High-energy emission from tidal disruption events in active galactic nuclei
HHigh-energy emission from tidal disruption events in active galactic nuclei
Chi-Ho Chan , Tsvi Piran , and Julian H. Krolik Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
January 6, 2021
ABSTRACTTidal disruption events (
TDE s) taking place in active galactic nuclei (
AGN s) are diο¬erent from ordinary
TDE s. In theseevents, the returning tidal debris stream drills through the pre-existing
AGN accretion disk near the stream pericenter,destroying the inner disk in the process, and then intersects with the disk a second time at radii ranging from a few tohundreds of times the pericenter distance. The debris dynamics of such
TDE s, and hence their appearance, are distinctfrom ordinary
TDE s. Here we explore the signature of this βsecond impactβ of the stream with the disk. Strong shocksform as the dilute stream is stopped by the denser disk. Compton cooling of the shocked material produces hard X-rays,even soft πΎ -rays, with most of the energy emitted between βΌ
10 keV and 1 MeV. The luminosity follows the mass-returnrate, peaking between βΌ and 10 erg s β . The X-ray hardness and the smoothness of the light curve providepossible means for distinguishing the second impact from ordinary AGN ο¬ares, which exhibit softer spectra and moreirregular light curves.
Key words: galaxies: nuclei β accretion, accretion disks β black hole physics β hydrodynamics
1. INTRODUCTIONSupermassive black holes at galactic centers can generate copiousamounts of radiation. When a black hole is fed a steady dietof gas from galactic scales, the gas forms an accretion diskaround the black hole, and the black hole manifests itself asan active galactic nucleus (
AGN ) that shines across the entireelectromagnetic spectrum. The luminosity of an AGN varies overtime, exhibiting variations from mundane, βΌ
10% ο¬uctuations tomore dramatic ο¬ares.Once in a while, a star in the nuclear cluster of the host galaxymay be scattered onto an orbit grazing the black hole. A tidaldisruption event (
TDE ) takes place when the tidal gravity of theblack hole overwhelms the self-gravity of the star and breaks thestar apart (Hills 1975). Half of the star is gravitationally unboundfrom the black hole (e.g., Rees 1988) and produces synchrotronradiation through its interaction with the circumnuclear medium(Krolik et al. 2016; Yalinewich et al. 2019). The other half returnsto the neighborhood of the black hole as an elongated stream.Ordinarily, the bound material shocks against itself, settlinginto an accretion ο¬ow (e.g., Rees 1988); the resulting radiationemerges primarily in the optical/ultraviolet ( UV ). However, whenthe supermassive black hole is an AGN , and therefore alreadypossesses a disk, the returning bound material faces a verydiο¬erent environment.Except for the general tendency that AGN s have more massiveblack holes, there is no particular reason why
TDE s should avoid
AGN s (see also Karas & Ε ubr 2007; Kennedy et al. 2016). Wethus face the challenge of separating
TDE s from common
AGN ο¬ares. Strategies for identifying
TDE s often depend on light-curve timescales and optical colors (e.g., van Velzen et al. 2020),but the identiο¬cation of an event is often disputed (Komossa2015; Kankare et al. 2017; Auchettl et al. 2018; Trakhtenbrotet al. 2019). The diο¬culty is compounded by the possibility that
TDE s in
AGN s may look very diο¬erent from those in inactive galaxies.We were the ο¬rst to explore the hydrodynamic and radiativeproperties of
TDE s in
AGN s (Chan et al. 2019, 2020). Thedisruption itself is unaο¬ected by the disk because both the starand the resulting tidal debris are much denser than the disk,but the situation is diο¬erent for the more dilute debris streamfalling back to pericenter. We call the pericentric collision ofthe returning stream with the disk the ο¬rst impact . An importantquantity to consider is the disk mass interior to the impact point.For example, for a black hole of mass π h = Γ M (cid:12) anda Sun-like star, the physical tidal radius R t , or the maximumpericenter for total disruption, is βΌ π g (Ryu et al. 2020a),where π g β‘ πΊ π h / π is the gravitational radius. A Shakura &Sunyaev (1973) disk accreting at 0.01 times Eddington has ameager βΌ β M (cid:12) inside this radius. It follows immediately thatthe ο¬rst impact can signiο¬cantly reshape the inner disk.This expectation is conο¬rmed by the hydrodynamics sim-ulations in Chan et al. (2019). Shocks emanating from theο¬rst impact dissipate energy and remove angular momentumso vigorously that they vacate the inner disk within tens ofdays. The dissipated energy keeps the bolometric luminosityconstant at Eddington levels for a similar amount of time (Chanet al. 2020). Unfortunately, the complicated hydrodynamicand radiative environment of the inner disk prevents us fromestimating ο¬rst-impact spectra without detailed simulations andradiative-transfer calculations.There is, however, another way by which TDE s in
AGN s canglow. Most streams have enough inertia to punch through thedisk, all the more so after shocks have gotten rid of the inner disk.As illustrated in Figure 1, the stream, tidally compressed duringits pericenter passage and ruο¬ed by the ο¬rst impact, spews outfan-shaped from the other side. As we shall see later, streammaterial can be sprayed as far as βΌ
100 times the pericenterdistance, and when it ο¬nally meets the disk again, it is much1 a r X i v : . [ a s t r o - ph . H E ] J a n CHAN ET AL. β5 β4 β3 β2 β1 0 1 2 3 4 5β3β2β101 Μπ s / Μπ d β 8
100 disk orbits β3 β2 β1 radial coordinate v e r ti ca l c oo r d i n a t e blackhole outer diskclearedinner disk unperturbedstream ο¬rstimpactboundmaterialunboundmaterial domain ofhydrodynamics simulationdomain ofsecond-impact calculationsfocus ofFigure 5 π p π₯π§π¦ Figure 1.
Interaction of a TDE stream with an AGN disk.
Top panel:
Densityslice of one of the hydrodynamics simulations this work is based on, set upaccording to Chan et al. (2019). The white ellipse around the origin is due tothe numerical cutout, whose purpose is to exclude the cylindrical axis from thesimulation domain. The stream, with its much greater inertia, penetrates the diskat the ο¬rst impact. Shocks excited at the ο¬rst impact nearly evacuate the diskinterior to the impact point. Subjected to tidal compression during its pericenterpassage, the stream widens on exit from the disk.
