The effect of radiation pressure on dusty absorbing gas around AGN
aa r X i v : . [ a s t r o - ph ] D ec Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 25 October 2018 (MN L A TEX style file v2.2)
The effect of radiation pressure on dusty absorbing gas around AGN
A.C. Fabian , R.V. Vasudevan and P. Gandhi Institute of Astronomy, Madingley Road, Cambridge CB3 0HA RIKEN Cosmic Radiation Lab, 2-1 Hirosawa, Wakoshi, Saitama 351-0198, Japan25 October 2018
ABSTRACT
Many Active Galactic Nuclei (AGN) are surrounded by gas which absorbs the radiation pro-duced by accretion onto the central black hole and obscures the nucleus from direct view.The dust component of the gas greatly enhances the effect of radiation pressure above thatfor Thomson scattering so that an AGN which is sub-Eddington for ionized gas in the usualsense can appear super-Eddington for cold dusty gas. The radiation-pressure enhancementfactor depends on the AGN spectrum but ranges between unity and about 500, dependingon the column density. It means that an AGN for which the absorption is long-lived shouldhave a column density N H > × λ cm − , where λ is its Eddington fraction L bol /L Edd ,provided that N H > × cm − . We have compared the distribution of several samplesof AGN – local, CDFS and Lockman Hole – with this expectation and find good agreement.We show that the limiting enhancement factor can explain the black hole mass – bulge massrelation and note that the effect of radiation pressure on dusty gas may be a key component inthe feedback of momentum and energy from a central black hole to a galaxy. Key words: galaxies: nuclei - galaxies: ISM - quasars: general - radiative transfer
Active Galactic Nuclei are powered by accretion onto a centralmassive black hole. The gas surrounding the nucleus, some ofwhich provides the fuel for the accretion process, often obscuresit from direct view. Indeed, the hard shape of the spectrum of theX-ray Background argues that most accretion onto galactic nucleiis obscured (Fabian & Iwasawa 1999). This is confirmed by deepChandra and XMM-Newton imaging of the Sky with many AGNfound to lie behind a column density of − cm − or more(Giacconi et al. 2002; Brandt & Hasinger 2005).Much of the obscuring material must lie within the in-ner 100 pc, or its total mass would be prohibitive (seeMaiolino & Risaliti 2007 for a review). It is therefore part of the in-ner bulge of the host galaxy. Stars can also form from this gas, giv-ing a nuclear starburst. The gas is subject to the radiation pressureof the AGN, and can be ejected from the bulge if the nucleus be-comes too bright. Such AGN feedback may thereby remove the gaswhich fuels the nucleus and from which new stars form, so termi-nating the growth of both the central black hole and its host bulge.Simple calculations of when this occurs (Fabian 1999; Fabian et al.2002; King 2003, Murray et al. 2005; Fabian et al. 2006) lead to thefollowing relation between the mass of the black hole M BH and thevelocity dispersion of the bulge σ : M BH = fσ πG m p σ T . (1)Assuming a gas fraction f ∼ . , this gives an M BH − σ relation in good agreement with observations (Kormendy & Richstone 1995;Magorrian et al. 1998; Gebhardt et al. 2000; Ferrarese et al. 2001).The limit when radiation pressure ejects mass is an effectiveEddington limit relying on absorption of radiation by dust, not elec-tron scattering. The radiation pressure is amplified or boosted by afactor A which is the ratio of the effective, frequency weighted, ab-sorption cross section for dusty gas, σ d to that for electrons alone: σ T . A = σ d σ T . (2)The dust absorption is greatest in the UV and the value of A de-pends on the spectrum of the AGN. The X-ray emission from thenucleus ensures that the gas and dust remain weakly ionized, andare effectively coupled by Coulomb forces so that pressure on thegrains is shared with the surrounding gas .Boost factors computed for a standard AGN spectrum, usingthe radiation code CLOUDY are shown in Fabian et al. (2006) andFig. 1. They range from several hundred for low column densitiesand drop as the column density of gas increases until they approachunity when the gas becomes Compton thick, i.e. N H ∼ /σ T =1 . × cm − . Under the assumptions used, the main reductionof A with column density N H is merely due to the increased col-umn acting as a dead weight since the UV part of the spectrum isused up after traversing a column of a few cm − . The outer’dead weight’ is then pushed by the inner gas which experiencesthe full force of the radiation.In this paper we explore further the implications of the boostfactor on the limit to the column density of dusty gas that can re- c (cid:13) A.C. Fabian, R.V. Vasudevan & P. Gandhi l og ( A ) log(N H /cm -2 )
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Figure 1.
