Fuelling Active Galactic Nuclei

0.13 MB·English

by  A. R. King

Mon.Not.R.Astron.Soc.000,1–4(2006) Printed5February2008 (MNLATEXstylefilev2.2)
Fuelling Active Galactic Nuclei
A. R. King1 and J.E. Pringle1,2
1Theoretical Astrophysics Group, Universityof Leicester,LeicesterLE1 7RH
2Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA
7
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5February2008
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2

n ABSTRACT
a
J
We suggest that most nearby active galactic nuclei are fed by a series of small–

4 scale, randomly–oriented accretion events. Outside a certain radius these events pro-
2
mote rapid star formation, while within it they fuel the supermassive black hole. We

show that the events have a characteristic time evolution. This picture agrees with
1
severalobservationalfacts. The expected luminosity function is broadly in agreement
v
with that observed for moderate–mass black holes. The spin of the black hole is low,
9
7 andaligns with the inner disc in eachindividual feeding event.This implies radiojets
6 aligned with the axis of the obscuring torus, and uncorrelated with the large–scale
1 structure of the host galaxy. The ring of young stars observed about the Galactic
0 Centre are close to where our picture predicts that star formation should occur.
7
0 Key words: accretion, accretion discs – black holes, galaxies – active
/
h
p
-
o 1 INTRODUCTION of our own Galactic Centre. It seems likely that all of the
r
t fuellingprocessesdiscussedsofarmayplayaroleinatleast
as Itisnowgenerallyacceptedthatthenucleiofmostgalaxies some galaxies. In this paper we focus attention on the fu-
: contain supermassive black holes. Assembling the observed ellingof thenucleusin anormalSeyfert galaxy,with acen-
v holemasses byaccretion at plausibleefficiency accountsfor tral black hole of mass M ∼ 107 −108 M⊙, (Ferrarese et
i
X the emission of active galactic nuclei (AGN) over cosmic al., 2001; Heckman et al., 2004; Denney et al., 2006) and
time(Soltan,1982;Yu&Tremaine,2002).Thisimpliesthat luminosity L ∼ 0.1L (with L the Eddington luminos-
r E E
a essentially every galaxy is intermittently active, in phases ity) thus accreting at a rate M˙ ∼0.2M⊙ yr−1. In a typical
when its black hole grows. Onlya small fraction of galaxies Seyfert event lasting, say, 106 yr, this would imply an ac-
areobserved tobeactive(e.g. Heckmanet al., 2004), so we creted mass ∆M ∼2×105 M⊙ (e.g. Emsellem, 2002, 2004;
knowthat these phases are short. Martini,2004).Thisisridiculouslysmallcomparedwiththe
Yet we still do not understand how gas gets down to gas available in atypical spiral galaxy, and weimmediately
the black hole. There are a number of candidates, includ- see that we are not concerned with major gas flows involv-
ing galaxy mergers (major and minor), bars, bars within ing spiral arms or galactic bars. Feeding the black hole at
bars, turbulence in the ISM, stellar mass loss, and viscous suchmodestratesneedsonlysomesmall–scaleeventtodrop
accretion discs. However, the nature of the problem is of- a little material of low angular momentum into the central
tenunderestimated.Forexample,inarecentreviewarticle, regions of thegalaxy.
Wada (2004) discusses ‘Fuelling Gas to the Central Region Wehavetwopiecesofevidencesuggestingwhatsuchan
of Galaxies’ in terms of bringinggas inwards toaround 100 eventmightbe.First,Kinneyetal.(2000;seealsoNagar&
pcfromthecentralblackhole.But,asemphasisedbyShlos- Wilson, 1999) found that in a sample of nearby(z≤0.031)
man,Begelman&Frank(1990),thegasmustgettoremark- Seyfert galaxies, the direction of the jet from the central
ably small radii before the inner viscous accretion disc can black hole, and therefore presumably the orientation of the
takeoverand bring thegas tothehole within theobserved central regions of the accretion disc, were unrelated to the
activitytimescale.Theinflowtimescalethroughadiscofsize orientation of the disc of the host galaxy. Second, Schmitt
1 pc is already ∼ 109 yr, even with maximal assumptions et al (2003) surveyed extended [O III] emission in a sample
aboutviscosity.ForshorterAGNphases,orlessefficientvis- of nearby Seyfert galaxies, and found that although the [O
cosity,thegasmustbefedtothecentraldiscatstillsmaller III] emission is well aligned with the radio, there is no cor-
radii. relation between its orientation and the major axis of the
Observationsshowawiderangeofactivity,fromhighly host galaxy. Assuming that the orientation of the [O III]
luminous quasars at redshifts up to z ≃ 6, through the emission is governed by the geometry of the inner torus, of
barely detectable nuclei in LINERS, to the weak activity typicalradius0.1–1.0pc(e.g.Antonucci,1993),thismeans
2 A. R. King and J. E. Pringle
thatthecentraldiscflowhasangularmomentum unrelated rapid (almost dynamical) timescale (see also Shlosman &
to that of most of the gas in thehost galaxy. Begelman, 1989). This corresponds to a nuclear starburst
This tells ustwo things(seealso thediscussion in Kin- of the kind often associated with AGN (e.g. Scoville 2002).