Bottom panel:
Schematicdiagram of the framework employed to calculate the properties of the secondimpact. Most of the stream material is gravitationally unbound, and the rest isdispersed over a large swath of the outer disk. The much lower density of thestream at this second impact means it can be completely absorbed by the disk.The skinny dashed box picks out an arbitrary annulus of the disk, and Figure 5shows how the second impact along this annulus looks like as viewed from theblack hole. more dilute than the disk it lands on. The relation betweenstream mass and disk mass is also very diο¬erent: for the exampleabove, the disk within βΌ R t contains βΌ M (cid:12) . Even thoughthe disk does not carry much more mass than the stream, it isstill much denser, mostly because all that mass is concentratedwithin a small scale height. Because of the density disparity,the stream is likely absorbed in its entirety by the disk withoutaltering the disk to any appreciate extent.The energy dissipated at this second impact powers anotherο¬are, on top of that from the ο¬rst impact. Diο¬erent circum-stances suggest diο¬erent observational signatures; speciο¬cally,the simpler geometry of the second impact allows us to moreeasily model the cooling process and compute the spectrum. We begin by accentuating in Β§2 the dissimilar nature of TDE s in vacuum and
TDE s in
AGN s. Our investigation of thesecond impact begins in Β§3 with a survey of system parameters.The dynamical and energetic aspects of the second impact areaddressed in Β§4. The core of our exposition is Β§5, where wetranslate the energy dissipation rates from the previous sectionto spectra using a simple Compton-cooling model. A discussionof the results is found in Β§6, followed by our conclusions in Β§7.2. TDES IN AGNS AS A DISTINCT POPULATION FROMTDES IN VACUUMA primary point of contention about
TDE s in vacuum is whethershocks can transform the eccentric stream to a more circularaccretion ο¬ow, and how. In the classical picture, general rela-tivistic apsidal precession makes the stream self-intersect nearpericenter; the resulting strong shocks dissipate energy briskly,forcing the stream to circularize and settle into a compact accre-tion disk (e.g., Rees 1988). The radiation from this disk mightbe reprocessed by surrounding optically thick matter (e.g., Loeb& Ulmer 1997; Metzger & Stone 2016; Lu & Bonnerot 2020;but see Matsumoto & Piran 2020). However, if the disruptiontakes place at (cid:38) π g , precession leads instead to shocks that arecloser to apocenter (Shiokawa et al. 2015; Dai et al. 2015). Theseapocentric shocks are the result of the stream interacting with thecomplex, eccentric accretion ο¬ow created by earlier-returningtidal debris. They are too weak to eο¬ciently circularize thestream, but they can generate optical/ UV light (Piran et al. 2015).The picture is fundamentally diο¬erent for TDE s in
AGN s.The obstruction posed by the disk means the stream cannot ingeneral self-intersect; speciο¬cally, the ο¬rst impact prevents rapidcircularization, while the second impact precludes apocentricshocks. Mechanisms discussed in the context of
TDE s in vacuum,including reprocessing and apocentric shocks as the origin ofoptical/ UV emission, are therefore wholly inapplicable to TDE sin
AGN s.The physics of
TDE s in
AGN s must be studied in its own right.The most energetic streamβdisk interaction comes about whenthe stream ο¬rst returns to pericenter, at the ο¬rst impact. Shocksexcited by the impact accelerate inο¬ow in the inner disk, whichleads to vigorous energy dissipation, often super-Eddington inpower (Chan et al. 2019). The bolometric luminosity dependson a balance between energy dissipation, radiation diο¬usion, andphoton trapping (Chan et al. 2020). These mechanisms operatein qualitatively the same way no matter how close the streamapproaches to the black hole, or how much apsidal precessionit suο¬ers on its pericentric ο¬yby. The second impact, the focusof this article, happens when the stream is arrested near itsapocenter as it ο¬ies over the disk. As expanded upon in Β§5.4, thesecond-impact shocks likely emit primarily hard X-rays to soft πΎ -rays.Even the energy reservoir is diο¬erent for the two kinds of TDE s. For
TDE s in vacuum, the energy radiated by the bounddebris must ultimately be sourced from its orbital energy. Bycontrast,
TDE s in
AGN s can tap into the orbital energy of the diskas well. In most
TDE s of the latter kind, the returning debrisplays the role of a catalyst, causing orbital energy to be liberatedat much higher rates than in the unperturbed disk. This statementis true for the ο¬rst impact, whose near-Eddington luminosityresults from the speedy infall of the inner disk (Chan et al. 2019,IGH-ENERGY EMISSION FROM TDES IN AGNS 32020). It is also true for the second impact: we shall see in Β§4.2that stream material dissipates the kinetic energy of the part ofthe disk it lands on, at a rate proportional to its mass ο¬ux.Thus,
TDE s in vacuum and
TDE s in
AGN s have entirely distinctappearances.
Searches tailored to one type may be insensitiveto the other. To ο¬nd
TDE s in
AGN s, a completely new setof distinguishing features must be constructed for this novelclass of transients. In addition, there is a second diο¬culty:winnowing away the cases in which βο¬aresβ are merely intrinsic
AGN variability. 3. PARAMETERSWe consider the case where the pericenter distance π p of thedebris stream equals the physical tidal radius R t , the maximumpericenter for complete disruption. This radius is a function ofthe black-hole mass π h and the stellar mass π β . Both R t andthe peak rate (cid:164) π s at which bound tidal debris returns to pericenterare given by the following expressions, derived from generalrelativistic hydrodynamics simulations of the disruption of starswith realistic internal structure (Ryu et al. 2020a): R t β . Γ cm Γ Ξ¨ (cid:18) π h Γ M (cid:12) (cid:19) / (cid:18) π β M (cid:12) (cid:19) β / (cid:18) π β r (cid:12) (cid:19) , (1) (cid:164) π s β . M (cid:12) yr β Γ Ξ / (cid:18) π h Γ M (cid:12) (cid:19) β / (cid:18) π β M (cid:12) (cid:19) (cid:18) π β r (cid:12) (cid:19) β / . (2)Unlike Ryu et al. (2020a), here we use 3 Γ M (cid:12) as our ο¬ducial π h . In these equations, π β β . r (cid:12) Γ (cid:18) π β M (cid:12) (cid:19) . (3)is the stellar radius (Ryu et al. 2020b), and the dimensionlessfactors Ξ¨ ( π h , π β ) β‘ { . + . [ π h /( Γ M (cid:12) )] . } Γ . + exp (( π β / M (cid:12) β . )/ . ) + .
34 exp (( π β / M (cid:12) β . )/ . ) , (4) Ξ ( π h , π β ) β‘ { . β . [ π h /( Γ M (cid:12) )] . } Γ . + exp (( π β / M (cid:12) β . )/ . ) + .
