Observing white dwarfs orbiting massive black holes in the gravitational wave and electro-magnetic window

A. Sesana 2 A. Vecchio 1 M. Eracleous 0 2 S. Sigurdsson 0 2 0 Department of Astronomy & Astrophysics, The Pennsylvania State University, University Park , PA 16802, USA 1 School of Physics and Astronomy, University of Birmingham , Edgbaston, Birmingham , B15 2TT 2 Center for Gravitational Wave Physics, The Pennsylvania State University, University Park , PA 16802, USA A B S T R A C T We consider a potentially new class of gravitational wave sources consisting of a white dwarf (WD) coalescing into a massive black hole (MBH) in the mass range 104-105 M . These sources are of particular interest because the gravitational wave signal produced during the inspiral phase can be detected by the Laser Interferometer Space Antenna (LISA) and is promptly followed, in an extended portion of the black hole and WD mass parameter space, by an electro-magnetic signal generated by the tidal disruption of the star, detectable with X-ray, optical and ultraviolet (UV) telescopes. This class of sources could therefore yield a considerable number of scientific payoffs, that include precise cosmography at low redshift, demographics of black holes in the mass range 104-105 M , insights into dynamical interactions and populations of WDs in the cores of dwarf galaxies, as well as a new probe into the structure and equation of state of WDs. By modelling the gravitational and electromagnetic radiation produced by these events, we find them detectable in both observational windows at a distance 200 Mpc, and possibly beyond for selected regions of the parameter space. We also estimate the detection rate for a number of model assumptions about black hole and WD mass functions and dynamical interactions: the rate is (not surprisingly) highly uncertain, ranging from 0.01 to 100 yr1. This is due to the current limited theoretical understanding and minimal observational constraints for these objects and processes. However, capture rate scaling arguments favour the high end of the above range, making likely the detection of several events during the LISA lifetime. 1 I N T R O D U C T I O N The simultaneous detection of sources in both the electro-magnetic band which provides a measurement of the source redshift, z and the gravitational wave (GW) window which yields a direct determination of the luminosity distance DL to the source could revolutionize cosmography by determining the distance scale of the Universe in a precise, calibration-free way. This was pointed out initially by Schutz (1986) in the context of groundbased observations of GWs from coalescing compact binaries with the network of ground-based laser interferometers now in operation (Whitcomb 2008). The observational capability of space-based instruments such as the Laser Interferometer Space Antenna (LISA; Bender et al. 1998), which could observe many sources at high signal-to-noise ratio (SNR) and large redshift, has attracted much attention recently. Several scenarios have been considered, primarily related to the identification of the host galaxy or galaxy cluster of MBH binary systems detected in GWs (Cutler 1998; Hughes 2002; Menou 2003; Vecchio 2004; Holz & Hughes 2005; Kocsis et al. 2006; Lang & Hughes 2006; Arun et al. 2007; Kocsis et al. 2007a,b; Porter & Cornish 2008; Lang & Hughes 2008; Trias & Sintes 2008), and the possible electro-magnetic signatures produced by the pre-glow/afterglow of the MBH mergers (Milosavljevic & Phinney 2005; Dotti et al. 2006). The main obstacles to such groundbreaking observations are either the possible paucity of sources likely to produce significant gravitational and electro-magnetic radiation detectable to cosmological distances and/or the rather poor angular resolution of GW instruments (e.g. Cutler 1998; Hughes 2002; Vecchio 2004; Lang & Hughes 2006; Arun et al. 2007; Porter & Cornish 2008; Trias & Sintes 2008), which could inhibit the electro-magnetic identification of the host. In this paper, we discuss a new class of GW sources that have received little attention so far (Menou, Haiman & Kocsis 2008): the inspiral of a white dwarf (WD) around a MBH in the mass range 104105 M followed by the tidal disruption of the star before it plunges into the MBH. As we will show, these sources may be observable at low redshift (a few hundreds Mpc) with LISA and their electro-magnetic emission may be detectable with X-ray observatories and optical ground based telescopes. From the GW point of view, a MBH-WD binary is a different flavour of the socalled Extreme-Mass Ratio Inspirals (EMRIs). Traditionally, the fiducial EMRI is taken to be a stellar-mass 10 M black hole orbiting a 106 M MBH (Barack & Cutler 2004, hereafter BC04). The key difference between a [traditional EMRI] and a MBH-WD system considered in this paper is that for a range of MBH and WD masses, the inspiral does not proceed all the way until the compact object falls into the MBH horizon, but it terminates with the tidal disruption of the WD producing an electro-magnetic signature (for a MBH mass 3 105 M , a WD survives throughout the whole inspiral and the system behaves just like a traditional EMRI). The observation of both gravitational and electro-magnetic signals from the same source provides a direct and calibration-free measurement of the DL(z) relationship and opens new avenues for cosmography and, more directly (due to the low redshift of most of the expected sources) a completely independent determination of the Hubble parameter H0 that does not depend on any distance calibration. This class of sources can also provide new insights into a number of unanswered questions in relativistic astrophysics: (i) the demographics of MBHs in the mass range 104105 M only a handful of MBH candidates with masses below 106 M (Greene & Ho 2004; Barth, Greene & Ho 2005) is known to date, their mass estimate is rather uncertain, since it is based on the emission-line spectra of the active nuclei, and none of them has masses below 105 M (ii) the populations of WDs and the dynamical processes that take place in the cores of dwarf galaxies, that are unknown and unconstrained by observations and (iii) the structure and equation of state of WDs the exact point at which tidal disruption occurs indeed depends on the WD equation of state (e.g. Magorrian & Tremaine 1999), and the electro-magnetic signature carries information about the WD composition. The paper is organized as follows. In Section 2, we identify the mass range of WDs and central MBHs that lead to the tidal disruption of the star before it plunges on to the black hole and we determine the volume of the Universe that LISA will be able to survey. In Section 3, we derive the GW detection rate of these sources and discuss its uncertainties. In Section 4, we model the electromagnetic counterpart to MBH-WD EMRIs. Finally, in Section 5, we summarize the main results and our conclusions. 2 T H E G R AV I TAT I O N A L WAV E S I G N A L 2.1 Mass parameter space Let us consider a MBH of mas (...truncated)