#### Distances and peculiar velocities of spiral galaxies in the 2MFGC and SFI++ samples

Yu. N. Kudrya
2
V. E. Karachentseva
2
I. D. Karachentsev
1
S. N. Mitronova
1
W. K. Huchtmeier
0
0
Max-Planck-Institut fr Radioastronomie
,
Bonn, Germany
1
Special Astrophysical Observatory,
Russian Academy of Sciences
,
Russia
2
Astronomical observatory of the Kiev Taras Shevchenko National University
,
Ukraine
We compare infrared Tully-Fisher (TF) distances and peculiar velocities derived for spiral galaxies from the two largest datasets: the 2MASS selected Flat Galaxy Catalog 2MFGC and the Arecibo General Catalog with I-band photometry, SFI++. These samples contain peculiar velocities for ~3000 and ~4000 objects, respectively. Based on a sub-sample of ~1000 common very inclined galaxies, we reach the following conclusions. Irrespective of high (SFI++) or low (2MFGC) quality of the photometric data used, both the samples have ~10% fraction of galaxies deviating considerably from the main body of the TF relation. After their deletion, the standard TF scatter drops to 0m.47 (2MFGC) and 0m.40 (SFI++). The TF distances, derived from two samples, demonstrate a high degree of mutual agreement with a correlation coefficient = +0.95 and (H 0r ) = 837 km/s. Peculiar velocities of the galaxies are also correlated with = 0.56 0.59 and (Vpec ) = 610 km/s. We find that the bulk motion of the 2MFGC and SFI++ galaxies on a typical scale of H 0r 5700 km/s can be represented by a dipole solution with the amplitude V = (297 23) km/s directed towards {l = 2920 40 , b = 120 30 }, being only slightly sensitive to different modifications of the TF relaton.
1. Introduction
compiling this catalog, they make use of digital optical images, optical long-slit spectra and global HI line profiles
to extract parameters of relevance to disk scaling relations, incorporating several previously published datasets as well
as a new photometric sample of some 2000 objects. In this paper we intend to find out how estimates of TF-distances
and peculiar velocities of spiral galaxies depend on the properties of the initial sample, as well as the method of
correction of observables and the manner of data analysis. With this idea in mind, we compare distances and peculiar
velocities contained in the catalogs [20,7].
2. Determination of distances and peculiar velocities by the Tully-Fisher method
Fig. 1. Sky distribution of galaxies from the 2MFGC sample (top panel)
and the SFI++ sample (bottom panel) in galactic coordinates.
M = c 0 + c1 log W5c0 + c2 log (a b )+ c3 Jhl + c 4 (J cfe K cfe )+ c5 Jc dex ,
M = J cfe 25 5log r ,
r = V3 K {1 (q0 1)V3K 2 c} H 0 ,
where the photometric distance r (in Mpc) was expressed via the radial velocity by the post-Hubble relation
Fig. 2. Top: The Tully-Fisher diagram for the 2MFGC sample
before cleaning (left) and after it (right panel). Bottom: The TF
diagram for the initial (left panel) and cleaned (right panel)
sample of SFI++ galaxies.
deviations are caused by observational errors, but not physical reasons. After making several consecutive eliminating
At the second step, after calibrating the TF relation, we determined individual galaxy distances H0r from (1)
and (2) and calculated their individual peculiar velocities as
Vpec = V3K H0r{1+ (q0 1)H0r 2 c}.
As a result, individual distances and peculiar velocities of 2724 2MFGC galaxies were presented in [20].
2.2. The SFI++ sample. This sample was compiled as a sum of the following subsamples.
a) The SCI (24 clusters having mean velocities less than 10000 km/s).
b) The SC2 (52 all sky clusters with recessional velocities 5000 < cz < 2500km/s).
c) The SFI was comprised of a TF sample of 2000 field galaxies limited to cz < 7500 km/s, blue magnitude
3. Common galaxies in the 2MFGC and SFI++ samples.
Fig.3. Comparison of corrected line-widths in the SFI++
and 2MFGC samples for 983 common edge-on
galaxies. Galaxies outside the 3 band are marked by
their 2MFGC numbers.
Fig. 4. Comparison of corrected I-band and
J-band magnitudes for 983 common galaxies
in the considered samples. Deviating galaxies
are denoted by their 2MFGC numbers.
to a photometric error ~ 0m.25 in the 2MASS sample.
Figure 4 demonstrates the relation between apparent magnitudes of 983 common galaxies. The I-band
magnitudes corrected for internal and external (Galactic) extinction are taken from [7], and J-band magnitudes
It is caused mostly by underestimating total luminosities of galaxies with faint extended periphery based on the
shallow 2MASS photometry.