55 exp (( π β / M (cid:12) β . )/ . ) (5)reο¬ne earlier order-of-magnitude estimates (e.g., Rees 1988).For π h = Γ M (cid:12) and π β = M (cid:12) , the revised π p is β π g ,roughly half the value used in Chan et al. (2019, 2020). Thischanges the dependence of timescales and stream mass currenton TDE parameters.In our previous work, we investigated the interaction of thestream with the disk at the ο¬rst impact using a suite of Newto-nian hydrodynamics simulations (Chan et al. 2019). In thosesimulations, a disk was set up along the midplane, and a streamon a parabolic orbit was injected from above in such a way that itmade perpendicular contact with the disk exactly when it reachedpericenter. Because the simulations lasted only a fraction of themass-return time, the stream mass current was kept constant at (cid:164) π s . The same simulation setup is employed to study the secondimpact. The chief parameter characterizing both impacts is (cid:164) π s / (cid:164) π d ,where (cid:164) π d is the mass current of the unperturbed disk rotatingunder the stream footprint at the ο¬rst impact. Assuming a Shakura& Sunyaev (1973) disk, we found that (cid:164) π s / (cid:164) π d has a minimum,and (cid:164) π s / (cid:164) π d (cid:38) TDE and
AGN parameters (Chanet al. 2019); therefore, we consider here (cid:164) π s / (cid:164) π d β {β , β , β , β } , which are typical for TDE s in
AGN s. The last threevalues of (cid:164) π s / (cid:164) π d necessitate new runs not reported in Chan et al.(2019).We characterize the AGN in terms of its unperturbed disk lumi-nosity π (cid:164) π a π , where π = . (cid:164) π s / (cid:164) π d above the minimum corresponds to twovalues of (cid:164) π a , the larger and smaller values appropriate for a diskwhose pressure is dominated by radiation and gas, respectively(Chan et al. 2019). We adopt the larger value here.4. SECOND IMPACT4.1. Trajectory calculations
Figure 1 combines a density slice from the actual simulationswith a schematic depiction of the bigger picture. A stream with (cid:164) π s / (cid:164) π d (cid:38) (cid:46) . [ πΊ π h /( π + π§ ) / ] / (Chan et al. 2019), we assume it follows ballistic trajectories fromthe boundaries of the simulation domain until they strike the disk.For each time step in each run, we determine which boundarycells have outο¬owing gas with speciο¬c angular momentum β₯ . ( πΊ π h π p ) / in the π¦ -direction; these cells have outο¬owingstream material, as opposed to vertically expanding disk gas.For each of these cells, we assume that all the outο¬owingmaterial over the time step is launched outward on a Kepleriantrajectory. We calculate when, where, and with what velocitythis trajectory hits the midplane. Even gravitationally unboundgas can be intercepted if its hyperbolic trajectory crosses thedisk. Trajectory calculations are continued until the end ofthe simulations, at time 1400 ( πΊ π h / π ) β / , which is morethan double the simulation duration in Chan et al. (2019); for π h = Γ M (cid:12) and π β = M (cid:12) , this translates to βΌ
10 d, orabout a quarter of the orbital period of the most bound debriswhen these parameters apply. The mass fallback rate as a functionof time is a convolution of the outο¬ow rate and the ο¬ight-timedelay. 4.2.
Dynamics and energetics
Figure 2 contrasts the rate at which stream material crashes backto the disk as a function of time with the rate at which it exits theο¬rst-impact region. Most of the material is unbound, and only βΌ
20% is involved in the second impact.Figure 3 is a map of where the material lands on the disk overthe course of the simulation, and the left panel of Figure 4 displaysthe azimuthally integrated mass fallback rate. The trajectoriesfollowed by the bulk of the material from the ο¬rst impact to thesecond have eccentricities β
1, and the planes of the trajectories CHAN ET AL. β2 β1 Μπ s / Μπ d β 4 Μπ s / Μπ d β 80 2 4 6 8 1010 β2 β1 Μπ s / Μπ d β 16 2 4 6 8 10Μπ s / Μπ d β 32 days since first impact m a ss c u rr e n t a s fr ac ti ono f unp e r t u r b e d s t r ea m Figure 2.
Rate at which stream material leaves the simulation domain as athin curve, and rate at which it falls back to the midplane as a thick curve, for π h = Γ M (cid:12) and π β = M (cid:12) . All rates are normalized by the unperturbedstream mass current (cid:164) π s . are almost perpendicular to the disk. These trajectories dumpthe material along the projection of the unperturbed stream ontothe disk. A tiny portion of the material is heavily deο¬ected andput on mildly eccentric, highly inclined trajectories with a rangeof orientations; this material ends up at π (cid:46) π p . Although thedetailed shape of the splash zone and the rate at which materialis dumped onto it vary with time and (cid:164) π s / (cid:164) π d , overall they areremarkably independent of these two variables. This means theproperties of the second impact depend less on AGN properties( (cid:164) π a ) and more on TDE properties ( π h , π β ).The right panel of Figure 4 shows the azimuthally integratedenergy dissipation rate per logarithmic radius: π β« ππ π f π£ f ,π§ πΎ, (6)where π f and v f are the density and velocity of the material fallingback, πΎ β‘ (cid:107) v f β π Ξ© Λ e π (cid:107) is the speciο¬c energy dissipation rate, Ξ© = ( πΊ π h / π ) / is the Keplerian orbital frequency, and theintegral is over where the stream hits. At radii greater than afew π p , material hits the disk with (cid:107) v f (cid:107) (cid:28) π Ξ© ; as a result, thedissipated energy is mainly derived from the kinetic energy ofthe disk, that is, πΎ β / π . At all radii, the energy dissipationrate due to the second impact is orders of magnitude greater thanthat of the underlying disk; in fact, the energy dissipated perorbital time can reach βΌ β times the local binding energy atcertain radii. The expedited inο¬ow this entails could help feedthe small-scale disk emptied by the shocks from the ο¬rst impact(Chan et al. 2019).The spatial distribution and energy dissipation of the secondimpact depend on the strength of the pericentric tidal compres-sion. This in turn depends on the kinematic properties of theunperturbed stream, which cannot be accurately determinedwithout simulating the full disruption process. Therefore, theresults presented here should be understood as capturing thequalitative, not quantitative, aspects of the second impact. 5. COMPTON COOLINGThe next step is to estimate the photon energies at which thedissipated energy is radiated from the disk. The task is non-trivial because, at the same time the stream material shocks anddissipates its energy, its internal energy is converted to radiationthrough Compton cooling and carried away with the escapingradiation. Here we construct a crude model that captures theessence of these concurrent processes; characterization of thepotentially radiation-dominated shocks and detailed spectralcalculations are left to future work.5.1. Overall picture