neyetal.,2000).First,inlinewithourinferenceabove,ifthe A starburst like this lasts around 3×106 yr in terms of
galacticdiscsuppliedthetorusmaterialviabar–drivendisc its ionising flux (O and early B stars). We suppose further
evolution, or grand–design nuclear spirals, or similar mech- that all the gas which is initially at radii R < Rsg forms a
anisms, some means of randomising its rotation axis in the standardaccretiondisc,whichslowlydrainsontotheblack
centralregionsisneeded.Forwithoutsomesuchmechanism hole and powers theAGN. Westress that underthesimple
we expect such processes to leave evidence of the angular form of this hypothesis the nuclear starburst and the AGN
momentum of the galactic disc, which is not seen. There is aretwodifferentmanifestationsofthesameaccretionevent,
currently no suggestion as to what this mechanism might but do not feed one another. We note that such a picture
be, although one can appeal to the fact that the galactic provides at least a qualitative explanation for the existence
disc is much thicker than the radial scale of a few parsecs of the ring(s) of young stars seen around the black hole in
that we are interested in. In the absence of a randomising thecentreof theMilky Way (Genzel et al., 2003).
mechanism the gas must come from outside the galaxy as InSection2,weinvestigatethepropertiesoftheaccre-
part of a succession of (very) minor mergers. Where in a tion disc at radii R < Rsg. In Section 3, we consider the
galaxy a very small merging satellite deposits its gas is not time-dependence of such an event and in Section 4 present
straightforwardtocompute(Velasquez&White,1999;Tay- a simplified luminosity function under the assumption that
lor & Babul, 2001). Kendall, Magorrian & Pringle (2003) all eventsare identical, but randomly timed.
find that if such small merging satellites are to deposit gas
near the nucleus then their initial orbits must be fairly ac-
curate shots. Kendall et al. (2003) also conclude that such 2 PROPERTIES OF THE DISC
small merging satellites which do manage to reach the nu-
WeusethesteadydiscpropertiesderivedbyCollin–Souffrin
cleus arrive there on more or less randomly oriented orbits.
& Dumont (1990) in the context of AGN, which are es-
Second, the inner disc (specifying the radio jet axis)
sentially the same as those derived by Shakura & Sunyaev
remains aligned with the torus. In an earlier paper (King
(1973)forsteadydiscsinthecontextofX–raybinaries.The
&Pringle,2006, Section3)weshowedthatrepeatedsmall–
disc surface density is given as
scalefuellinghaspreciselythiseffect.Itcausescounteralign-
mentof thehole(Kinget al., 2005) in about one–half ofall
accretion events,andthusspindown,whichismoreefficient α −4/5 ǫ −3/5
Σ=7.5×106
than spinup. Once the hole’s mass has doubled, its angular 0.03 0.1
(cid:16) (cid:17) (cid:16) (cid:17)
momentumisalwayssmallerinmagnitudethanthatofany L 3/5 R −3/5
accretionevent.Itthenalwaysalignsitsspinwiththeinner × 0.1L M81/5 R gcm−2. (2)
(cid:16) E(cid:17) (cid:16) s(cid:17)
disc and thusthe torus.