3.2. Comparison of distances
The panels in Fig. 5 reproduce a comparison of distances determined for 983 objects common in the 2MFGC
catalog and the SFI++ sample without (left panel) and with (right panel) allowance made for the Malmquist bias. The
dashed line denotes the line of direct regression and the solid line is the diagonal (in the right panel it is practically
indistinguishable from the regression line). From the adduced analysis it follows that the 2MFGC distances are in
a bit better agreement with the SFI++ distances obtained with allowance made for the Malmquist bias. Since we
determined the 2MFGC distances on the basis of a multiparameter generalization of the TF relation, it can be assumed
that the use of additional regressors reduces the Malmquist bias, at least, partially. We note also that in the case of
orthogonal regression with
H 0r(SFI + +) = (1.024 0.005) H 0r (2MFGC )
the Fisher statistics is equal to 1.8. Comparing this value with the Fisher quantile for the 95% significance level (3.84),
Fig. 5. Comparison of distances to 983 SFI++ galaxies calculated without (left
panel) and with (right panel) allowance made for the Malmquist bias with
distances to the same galaxies calculated for the 2MFGC sample.
Vpec (2MFGC), km/s
Vpec (2MFGC), km/s
Fig. 6. Peculiar velocities obtained from the SFI++ sample without (left panel)
and with (right panel) allowance made for the Malmquist bias versus peculiar
velocities of the same 983 galaxies derived from the 2MFGC catalog.
we conclude that this hypothesis may be statistically consistent. In such a case, we have the straight proportion of
distances with the rms scatter (H 0r )= 840 km/s and = +0.95 .
3.3. Comparison of peculiar velocities. The two panels in Fig. 6 present a comparison of peculiar velocities
for 983 common galaxies. Ellipses in the figure are boundaries of the 95% probability level if one accepts the plane
distribution of points to be a two-dimensional Gaussian one with averages, dispersions, and a correlation coefficient
peculiar velocities in the SFI++ sample with allowance made for the Malmquist bias, than to peculiar velocities
The outermost dashed lines in Fig. 6 correspond to the direct and inverse regressions, and the middle dashed
line denotes the orthogonal regression. In the case of peculiar velocities with allowance made for the Malmquist bias,
the orthogonal regression takes the form
V pec (SFI + +) = (1.00 0.04)V pec (2MFGC ) (230 28),
i.e. the velocities Vpec (SFI + +) are, on average, 230 km/s less than the peculiar velocities Vpec (2MFGC).
4. Parameters of dipole solution.
4.1. The 2MFGC sample. Now we use arrays of peculiar velocities Vpec to calculate orthogonal components
V pec,i = V ei + V p,i
by minimizing the sum of squares of a "noise" component Vp,i of the peculiar velocity (i is the order number of a
These quantities manifest different statistical significances of the regressors used in the multiparameter TF
2MFGC 3074 (1) 0.763 -4.66 0.10 1668 169 56 314 19 -7 15 3.1
2MFGC(cln) 2724 (1) 0.471 -6.53 0.08 1018 199 37 304 11 -8 8 9.8
2MFGC 3074 (6) 0.874 -6.01 0.09 1892 411 65 314 9 -32 7 14
2MFGC(cln) 2676 (6) 0.482 -7.53 0.06 1050 313 39 304 7 -20 5 21
2MFGC 3074 (7) - -9.07 2073 463 72 300 9 -32 7 14
2MFGC(cln) 2663 (7) - -9.07 1091 334 41 291 7 -19 5 22
M J 5 log(h) = 21.00 9.07 (logW50 2.5).
c
The results are presented in the last two rows of Table 1. Surprisingly, despite considerably increasing the slope of
the TF relation, the dipole parameters turned out to be close to those obtained with the TF relation (6) calibrated
directly by the 2MFGC data.
4.2. The SFI++ sample. Then we processed data on the SFI++ sample following the scheme accepted before
a) We repeated the calculation using the simple TF relation instead of (1)
M 5 log(h) = c0 + c1 logW5c0 ,
M I 5 log(h) = c0 + c1 log Wcorr + c2 log(1 e)+ c3 log(r23.5 r83 L )+ c4 T
applying it to the initial and cleaned SFI++ samples. A number of galaxies fell out of analysis because of lack of
additional data for them. Results of our calculation are shown in the last two rows of Table 2. The coefficients ci in
the relation (9) for the cleaned sample together with their significance according to the Fisher criterion (given in
parentheses) turn out to be
c0 = 3.86 0.15 (661), c1 = 6.87 0.05 ( (13890),
c2 = 0.421 0.038 (123), c3 = 0.63 0.10 (36),
c4 = 0.0188 0.0054 (12).
5. Discussion and conclusions In this paper we tried to outline how much the estimates of distances and peculiar velocities of spiral galaxies determined by the Tully-Fisher method depend on the features of forming the initial sample and the manner of 346
km/s, lB = 292o 4o , bB = 12o 3o . The obtained values are in satisfactory fit with the estimates { VB , lB , bB }
derived by the MarkIII team [31] and some other samples, with due regard to their lower goodness. The observed
agreement between directions and amplitudes of bulk motions for different samples of spiral galaxies on the scale
~6000 km/s allows us to assume that a combined sample of N ~ 6000 disk-dominated galaxies (with the expected
goodness of G ~ 20) will serve as a firm ground for studying in detail the local peculiar velocity field.