lyman edges in supermassive black hole binaries

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Lyman edges in supermassive black hole binaries

Aleksey Generozov and Zoltan HaimanDepartment of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027

4 March 2014

ABSTRACT

We propose a new spectral signature for supermassive black hole binaries (SMBHBs) withcircumbinary gas disks: a sharp drop in flux blueward of the Lyman limit. A prominentedge is produced if the gas dominating the emission in the Lyman continuum region ofthe spectrum is sufficiently cold (T

< 20,000K) to contain significant neutral hydrogen.Circumbinary disks may be in this regime if the binary torques open a central cavity in thedisk and clear most of the hot gas from the inner region, and if any residual UV emissionfrom the individual BHs is either dim or intermittent. We model the vertical structure

and spectra of circumbinary disks using the radiative transfer code TLUSTY, and identifythe range of BH masses and binary separations producing a Lyman edge. We find thatcompact supermassive (M

>108 M) binaries with orbital periods of0.110yr, whosegravitational waves (GWs) are expected to be detectable by pulsar timing arrays (PTAs),could have prominent Lyman edges. Such strong spectral edge features are not typicallypresent in AGN spectra and could serve as corroborating evidence for the presence of aSMBHB.

Key words: accretion, accretion discs black hole physics galaxies: active

1 INTRODUCTION

Supermassive black holes (SMBHs) are present in the centers ofmost, if not all nearby galaxies (see reviews by, e.g.Kormendy &Richstone 1995; Ferrarese & Ford 2005). Furthermore, SMBHsare abundant at all redshifts, manifesting themselves as quasarsat higher redshifts. If two galaxies containing SMBHs merge,this should then result in the formation of a SMBH binary (e.g.Begelman et al. 1980). Thus, given the hierarchical model forstructure formation, in which galaxies are built up by mergers,one would naively expect SMBH binaries to be quite common.

Many candidates for binary BHs have been identified onkiloparsec scales, including two galaxies with spatially resolvedactive binary nuclei (Komossa et al. 2003;Fabbiano et al. 2011;see, e.g. the review byKomossa 2006andShen et al. 2013andreferences therein). At parsec scales, however, there is a dearth

of evidence for binary black holes, with only one clear example:a radio observation of a black hole pair with a projectedseparation of7 pc(Rodriguez et al. 2006). There remain noconfirmed binary black holes at subparsec separations.

The lack of observational evidence for binaries at smallseparations suggests that the SMBHs either remain inactiveduring the merger, or that they merge within a small fraction ofa Hubble time and are consequently rare (Haiman et al. 2009).Another possibility is that the spectrum of a compact binarydiffers significantly from those of single-BH active galacticnuclei (AGN). A better understanding of the spectral energy

E-mail: (alekseygenerozov,zoltan)@astro.columbia.edu

distributions (SEDs) and lightcurves from circumbinary disksis necessary to determine whether binaries may therefore be

missing from AGN surveys or catalogs(Tanaka 2013).Understanding the electromagnetic (EM) signatures of

binary black holes is also important for gravitational waveastronomy. Gravitational waves (GWs) from a merging SMBHbinary may be detected in the next decade by pulsar timingarrays (PTAs;Bizouard et al. 2013). Identifying the gravita-tional wave source in EM bands would also have considerablepayoffs for cosmology and astrophysics (e.g. Phinney 2009).Unfortunately, GWs yield limited precision on the sky position.For a PTA source, of order 102 (and perhaps as many as 104)plausible candidates may be present within the 3D measurementerror box (Tanaka et al. 2012). Concurrent EM observationswould then be necessary to identify the GW source.

Many different EM signatures have been proposed forSMBH binaries. These include periodic luminosity variationscommensurate with the orbital frequency of the source (Haimanet al. 2009 and references therein) and broad emission linesthat are double-peaked and/or offset in frequency (Shen et al.2013and the references therein). Additionally, the evacuationof a central cavity by the binary could lead to a spectrum thatis a distinctively soft (Milosavljevic & Phinney 2005; Tanaka &Menou 2010), and has unusually weak broad optical emissionlines, compared to typical AGN (Tanaka et al. 2012).

We here propose that, in addition to the above signatures,the presence of a central cavity in a circumbinary disk couldproduce distinct absorption edges in the optical/UV (inparticular, at the Lyman limit). This is analogous to the

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prominent Lyman break in galactic spectra a >few10 Myr

after a starburst, when the composite emission is dominated byless massive stars with cooler atmospheres (Leitherer et al. 1999;Schaerer 2003). Physically, such an edge would be present if thedisk is cold enough (Teff

10,000

K); for yet cooler disks, the continuum emission redward of theLyman limit may be obscured by metal absorption features.