Figure 5 shows an idealized picture of the second impact inthe inertial frame. Falling stream material is slowed down,compressed, and heated by a strong, standing reverse shock. Thelayer of shocked material, sitting on the disk, is ferried away bydisk rotation. This material cools quite swiftly; with the loss ofpressure support, presumably it sinks into the disk within oneorbit. As is evident from the narrowness of the splash zonesdisplayed in Figure 3, the time for the disk to rotate through thestream is much shorter than an orbital period. The structure inFigure 5 is thus time-steady: the unperturbed disk enters fromthe left side, and exits to the right topped with cooled shockedmaterial.Over longer timescales, this time-steady picture changes grad-ually as the rate at which stream material descends on the diskvaries. The mass current of the second impact slowly builds upin the early stages of the
TDE because the stream takes time toο¬y from the ο¬rst impact to the second. In addition, on timescalescomparable to the mass-return time of the
TDE , the rate at whichstellar material returns to pericenter declines, and so does themass current going to the second impact.Our simulations, which last for βΌ
10 d when π h = Γ M (cid:12) and π β = M (cid:12) , are long enough to cover only the buildup period.To study how the second impact changes over this period, wedivide the simulation duration into ο¬ve equal intervals. The fall-back material is characterized by its speed, mass ο¬ux, and energydissipation rate; for simplicity, we assume these three quantitiesare time-independent within each interval and π -independentacross the stream, so we can consider their averages (cid:104) π£ f ,π§ (cid:105) , (cid:104) π f π£ f ,π§ (cid:105) , and (cid:104) π f π£ f ,π§ πΎ (cid:105) .5.2. Cooling model
To calculate the cooling emission, we follow a point on the diskat radius π from the moment it enters the stream, which wetake to be π‘ =
0. A column of shocked material accumulatesabove the point as it moves through the stream; meanwhile, thecolumn cools by radiating away the dissipated energy. The pointleaves the stream at π‘ dep = Ξ π / Ξ© , where Ξ π is the characteristicazimuthal width of the second impact at radius π ; we neverthelesscontinue tracking the cooling over the entire orbit to ensure thecolumn has largely cooled oο¬ by the time it returns to the stream.The observed cooling emission is the sum from columns all overthe disk, each in a diο¬erent cooling stage.The dominant cooling mechanism is inverse Compton scatter-ing of seed photons from the disk. In this sense, the shocked layerbehaves similarly to an AGN corona (e.g., Haardt & Maraschi1991), except that the shocked layer can be quite Compton thick.IGH-ENERGY EMISSION FROM TDES IN AGNS 5 β202 Μπ s / Μπ d β 40.00 d β€ π‘ < 2.06 d β202 2.06 d β€ π‘ < 4.11 d β202 4.11 d β€ π‘ < 6.17 d β202 6.17 d β€ π‘ < 8.23 d β40 β30 β20 β10 0β202 8.23 d β€ π‘ < 10.28 d β3 β2 g cm β2 s β1 β202 Μπ s / Μπ d β 80.00 d β€ π‘ < 2.06 d β202 2.06 d β€ π‘ < 4.11 d β202 4.11 d β€ π‘ < 6.17 d β202 6.17 d β€ π‘ < 8.23 d β40 β30 β20 β10 0β202 8.23 d β€ π‘ < 10.28 d β3 β2 g cm β2 s β1 β202 Μπ s / Μπ d β 160.00 d β€ π‘ < 2.06 d β202 2.06 d β€ π‘ < 4.11 d β202 4.11 d β€ π‘ < 6.17 d β202 6.17 d β€ π‘ < 8.23 d β40 β30 β20 β10 0β202 8.23 d β€ π‘ < 10.28 d β3 β2 g cm β2 s β1 β202 Μπ s / Μπ d β 320.00 d β€ π‘ < 2.06 d β202 2.06 d β€ π‘ < 4.11 d β202 4.11 d β€ π‘ < 6.17 d β202 6.17 d β€ π‘ < 8.23 d β40 β30 β20 β10 0β202 8.23 d β€ π‘ < 10.28 d β3 β2 g cm β2 s β1 π₯ -coordinate of second impact π₯/π p π¦ - c oo r d i n a t e o f s ec ond i m p ac t π¦ / π p π₯ -coordinate of second impact π₯/π p π¦ - c oo r d i n a t e o f s ec ond i m p ac t π¦ / π p π₯ -coordinate of second impact π₯/π p π¦ - c oo r d i n a t e o f s ec ond i m p ac t π¦ / π p π₯ -coordinate of second impact π₯/π p π¦ - c oo r d i n a t e o f s ec ond i m p ac t π¦ / π p focus ofFigure 5 Figure 3.
Flux of stream material falling back to the midplane for π h = Γ M (cid:12) and π β = M (cid:12) . The ο¬ux is the time-integral of mass landing in a cell over one ofthe ο¬ve intervals indicated in each panel, divided by the length of the interval. The black hole is at the origin, and the cross marks the ο¬rst impact. Figure 5 shows howthe second impact along an arbitrary annulus of the disk, such as the dashed one in the top-left panel, looks like as viewed from the black hole. Synchrotron emission should not contribute greatly because itis strongly self-absorbed, and we shall see later that freeβfreecooling is also unlikely to be important.We assume the shocked layer is vertically homogeneous, andions and electrons are thermal at the same temperature. Thermalelectrons at the temperatures we ο¬nd are mildly relativistic;therefore, we ignore electronβpositron pair production and theKleinβNishina reduction in cross section, both aο¬ecting only asmall fraction of photons.The spectrum of the Comptonized photons is taken to be apower law with a cutoο¬. Seed photons from the disk carry aradiative ο¬ux πΉ d = πΊ π h (cid:164) π a ππ , (7)and their spectrum is black-body at temperature π d = ( πΉ d / π SB ) / , where π SB is the StefanβBoltzmann constant. Be-cause the seed spectrum is much narrower than the Comptonizedspectrum, we approximate the former as a delta function. Weuse πΉ d of the unperturbed disk here, but spiral shocks extendingoutward from the ο¬rst impact (Chan et al. 2019) could modifythe disk and thus πΉ d .At each moment, the model is characterized by πΈ g and πΈ r ,which are, respectively, the vertically integrated gas and radiation energy densities; by πΈ β , the energy per area that has escapedfrom the top of the column; and by π» sh , the height of the columnof shocked material. They obey the equations ππΈ g ππ‘ = (cid:104) π f π£ f ,π§ πΎ (cid:105) π ( π‘ dep β π‘ ) β ( π΄ β Ξ C ) πΈ r π‘ sca , (8) ππΈ r ππ‘ = πΉ d + ( π΄ β Ξ C ) πΈ r π‘ sca β πΈ r π‘ esc , (9) ππΈ β ππ‘ = πΈ r π‘ esc , (10) ππ» sh ππ‘ = (cid:26) π£ sh if π‘ < π‘ dep , ( π» eq / π» sh β ) π s if π‘ β₯ π‘ dep , (11)where π is the step function, and other symbols are deο¬ned in therest of the section. The initial condition is ( πΈ g , πΈ r , πΈ β , π» sh ) = ( , , , ) ; the results are insensitive to small perturbations tothe initial condition.Equation (8) characterizes the accrual of dissipated energyin the column and its conversion to radiation through Comptonscattering. Equation (9) follows the increase in radiation energyas a result of disk injection and Compton scattering, and itsdecrease due to radiative losses. Equation (11) describes howthe column grows during deposition while mass and heat areadded to it, and collapses after deposition as it cools. We ignore CHAN ET AL. Μπ s / Μπ d β 40.00 d β€ π‘ < 2.06 d d β€ π‘ < 4.11 d d β€ π‘ < 6.17 d Μπ s / Μπ d β 86.17 d β€ π‘ < 8.23 d d β€ π‘ < 10.28 d Μπ s / Μπ d β 16 10 Μπ s / Μπ d β 32 10 Μπ s / Μπ d β 4 Μπ s / Μπ d β 810 Μπ s / Μπ d β 16 10 Μπ s / Μπ d β 32 radial coordinate π /π p m a ss f a ll b ac k r a t e p e r l og a r it h m i c r a d i u s ( g s β ) radial coordinate π /π p e n e r gyd i ss i p a ti on r a t e p e r l og a r it h m i c r a d i u s ( e r g s β ) Figure 4.
