The mass density in black holes inferred from the X-ray background

4 Pages·0.11 MB·English

by  A. C. Fabian

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed1February2008 (MNLATEXstylefilev1.4)
The mass density in black holes inferred from the X-ray
background
A.C. Fabian and K. Iwasawa
InstituteofAstronomy,MadingleyRoad,CambridgeCB30HA
1February2008
9
9
9 ABSTRACT
1
TheX-rayBackground(XRB)probablyoriginatesfromtheintegratedX-rayemission

n of active galactic nuclei (AGN). Modelling of its flat spectrum implies considerable
a absorption in most AGN. Compton down-scattering means that sources in which the
J
absorptionis Compton thick are unlikely to be majorcontributors to the background

1 intensity so the observed spectral intensity at about 30 keV is little affected by pho-
1 toelectric absorption.Assuming that the intrinsic photon index of AGN is 2, we then

use the 30 keV intensity of the XRB to infer the absorption-correctedenergy density
1
of the background. Soltan’s argument then enables us to convert this to a mean lo-
v
cal density in black holes, assuming an accretion efficiency of 0.1 and a mean AGN
1
redshift of 2. The result is within a factor of two of that estimated by Haehnelt et al
2
1 fromthe optically-determinedblackhole massesofMagorrianetal.We concludethat
1 there is no strong need for any radiatively inefficient mode of accretion for building
0 the masses of black holes. Furthermore we show that the absorption model for the
9 XRB implies that about 85 per cent of accretion power in the Universe is absorbed.
9 This power probably emerges in the infrared bands where it can be several tens per
/ cent ofthe recently inferred backgroundsthere. The totalpower emitted by accretion
h
p is then about one fifth that of stars.
- Key words: galaxies:active – quasars:general–galaxies:Seyfert– infrared:galaxies –
o
r X-rays:general
t
s
a
:
v
i 1 INTRODUCTION We show that the mean mass density of black holes
X
is within a factor of two of direct estimates based on the
r
detectionofblackholesinnearbygalaxies.Thereisthenno
a Many current models for the X-ray Background (XRB) as-
strongrequirementforanysignificantmassbuildupinblack
sume that it is due to the summed emission from many
holes from some radiatively inefficient mode of accretion.
ActiveGalactic Nuclei(AGN)with strong intrinsicabsorp-
MostaccretionpowerintheUniverseisabsorbed,andlikely
tion (Setti & Woltjer 1989; Madau et al 1994; Comastri et
reradiated intheinfrared wavebands.Thishasimplications
al 1995; Celotti et al 1995). In this case most X-ray emis-
for theIR background and source counts.
sion from AGN in the Universe must be highly absorbed
(Fabian et al 1998). Here we make a representative correc-
tion of the spectrum of the XRB in order to deduce the
currentradiationenergydensityoftheXRBhadabsorption 2 THE MASS DENSITY IN BLACK HOLES
notbeenpresent.Thisisconvertedtoabolometricradiation
density using the X-ray to bolometric ratio of a sample of Wemodel the spectrum of theXRBas
unobscured AGN. Then from the simple cosmology-free ar- Iν =9E−0.4exp(−E/50keV)keVcm−2s−1sr−1 keV−1.
gumentofSoltan(1982)weconvertthisenergydensityinto
a mean mass density of black holes at the current epoch. This agrees with both the Marshall et al (1980) result
Soltan (1982) took thequasar countsin theoptical B-band (HEAO A2 spectra taken in the 3–60 keV band) above
for his estimate so was only using unobscured AGN. Our ∼7keVandthatofGendreauetal(1995)result(ASCA0.5–
result exceeds his earlier estimate by a factor of about 7.5 7 keV spectra) below that energy. The EFE spectrum then
andtheupperlimitofthemorerecentestimatesofChokshi peaksat30keVwithanintensityof38.1keVcm−2s−1sr−1.
&Turner(1992),whichalsouseopticalquasarcounts,bya The major assumption made in this paper is that the
factorof3.ItagreeswiththeveryrecentestimateofSalucci XRB spectrum above 30 keV is unaffected by absorption.
et al (1998), based on X-raysource counts. Thisisbecausethelikelymaximumphotoelectricabsorption
(cid:13)c 0000RAS
2
nowassume,followingSoltan(1982),thatthisradiationhas
been produced by accretion at an efficiency of 10 per cent
(noting that (comoving) radiation energy density decays as
1+z whereasmassdensitydoesnot)wefindamassdensity
ρ=10(1+z)E0′/c2 =4.1×10−35gcm−3.
This corresponds to 6 × 1014M⊙ Gpc−3 = 6 ×
105M⊙ Mpc−3.Aredshiftof2isusedhere(seeMiyajietal
1998foradiscussionofevolutionmodelsforX-rayobserved
AGN).
ThismassdensityismuchgreaterthanSoltan’soriginal
estimate and about three times higher than that estimated