This Letter is organized as follows. In2, we describethe details of our disk and emission models. In 3,we showexamples of spectra for binary BH disks, and compare theseto those of single BH disks. In 4, we discuss caveats, includingemission from mini-disks around each of the individual BHsthat could mask the Lyman edge. We summarize our mainconclusions and the implications of this work in 5.

2 DISK MODELS

In order to model disk spectra, we must begin with a model forthe disk. In particular, we need the energetics (i.e. how much en-ergy is dissipated from tidal torques and viscous heating through-out the disk). We here adopt the analytic models in Kocsis et al.(2012,hereafter KHL12). These are modified versions of a stan-dardShakura & Sunyaev(1973) accretion disk, to incorporatethe angular momentum transfer and the corresponding heatingof the disk by the binary torques. The models self-consistentlytrack the co-evolution of the disk and the binary orbit, througha series of quasi-steady, axisymmetric configurations.

There are several qualitatively different solutions for such asystem, depending on the parameters of the binary (i.e. massesand orbital separation) and the disk (i.e. viscosity and accretionrate). For the purposes of this Letter, we concentrate on regionsof parameter space in which a central cavity is opened andmaintained, as the lack of the hot inner regions is responsible forthe Lyman edges in the spectrum. Generally, a cavity is presentwhen the lower-mass (secondary) BH has a mass higher thanthe local disk mass: in this case, the secondary migrates inwardon a timescale longer than the viscous time, allowing most of theinner disk to drain onto the primary. The corresponding pile-upof material outside the secondarys orbit creates a hot rim, andthe increase in viscosity can cause the gas to overflow and closethe gap. The gap-opening criterion we adopt from KHL12 is thusmore conservative than in previous works (e.g. Syer & Clarke1995; del Valle & Escala 2012). Our conclusions on Lymanedges simply rely on emission from disk patches with effectivetemperatureTeff10,00020,000K dominating the compositeUV spectrum, and should not be sensitive to model details.

Fig.1 shows illustrative examples of radial profiles of theeffective temperature (defined by SBT4

eff F, where SB isthe Stefan-Boltzmann constant, andFis the total dissipationrate per unit disk surface area, including both viscous andtidal heating). The solid curve shows Teff(r) for a circumbinarydisk around a Mtot= M1 +M2= 10

8M binary, with massratio q=M2/M1=0.05 and accretion rate M/ MEdd=0.1 (withMEddassuming a radiative efficiency of 10%). The secondaryis located at the radius rs= 270 Rg (RgGMtot/c

2), creatinga cavity inside 340Rg. We assume in all of our models that theblack holes are non-spinning, and adopt a viscosity parameter= 0.1. For the other less important parameters, we use thesame fiducial parameters as KHL12, except we set fT= 3/8to be consistent with our assumption of vertically uniform

101

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Figure 1. Temperature profiles for a circumbinary disk around a108M, q = 0.05 binary (solid) and for a thin disk around a single108M black hole (dashed). Both disks assume an accretion rate

M/ MEdd= 0.1, and the radial distance is shown in gravitationalunits. The solid curve is truncated at a radius of 340Rg due to the

presence of a cavity in the disk. The black dot marks the radius ofthe secondary.

dissipation The dashed curve shows, for comparison, Teff(r)

for a disk around a single BH with the same mass. Mostimportantly, this figure shows that outside the cavity, thecircumbinary disk is hotter (by a factor oftwo; see alsoLodatoet al. 2009)than the corresponding single-BH disk, but still notnearly as hot as the innermost regions of this single-BH disk.

2.1 Spectral energy distributions: previous models

The simplest model for the emerging spectrum is that of acomposite blackbody. In this model, each disk annulus emits asa blackbody, with the effective temperature determined by theheating rate from viscous and tidal torques in that annulus. Amore sophisticated version is a composite graybody spectrum.The blackbody emission in each disk annulus is modified by a

correction factor, accounting for the effects of electron scatteringopacity (Milosavljevic & Phinney 2005; Tanaka & Menou 2010),to obtain

F 2

1/2

1+1/2

B. (1)

Here, abs,/(abs,+es,) is the ratio of absorption tototal opacity. We adopt the Kramers bound-free opacity atsolar metallicity for abs, andes,= 0.4 cm

2 g1 (we stressthat these are used only for our reference graybody spectra).We refer the reader toTanaka & Menou(2010) for a detaileddiscussion of the graybody disk model.

