Search

Among the potential milliHz gravitational wave (GW) sources for the upcoming space-based interferometer LISA are extreme- or intermediate-mass ratio inspirals (EMRI/IMRIs). These events involve the coalescence of supermassive black holes in the mass range $10^5 M_{\odot} \lesssim M \lesssim 10^7 M_{\odot}$ with companion BHs of much lower masses. A subset of E/IMRIs are expected to occur in the accretion discs of active galactic nuclei (AGN), where torques exerted by the disc can interfere with the inspiral and cause a phase shift in the GW waveform. Here we use a suite of two-dimensional hydrodynamical simulations with the moving-mesh code DISCO to present a systematic study of disc torques. We measure torques on an inspiraling BH and compute the corresponding waveform deviations as a function of the binary mass ratio $q\equiv M_2/M_1$, the disc viscosity ($\alpha$), and gas temperature (or equivalently Mach number; $\mathcal{M}$). We find that the absolute value of the gas torques is within an order of magnitude of previously determined planetary migration torques, but their precise value and sign depends non-trivially on the combination of these parameters. The gas imprint is detectable by LISA for binaries embedded in AGN discs with surface densities above $\Sigma_0\ge10^{4-6} \rm \, g cm^{-2}$, depending on $q$, $\alpha$ and $\mathcal{M}$. Deviations are most pronounced in discs with higher viscosities, and for E/IMRIs detected at frequencies where LISA is most sensitive. Torques in colder discs exhibit a noticeable dependence on the GW-driven inspiral rate as well as strong fluctuations at late stages of the inspiral. Our results further suggest that LISA may be able to place constraints on AGN disc parameters and the physics of disc-satellite interaction.

The community may be on the verge of detecting low-frequency gravitational waves from massive black hole binaries (MBHBs), but no examples of binary active galactic nuclei (AGN) have been confirmed. Because MBHBs are intrinsically rare, the most promising detection methods utilize photometric data from all-sky surveys. Recently D'Orazio & Di Stefano 2018 (arXiv:1707.02335) suggested gravitational self-lensing as a method of detecting AGN in close separation binaries. In this study we calculate the detectability of lensing signatures in realistic populations of simulated MBHBs. Within our model assumptions, we find that VRO's LSST should be able to detect 10s to 100s of self-lensing binaries, with the rate uncertainty depending primarily on the orientation of AGN disks relative to their binary orbits. Roughly a quarter of lensing detectable systems should also show detectable Doppler boosting signatures. If AGN disks tend to be aligned with the orbit, lensing signatures are very nearly achromatic, while in misaligned configurations the bluer optical bands are lensed more than redder ones. Whether substantial obscuring material (e.g.~a dusty torus) will be present in close binaries remains uncertain, but our estimates suggest that a substantial fraction of systems would still be observable in this case., 10+3 pages, 4+2 figures, comments welcome and appreciated

We show that nearly half of all binary black hole (BBH) mergers dynamically assembled in globular clusters have measurable eccentricities ($e>0.01$) in the LISA band ($10^{-2}$ Hz), when General Relativistic corrections are properly included in the $N$-body evolution. If only Newtonian gravity is included, the derived fraction of eccentric LISA sources is significantly lower, which explains why recent studies all have greatly underestimated this fraction. Our findings have major implications for how to observationally distinguish between BBH formation channels using eccentricity with LISA, which is one of the key science goals of the mission. We illustrate that the relatively large population of eccentric LISA sources reported here originates from BBHs that merge between hardening binary-single interactions inside their globular cluster. These results indicate a bright future for using LISA to probe the origin of BBH mergers., accepted version. MNRAS

The optical and UV emission from sub-parsec massive black hole binaries (MBHBs) in active galactic nuclei (AGN) is believed to vary periodically, on timescales comparable to the binary's orbital time. If driven by accretion rate fluctuations, the variability could be isotropic. If dominated by relativistic Doppler modulation, the variability should instead be anisotropic, resembling a rotating forward-beamed lighthouse. We consider the infrared (IR) reverberation of either type of periodic emission by pc-scale circumbinary dust tori. We predict the phase and amplitude of IR variability as a function of the ratio of dust light crossing time to the source variability period, and of the torus inclination and opening angle. We enumerate several differences between the isotropic and anisotropic cases. Interestingly, for a nearly face-on binary with an inclined dust torus, the Doppler boost can produce IR variability without any observable optical/UV variability. Such orphan-IR variability would have been missed in optical searches for periodic AGN. We apply our models to time-domain WISE IR data from the MBHB candidate PG 1302-102 and find consistency with dust reverberation by both isotropically emitting and Doppler-boosted sources in the shorter wavelength W1-W2 (2.8-5.3 micrometer) bands. We constrain the dust torus to be thin (aspect ratio ~0.1), with an inner radius at 1-5 pc. More generally, our dust echo models will aid in identifying new MBHB candidates, determining their nature, and constraining the physical properties of MBHBs and their dust tori., We dedicate this work to the memory of Arlin Crotts, an expert on supernova light echoes who passed away on November 19, 2015