Hereαisthestandard Shakura&Sunyaev(1973) viscosity
Thuswehavearguedthatthefuellingoflowluminosity
parameter,ǫistheaccretionefficiency,sothattheluminos-
AGNproceedsviaaseriesofrandomlyoriented,small–scale
ity L and accetion rate M˙ are related by
accretion events,acting directly in theregion of thecentral
blackhole.Thematerialdepositedinsuchaneventislikely L=ǫM˙c2, (3)
to settlequickly intoa ring ordisc of material within afew
also
local dynamical (or orbital) timescales t ,where
dyn
−1/2 3/2 LE =1.4×1046M8ergs−1, (4)
M R
tdyn =2.9×102(cid:18)108M⊙(cid:19) (cid:18)0.1pc(cid:19) yr. (1) iisntuhneitEsdodfin10g8toMn⊙lu,mRiniosstithye,rMad8iuisstahnedblack hole mass, M,
It is well known that such a disc is likely to be self– Rs=2.96×1013M8cm (5)
gravitating outside some radius Rsg ∼0.01−0.1 pc (Shlos-
man et al., 1990; Collin–Souffrin & Dumont, 1990, Hur´e et is theSchwarzschild radius of thecentral black hole.
al., 1994). Further, in the outer regions of these discs the Thenthemassofthedisc M(<R)interiortoradiusR
cooling timescales are sufficiently short that self–gravity is is given by
likelytocausestarformation,ratherthanenhancedangular α −4/5 ǫ −3/5
momentum transport (Shlosman & Begelman, 1989; Collin M(<R)=2.94×1034
0.03 0.1
(cid:16) (cid:17) (cid:16) (cid:17)
&Zahn,1999).Forthediscsweconsiderinthispaper,which
L 3/5 R 7/5
are relatively thin (because of efficient cooling) and of low × M11/5 g. (6)
0.1L 8 R
mass (M ≪ M ) self–gravity appears first in modes (cid:16) E(cid:17) (cid:16) s(cid:17)
disc hole
withazimuthalwavenumberm≈R/H,producingtransient The disc semi–thickness H is given by
spiral waves which transport angular momentum (Anthony
H α −1/10 ǫ −1/5
& Carlberg, 1988; Lodato &Rice, 2004, 2005). Itis reason- =1.94×10−3
R 0.03 0.1
abletosupposethatwherethediscislocallygravitationally (cid:16) (cid:17) (cid:16) (cid:17)
unstable in this way, most of thegas forms stars. × L 1/5M−1/10 R 1/20. (7)
0.1L 8 R
Wethereforeproposethehypothesisthatall,oratleast (cid:16) E(cid:17) (cid:16) s(cid:17)
most of, the gas initially at radii R > Rsg is either turned Theconditionforthedisctobecomeself–gravitating is
into stars, or expelled by those stars which do form, on a approximately (e.g. Pringle, 1981)
Fuelling Active Galactic Nuclei 3
M(<R) H
≥ . (8)
M R -1
This occurs at radii R≥Rsg, where
Rsg =1.13×103 α 14/27 ǫ 8/27
R 0.03 0.1
s (cid:16) (cid:17) (cid:16) (cid:17)
×. L −8/27M−26/27 (9) -2
0.1L 8
(cid:16) E(cid:17)
We notethat thisimplies
α 14/27 ǫ 8/27 L −8/27
Rsg =0.01 0.03 0.1 0.1L M81/27pc(10)
(cid:16) (cid:17) (cid:16) (cid:17) (cid:16) E(cid:17)
almost independently of the black hole mass. This arises -3
because (10) is an integrated form of the standard steady–
statediscequationM˙ =3πνΣcombinedwith(8),whichwe
can expressas
3H M
Rsg ≃ 2RαcsM˙ (11) -4
where c is a mean sound speed and we note from (7) that
s
H/R ≃ constant. Encouragingly, we see that Rsg is only
slightly smaller than theinneredge R∼0.03 pcof thering -3 -2 -1 0 1
of young stars seen around the black hole in the centre of
theMilkyWay(Genzeletal.,2003).Thisistobeexpected,
as the disc within Rsg must pass its angular momentum to Figure 1. Form of the AGN luminosity function predicted by
the self–gravitating region further out which in our picture the fuelling process, and subsequent disc evolution, discussed in
produces thesestars. thispaper.ThefractionF,ofthosesourceswithluminositiesless
The mass inside theradius Rsg is given by than L/LE is shown as a function of L/LE. This is similar in
formtothosepresentedinFigure3ofHeckmanetal.,2004
α −2/27 ǫ −5/27
Msg =2.76×105
0.03 0.1
(cid:16) (cid:17) (cid:16) (cid:17)
L 5/27 at most τsg given by eq.(14) the disc evolves to resemble a
× 0.1L M823/27M⊙, (12) steadydiscatradiiR≤Rsg (e.g.Pringle,1981).Thususing
(cid:16) E(cid:17) the formulae derived in Section 2 gives a good approxima-
whichisofcoursejust(H/R)M withH/RevaluatedatRsg tiontotheactualdiscpropertiesafterabriefinitialperiod.
