The Telltale Heartbeat: Detection and Characterization of Eccentric Orbiting Planets via Tides on their Host Star

We present an analytic description of tides raised on a star by a small orbiting body. In particular, we highlight the disproportionate effect of eccentricity and thus the scope for using these tides to detect and characterise the orbits of exoplanets and brown dwarfs. The tidal distortions of the star produced by an eccentric orbit are, in comparison to a circular orbit, much richer in detail, and potentially visible from any viewing angle. The magnitude of these variations is much larger than that in a circular orbit of the same semi-major axis. These variations are visible in both photometric and spectroscopic data, and dominate other regular sources of phase variability (e.g reflection and Doppler beaming) over a particularly interesting portion of parameter space. These tidal signatures will be a useful tool for planet detection on their own, and used in concert with other methods provide powerful constraints on planetary and stellar properties.Comment: Accepted by ApJ, 23 pages, 13 figure

A Bright Year for Tidal Disruptions?

When a star is tidally disrupted by a supermassive black hole (BH), roughly half of its mass falls back to the BH at super-Eddington rates. Being tenuously gravitationally bound and unable to cool radiatively, only a small fraction f_in << 1 of the returning debris will likely be incorporated into the disk and accrete, with the vast majority instead becoming unbound in an outflow of velocity ~1e4 km/s. This slow outflow spreads laterally, encasing the BH. For months or longer, the outflow remains sufficiently neutral to block hard EUV and X-ray radiation from the hot inner disk, which instead becomes trapped in a radiation-dominated nebula. Ionizing nebular radiation heats the inner edge of the ejecta to temperatures of T > few 1e4 K, converting the emission to optical/near-UV wavelengths where photons more readily escape due to the lower opacity. This can explain the unexpectedly low and temporally constant effective temperatures of optically-discovered TDE flares. For BHs with relatively high masses M_BH > 1e7 M_sun the ejecta can become ionized at an earlier stage, or for a wider range of viewing angles, producing a TDE flare which is instead dominated by thermal X-ray emission. We predict total radiated energies consistent with those of observed TDE flares, and ejecta velocities that agree with the measured emission line widths. The peak optical luminosity for M_BH < 1e6 M_sun is suppressed due to adiabatic losses in the inner disk wind, possibly contributing to the unexpected dearth of optical TDEs in galaxies with low mass BHs. In the classical picture, where f_in ~ 1, TDEs de-spin supermassive BHs and cap their maximum spins well below theoretical accretion physics limits. This cap is greatly relaxed in our model, and existing Fe K-alpha spin measurements provide suggestive preliminary evidence that f_in < 1.Comment: 13 pages, 7 figures, submitted to MNRA

Periodic accretion-powered flares from colliding EMRIs as TDE Imposters

When a main sequence star undergoes Roche lobe overflow onto a supermassive black hole (SMBH) in a circular extreme mass ratio inspiral (EMRI), a phase of steady mass transfer ensues. Over millions of years, the binary evolves to a period minimum before reversing course and migrating outwards. Because the time interval between consecutive EMRIs is comparable to the mass-transfer timescale, the semi-major axes of two consecutive mass-transferring EMRIs will cross on a radial scale < few AU. We show that such EMRI crossing events are inevitably accompanied by a series of mildly relativistic, grazing physical collisions between the stars. Each collision strips a small quantity of mass, primarily from the more massive star, which generally increases their radial separation to set up the next collision after a delay of decades to centuries (or longer) set by further gravitational radiation. Depending on the mass of the SMBH, this interaction can result in N ~ 1-1e4 gas production events of mass Msun/N, thus powering a quasi-periodic sequence of SMBH accretion-powered flares over a total duration of thousands of years or longer. Although the EMRI rate is 2-3 orders of magnitude lower than the rate of tidal disruption events (TDE), the ability of a single interacting EMRI pair to produce a large number of luminous flares - and to make more judicious use of the available stellar fuel - could make their observed rate competitive with the TDE rate, enabling them to masquerade as "TDE Imposters." We predict flares with luminosities that decay both as power laws shallower than t^(-5/3) or as decaying exponentials. Viscous spreading of the gas disks produced by the accumulation of previous mass-stripping events places substantial mass on radial scales > 10-100 AU, providing a reprocessing source required to explain the unexpectedly high optical luminosities of some flares.Comment: 13 pages, submitte

An enhanced rate of tidal disruptions in the centrally overdense E+A galaxy NGC 3156

