E14 1.00E15 1.42E14 7.11E16 Note. P = probability where T = true, L = likely, P = possible. A detailed review of T, L and P is given in RPb. aA flux measured directly from long-slit spectra. bPNe with extremely high H/H > 10 ratios which may have been affected by power-law photoionization or shock-heating (see Section 3.3). This paper has been typeset from a TEX/LATEX file prepared by the author.

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Warren A. Reid, Quentin A. Parker. A new population of planetary nebulae discovered in the Large Magellanic Cloud – III. The luminosity function, Monthly Notices of the Royal Astronomical Society, 2010, 1349-1374, DOI: 10.1111/j.1365-2966.2010.16635.x