(cf. equation 7). We can now use this to estimate the properties of the disc,
TheaccretionrateisgivenbyM˙ =L/ǫc2,whichimplies and therefore of theAGN event,as it evolves.
ǫ −1 L Fromeqn.(2)weseethatΣ∝M˙3/5R−3/5.Forasteady
M˙ =0.245 M8M⊙y−1. (13) disc we know (Pringle 1981) that M˙ ∝ νΣ, where ν is the
0.1 0.1L
(cid:16) (cid:17) (cid:16) E(cid:17)
viscosity. From these two relationships we can deduce that
Then the evolution timescale of the disc is given by τsg = forthesediscsν ∝Σ2/3R.Forsuchdiscs,similaritysolutions
Msg/M˙, which gives (Pringle 1991) imply that at late times the accretion rate,
α −2/27 ǫ 22/27 andhenceluminosity,varieswithtimeasL∝t−19/16.Thus
τsg =1.12×106 0.03 0.1 we expect luminosity evolution roughly to follow
(cid:16) (cid:17) (cid:16) (cid:17)
×. L −22/27M−4/27y (14) L=Linit[1+(t/τsg)]−19/16. (15)
0.1L 8
(cid:16) E(cid:17)
Again we note that τsg ∼(H/R)(M/M˙).
4 IMPLICATIONS FOR THE LUMINOSITY
FUNCTION
3 PROPERTIES OF AN ACCRETION EVENT
Heckmanetal.(2004)findthatmostofthecurrentaccretion
InthepreviousSectionweestablishedthegeneralproperties on to black holes is on to those with masses in the range
of the non–self–gravitating disc, assuming that it was ac- 107−108 M⊙. In addition they findthat of low mass black
cretingsteadily,andgivingrisetoaluminosityL.Ofcourse holes, with masses M < 3 × 107 M⊙, only 0.2 per cent
this is not precisely what we require for the present prob- are growing at a rate which accounts for 50 per cent of the
lem. What we are assuming is that the disc, of initial mass fuelling.Theypointoutthatthisimpliesthatstrongfuelling
Msg, is deposited by the accretion event in some unknown therefore only lasts for a time tfuel ∼ 0.002 ×tH, where
configuration,andthenevolvesduetoviscosity.Asformost t ∼ 1.4×1010 years is the age of the universe. Thus the
H
accretion discs it is fair toassume that initially most of the total time during which strong fuelling is taking place is
mass, and most of the angular momentum of the disc, is aroundt ∼3×107 years,or,ifthereareN fuellingevents
fuel
predominantlyatlargeradius,andthereforeataroundRsg. per black hole per Hubble time, it implies that each event
Butwhatevertheinitialconfiguration,withinatimescaleof lasts around tev ∼3×107/N yr(Heckman et al., 2004).
4 A. R. King and J. E. Pringle
Accordingly we make some simplifying assumptions to offers a promising explanation of the growth of most su-
work outtheluminosity function wemight expectfrom our permassive black holes, and thusfor theactivity of galactic
model. We take α = 0.03 and ǫ = 0.1, and consider black nuclei.
holeswith mass107M⊙ asrepresentativeoftherangemak-
ing the major contribution to the distribution of accreting
black holes. Weassume that theseblack holes undergoran- 6 ACKNOWLEDGMENTS
dom, but identical, accretion events such that the initial
ARKacknowledgesaRoyalSociety–WolfsonResearchMerit
luminosity of each event is L . In this case, we see from
E
the above that the initial disc mass is Msg ∼ 5.95×104 Award. We thank Sergei Nayakshin for stimulating discus-
M⊙, and the initial evolution timescale is τsg ∼ 2.41×105 sions, and the referee, Isaac Shlosman, for a very helpful
report.
yr. Equating this timescale to the length of each event,
tev we see that the number of events has to be about
N = 0.002tH/τsg ∼ 116, and therefore the average time
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