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Stellar tidal disruption events in general relativity

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Abstract

A tidal disruption event (TDE) ensues when a star passes too close to a supermassive black hole (SMBH) in a galactic center, and is ripped apart by its tidal field. The gaseous debris produced in a TDE can power a bright electromagnetic flare as it is accreted by the SMBH; so far, several dozen TDE candidates have been observed. For SMBHs with masses above \(\sim 10^7 M_\odot \), the tidal disruption of solar-type stars occurs within ten gravitational radii of the SMBH, implying that general relativity (GR) is needed to describe gravity. Three promising signatures of GR in TDEs are: (1) a super-exponential cutoff in the volumetric TDE rate for SMBH masses above \(\sim 10^8 M_\odot \) due to direct capture of tidal debris by the event horizon, (2) delays in accretion disk formation (and a consequent alteration of the early-time light curve) caused by the effects of relativistic nodal precession on stream circularization, and (3) quasi-periodic modulation of X-ray emission due to global precession of misaligned accretion disks and the jets they launch. We review theoretical models and simulations of TDEs in Newtonian gravity, then describe how relativistic modifications give rise to these proposed observational signatures, as well as more speculative effects of GR. We conclude with a brief summary of TDE observations and the extent to which they show indications of these predicted relativistic signatures.

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Notes

  1. The third parameter of the general Kerr–Newman metric, electric charge, is expected to be effectively zero for any astrophysical black hole.

  2. The presence of massive black holes in the nuclei of smaller galaxies is poorly constrained due to instrumental limitations.

  3. The strength of the tidal encounter is sometimes quantified with the alternative dimensionless impact parameter \(\eta _t \equiv (M_\star /M_\bullet )^{1/2}(r_p/R_\star )^{3/2}= \beta ^{-3/2}\).

  4. Although see Refs. [35, 41].

  5. Although the late-time power law index can be somewhat shallower or steeper for partial disruptions [40].

  6. See Refs. [36, 54] for a more elaborate generalization of the affine model.

  7. This is not true for deeply plunging encounters (\(\beta \gtrsim 3\)) where compression shocks inject so much heat into the disrupting star that the debris streams never recollapse [79].

  8. Further fragmentation is possible for very stiff gas equations of state [85].

  9. This model is also in rough qualitative agreement with some of the earliest expectations for disk accretion following tidal disruption [93].

  10. However, at very late times, thermal instability may cause significant fluctuations in the accretion rate; see Ref. [105] for more recent one-dimensional \(\alpha \)-disk modeling that accounts for limit-cycle instabilities in a viscously spreading TDE disk.

  11. Although see Ref. [156].

  12. Three or more vertical collapses are possible in a small portion of parameter space.

  13. Note, however, that low-frequency GWs from white dwarf disruption can be visible to larger distances [159].

  14. This discrepancy may be due to the low particle number used in these SPH simulations.

  15. If the star cluster and potential surrounding the SMBH are spherical, the distribution of angular momenta \(\mathbf {L}\) of tidally disrupted stars will be isotropic (flat in \(\cos \iota \), \(\omega \), and \(\varOmega \)) in Newtonian gravity. If these quantities are non-spherical, they may imprint anisotropies in the distribution of \(\mathbf {L}\). These anisotropies will reflect features of the potential on the scale of the influence radius \(r_h \sim \mathrm{pc}\), and are thus unlikely to favor or disfavor equatorial orbits unless the SMBH and nuclear star cluster share a common origin.

  16. Here we refer to “high blackbody temperature” only in comparison to supernova explosions; this blackbody temperature is of course quite low in comparison to that of the X-ray selected TDE sample.

  17. Tidal disruption of much more massive stars, which have larger Hills masses, is disfavored both by their short lifetimes and the paucity of star formation in the ASASSN-15lh host.

  18. A further challenge is the short rise time of the flare, which appears much shorter than the predicted \(t_{\mathrm{min}}\) for such a large SMBH.

  19. There are other interesting questions in the field of TDEs as well, such as the apparent preference of TDEs for rare post-starburst host galaxies [216, 244, 245], but these have less bearing on the relativistic focus of this review.

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Acknowledgements

Financial support was provided to NCS by NASA through Einstein Postdoctoral Fellowship Award Number PF5-160145. MK is supported by the Alfred P. Sloan Foundation Grant FG-2015-65299, NSF Grant PHY-1607031, and NASA Grant 17-ATP17-0045. The work of RMC was funded by a Nicholas C. Metropolis Postdoctoral Fellowship under the auspices of the U.S. Dept. of Energy, and supported by its contract W-7405-ENG-36 to Los Alamos National Laboratory.

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  1. Columbia Astrophysics Laboratory, Columbia University, New York, NY, 10027, USA

    Nicholas C. Stone

  2. Department of Physics, The University of Texas at Dallas, 800 W. Campbell Rd., Richardson, TX, 75080, USA

    Michael Kesden

  3. Computational Physics and Methods Group, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM, 87545, USA

    Roseanne M. Cheng

  4. Center for Cosmology and Particle Physics, New York University, New York, NY, 10003, USA

    Sjoert van Velzen

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Stone, N.C., Kesden, M., Cheng, R.M. et al. Stellar tidal disruption events in general relativity. Gen Relativ Gravit 51, 30 (2019). https://doi.org/10.1007/s10714-019-2510-9

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