The bright quasar PG1302-102 has been identified as a candidate supermassive black hole binary from its near-sinusoidal optical variability. While the significance of its optical periodicity has been debated due to the stochastic variability of quasars, its multi-wavelength variability in the ultraviolet (UV) and optical bands is consistent with relativistic Doppler boost caused by the orbital motion in a binary. However, this conclusion was based previously on sparse UV data which were not taken simultaneously with the optical data. Here we report simultaneous follow-up observations of PG1302-102 with the Ultraviolet Optical Telescope on the Neil Gehrels Swift Observatory in six optical + UV bands. The additional nine Swift observations produce light curves roughly consistent with the trend under the Doppler boost hypothesis, which predicts that UV variability should track the optical, but with a ~2.2 times higher amplitude. We perform a statistical analysis to quantitatively test this hypothesis. We find that the data are consistent with the Doppler boost hypothesis when we compare the the amplitudes in optical B-band and UV light curves. However, the ratio of UV to V-band variability is larger than expected and is consistent with the Doppler model, only if either the UV/optical spectral slopes vary, the stochastic variability makes a large contribution in the UV, or the sparse new optical data underestimate the true optical variability. We have evidence for the latter from comparison with the optical light curve from ASAS-SN. Additionally, the simultaneous analysis of all four bands strongly disfavors the Doppler boost model whenever Swift V-band is involved. Additional, simultaneous optical + UV observations tracing out another cycle of the 5.2-year proposed periodicity should lead to a definitive conclusion., Comment: accepted in MNRAS

We study the formation rate of binary black hole mergers formed through gravitational-wave emission between unbound, single black holes in globular clusters. While the formation of these binaries in very dense systems such as galactic nuclei has been well studied, we show here that this process can operate in lower-density stellar systems as well, forming binaries at a rate similar to other proposed pathways for creating eccentric mergers. Recent advances in post-Newtonian cluster dynamics indicate that a large fraction of dynamically-assembled binary black holes merge inside their host clusters during weak and strong binary-single and binary-binary interactions, and that these systems may retain measurable eccentricities as they travel through the LIGO and LISA sensitivity bands. Using an analytic approach to modeling binary black holes from globular clusters, we show that the formation of merging binaries from previously unbound black holes can operate at a similar rate to mergers forming during strong binary encounters, and that these binaries inhabit a unique region of the gravitational-wave frequency space which can be identified by proposed deci-Hertz space-based detectors., Comment: 16 pages, 5 figures. Accepted version (PRD)

We consider binary black holes (BBHs) in a hierarchical triple system where a more compact, less-massive binary is emitting detectable gravitational waves (GWs), and the tertiary is a supermassive BH at the center of a nuclear star cluster. As previous works have shown, the orbital motion of the outer binary can generate a detectable relativistic Doppler boost of the GWs emitted by the orbiting inner binary. We show here that for outer-binary orbits with a period of order one year, there can be a non-negligible probability for repeated gravitational lensing of the GWs emitted by the inner binary. Repeating gravitational lensing events could be detected by the LISA observatory as periodic GW amplitude spikes before the BBH enters the LIGO band. Such a detection would confirm the origin of some BBH mergers in nuclear star clusters. GW lensing also offers new testing grounds for strong gravity., Comment: Accepted to Physical Review D. Comments welcome

We present analysis of Chandra X-ray observations of seven quasars that were identified as candidate subparsec binary supermassive black hole (SMBH) systems in the Catalina Real-Time Transient Survey based on the apparent periodicity in their optical light curves. Simulations predict that close-separation accreting SMBH binaries will have different X-ray spectra than single accreting SMBHs, including harder or softer X-ray spectra, ripple-like profiles in the Fe K-α line, and distinct peaks in the spectrum due to the separation of the accretion disk into a circumbinary disk and mini disks around each SMBH. We obtained Chandra observations to test these models and assess whether these quasars could contain binary SMBHs. We instead find that the quasar spectra are all well fit by simple absorbed power-law models, with the rest-frame 2–10 keV photon indices, Γ, and the X-ray-to-optical power slopes, α_(OX), indistinguishable from those of the larger quasar population. This may indicate that these seven quasars are not truly subparsec binary SMBH systems, or it may simply reflect that our sample size was too small to robustly detect any differences. Alternatively, the X-ray spectral changes might only be evident at energies higher than probed by Chandra. Given the available models and current data, no firm conclusions are drawn. These observations will help motivate and direct further work on theoretical models of binary SMBH systems, such as modeling systems with thinner accretion disks and larger binary separations.