Left panel:
Mass fallback rate per logarithmic radius at the second impact for π h = Γ M (cid:12) and π β = M (cid:12) . The legend applies to the right panel as well. Right panel:
Energy dissipation rate per logarithmic radius as given by Equation (6), for the same π h and π β . The thin solid line is 10 times the energy dissipation rateper logarithmic radius of the underlying disk. The thin dashed line is 10 β times the binding energy per logarithmic radius of the disk divided by the orbital time; thebreak in this line is at the radius where disk pressure changes from radiation-dominated on the inside to gas-dominated on the outside.unperturbeddisk r e v e r s e s h o c k hotshockedcold Compton-cooledsoftphotonshardphotons Ξ π π¦ π§ π₯ Figure 5.
Schematic diagram of the second impact. This ο¬gure zooms in on theskinny dashed box in Figure 1 or the dashed annulus in Figure 3, and it is ο¬ippedupside down with respect to Figure 1. The unperturbed disk (gray) moves infrom the left. Cold stream material (blue) falls onto the disk and shocks (darkred). Soft seed photons from the disk undergo inverse Compton scattering andharden as they propagate upward through the shocked material. The materialis eο¬ciently cooled only when it has become somewhat Compton thick (lightred). Mostly cooled material (pale red) is transported away to the right by diskrotation. The cooled material likely sinks into the disk over the course of anorbit, meaning that the disk is rotated back into the stream in its unperturbedstate. the internal energy increase during this collapse due to adiabaticcompression and release of gravitational energy, both beingsecondary eο¬ects.In Equations (8) and (9), π΄ is the fractional photon energygain due to inverse Compton scattering, and Ξ C is the Comptontemperature in units of π e π / π B , with π e the electron mass and π B the Boltzmann constant. The Compton temperature is thetemperature of an electron gas in thermal balance with photonsthrough Compton scattering, and it is equal to one-fourth theintensity-weighted mean photon energy. Three timescales appear in the equations: π‘ dep = Ξ π / Ξ© , (12) π‘ sca = /( π e π T π ) , (13) π‘ esc = ( π» sh / π ) max ( , π T ) , (14)where π e is the electron number density, π T is the Thomson crosssection, and π T is the Thomson thickness. These timescales are,respectively, the duration of deposition, the mean timescale for aphoton to scatter oο¬ an electron, and the timescale for radiationto escape. We also deο¬ne π£ sh = [( πΎ β )/( πΎ + )](cid:104) π£ f ,π§ (cid:105) , (15) π» = π π /( πΊ π h ) , (16) π = ( πΈ g + πΈ r )/ Ξ£ sh , (17) π e = Ξ£ sh /( ππ» sh ) , (18) π T = π T Ξ£ sh / π H , (19) Ξ£ sh = (cid:104) π f π£ f ,π§ (cid:105) min ( π‘ dep , π‘ ) . (20)Here π£ sh is the upward speed of the reverse shock in the corotatingframe, π» eq is the scale height in hydrostatic equilibrium, π s isthe isothermal sound speed, Ξ£ sh is the column density, πΎ = isthe adiabatic index, Β― π = π H is the mean particle mass, and π H is the hydrogen mass.Although the electrons are mildly relativistic at the beginning,the radiative output is dominated by later stages when the gas iscooler; we therefore have π΄ β Ξ , (21)where Ξ β‘ π B π g /( π e π ) , (22)and π g = ( πΎ β ) Β― ππΈ g /( π B Ξ£ sh ) (23)IGH-ENERGY EMISSION FROM TDES IN AGNS 7is the gas temperature.We compute the Compton temperature in two diο¬erent ways,distinguished by whether the column is Compton-thin or thick.The dividing line π T = / π is chosen to be as large as possiblewhile being small enough that the probability of π scatters is β π π T . If π T < / π , most disk photons escape without beingscattered, so the spectrum of the radiation emerging from thecolumn consists of a delta-function disk component in additionto a Comptonized component: πΉ ( π ) ππ = (cid:20) ( β π T ) πΉ d πΏ ( π β π B π d )+ πΉ C π B π g (cid:18) ππ B π g (cid:19) π exp (cid:18) β ππ B π g (cid:19)(cid:21) ππ, (24)where π is the photon energy and πΉ C is the normalization of theComptonized component. In this regime, repeated Comptonscattering leads to a spectral index π = ln π T / ln ( + π΄ ) (Rybicki& Lightman 1979; Krolik 1999), and energy conservation andthe deο¬nition of Ξ C can be written as πΈ r π‘ esc = β« β π B π β d ππ πΉ ( π ) = ( β π T ) πΉ d + Ξ ( π + , π d / π g ) πΉ C , (25)4 Ξ C π e π = β« β π B π β d ππ π πΉ ( π ) β« β π B π β d ππ πΉ ( π ) = ( β π T )( π d / π g ) πΉ d + Ξ ( π + , π d / π g ) πΉ C ( β π T ) πΉ d + Ξ ( π + , π d / π g ) πΉ C π B π g , (26)with Ξ the incomplete gamma function. Solving these equationsyields πΉ C and Ξ C ; in case πΉ C <
0, we set Ξ C = π T β₯ / π , we assume every photon is scattered at least onceon its way out, so we retain only the Comptonized component: πΉ ( π ) ππ = πΉ C π B π g (cid:18) ππ B π g (cid:19) π exp (cid:18) β ππ B π g (cid:19) ππ . (27)The spectral parameters πΉ C , π , and Ξ C are determined in thisregime from photon conservation, energy conservation, and thedeο¬nition of Ξ C : πΉ d π B π d = β« β π B π d ππ π β πΉ ( π ) = Ξ ( π, π d / π g ) πΉ C π B π g , (28) πΈ r π‘ esc = β« β π B π d ππ πΉ ( π ) = Ξ ( π + , π d / π g ) πΉ C , (29)4 Ξ C π e π = β« β π B π d ππ π πΉ ( π ) β« β π B π d ππ πΉ ( π ) = Ξ ( π + , π d / π g ) Ξ ( π + , π d / π g ) π B π g . (30)5.3. Solution