by Chokshi & Turner (1992) using optical counts of unob-
scured quasars. It is about half that estimated byHaehnelt
et al (1998) from the product of the mean black hole mass
to bulge mass, estimated from spectroscopic data on the
cores of nearby galaxies by Magorrian et al (1998), and the
mass density in galactic bulges (Fukugita et al 1998). The
Figure 1. XRB spectrum (solid line) with the assumed unab-
Haehnelt et al estimate is likely to befairly uncertain since
sorbedspectrumofphotonindex2(dottedline).AtypicalAGN
spectrumwithreflection,inwhichthedirectemissionisapower the method for black hole mass measurement of Magorrian
law of photon index 2 with an exponential cutoff of 300 keV is et al may overestimate the masses. Our result agrees with
shown by the dot-dash line, matching around the XRB peak. If the very recent, and more complicated, estimate of Salucci
unabsorbedquasarscontribute50percentoftheXRBat1keV, etal(1998)whouseX-raysourcecountstogetherwithother
thentheircontributionliesalongthebottom ofthefigure. factors.Ifafurther50percentofsourcesareCompton-thick
and, due to Compton down-scattering, contribute little to
the XRB spectral intensity,then our estimate rises propor-
forsourcesmakingasignificantcontributiontotheXRBin- tionately.
tensity occurs at column densities of about 2×1024cm−2, An important conclusion of our result is that the
which has little effect above 30 keV in the rest frame, and absorption-corrected XRB estimate and the more direct
of course even less in redshifted sources. (We assume ap- galaxy-core estimate of the local density of massive black
proximate Solar metallicity for absorption purposes.) At holes are within a factor of two. There is thus no strong
higher column densities the Thomson depth exceeds unity need to invoke very low efficiency accretion or any excep-
and Compton scattering significantly reduces the transmit- tional accretion flows. What is required is that most accre-
ted power at all energies (see e.g. Madau et al 1994). Such tionpowerisabsorbedbysurroundinggas.Thismayrequire
Compton-thicksourcesarethereforeunlikelytoplayamajor thegeometries discussed by Fabian et al (1998).
roleintheXRB,althoughtheymaybesignificantinnumber The fraction which is unabsorbed, in the hard X-ray
(perhapsone third of all sources; Maiolino et al 1998). spectrum, is about 6 per cent of the total spectrum. Here
We now assume that the intrinsic spectrum of the weassumethatalltheopticalandUVemissionareabsorbed
sourcesresponsiblefortheXRBhasaphotonindexof2and and that the infrared emission from AGN is already due to
matchestheabovespectrumatitsEFE peak.Amorecom- reprocessing. The fraction is obtained by noting that only
plexspectrumincludingreflectioncanhaveaslightlyhigher about one half the 0.1–60 keV intrinsic X-ray spectrum is
intensity (Fig. 1), particularly if redshifted. The caveats transmitted to make the XRB spectrum (this is the ratio
noted so far mean that thetrue intrinsic spectrum is above of the observed 0.1–60 keV intensity to that in the inferred
thesimple power-law estimate, by some small factor. unabsorbed spectrum). The ratio of the 0.1–60 keV to 2–
The unabsorbed 0.66–3.33 keV (2–10 keV in the as- 10 keV fluxes for our assumed intrinsic spectrum is r ∼ 4,
sumed mean restframe redshift of 2, but with our adopted so if the 2–10 keV flux is 3 per cent of the total flux of an
photon index this is independent of redshift) intensity of AGN, the transmitted fraction of the XRB, assuming the
the sources is I0 = 9.8×10−8ergcm−2s−1sr−1. The un- spectrum of Fig. 1, is fr/2∼6 per cent.
absorbed radiation energy density is then E′ = 4πI0/c = ThespectrumoftheobservedXRBdoesturnupbelow
4.1×10−17ergcm−3s−1.To convertthisto an unabsorbed 1 keV in part due to unabsorbed quasars and AGN, which
bolometric radiation density, we note that the mean ra- from the integration of ROSAT source counts (Hasinger et
tio of the 2–10 keV to bolometric luminosities for radio- al 1993) contribute about half the total XRB intensity at 1
quiet quasars in the compilation of spectral energy distri- keV.This corresponds to about 10 percent of the assumed
butions of Elvis et al (1994) is 3.3 per cent (we convert intrinsicpower-lawspectrumsothetotalfraction oftheac-
from the tabulated monochromatic value of LX to the 2– cretion power emitted in the Universe which escapes unab-
10keVvaluebymultiplyingbyafactor of1.6,usingapho- sorbed is therefore about 16 per cent. If we further assume
