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New Astronomy Reviews 51 (2008) 775–777

Hyperaccretion

Andrew King

Department of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK

Available online 18 March 2008

Abstract

I briefly review the physics of accretion at rates well above the Eddington value. In stellar-mass systems, the result is generally anultraluminous X-ray binary, and I show how SS433 fits into this picture. Conditions are relatively less extreme in active galactic nuclei,as the greatest likely accretion rates are not far above the electron-scattering Eddington value. However, even quite modest mass inflowrates exceed the corresponding value for dust opacity. I show that the obscuring torus invoked in unified AGN schemes is the probableresult, and note that the matter in the torus probably does not supply the matter accreting on to the central black hole and thus poweringthe AGN.� 2008 Published by Elsevier B.V.

1. Introduction

Accretion is the most efficient way of using normal mat-ter to release radiant energy. Accordingly, radiation pres-sure imposes a natural limit on the accretion luminosity,usually expressed as the Eddington limit

LEdd ’4pGMc

jð1Þ

where j is the opacity and M is the accretor mass.However, there is no reason why the source of the

accreting matter should know about this limit. This raisesthe obvious question of what happens in hyperaccretingsystems, i.e. ones where the accretor is fed matter at rates_M far above the value _MEdd ¼ LEdd=�c2 which would pro-

duce LEdd, where � � 0:1 is the efficiency. We note thatfor electron-scattering opacity j ’ 0:34 we have _MEdd ’10�7M� year�1ðM=10M�Þ ’ 1M� year�1ðM=108M�Þ. Thisquestion is particularly acute for accreting binary systems,since here there are several generic situations in which masstransfer naturally proceeds at values� _MEdd. An extremelycommon case occurs when a massive star fills its Rochelobe and transfers mass to a less massive accretor (allhigh-mass supergiant X-ray binaries will pass through thisstage for example). It is easy to show (e.g. King and Ritter,

1387-6473/$ - see front matter � 2008 Published by Elsevier B.V.

doi:10.1016/j.newar.2008.03.005

E-mail address: ark@astro.le.ac.uk

1999) that if the donor is largely radiative, it then transfersits mass M2 mass to the accretor on its thermal timescaletKH, i.e. _M ¼ � _M2 � M2=tKH, leading to rates _M �10�5–10�3M� year�1 or more, i.e. _M > 102–104 _MEdd. Ifthe donor is largely convective, the mass transfer rateincreases towards the still larger dynamical timescale rate� M2=P , where P is the orbital period.

Such accretion rates mean that the accreting luminosityreaches the Eddington value even before the matter hasfallen all the way down the accretor’s gravitational poten-tial well, that is, well above its surface. At this point, radi-ation pressure must start to blow some of the accretingmatter away, presumably self-limiting so that accretionwithin this point proceeds only at the (decreasing) Edding-ton rate corresponding to each radius. This is essentiallythe picture derived by Shakura and Sunyaev (1973), whocall the critical point the spherization radius, withRsph � ð _M= _MEddÞRs, where Rs is the accretor’s Schwarzs-child radius. Within Rsph the local accretion rate decreasesroughly as _MðRÞ ’ _MEddðR=RsphÞ, implying a total accre-tion luminosity

Lacc ’ LEddð1þ lnð� _M2= _MEddÞÞ ð2Þwhich can be as large as � 10LEdd for mass transfer rates� _M2 � 104 _MEdd.

Clearly, we would like to know how this thermal-timescale phase appears to observation. In particular, one

776 A. King / New Astronomy Reviews 51 (2008) 775–777

might imagine that it should have a fairly spectacular man-ifestation, given the high energies and prodigious outflowsinvolved. Begelman et al. (2006) show that the answerdepends on our viewing angle. If we observe the systemfrom an angle close to the axis of the inner accretion disc(which is probably close to the spin axis of a black hole acc-retor) we see an ultraluminous X-ray source (ULX). Thesesources appear very bright partly because they are intrinsi-cally somewhat super-Eddington (cf. Eq. (2)), and alsobecause this luminosity can only escape along the axis ofthe dense outflow. Given collimation solid angles X ¼4pb with b � 0:1, we see that a 10M� black hole can haveapparent luminosity L � Lacc=b � 1041 erg s�1.