The merger of stellar-mass black holes (BHs) is not expected to generate detectable electromagnetic (EM) emission. However, the gravitational wave (GW) events GW150914 and GW170104, detected by the Laser Interferometer Gravitational Wave Observatory (LIGO) to be the result of merging, ~60 solar mass binary black holes (BBHs), each have claimed coincident gamma-ray emission. Motivated by the intriguing possibility of an EM counterpart to BBH mergers, we construct a model that can reproduce the observed EM and GW signals for GW150914- and GW170104-like events, from a single-star progenitor. Following Loeb (2016), we envision a massive, rapidly rotating star within which a rotating bar instability fractures the core into two overdensities that fragment into clumps which merge to form BHs in a tight binary with arbitrary spin-orbit alignment. Once formed, the BBH inspirals due to gas and gravitational-wave drag until tidal forces trigger strong feeding of the BHs with the surrounding stellar-density gas about 10 seconds before merger. The resulting giga-Eddington accretion peak launches a jet that breaks out of the progenitor star and drives a powerful outflow that clears the gas from the orbit of the binary within one second, preserving the vacuum GW waveform in the LIGO band. The single-progenitor scenario predicts the existence of variability of the gamma-ray burst, modulated at the ~0.2 second chirping period of the BBH due to relativistic Doppler boost. The jet breakout should be accompanied by a low-luminosity supernova. Finally, because the BBHs of the single progenitor model do not exist at large separations, they will not be detectable in the low frequency gravitational wave band of the Laser Interferometer Space Antenna (LISA). Hence, the single-progenitor BBHs will be unambiguously discernible from BBHs formed through alternate, double-progenitor evolution scenarios., Comment: Published in Physical Review D

We derive the observable gravitational wave (GW) peak frequency ($f$) distribution of binary black holes (BBHs) that currently reside inside their globular clusters (GCs), with and without 2.5 Post-Newtonian (2.5PN) effects included in the dynamical evolution of the BBHs. Recent Newtonian studies have reported that a notable number of nearby non-merging BBHs, i.e. those BBHs that are expected to undergo further dynamical interactions before merger, in GCs are likely to be observable by LISA. However, our 2.5PN calculations show that the distribution of $\log f$ for the non-merging BBH population above $\sim 10^{-3.5}$ Hz scales as $f^{-34/9}$ instead of the $f^{-2/3}$ scaling found in the Newtonian case. This leads to an approximately two-orders-of-magnitude reduction in the expected number of GW sources at $\sim 10^{-3}$ Hz, which lead us to conclude that observing nearby BBHs with LISA is not as likely as has been claimed in the recent literature. In fact, our results suggest that it might be more likely that LISA detects the population of BBHs that will merge before undergoing further interactions. This interestingly suggests that the BBH merger rate derived from LIGO can be used to forecast the number of nearby LISA sources, as well as providing insight into the fraction of BBH mergers forming in GCs., Comment: 9 pages. 1 figure

We show that a 10 year Gaia mission could astrometrically detect the orbital motion of ~1 sub-parsec separation supermassive black hole binary in the heart of nearby, bright active galactic nuclei (AGN). Candidate AGN lie out to a redshift of z=0.02 and in the V-band magnitude range $10 \lesssim m_V \lesssim 13$. The distribution of detectable binary masses peaks at a few times $10^7$ solar masses and is truncated above a few times $10^8$ solar masses., Comment: Published in Phys. Rev. D