ton index of 2; 6 out of every 7 objects have a luminosity 50percentmoreAGNareCompton-thickwithcolumnden-
ratio between 1 and 7.6 per cent).This is similar to thera- sitiesabove2×1024cm−2 (cf.Maiolinoetal1998)thenthis
tio of 2 per cent found using Ferland’s (1996) ’Table AGN’ finalnumberdrops to about 12 percent.
model,whichreproducesemission lineratioswell.Denoting
this fraction as (f/0.03), we find a total energy density of
E0′ = 4πI0/fc = 1.2×10−15(f/0.03)−1ergcm−3s−1. If we
(cid:13)c 0000RAS,MNRAS000,000–000
The mass density in black holes inferred from the X-ray background 3
3 THE INFRARED BACKGROUND LIGHT effect on the final result). There is insufficient information
to assess the second assumption, but we do note that it is
The absorbed intensity can now be used to estimate the
plausible that the intrinsic X-ray emission region is unaf-
IR background.Assumingthe absorber tobe dustygas, we
fected by the absorption which is usually assumed to occur
havefoundthatat least 85percentof theemittedintrinsic
at much greater radii from the central black hole. Finally,
flux for our adopted XRB spectrum is absorbed, or an in-
the total X-ray intensity is reduced by about 30 per cent if
tensity Iabs = 0.85I0/f ≈ 3×10−6ergcm−2s−1sr−1. This the photon index drops to 1.5, but the contribution of re-
is 3 nW m−2 sr−1, for comparison with the limits and de-
flection in all cases increases our estimate (by about 10 per
tections derived of the infrared backgrounds derived and
cent for a photon index of 2).
reviewed by Hauser et al (1998) and Fixsen et al (1998).
Weareconcerned that thesimpleuseof theElvis et al
If much of the absorbed flux emerges longward of 100µ,
(1994)spectralenergydistributionforAGNleadstotheUV
which requires a significant contribution occurring at red-
emission being counted twice. This is because the infrared
shifts much greater than 2, it will dominate the FIR back-
emission may be dominated by absorbed UV (and soft X-
ground and source counts (see also Almaini, Lawrence &
ray)emission (assumingthatweviewtheUVsourcedirect,
Boyle1998). Whereverthereprocessed emission emerges,it
but the absorbing matter which reradiates UV as infrared
correspondstoseveraltenspercentofthelikelybackground
coversotherlines ofsight). Ifweomit theinfrared emission
in the 10–100µm infrared bands (Hauser et al 1998; Fixsen
from that distribution the bolometric luminosities drop by
etal1998)tomostofthebackgroundlongwardof∼200µm, about one third. This increases f ∼0.05 and decreases our
which is generally assumed to be dominated by the repro-
mass density estimate by one third. It also means that the
cessed radiation from stars. This meansthat theintegrated
total absorbed fraction of the power drops to about 80 per
intrinsicradiationfromAGNisseveraltenspercentofthat
cent.
dueto stars.
In conclusion, the spectrum of the XRB provides a ro-
A check on this result is obtained by adapting an ar-
bust estimate of the total radiation emitted byAGN in the
gument due to G. Hasinger (priv. comm.). Magorrian et al
Universe. The agreement of the local black hole density re-
(1998) find that the mass of a central black hole MBH is
sultingfromtheconversionoftheimpliedenergydensityto
about 0.006 times the mass of the host bulge Mb. If the mass with direct estimates from other wavebands indicates
presentbulgemassisafractionabofthemassofthestarsas- thatthereisnoobviousneedforsomeradiativelyinefficient
sociatedwiththatgalaxywhichhavealreadyburnt,thenthe
form of accretion. Most of the accretion power in the Uni-
totalradiationemittedovertimeis0.0006a−b1Mbc2,whereit verse has been absorbed and presumably reradiated in the
isassumedthatonetenthofastarundergoesnuclearburn-
infrared.
ing with an efficiency of 0.6 per cent. The total accretion
energy radiated from the black hole, at an efficiency of 0.1,
is 0.1MBHc2 =0.0006Mbc2. If the history of star formation
and accretion are similar (see e.g. Boyle & Terlevich 1998), 5 ACKNOWLEDGEMENTS
then the contribution of AGN to the background radiation
We thank Omar Almaini, Guenther Hasinger and Andy
densityisab timesthatofstars.ForaSalpeterIMFextend-
ingto0.4M⊙,ab ∼0.2.Thisfractioncanbeincreasedifthe Lawrence for discussions and Elihu Boldt for comments.
ACFthanksthe RoyalSociety for support.
radiativeefficiencyoftheaccretionishigher(e.g.Kerrblack
holes)ortheIMFissteeperthanassumed,anddecreased if
the IMF is flatter and a large non-bulge stellar component
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4 DISCUSSION AND CONCLUSION
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