2.2 Spectral energy distributions: new RT models

Although the graybody model is an improvement over a black-body, it ignores important radiative transfer (RT) effects. Inparticular, the opacity is assumed to be a smooth function of fre-quency. In reality, the bound-free opacities have sharp thresholds,corresponding to the onset of absorption from various species inthe disk. For example, photons with energies above the Lymanlimit 13.6eV (or frequency 3.28 1015 Hz) can be absorbed byneutral (ground-state) hydrogen (H) within the disk. This sharpchange in opacity can cause a corresponding prominent edge inthe emerging disk spectrum. This may be understood in termsof the Eddington-Barbier approximation: in a plane-parallel in-finite atmosphere, one sees the source function at optical depth

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unity along the line of sight. Thus, the smaller opacity redwardof the Lyman limit means we see the source function from deeperin the disk, where the temperature is (generally) higher. Thehigher temperature then translates into a greater flux redwardof the Lyman limit in other words, an absorption edge willbe present in the spectrum (e.g. Hubeny & Hubeny 1997).

As the temperature increases, H is more ionized, decreasing

the H bound-free opacity. Eventually, the combined electronscattering and free-free opacities overwhelm the discontinuityin the bound-free opacity, and the opacity on both sides of theLyman edge becomes nearly equal, washing out any absorptionedge in the spectrum. As the temperature continues to increase,NLTE effects may cause an emission edge instead.

To model the emission from the disk, we use the radiativetransfer code TLUSTY (Hubeny & Lanz 1995). This codeself-consistently solves the equations of vertical hydrostaticequilibrium, energy balance, radiative transfer, and the fullnon-LTE statistical equilibrium equations for all species thatare present in the disk. Contributions from all bound-free andfree-free transitions at all frequencies of interest are included,while bound-bound transitions are assumed to be in detailed

balance. We model H as a 9level atom and He as a 4levelatom. Electron scattering, including Comptonization is alsoincluded. We assume the disk is composed of H and He (attheir Solar ratio). Metals are not included, but would makelittle difference to continuum spectra for 104 K Teff10

5 K.For any given annulus, we calculate the vertical structure byspecifying the vertical gravity gz, disk surface density , andthe total energy dissipation rate Teff. Spectra are insensitive tothe surface density (provided the disk remains optically thick)and, for computational convenience, we fix =2105 g cm2

throughout this Letter. Thus, specifying the radial profile Teff(r)and vertical gravity gz(r) fully determines the spectrum emerg-ing from the disk annulus at radius r. gz(r) is approximatedto be linear in zand proportional to the square of the localKeplerian angular frequency,qg2K. The composite spectrummay be computed by summing over all annuli.

Although we have assumed flux is radiatively transmittedthrough the disk, most of our model annuli have convectivelyunstable zones. Models with small density inversions (densityincreasing outward) also occur. Such density profiles areequilibrium solutions, but are unstable. Finally, we assume thattidal and viscous torques dissipate energy locally, and uniformlyin height (i.e. equal dissipation per unit column mass). Thevertical energy distribution is poorly understood, and realdisks may be advective, or the energy may be carried away bydensity waves (Dong et al. 2011;Duffell & MacFadyen 2012).

3 RESULTS: EDGES IN DISK SPECTRA

In this section, we show examples of composite circumbinary diskspectra, and compare these to the simpler black and graybodymodels, as well as to the corresponding singleBH disk spectra.

In the left panel of Fig.2,the solid (dashed) curves showcomposite disk spectra corresponding to the circumbinary (single-BH) disk in Fig.1.Realistically, the disk may extend to 2000Rg, where it would become gravitationally unstable, accordingto the Toomre criterion. However, due to practical issues withconvergence, we were only able to get models within 100Rgofthe inner disk edge, and we only integrate the emission from this

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Figure 2. Left panel:Spectra from disks with the temperature profiles

shown in Figure1.The black, blue and red solid curves are TLUSTY,blackbody, and graybody spectra for circumbinary disks. The dashedcurves with the same colors refer to the same models for a single-BHdisk. Right panel: Same as the left, except for disks around 2.5 times

lower-mass (Mtot=4107M) black holes.

region. However, the excluded region is cooler than the inner edgeof the disk and its emission should not mask the Lyman edge.

The TLUSTY binary spectrum (in black), shows a promi-nent break at the Lyman limit (3.281015 Hz), which is notpresent in the black or graybody disk models (shown in blue

and red, respectively). Overall, the blackbody model overpredictsthe flux at both low and high frequencies, but underpredictsit immediately below the Lyman limit. The graybody modeldoes a better job at frequencies below the Lyman limit, butoverpredicts the flux more significantly at higher frequencies.