Figure 6 shows one solution of the model; other solutions arequalitatively similar, diο¬ering only in the durations of the variousstages of evolution. The ο¬rst stage is so optically thin that ( π΄ β Ξ C ) π‘ esc / π‘ sca = ( π΄ β Ξ C ) π T π H /( π ) (cid:28)
1; thus, the netampliο¬cation of the disk emission is small. The third term on the right-hand side of Equation (9) largely oο¬sets the ο¬rst term,so πΈ r grows slowly and π g remains large. Indeed, πΈ g β (cid:104) π f π£ f ,π§ πΎ (cid:105) π‘, (31) πΈ r β πΉ d π‘ /( + π / π£ sh ) , (32) πΈ β β πΉ d π‘. (33)The second stage commences when ( π΄ β Ξ C ) π‘ esc / π‘ sca = ( π΄ β Ξ C ) π T π H /( π ) βΌ
1. Although the column is stillCompton-thin, the scattered photons gain so much energy thatthe luminosity of a cohort of injected photons is at least doubled.This drives up πΈ r , which in turn accelerates Compton cooling,resulting in an exponential surge in πΈ r . The oscillations inthis stage are due to the mutual feedback between πΈ g and πΈ r in our model, in which a column evolves independently of itsneighbors; if adjacent columns interacted by photon diο¬usion,these oscillations would likely be damped.The growth of πΈ r comes to an end when the system ο¬nds a newequilibrium. In this equilibrium, dissipated energy is eο¬cientlyconverted to radiation energy, which in turn is lost rapidly tooutward streaming. This means the two terms of Equation (8)are comparable, while the second term of Equation (9) is coun-teracted by the third. The eο¬ective temperature of the emergentradiation is then π eff = (cid:18) πΈ r π‘ esc π SB (cid:19) / βΌ (cid:18) (cid:104) π f π£ f ,π§ πΎ (cid:105) π SB (cid:19) / . (34)The third stage goes from the moment when π T βΌ
1, should ithappen, to the end of deposition. Compton cooling is faster in theCompton-thick column, but the gas is kept warm by continual en-ergy dissipation. The balance of terms is the same as in the secondstage; hence, ( π΄ β Ξ C ) π‘ esc / π‘ sca = ( π΄ β Ξ C ) π π H /( π ) βΌ π and Ξ C increase over time in all threestages as long as material continues to be deposited, but π neverrises to above 3, its value in the RayleighβJeans limit. Bycontrast, Ξ is almost constant in the ο¬rst stage, but falls graduallyin the next two stages, bounded below by Ξ C . This observationcan be further generalized: a Compton-thicker layer tends tohave a larger π and a smaller Ξ . Consequently, the spectrumemerging from the column transforms from a soft power lawwith a high-energy cutoο¬ to a hard power law with a low-energycutoο¬ as cooling progresses.Freeβfree cooling is more eο¬cient for small π h , large π β , andlarge π / π p . It can be orders of magnitude faster than Comptoncooling at converting πΈ g to πΈ r in the ο¬rst phase, but for most ofthe cases we considered, Compton cooling quickly catches up inthe second and third phases, and even monopolizes the coolingbudget toward the end of deposition. Therefore, the eο¬ect ofearly-time freeβfree cooling is likely limited to creating extraseed photons for Compton cooling. Freeβfree cooling can alsodominate after the end of deposition; however, in most casesonly a small fraction of the total dissipated energy remains inthe column by the time stream material stops arriving, so thecontribution of late-time freeβfree cooling is minor. CHAN ET AL. c o l u m n - i n t e g r a t e d e n e r gyd e n s it y ( e r g c m β ) π h = 3 Γ 10 π β π β = π β Μπ s / Μπ d β 84.11 d β€ π‘ < 6.17 d π /π g β 126πΈ g πΈ r πΈ β β1 ti m e s ca l e ( s ) on s e t o f e ffi c i e n t c oo li ng e ndo f Z e l β dov i c h a pp r ox i m a ti on on s e t o f C o m p t on t h i c kn e ss e ndo f d e po s iti on π‘ sca /(π΄ β 4Ξ C )π‘ esc β6 β4 β2 t e m p e r a t u r e no r m a li ze d t o e l ec t r on r e s t e n e r gy π B π d /(π e π )π B (β¨π f v f β Μ e z πΎβ©/π SB ) /(π e π )ΞΞ C π B π eff /(π e π )10 time (s) β2.0β1.5β1.0β0.50.00.51.0 s p ec t r a li nd e x flat logarithmic spectrum π Figure 6.
One solution of the cooling model; see Β§5.2 for deο¬nitions. The verticallines from left to right mark the times when ( π΄ β Ξ C ) π‘ esc / π‘ sca = π T = / π ,and π T =
1, respectively; the ο¬rst two times may be interchanged in othersolutions. The inclined lines in the ο¬rst panel are given by Equations (31)β(33).The inclined line in the second panel follows a one-to-one ratio.
Another source of seed photons is the disk interior to the ο¬rstimpact, which could be emitting at Eddington levels (Chan et al.2019, 2020). Although this could, in principle, be a competitivesource of seed photons, the luminosity and angular distributionof this light remain so uncertain that we do not include it here. 5.4.