Supermassive black hole binaries (SMBHBs) should be common in galactic nuclei as a result of frequent galaxy mergers. Recently, a large sample of sub-parsec SMBHB candidates was identified as bright periodically variable quasars in optical surveys. If the observed periodicity corresponds to the redshifted binary orbital period, the inferred orbital velocities are relativistic (v/c~0.1). The optical and UV luminosities are expected to arise from gas bound to the individual BHs, and would be modulated by the relativistic Doppler effect. The optical and UV light curves should vary in tandem with relative amplitudes which depend on the respective spectral slopes. We constructed a control sample of 42 quasars with aperiodic variability, to test whether this Doppler colour signature can be distinguished from intrinsic chromatic variability. We found that the Doppler signature can arise by chance in ~20% (~37%) of quasars in the nUV (fUV) band. These probabilities reflect the limited quality of the control sample and represent upper limits on how frequently quasars mimic the Doppler brightness+colour variations. We performed separate tests on the periodic quasar candidates, and found that for the majority, the Doppler boost hypothesis requires an unusually steep UV spectrum or an unexpectedly large BH mass and orbital velocity. We conclude that at most ~1/3rd of these periodic candidates can harbor Doppler-modulated SMBHBs., Comment: submitted in MNRAS

In paper I of this series we showed that a large percentage of the binary black hole (BBH) mergers that form through dynamical interactions in globular clusters will have significant eccentricity in the ~10^{-3}-10^{-1} Hz LISA band. In this work we quantify the evolution of these highly eccentric binaries through the LISA and LIGO bands, and compute the stochastic gravitational wave background from the merging, eccentric population. We find that the population of BBHs that merge in-between three-body encounters inside their cluster (~50% of all cluster-formed BBH mergers) will have measurable eccentricity for their entire lifetime in the LISA band. The population of BBHs that merge during three-body encounters (~5% of all cluster-formed BBH mergers), will be detectable by LIGO with eccentricities of e~0.1. The gravitational wave background from dynamically assembled BBHs encodes a characteristic bump due to the high initial eccentricities of these systems. The location and amplitude of this bump depends on globular cluster properties., Comment: Published in MNRAS. Companion paper to arxiv:1804.06519

The rate of tidal disruption flares (TDFs) per mass of the disrupting black hole encodes information on the present-day mass function (PDMF) of stars in the clusters surrounding super massive black holes. We explore how the shape of the TDF rate with black hole mass can constrain the PDMF, with only weak dependence on black hole spin. We show that existing data can marginally constrain the minimum and maximum masses of stars in the cluster, and the high-mass end of the PDMF slope, as well as the overall TDF rate. With of order 100 TDFs expected to be identified with the Zwicky Transient Facility, the overall rate can be highly constrained, but still with only marginal constraints on the PDMF. However, if less than of order 10% of the TDFs expected to be found by LSST over a decade (of order 1000 TDFs) are identified, then precise and accurate estimates can be made for the minimum stellar mass (within a factor of two) and the average slope of the high-mass PDMF (to within ~10%) in nuclear star clusters. This technique could be adapted in the future to probe, in addition to the PDMF, the local black hole mass function and possibly the massive black hole binary population., Comment: Accepted for publication in MNRAS

The coalescence of a compact object with a $10^{4}-10^{7} {\rm M_\odot}$ supermassive black hole (SMBH) produces mHz gravitational waves (GWs) detectable by the future Laser Interferometer Space Antenna (LISA). If such an inspiral occurs in the accretion disc of an active galactic nucleus (AGN), the gas torques imprint a small deviation in the GW waveform. Here we present two-dimensional hydrodynamical simulations with the moving-mesh code DISCO of a BH inspiraling at the GW rate in a binary system with a mass ratio $q\!=\!M_2/M_1\!=\!10^{-3}$, embedded in an accretion disc. We assume a locally isothermal equation of state for the gas (with Mach number $\mathcal{M}=20$) and implement a standard $\alpha$-prescription for its viscosity (with $\alpha = 0.03$). We find disc torques on the binary that are weaker than in previous semi-analytic toy models, and are in the opposite direction: the gas disc slows down, rather than speeds up the inspiral. We compute the resulting deviations in the GW waveform, which scale linearly with the mass of the disc. The SNR of these deviations accumulates mostly at high frequencies, and becomes detectable in a 5-year LISA observation if the total phase shift exceeds a few radians. We find that this occurs if the disc surface density exceeds $\Sigma_0 \gtrsim 10^{2-3}\rm g\,cm^{-2}$, as may be the case in thin discs with near-Eddington accretion rates. Since the characteristic imprint on the GW signal is strongly dependent on disc parameters, a LISA detection of an intermediate mass ratio inspiral would probe the physics of AGN discs and migration., Comment: Incorporates published erratum - revised figures in Section 5, results unchanged