In contrast to the binary-BH spectrum, the single-BHspectrum has no sharp absorption edge at the Lyman limit(although there is a weak kink). This is because, as shown inFig.1,the innermost region of the single-BH disk is much hotterthan the inner edge of the binary disk. Specifically, the binarydisk has a maximum Teffof 12,000, whereas, the single-BH diskis considerably hotter, with a maximum Teffof 63,000 K. Fora spinning black hole, the inner edge is expected to be closer tothe black hole horizon (following the innermost stable circular

orbit), which would further increase the maximum temperaturein the single-BH case. However, winds may limit the maximumTeffin single-BH disks to 50,000 K (Laor & Davis 2014).

In the right panel of Fig. 2, we show another set ofillustrative disk spectra, with the same parameters as in theleft panel, except for a lower mass (Mtot=410

7M). In thiscase, the binary disk is hotter (Teff=18,600K at the inner edge)and the Lyman edge feature is correspondingly weaker. Thesingle-BH model looks similar to the one shown in the left.

3.1 Binary parameter space with edges

We now discuss under what conditions binary disks are likely

to have prominent Lyman edges.If the inner edge of the disk falls below a particular thresholdtemperature, the composite disk spectrum will have a prominentLyman absorption edge. An example of a spectrum close to thethreshold temperature is the one shown in the right panel of Fig-ure 2: if the disk were much hotter, the Lyman edge feature wouldbe wiped out. The precise threshold will depend on the verticalgravity and other parameters. Physically, the vertical gravity setsthe scale height, which determines the vertical density. The den-sity, in turn, determines the ionization state, which then affectsthe opacity difference between the two sides of the Lyman limit.

To establish a quantitative criterion for the threshold Teff,we find the maximum effective temperature such that there is atleast an order of magnitude drop in the flux at the Lyman limit

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Figure 3. Regions of binary parameter space with a prominent

Lyman edge. In both panels, the blue region corresponds to binarieswith a prominent Lyman edge forq = 0.05 and M/ MEdd= 0.1. Onthe left, the red region corresponds to Lyman edges forq = 1 and

M/ MEdd=0.1. On the right, the red region corresponds toq =0.05and M/ MEdd = 1. The bends below r

10

9s2 lies outside ourparameter space of interest. At lower qg we were unable toconstruct models at the threshold, and simply extrapolated thisfit. qg= 10

12s2 at 160 Rg for a 108M BH. Note that the

spectrum in the right panel of Fig. 2 would not satisfy our con-servative criterion. We also impose a low-temperature thresholdof 104 K, below which metal absorption becomes important and

possibly causes metal edges to appear in the spectrum. Compar-ing the maximum disk temperature to the fitting formula above,we identify regions in binary parameter space which are coolenough to have Lyman edges.2 In Fig.3, we show the rangesof masses and separations for which a prominent Lyman edgeis produced, for two different accretion rates and mass ratios.

4 MINI-DISKS

In general, we would not expect any central cavity to becompletely empty. As first discussed in the SPH simulationsof Artymowicz & Lubow (1996) and confirmed by severalrecent works(Hayasaki et al. 2007; MacFadyen & Milosavljevic

2008;Cuadra et al. 2009; Shi et al. 2012; Roedig et al. 2012;DOrazio et al. 2013; Farris et al. 2013; Gold et al. 2013) gasleaks into the cavity through non-axisymmetric streams. Thesestreams can feed mini-disks around each individual BH, atrates set by the viscous timescale of each mini-disk. The recentsimulations suggest that accretion rates inside the cavity maybe comparable to those onto a single-BH.

The emission from hot mini-disks may mask the Lyman

1 Assuming =2105 g cm2. In the optically thick limit changesin the may affect the threshold by 5%2 Using the hottest annulus, as opposed to full composite spectra,

is a good proxy to identify the presence/absence of the Lyman edge.

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Figure 4. Left: Time average of the surface density distribution,

reproduced with permission fromFarris et al. (2013,Fig. 8b). Right:spectra for the circumbinary and circumsecondary disks. The solid(black) curve is for the circumbinary disk, and the other curves are

for the mini-disk, corresponding to a different assumed fraction of thecircumbinary Mfueling the secondary BH: 50% (purple), 10% (blue),and 5% (red).

edge feature. To illustrate this, we calculate spectra for the disksshown in Fig. 8b ofFarris et al. 2013(reproduced here as theleft panel of Fig.4). This figure shows a time averaged surfacedensity profile for aq=0.43 binary. The simulation is scale-freeso the masses, separation, and accretion rate are arbitrary.We adopt a Mtot= 510

7M and separationrs =460Rg. Forq= 0.43, the masses of the primary and secondary are then3.5107Mand 1.510

7M, and the system is on the vergeof the GW inspiral stage.