Time domain optical surveys have discovered roughly a dozen candidate stellar tidal disruption flares in the last five years, and future surveys like the {\it Large Synoptic Survey Telescope} will likely find hundreds to thousands more. These tidal disruption events (TDEs) present an interesting puzzle: a majority of the current TDE sample is hosted by rare post-starburst galaxies, and tens of percent are hosted in even rarer E+A galaxies, which make up $\sim 0.1\%$ of all galaxies in the local universe. E+As are therefore overrepresented among TDE hosts by 1-2 orders of magnitude, a discrepancy unlikely to be accounted for by selection effects. We analyze {\it Hubble Space Telescope} photometry of one of the nearest E+A galaxies, NGC~3156, to estimate the rate of stellar tidal disruption produced as two-body relaxation diffuses stars onto orbits in the loss cone of the central supermassive black hole. The rate of TDEs produced by two-body relaxation in NGC~3156 is large when compared to other galaxies with similar black hole mass: $\dot{N}_{\rm TDE}\sim 1\times 10^{-3}~{\rm yr}^{-1}$. This suggests that the preference of TDEs for E+A hosts may be due to central stellar overdensities produced in recent starbursts.Comment: 8 pages, 4 figures, 2 tables. Minor changes made to match published version in ApJ

A Dynamical Potential-Density Pair for Star Clusters With Nearly Isothermal Interiors

We present a potential-density pair designed to model nearly isothermal star clusters (and similar self-gravitating systems) with a central core and an outer turnover radius, beyond which density falls off as $r^{-4}$. In the intermediate zone, the profile is similar to that of an isothermal sphere (density $\rho \propto r^{-2}$), somewhat less steep than the King 62 profile, and with the advantage that many dynamical quantities can be written in a simple closed form. We derive new analytic expressions for the cluster binding energy and velocity dispersion, and apply these to create toy models for cluster core collapse and evaporation. We fit our projected surface brightness profiles to observed globular and open clusters, and find that the quality of the fit is generally at least as good as that for the surface brightness profiles of King 62. This model can be used for convenient computation of the dynamics and evolution of globular and nuclear star clusters.Comment: 6 pages, 5 figures. Published in ApJL; changes to match published versio

Circularization of Tidally Disrupted Stars around Spinning Supermassive Black Holes

We study the circularization of tidally disrupted stars on bound orbits around spinning supermassive black holes by performing three-dimensional smoothed particle hydrodynamic simulations with Post-Newtonian corrections. Our simulations reveal that debris circularization depends sensitively on the efficiency of radiative cooling. There are two stages in debris circularization if radiative cooling is inefficient: first, the stellar debris streams self-intersect due to relativistic apsidal precession; shocks at the intersection points thermalize orbital energy and the debris forms a geometrically thick, ring-like structure around the black hole. The ring rapidly spreads via viscous diffusion, leading to the formation of a geometrically thick accretion disk. In contrast, if radiative cooling is efficient, the stellar debris circularizes due to self-intersection shocks and forms a geometrically thin ring-like structure. In this case, the dissipated energy can be emitted during debris circularization as a precursor to the subsequent tidal disruption flare. The possible radiated energy is up to ~2*10^{52} erg for a 1 Msun star orbiting a 10^6 Msun black hole. We also find that a retrograde (prograde) black hole spin causes the shock-induced circularization timescale to be shorter (longer) than that of a non-spinning black hole in both cooling cases. The circularization timescale is remarkably long in the radiatively efficient cooling case, and is also sensitive to black hole spin. Specifically, Lense-Thirring torques cause dynamically important nodal precession, which significantly delays debris circularization. On the other hand, nodal precession is too slow to produce observable signatures in the radiatively inefficient case. We also discuss the relationship between our simulations and the parabolic TDEs that are characteristic of most stellar tidal disruptions.Comment: 23 pages, 18 figures, 1 appendix, accepted for publication in MNRAS (with significant improvement

Circumnuclear Media of Quiescent Supermassive Black Holes

We calculate steady-state, one-dimensional hydrodynamic profiles of hot gas in slowly accreting ("quiescent") galactic nuclei for a range of central black hole masses $M_{\bullet}$, parametrized gas heating rates, and observationally-motivated stellar density profiles. Mass is supplied to the circumnuclear medium by stellar winds, while energy is injected primarily by stellar winds, supernovae, and black hole feedback. Analytic estimates are derived for the stagnation radius (where the radial velocity of the gas passes through zero) and the large scale gas inflow rate, $\dot{M}$, as a function of $M_{\bullet}$ and the gas heating efficiency, the latter being related to the star-formation history. We assess the conditions under which radiative instabilities develop in the hydrostatic region near the stagnation radius, both in the case of a single burst of star formation and for the average star formation history predicted by cosmological simulations. By combining a sample of measured nuclear X-ray luminosities, $L_x$, of nearby quiescent galactic nuclei with our results for $\dot{M}(M_{\bullet})$ we address whether the nuclei are consistent with accreting in a steady-state, thermally-stable manner for radiative efficiencies predicted for radiatively inefficiency accretion flows. We find thermally-stable accretion cannot explain the short average growth times of low mass black holes in the local Universe, which must instead result from gas being fed in from large radii, due either to gas inflows or thermal instabilities acting on larger, galactic scales. Our results have implications for attempts to constrain the occupation fraction of SMBHs in low mass galaxies using the mean $L_x-M_{\bullet}$ correlation, as well as the predicted diversity of the circumnuclear densities encountered by relativistic outflows from tidal disruption events.Comment: 24 pages, 11 figures, 2 tables. Published in MNRA