Very long baseline interferometry (VLBI) at millimeter (mm) wavelengths is being employed to resolve event-horizon scale structure of the environment surrounding the Milky-Way black hole, at an angular resolution of a few tens of micro-arcseconds. The same approach could also resolve the orbital separation of a population of massive black hole binaries (MBHBs). Modeling the inspiral of binaries due to gravitational wave emission and gas and requiring binary orbital periods of less than 10 years, we estimate that there may exist ~100 resolvable MBHBs that are bright enough to be observed by mm-wavelength VLBI instruments over the entire sky, at redshifts z, Published in The Astrophysical Journal

Nearly 150 massive black hole binary (MBHB) candidates at sub-pc orbital separations have been reported in recent literature. Nevertheless, the definitive detection of even a single such object remains elusive. If at least one of the black holes is accreting, the light emitted from its accretion disc will be lensed by the other black hole for binary orbital inclinations near to the line of sight. This binary self-lensing could provide a unique signature of compact MBHB systems. We show that, for MBHBs with masses in the range 10^6 - 10^10 solar masses and with orbital periods less than ~10 yr, strong lensing events should occur in one to 10s of percent of MBHB systems that are monitored for an entire orbit. Lensing events will last from days for the less massive, shorter period MBHBs up to a year for the most massive ~10 year orbital period MBHBs. At small inclinations of the binary orbit to the line of sight, lensing must occur and will be accompanied by periodicity due to the relativistic Doppler boost. Flares at the same phase as the otherwise average flux of the Doppler modulation would be a smoking gun signature of self-lensing and can be used to constrain binary parameters. For MBHBs with separation >100 Schwarzschild radii, we show that finite-sized source effects could serve as a probe of MBH accretion disc structure. Finally, we stress that our lensing probability estimate implies that ~10 of the known MBHB candidates identified through quasar periodicity should exhibit strong lensing flares., Accepted to MNRAS

Among the growing list of confirmed exoplanets, the number of planets identified in dense star clusters remains sparse. Previous analyses have suggested this may be due in part to dynamical interactions that unbind large fractions of planets from their host stars, limiting the survival of planetary systems in clusters. Thus, alternative detection strategies may be necessary to study planets in clusters that may no longer be bound to a host star. Here, we use the cluster Monte Carlo code CMC to explore the evolution of planetary systems in dense star clusters. Depending on a number of initial conditions, we show that $10-50\%$ of primordial planetary systems are broken through dynamical encounters over a cluster's full lifetime, populating clusters with "free-floating" planets. Furthermore, a large number ($30-80\%$) of planets are ejected from their host cluster through strong dynamical encounters and/or tidal loss. Additionally, we show that planets naturally mix with stellar-mass black holes (BHs) in the central regions of their host cluster. As a consequence, up to a few hundreds of planets will be tidally disrupted through close passages of BHs. We show these BH-planet tidal disruption events (TDEs) occur in clusters at a rate of up to $10^{-5}\,\rm{yr}^{-1}$ in a Milky Way-type galaxy. We predict BH-planet TDEs should be detected by upcoming transient surveys such as LSST at a rate of roughly a few events per year. The observed rate of BH-planet TDEs would place new constraints upon the formation and survival of both planetary systems and BHs in dense star clusters. Additionally, depending on various assumptions including the initial number of planets and their orbital properties, we predict that typical globular clusters may contain a few dynamically-formed NS-planet systems at present as well as up to roughly 100 dynamically-formed WD-planet systems., 18 pages, 8 figures. Submitted to ApJ. Comments welcome

Because most large galaxies contain a central black hole, and galaxies often merge, black-hole binaries are expected to be common in galactic nuclei. Although they cannot be imaged, periodicities in the light curves of quasars have been interpreted as evidence for binaries, most recently in PG~1302-102, with a short rest-frame optical period of 4 years. If the orbital period matches this value, then for the range of estimated black hole masses the components would be separated by 0.007-0.017 pc, implying relativistic orbital speeds. There has been much debate over whether black hole orbits could be smaller than 1 pc. Here we show that the amplitude and the sinusoid-like shape of the variability of PG~1302-102 can be fit by relativistic Doppler boosting of emission from a compact, steadily accreting, unequal-mass binary. We predict that brightness variations in the ultraviolet light curve track those in the optical, but with a 2-3 times larger amplitude. This prediction is relatively insensitive to the details of the emission process, and is consistent with archival UV data. Follow-up UV and optical observations in the next few years can test this prediction and confirm the existence of a binary black hole in the relativistic regime., To appear as a Letter in the September 17, 2015 issue of Nature. Press embargo until 18:00 London time / 13:00 US Eastern Time on 16 September 2015