Interestingly, Begelman et al. (2006) did not set out toinvestigate ULXs, but reached this conclusion by consider-ing the famous source SS433, which turns out to be what ahyperaccreting binary looks like when viewed ‘from theside’, i.e. away from the inner disc axis. Here the dense out-flow obscures our view of the most energetic part of theaccretion flow. Our only evidence for this in SS433 is therelativistic jets, which themselves carry mechanical energy> LEdd. The clue allowing insight here is the fact that theseprecessing jets also show a nodding motion at one-half ofthe orbital period. This is clear evidence of the m ¼ 2 tidaltorque acting on the outer accretion disc. Begelman et al.(2006) show that the only plausible way of conveying thistorque to the inner regions of the disc involved in jet forma-tion is the dense outflow. The jet are presumably launchedalong the local disc axis, and the outflow imprints the longprecession period and the nodding motion on them bydeflecting them along the outflow axis, which already hasthese motions.

A suggested configuration with some of these features(Paczynski and Wiita, 1980; Jaroszynski et al., 1980; Abra-mowicz et al., 1980) postulates an accretion disc whoseinner regions are geometrically thick, and a central pairof scattering funnels through which the accretion radiationemerges. Of course this configuration does not incorporatethe characteristic outflow discussed here. Note that thisform of ‘beaming’ does not involve relativistic effects,although Doppler boosting in a relativistic jet has also beensuggested as a way of explaining the high luminosities(Koerding et al., 2001; Markoff et al., 2001). The thick-discplus funnels anisotropy mechanism explicitly requires ahigh mass inflow rate near the black hole or neutron staraccretor, much of which must be ejected, probably someof it in the form of a jet. (In fact, the motivation of the ori-ginal papers, Jaroszynski et al., 1980; Abramowicz et al.,1980, was to produce a geometry favouring jet production).

The balance between the two factors producing the highapparent luminosity of ULXs is discussed further in King(2008). Extreme beaming factors b are not needed to explainULXs as stellar-mass binaries. For neutron star accretorsone typically requires b � 0:13, and for black holes almostno beaming (b � 0:8). The main reason for the high appar-ent luminosity is the logarithmic increase in the limitingluminosity for super-Eddington accretion. The required

accretion rates are explicable in terms of thermal-timescalemass transfer from donor stars of mass 6–10M�, or possiblytransient outbursts. Beaming factors <0.1 would be neededto explain luminosities significantly above 1040 erg s�1, butthese requirements are relaxed somewhat if the accretingmatter has low hydrogen content.

2. Hyperaccreting AGN

The last section shows that the hyperaccretion problemis specified purely by _MEdd and Rs. We can obviously extendall this work to hyperaccreting AGN. The major differenceis that AGN have a much more limited Eddington factor,i.e. _M= _MEdd does not attain such large values for AGNas for binaries. We can see this from a simple argument.Whatever process fuels the supermassive black holes inactive galactic nuclei (e.g. minor mergers with small satel-lite galaxies) presumably feeds gas in dispersed form intoorbit near the hole before it gets accreted. The maximumlikely accretion rate then comes from assembling the largestgas mass which can orbit, and assuming that some trigger-ing event causes it to fall freely on to the black hole.

We can assume that the host galaxy is roughly repre-sented by an isothermal sphere of ‘gas’ (=all normal mat-ter) and dark matter. Then the ‘gas’ mass inside radius R is

MgðRÞ ¼2r2Rfg

Gð3Þ

where r is the velocity dispersion and fg the gas fraction.The highest plausible accretion rate is given by getting allthis mass to fall inwards on the dynamical timescale R=r,i.e.

_Mmax ’2r3

Gfg ð4Þ

Note that this is independent of R. Now the black holemass is related to r by

M ¼ fgj

pG2r4 ð5Þ

(King, 2003, 2005) which implies an Eddington luminosityfor gas-rich matter

LEdd ¼4cfg

Gr4 ð6Þ

and thus an Eddington accretion rate

_MEdd ¼4f g

�Gcr4 ð7Þ

where � is the accretion efficiency. Hence, we get the Edd-ington ratio

rE ¼_Mmax

_MEdd

¼ �c2r

ð8Þ

For typical values (� ¼ 0:1; r ¼ 150M1=48 km s�1), we have

rE � 100M�1=48 ð9Þ

where M8 ¼ M=108M�.