To model the spectrum of the circumbinary disk, we useTeff(r) from an axisymmetric KHL12 circumbinary disk modelwith inner radius at 460 Rg (even though the simulated diskis in fact lopsided; note that the simulations are isothermaland do not predict Teff). To obtain the Teffprofile, we setM/ MEdd= 0.1. We likewise model the circumsecondary diskas a standard thin disk around a non-spinning BH (withtruncation radius of 400Rg, whereRgis defined in terms of justthe secondary mass. This is roughly consistent with the size ofthe circumsecondary disk in Fig.4). Fig.4 shows spectra of thecircumbinary and circumsecondary disks, assuming that 50%(purple), 10% (blue), and 5% (red) of the external Mfuels thesecondary. For the 5% case, the Lyman edge is still prominent.However, it is greatly reduced for 10%, and for 50% it iscompletely obscured. Thus, if more than a few % of the M inthe cicumbinary disk leaks into the cavity and fuels a radiativelyefficient, hot accretion flow, the Lyman edge can be obscured.For highermass black holes, an even smaller Mwould be re-quired to hide the edge as inner portion of the circumbinary diskwould be cooler, reducing the flux redward of the Lyman edge.As discussed above,Farris et al. (2013) find circumsecondaryaccretion rates comparable to the rate onto a single BH, which

would favor the>50% case. There should also be some emissionfrom the circumprimary disk, which we have not included.However, there are two reasons why Lyman edges could

remain detectable, even with efficient fueling of the individualBHs. First, most of the gas entering the cavity may fuel thesecondary (rather than the primary) BH. This could then lead toa radiatively inefficient, super-Eddington accretion flow, ratherthan a thin mini-disk; such disks have much fainter fluxes inthe UV (see, e.g.Kawaguchi 2003). Second, the fueling of theindividual BHs may be intermittent. The simulations listed in thepreceding paragaphs show that the rate at which the gas entersthe cavity fluctuates strongly, tracking the binarys orbital period.Whether the BHs can accept this fuel depends on the viscoustimescale in their vicinity. There is some evidence from 3D MHD

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simulations that the effective may strongly increase insidethe cavity (Shi et al. 2012;Noble et al. 2012; Gold et al. 2013).The streams from the circumbinary disk would then rapidlyaccrete onto the individual BHs, and mini-disks would eithernot form or would be intermittent (Tanaka 2013). Ultimately,the prominence of the Lyman edge features is tied to the natureof the accretion flows onto the individual BHs, and requires a

better understanding of the effective viscosity, time-dependence,and radiative efficiency (in the UV bands) of these flows.

5 SUMMARY AND CONCLUSIONS

In this Letter, we have proposed that spectral edges, in particularat the Lyman limit, may be characteristic signatures of a cir-cumbinary disk. Our conclusions can be summarized as follows.

(i) If binary torques clear a cavity in the circumbinary disk,the disk spectrum may exhibit a sharp drop at the Lymanlimit. This is because the hottest region (i.e. the inner edge)of the disk is cool enough to have neutral H, absorbing nearly

all flux blueward of the Lyman limit. This occurs below acritical Teffwhich generally lies in the range 10,000 K-20,000K, depending on vertical gravity and other parameters. Atlower temperatures, absorption from metals (i.e. C) may causespectral edges redward of the Lyman limit.

(ii) Observationally, AGN spectra only show Lyman edgesdue to absorption by intervening neutral gas. The inner regionsof a single-BH AGN disk are hotter than for binaries (Fig.1),and can mask any edge produced in the outer disk, leaving only asmall kink(Fig. 2). Such kinks are not seen observationally, andunderstanding what would smear them (e.g. general relativisticeffects or winds) is an open theoretical problem. For an overviewof the Lyman edge problem in AGN spectral modeling see, e.g.Kolykhalov & Sunyaev(1984) andKoratkar & Blaes(1999).

(iii) Neutral H in the binarys host galaxy, unrelated to thenuclear accretion disk itself, could cause a Lyman edge (asseen in a few AGNs). However, in the case of the disk, onecould look for rotational broadening of the edge due to orbitalmotions in the disk, with velocities of order 104 km/s. Thismay cause a 10% smearing on the edge.

(iv) A portion of the binary parameter space could havea truncated circumbinary disk, with Teff in the critical rangefor a prominent Lyman edge (Fig. 3). This parameter spacepartially overlaps with the expected typical parameters forindividually resolvable PTA sources. These are very massivebinaries, with 108M

lyman edges in supermassive black hole binaries

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