It is well known that the classical gravitational two body problem can be transformed into a spherical harmonic oscillator by regularization. We find that a modification of the regularization transformation has a similar result to leading order in general relativity. In the resulting harmonic oscillator, the leading-order relativistic perturbation is formally a negative centrifugal force. The net centrifugal force changes sign at three Schwarzschild radii, which interestingly mimics the innermost stable circular orbit (ISCO) of the full Schwarzschild problem. Transforming the harmonic-oscillator solution back to spatial coordinates yields, for both timelike and null weak-field Schwarzschild geodesics, a solution for $t,r,\phi$ in terms of elementary functions of a variable that can be interpreted as a generalized eccentric anomaly. The textbook expressions for relativistic precession and light deflection are easily recovered. We suggest how this solution could be combined with additional perturbations into numerical methods suitable for applications such as relativistic accretion or dynamics of the Galactic-centre stars.

We describe an undergraduate laboratory that combines an accurate measurement of the speed of light, a fundamental investigation of a basic laser system, and a nontrivial use of statistical analysis. Students grapple with the existence of longitudinal modes in a laser cavity as they change the cavity length of an adjustable-cavity HeNe laser and tune the cavity to produce lasing in the TEM$_{00}$ mode. For appropriate laser cavity lengths, the laser gain curve of a HeNe laser allows simultaneous operation of multiple longitudinal modes. The difference frequency between the modes is measured using a self-heterodyne detection with a diode photodetector and a radio frequency spectrum analyzer. Asymmetric effects due to frequency pushing and frequency pulling, as well as transverse modes, are minimized by simultaneously monitoring and adjusting the mode structure as viewed with a Fabry-Perot interferometer. The frequency spacing of longitudinal modes is proportional to the inverse of the cavity length with a proportionality constant equal to half the speed of light. By changing the length of the cavity, without changing the path length within the HeNe gas, the speed of light in air can be measured to be ($2.9972 \pm0.0002) \times 10^{8}$ m/s, which is to high enough precision to distinguish between the speed of light in air and that in a vacuum., Comment: 6 pages; 6 figures; Published in the American Journal of Physics

Graham et al. (2015) have detected a 5.2 year periodic optical variability of the quasar PG 1302-102 at redshift $z=0.3$, which they interpret as the redshifted orbital period $(1+z)t_{\rm bin}$ of a putative supermassive black hole binary (SMBHB). Here we consider the implications of a $3-8$ times shorter orbital period, suggested by hydrodynamical simulations of circumbinary discs (CBDs) with nearly equal--mass SMBHBs ($q\equiv M_2/M_1\gtrsim 0.3$). With the corresponding $2-4$ times tighter binary separation, PG 1302 would be undergoing gravitational wave dominated inspiral, and serve as a proof that the BHs can be fueled and produce bright emission even in this late stage of the merger. The expected fraction of binaries with the shorter $t_{\rm bin}$, among bright quasars, would be reduced by 1-2 orders of magnitude, compared to the 5.2 year period, in better agreement with the rarity of candidates reported by Graham et al. (2015). Finally, shorter periods would imply higher binary speeds, possibly imprinting periodicity on the light curves from relativistic beaming, as well as measurable relativistic effects on the Fe K$\alpha$ line. The CBD model predicts additional periodic variability on timescales of $t_{\rm bin}$ and $\approx 0.5 t_{\rm bin}$, as well as periodic variation of broad line widths and offsets relative to the narrow lines, which are consistent with the observations. Future observations will be able to test these predictions and hence the binary+CBD hypothesis for PG 1302., Comment: Published in MNRAS

Most standard descriptions of Type II migration state that massive, gap-opening planets must migrate at the viscous drift rate. This is based on the idea that the disk is separated into an inner and outer region and gas is considered unable to cross the gap. In fact, gas easily crosses the gap on horseshoe orbits, nullifying this necessary premise which would set the migration rate. In this work, it is demonstrated using highly accurate numerical calculations that the actual migration rate is dependent on disk and planet parameters, and can be significantly larger or smaller than the viscous drift rate. In the limiting case of a disk much more massive than the secondary, the migration rate saturates to a constant which is sensitive to disk parameters and is not necessarily of order viscous rate. In the opposite limit of a low-mass disk, the migration rate decreases linearly with disk mass. Steady-state solutions in the low disk mass limit show no pile-up outside the secondary's orbit, and no corresponding drainage of the inner disk., Comment: ApJ Accepted