Assisted Inspirals of Stellar Mass Black Holes Embedded in AGN Disks: Solving the "Final AU Problem"

We explore the evolution of stellar mass black hole binaries (BHBs) which are formed in the self-gravitating disks of active galactic nuclei (AGN). Hardening due to three-body scattering and gaseous drag are effective mechanisms that reduce the semi-major axis of a BHB to radii where gravitational waves take over, on timescales shorter than the typical lifetime of the AGN disk. Taking observationally-motivated assumptions for the rate of star formation in AGN disks, we find a rate of disk-induced BHB mergers ($\mathcal{R} \sim 3~{\rm yr}^{-1}~{\rm Gpc}^{-3}$, but with large uncertainties) that is comparable with existing estimates of the field rate of BHB mergers, and the approximate BHB merger rate implied by the recent Advanced LIGO detection of GW150914. BHBs formed thorough this channel will frequently be associated with luminous AGN, which are relatively rare within the sky error regions of future gravitational wave detector arrays. This channel could also possess a (potentially transient) electromagnetic counterpart due to super-Eddington accretion onto the stellar mass black hole following the merger.Comment: 10 pages, 3 figures, changes made to match MNRAS published versio

The Delay Time Distribution of Tidal Disruption Flares

Recent observations suggest that stellar tidal disruption events (TDE) are strongly overrepresented in rare, post-starburst galaxies. Several dynamical mechanisms have been proposed to elevate their TDE rates, ranging from central stellar overdensities to the presence of supermassive black hole (SMBH) binaries. Another such mechanism, introduced here, is a radial velocity anisotropy in the nuclear star cluster produced during the starburst. These, and other, dynamical hypotheses can be disentangled by comparing observations to theoretical predictions for the TDE delay time distribution (DTD). We show that SMBH binaries are a less plausible solution for the post-starburst preference, as they can only reproduce the observed DTD with extensive fine-tuning. The overdensity hypothesis produces a reasonable match to the observed DTD (based on the limited data currently available), provided that the initial stellar density profile created during the starburst, $\rho(r)$, is exceptional in both steepness and normalization. In particular, explaining the post-starburst preference requires $\rho \propto r^{-\gamma}$ with $\gamma \gtrsim 2.5$, i.e. much steeper than the classic Bahcall-Wolf equilibrium profile of $\gamma = 7/4$. For "ultrasteep" density cusps ($\gamma \ge 9/4$), we show that the TDE rate decays with time measured since the starburst as $\dot{N} \propto t^{-(4\gamma-9)/(2\gamma-3)} / \ln t$. Radial anisotropies also represent a promising explanation, provided that initial anisotropy parameters of $\beta_0 \approx 0.5$ are sustainable against the radial orbit instability. TDE rates in initially anisotropic cusps will decay roughly as $\dot{N} \propto t^{-\beta_0}$. As the sample of TDEs with well-studied host galaxies grows, the DTD will become a powerful tool for constraining the exceptional dynamical properties of post-starburst galactic nuclei.Comment: 15 pages, 10 figures, 2 appendices. Submitted to MNRAS, comments welcom

Formation of Massive Black Holes in Galactic Nuclei: Runaway Tidal Encounters

Nuclear star clusters (NSCs) and supermassive black holes (SMBHs) both inhabit galactic nuclei, coexisting in a range of bulge masses, but excluding each other in the largest or smallest galaxies. We propose that the transformation of NSCs into SMBHs occurs via runaway tidal captures, once NSCs exceed a certain critical central density and velocity dispersion. The bottleneck in this process, as with all collisional runaways, is growing the first e-fold in black hole mass. The growth of a stellar mass black hole past this bottleneck occurs as tidally captured stars are consumed in repeated episodes of mass transfer at pericenter. Tidal captures may turn off as a growth channel once the black hole reaches a mass ~100-1000 solar masses, but tidal disruption events will continue and appear capable of growing the seed SMBH to larger sizes. The runaway slows (becomes sub-exponential) once the seed SMBH consumes the core of its host NSC. While the bulk of the cosmic mass density in SMBHs is ultimately produced (via the Soltan-Paczynski argument) by episodic gaseous accretion in very massive galaxies, the smallest SMBHs have probably grown from strong tidal encounters with NSC stars. SMBH seeds that grow for a time $t$ entirely through this channel will follow simple power law relations with the velocity dispersion, $\sigma$, of their host galaxy. In the simplest regime it is $M_\bullet \sim \sigma^{3/2}\sqrt{M_\star t / G} \sim 10^{6}M_\odot (\sigma / 50~{\rm km~s}^{-1})^{3/2}(t/10^{10}~{\rm yr})^{1/2}$, but the exponents and prefactor can differ slightly depending on the details of loss cone refilling. Current tidal disruption event rates predicted from this mechanism are consistent with observations.Comment: 18 pages, 9 figures, comments welcom