Spectra
The analysis so far concerns a single column. Figure 7 shows thespectra resulting from the second impact for various values of π h and π β . These are obtained by adding together the contributionof every column on the disk. In all cases, it can be roughlyrepresented by a broken power law whose break coincides withthe peak in π πΏ π . Depending on π h and π β , the photon energyof the peak can be anywhere between βΌ
10 keV and 1 MeV, asexpected from Compton cooling of mildly relativistic electrons.Generally speaking, with increasing π h and decreasing π β , thepeak broadens and shifts toward higher energies. Additionalcooling at π‘ (cid:38) π‘ dep modiο¬es the spectrum, the most prominenteο¬ect being the creation of a secondary βΌ keV peak for small π h and large π β .The spectra in Figure 7 have bolometric luminosities rangingfrom 10 to 10 erg s β , on the level of weak AGN s. Becausethe shocked material cools eο¬ciently, these luminosities areclose to the total energy dissipation rate, which is βΌ . (cid:164) π s timesthe speciο¬c kinetic energy of the disk at the second impact (Β§4.2).Second-impact radii are multiples of π p , so the luminosity scalesas πΏ β πΊ π h (cid:164) π s / π p β π / π / β π β / β Ξ¨ β Ξ / β π / π . β Ξ¨ β Ξ / . (35)As seen in Figure 8, this equation best describes the luminositiesfrom the model when the constant associated with the ο¬rstproportionality is βΌ Γ β : πΏ βΌ . Γ erg s β Γ (cid:18) π h Γ M (cid:12) (cid:19) / (cid:18) π β M (cid:12) (cid:19) . Ξ¨ β Ξ / . (36)The proportionality constant is so small because merely βΌ
20% ofthe bound debris participates in the second impact, and because,according to Figure 3, the second impact happens at several tensof π p .In view of the weak βnominalβ dependence of πΏ on π h and π β , the correction factors Ξ¨ and Ξ actually control how πΏ scales with π h and π β . The combination Ξ¨ β Ξ / decreaseswith π h and increases with π β , counteracting the nominal π h -dependence but augmenting the nominal π β -dependence.As is apparent from Figures 7 and 8, πΏ is most sensitive to π h for π h (cid:38) Γ M (cid:12) , and to π β for 0 . M (cid:12) (cid:46) π β (cid:46) M (cid:12) .6. DISCUSSION6.1. Identifying second-impact signatures in
TDE searches
TDE s in
AGN s have observational signatures that are emphaticallyunlike
TDE s in vacuum. They do not have optical/ UV light curvesthat follow the mass-return rate, as is commonly expected for theirvacuum counterparts (e.g., Rees 1988). Instead, the destructionof the inner disk by the ο¬rst impact sustains an Eddington-levelluminosity plateau over tens of days (Chan et al. 2019, 2020). Ontop of that, the second impact begets a longer-lasting signal whoseluminosity does follow the mass-return rate thanks to eο¬cientcooling, but its typical photon energy is not in the optical/ UV :most of the spectra in Figure 7 peak between βΌ
10 keV and1 MeV. Such spectra bear no resemblance to the tens-of-eVthermal spectrum originally expected from the accretion diskIGH-ENERGY EMISSION FROM TDES IN AGNS 9 π h = 10 π β π β = 0.3 π β π p /π g β 31.93Ξπ‘ = 2.88 d πΏ β 7.5 Γ 10 erg s β1 πΏ/πΏ E β 6.0 Γ 10 β2 π h = 10 π β π β = π β π p /π g β 21.63Ξπ‘ = 1.61 d πΏ β 7.4 Γ 10 erg s β1 πΏ/πΏ E β 5.9 Γ 10 β1 π h = 10 π β π β = 3 π β π p /π g β 36.19Ξπ‘ = 3.47 d πΏ β 1.3 Γ 10 erg s β1 πΏ/πΏ E β 1.0 Γ 10 π h = 3 Γ 10 π β π β = 0.3 π β π p /π g β 18.10Ξπ‘ = 3.69 d πΏ β 6.3 Γ 10 erg s β1 πΏ/πΏ E β 1.7 Γ 10 β2 π h = 3 Γ 10 π β π β = π β π p /π g β 12.26Ξπ‘ = 2.06 d πΏ β 6.5 Γ 10 erg s β1 πΏ/πΏ E β 1.7 Γ 10 β1 π h = 3 Γ 10 π β π β = 3 π β π p /π g β 20.52Ξπ‘ = 4.45 d πΏ β 1.1 Γ 10 erg s β1 πΏ/πΏ E β 2.9 Γ 10 β1 π h = 10 π β π β = 0.3 π β π p /π g β 10.53Ξπ‘ = 5.45 d πΏ β 3.7 Γ 10 erg s β1 πΏ/πΏ E β 2.9 Γ 10 β3 π h = 10 π β π β = π β π p /π g β 7.13Ξπ‘ = 3.04 d πΏ β 4.7 Γ 10 erg s β1 πΏ/πΏ E β 3.7 Γ 10 β2 π h = 10 π β π β = 3 π β π p /π g β 11.93Ξπ‘ = 6.58 d πΏ β 8.1 Γ 10 erg s β1 πΏ/πΏ E β 6.5 Γ 10 β2 π h = 3 Γ 10 π β π β = 0.3 π β π p /π g β 6.94Ξπ‘ = 8.75 d πΏ β 7.5 Γ 10 erg s β1 πΏ/πΏ E β 2.0 Γ 10 β4 π h = 3 Γ 10 π β π β = π β π p /π g β 4.70Ξπ‘ = 4.88 d πΏ β 2.6 Γ 10 erg s β1 πΏ/πΏ E β 6.8 Γ 10 β3 π h = 3 Γ 10 π β π β = 3 π β π p /π g β 7.86Ξπ‘ = 10.56 d πΏ β 4.6 Γ 10 erg s β1 πΏ/πΏ E β 1.2 Γ 10 β2 photon energy π/ eV l u m i no s it y π πΏ π / ( e r g s β ) Figure 7.
Disk-integrated second-impact spectra for (cid:164) π s / (cid:164) π d β
8. All panels share the same legend, but the value of Ξ π‘ = ( πΊπ h / π ) β / varies from panel topanel. Here πΏ E = ππΊπ h ππ H / π T is the Eddington luminosity. formed by TDE s in vacuum (Cannizzo et al. 1990; Ulmer 1999)and is sometimes observed in soft X-ray
TDE s (see Saxton et al.2020 for a review).The hard second-impact spectrum could mean that
TDE searches focused on softer spectra would miss it altogether. Thehunt is made diο¬cult by the fact that, unlike jetted
TDE s withisotropic-equivalent X-ray luminosities of 10 to 10 erg s β (Bloom et al. 2011; Burrows et al. 2011; Levan et al. 2011;Cenko et al. 2012), the second impact emits at rates four ordersof magnitude lower. 6.2. Second-impact signatures versus
AGN variability
Another challenge to identiο¬cation of second-impact signaturesis to distinguish them from common
AGN variability. Twoaspects may provide means to do so: the spectral hardness andthe pattern of time-variation.The second impact has much harder spectra than ordinary
AGN s. The coronal component of unobscured
AGN spec-tra typically has β (cid:46) π log πΏ π / π log π (cid:46) β . βΌ black hole mass π h /π β l u m i no s it y πΏ ( e r g s β ) πΏ / πΏ E = β πΏ / πΏ E = β πΏ / πΏ E = β πΏ / πΏ E = β πΏ / πΏ E = π β = 0.3 π β π β = π β π β = 3 π β Figure 8.