A. King / New Astronomy Reviews 51 (2008) 775–777 777

As it stands this argument concerns ‘grand design’inflows occupying a major part of the galaxy. One mighttry to circumvent it with flows targetted within the blackhole’s sphere of influence Ri ¼ 2GM=r2, when the problemis more like Bondi accretion. However, it is easy to showthat this gives essentially the same limit. This � r3=G limitprobably always appears if the mass reservoir used for theaccretion was in any kind of equilibrium with the host gal-axy or the black hole before accreting. The most likely wayaround it is to bring in a mass reservoir which is self-grav-itating, like a star. If this can be disrupted very close to thehole one can presumably get higher _M .

Evidently in practice one rarely gets accretion at a rate> r3=G, and thus AGN Eddington ratios are generallymodest (cf. Eq. (9)). Since rE < 100 the bolometric lumi-nosity exceeds the formal LEdd by < ln rE � 4:6. One wouldexpect to see outflow at velocities < c=r1=2

E � 0:1c, which isindeed about the maximum seen, e.g. in PG1211+143(Pounds et al., 2003). It seems plausible that the collima-tion of the radiation by the outflow is weaker at such lowrE. Hence, quasars probably only rarely appear verysuper-Eddington, i.e. there are few extreme ULX ana-logues among them.

3. The dusty torus

So far we have assumed (in Eq. (6)) that the accretingmatter is gas, with electron scattering opacity j. Howeverat sufficient distance from the active nucleus there mustbe dusty matter, with opacity jd > j. Then the local Edd-ington accretion rate is smaller by k ¼ j=jd, which can be� 10�2, so that the effective rE increases by 1=k. This wouldgive a dusty outflow with spherization radius

Rd � 500Rs=k � 5� 104Rs ¼ 0:5M8 pc ð10ÞThe radiation temperature of the AGN is

T rad 6 3:5� 105ðlM8Þ1=4ðRsm=RÞ1=2K ð11Þ

where l is the (electron-scattering) Eddington ratio. If dustsublimates at 1200 K, the sublimation radius is at

Rsub ¼ 9� 104ðlM8Þ1=2Rs ¼ 0:9l1=2M3=28 pc ð12Þ

Hence for lM8 < 0:3 or so the dust survives at the spher-ization radius.

Eqs. (4) and (5) of Begelman et al. (2006) can now beused to show that the dust optical depth sd across the out-flow increases by 1=k3=2 to values 6 2� 104. It is clear thatsd > 1 even for quite modest amounts of matter near theAGN. We thus have a dusty outflow from typical radiusRd, which creates a toroidal geometry for the obscuringmatter near the AGN. This appears to offer a naturalexplanation for the dusty torus invoked in unified AGNschemes (Antonucci, 1993; Urry and Padovani, 1995).Note that there is no reason to assume that the dusty torusmust supply the matter needed to power the AGN. Indeedthe very long viscous times at such large radii suggest thatcentral AGN accretion probably results from an indepen-dent accretion flow on much smaller scales. Hence thisgeometry is likely to be similar in most AGN, regardlessof their central accretion rates.

References

Abramowicz, M.A., Calvani, M., Nobili, L., 1980. ApJ 242, 772.

Antonucci, R., 1993. ARA&A 31, 473.

Begelman, M.C., King, A.R., Pringle, J.E., 2006. MNRAS 370, 399.

Jaroszynski, M., Abramowicz, M.A., Paczynski, B., 1980. AcA 30, 1.

King, A.R., 2003. ApJ 596, L27.

King, A.R., 2005. ApJ 635, L121.

King, A.R., 2008. MNRAS 385, L113 (arXiv:0801.2025).

King, A.R., Ritter, H., 1999. MNRAS 309, 253.

Koerding, E., Falcke, H., Markoff, S., Fender, R., 2001. AGAb 18, P176.

Markoff, S., Falcke, H., Fender, R., 2001. A&A 372, L25.

Paczynski, B., Wiita, P.J., 1980. A&A 88, 23.

Pounds, K.A., Reeves, J.N., King, A.R., Page, K.L., O’Brien, P.T.,

Turner, M.J.L., 2003. MNRAS 345, 705.

Shakura, N., Sunyaev, R., 1973. A&A 24, 337.

Urry, C., Padovani, P., 1995. PASP 107, 116.