Luminosity of the second impact. The crosses are the luminositiespredicted by our cooling model; there is one cross for every (cid:164) π s / (cid:164) π d and forevery one-ο¬fth of the simulation duration (Β§5.1). For clarity, the crosses aredisplaced horizontally by a small amount according to their (cid:164) π s / (cid:164) π d , with (cid:164) π s / (cid:164) π d increasing from left to right. The luminosity depends weakly on (cid:164) π s / (cid:164) π d and time in most cases. The curves are given by Equation (36). Thatequation estimates the second-impact luminosity to be equal to its characteristicenergy dissipation rate, and the overall normalization of the estimate is chosento ο¬t the model luminosities. The goodness of the ο¬t suggests that the materialshocked at the second impact cools eο¬ciently. β (cid:46) π log πΏ π / π log π (cid:46)
0. The contrast between unobscured
AGN spectra and the signiο¬cantly harder second-impact spectrais enhanced to the degree that the corona is disrupted by the ο¬rstimpact, an outcome suggested in our earlier work (Chan et al.2019; Ricci et al. 2020).In addition to unobscured
AGN s, there is also a roughlycomparable number of obscured
AGN s (e.g., Huchra & Burg1992; Reyes et al. 2008; Brightman & Nandra 2011; Wilkeset al. 2013; Oh et al. 2015). Our sightlines to these
AGN s areobscured by neutral gas with hydrogen column densities π H of βΌ to 10 cm β or more. A column with π H βΌ cm β absorbs essentially all photons below βΌ π H βΌ cm β absorbs all photons under βΌ π H scatters all photons with energiesup to (cid:38)
100 keV. A signiο¬cant fraction of all obscured
AGN s,from βΌ
20 to 50%, may belong to this last category (Ricci et al.2015; Georgantopoulos & Akylas 2019; Kammoun et al. 2020).Because this obscuration is mostly located parsecs away fromthe black hole, if it blocks X-rays from an AGN , it will equallyblock those due to a TDE . The only photons we can see arerelatively high-energy, which makes the contrast between thesecond impact and the unperturbed
AGN especially large.The smooth brightening and fading of the second impact couldprovide another method of distinction. The X-ray light curvesof normal
AGN s generically exhibit βred noise,β that is, theirFourier power spectra are power laws declining from timescalesof months or years to timescales of hours (e.g., Lawrence et al.1987; McHardy & Czerny 1987; Lawrence & Papadakis 1993),and individual modes of the power spectra have little or no phasecoherence (Krolik et al. 1993). By contrast, the second impactshould brighten and fade smoothly over a period of months, inresponse to the variation of the mass-return rate. The existenceof a dominant timescale, and the phase coherence implied by the smoothness of the light curve, may help make a second-impactο¬are distinct. 6.3.
Caveats about the spectrum
Our treatment of light production at the second impact depends ona number of approximations and simpliο¬cations. A few warrantidentiο¬cation as possible starting points for future improvements.The simulations underlying our cooling model injected thestream on a parabolic orbit (Chan et al. 2019) when, in fact,the debris is weakly bound. Therefore, the stream energy isoverestimated by an amount comparable to its typical bindingenergy. After correcting for this oο¬set, the second impactwould happen at smaller radii. This would increase the energydissipated per unit stream mass somewhat, raise the luminosity,and change the spectrum. A greater fraction of the stream couldalso end up in the second impact, making the cooling emissionfrom it softer and more thermal (Β§5.3).As in Chan et al. (2019, 2020), we considered here a speciο¬cstream conο¬guration: the stream hits the disk perpendicularlywhile passing through its pericenter at radius R t . Our resultsmight change depending on stream orientation and pericenter,but preliminary estimates suggest that orientation does notqualitatively aο¬ect our conclusions.Our model ignores the production of electronβpositron pairsfor simplicity (Β§5.2), but many pairs should be produced inthe freshly shocked gas with temperatures π B π g (cid:38) π e π . Inpair equilibrium, some of the thermal energy is held in therest mass of pairs, while pair annihilation adds to the numberdensity of photons. The increase in scattering opacity due topairs combined with the presence of additional photons tends topromote lower gas and radiation temperatures, and more nearlythermal spectra.Lastly, as the mass-return rate of the debris rises, reaches apeak, and then falls, the bolometric luminosity should roughlytrack that rate, while the spectrum evolves from harder at lowermass-return rate, to softer and more thermal near the peak, andthen back to harder as the mass-return rate decays.7. CONCLUSIONSAs argued in Chan et al. (2019), some fraction of all TDE s shouldtake place in
AGN s. These
TDE s have drastically diο¬erent physicsand phenomenology from those in inactive galaxies due to thepre-existing
AGN disk. The disk does not aο¬ect the disruption,but it can block the returning debris stream. The dynamicsand observational properties of these
TDE s are thus deο¬ned bythe multiple interactions between the stream and the disk. Themechanisms commonly considered in connection with
TDE s invacuum cannot be applied to
TDE s in
AGN s, and they certainlycannot explain the optical/ UV emission from the latter.For TDE s in
AGN s, the ο¬rst impact of the stream with the disktakes place near stream pericenter. The shocks generated causethe disk interior to the impact point to fall rapidly into the blackhole, and they power a short-lived Eddington-limited luminosityplateau (Chan et al. 2019), possibly thermal in spectrum. Theplateau lasts tens of days (Chan et al. 2020) if the tidal radiusis estimated using an order-of-magnitude estimate (e.g., Rees1988). Accounting for the eο¬ects of general relativity and stellarstructure on the disruption changes the duration by a factor of aIGH-ENERGY EMISSION FROM TDES IN AGNS 11few (Ryu et al. 2020a); for example, the plateau duration for aSun-like star disrupted by a 3 Γ M (cid:12) black hole accreting at0.01 times Eddington is shortened from βΌ
10 d to βΌ βΌ
100 keV. Compton cooling produceshard X-rays to soft πΎ -rays with a strikingly hard spectrum: mostof the energy is carried by photons from βΌ
10 keV to 1 MeV.The luminosity tracks the mass return rate, reaching βΌ to 10 erg s β at peak; this means the timescale of the lightcurve is roughly a few months. The spectrum is harder whenthe luminosity is low, and softer and more thermal when theluminosity is high.Second-impact emission may be distinguished from intrinsic AGN light by its exceptionally hard spectrum, and the smoothtime-variation of its luminosity roughly following the mass-return rate. If the ο¬rst impact disrupts the inner diskβs corona(Chan et al. 2019; Ricci et al. 2020), then the few-keV coronalemission of the normal
AGN would be reduced, and the tens-of-keV second-impact radiation would stand out even more.A third source of radiation not discussed here arises from theunbound debris interacting with the circumnuclear environment;such debris can be unbound either during the disruption (Kroliket al. 2016; Yalinewich et al. 2019), or by a boost from the diskat the ο¬rst impact (Chan et al. 2019). Synchrotron radiation,similar to that of supernova remnants, would be produced at theshocks generated by the outο¬owing debris. Such radio signatureshave been observed in
TDE s such as
ASASSN -14li (Alexanderet al. 2016; van Velzen et al. 2016; Bright et al. 2018).
TDE s areexpected to produce stronger radio emission in
AGN s because ofthe higher circumnuclear densities.Finally, by severely disturbing the disk, a TDE can leavean enduring mark on an AGN . The
AGN accretion rate may beenhanced for years to come because half a star has been depositedin the disk. Alternatively, the accretion rate may be reduced afterthe end of the
TDE because the ο¬rst impact has emptied the innerdisk into the black hole.To summarize,
TDE s in
AGN s are expected to show a bolo-metric luminosity plateau extending for tens of days. This isfollowed by βΌ
10 keV to 1 MeV hard X-rays and soft πΎ -rays thatfollow the mass-return rate; the typical photon energy is muchharder than in non-jetted TDE s, and the observed luminosity isseveral orders of magnitude below jetted
TDE s. At the same time,the debris unbound during the disruption and at the ο¬rst impactcan interact with the circumnuclear gas and produce synchrotronradiation much brighter than
TDE s in vacuum.CHC and TP were partially supported by ERC advanced grantβTReX.β JHK was partially supported by NSF grant AST-1715032. REFERENCES
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