The radiation pressure boost factor A for dusty gas shown as afunction of column density N H . The continuum spectrum is assumed tobe that of high and low Eddington ratio objects (from Vasudevan & Fabian(2007)) for the upper and lower lines, respectively. main close to an AGN without being ejected by radiation pressure.The key feature is to cast the inverse of the boost factor as the (clas-sical) Eddington ratio λ : A − = L Bol L Edd = λ. (3)A cloud is long lived if Aλ < . If the boost factor for a particularcloud is 100 then it will be blown away when the Eddington ratioexceeds 1/100. This determines a relation between the column den-sity of long-lived absorbing gas close to a nucleus and its Eddingtonratio.Pier & Krolik (1992) have previously noted the role of theEddington ratio when explaining the geometrical thickness ofthe torus around AGN by the action of radiation pressure.H¨onig & Beckert (2007) have estimated the effective Eddingtonlimit for a torus around an AGN considering both smooth andclumpy dust distributions.Previous work on the luminosity dependence of absorp-tion has found that the incidence of absorption drops withluminosity (Ueda et al. 2003; La Franca et al. 2005, but seeDwelly & Page 2006, Treister & Urry 2005). The ’receding torus’model (Lawrence 1991; Simpson 1998) is often invoked to explainwhy quasars may show less absorption. In that model the reduc-tion in absorbed objects is attributed to (heating) destruction of dustwithin the inner regions of a torus of absoring gas surrounding thenucleus.Here we consider the relation between luminosity and absorp-tion from the point of view of the effective Eddington limit on dustygas. ABSORPTION LONG-LIVEDSTAR FORMATION?DUST LANES?OUTFLOWS l og ( N H / c m - ) bol /L Edd -4 -3 Figure 2.
Fig. 1 replotted in terms of column density versus /A . Long-lived absorption from clouds near the centre of the galaxy should occurin the shaded region. Absorption from clouds and dust lanes can occur athigher values of λ progressively further out. High column densities therewould require prohibitive gas masses so we restrict such a region to N H < × cm − , marked by a horizontal line. We determine the boost factor A as detailed in Fabian et al. (2006)using CLOUDY and AGN spectral energy distributions obtained byVasudevan & Fabian (2007). A is obtained from absorption only(the input spectrum minus the transmitted one) and assumes thatthe gas is optically thin to the infrared radiation thereby produced.Trapping of radiation is assumed to be negligible and the ionizationparameter ξ = L/nr is arranged to be about 10 (thereby fixing thegas density for a given incident AGN flux). Vasudevan & Fabian(2007) find that the UV – X-ray spectral energy distributions(SEDs) of AGN depend on Eddington ratio, with much more ion-izing radiation – and therefore higher boost factors – occurring athigher λ . We adopt mean SEDs for high ( > . ) and low ( < . ) λ when computing A as a function of absorption column density. N H is plotted against λ = A − in Fig. 2. The drift velocity of thegrains relative to the gas is computed by CLOUDY and found to below (about . − where most of the radiative force is applied)justifying our assumption that the dust and gas are coupled.Long-lived absorbing clouds can survive against radiationpressure in the shaded region of the Figure. Clouds to the rightof the dividing line, in the unshaded part, see the nucleus as abovethe effective Eddington luminosity and are thus ejected. Objectsfound in this region should be experiencing outflows and absorp-tion may be transient or variable. The Compton-thick objects neversee the source as exceeding the Eddington luminosity and so canbe long-lived at all Eddington ratios less than unity. Gas clouds inthis regime are more likely to change because of star formation.Absorbed objects in the unshaded part at higher Eddingtonratio should exhibit outflows, or the absorbing gas be far away fromthe nucleus where the retaining gravitational mass is much larger. c (cid:13) , 000–000 adiation pressure and absorption in AGN They could for instance be associated with dust lanes, as envisagedby Matt (2000). Such absorption cannot be too large or the gasmass required would be prohibitive. We show, for example, a limitat N H = 5 × cm − in Fig. 2.Our prediction is therefore that absorbed objects should lieabove the approximate dividing line given by N H > × λ cm − , provided that N H > × cm − . The simple model described above predicts that most highly-obscured AGN will be observed to have an intrinsic column densityplacing them in the shaded region of Fig. 2.In order to test our model, we have examined the absorptionand black hole mass of several samples. The first is a compositelow redshift sample consisting of the Markwardt et al. (2005) sam-ple of AGN detected by the Burst Alert Telescope (BAT) on the
SWIFT satellite, and the Dadina (2007) sample of Seyfert nucleiobserved by the
BeppoSAX satellite. The former is an all-sky, hard-X-ray-flux limited sample in the energy range 14–195 keV wheredetection should be independent of column density, provided thesource is not too Compton thick. The latter study presents an at-las of X-ray spectra for 39 Seyfert I and 42 Seyfert II nuclei overthe energy range 2–100 keV. All objects in the combined samplehave redshifts below 0.05. Black hole masses are estimated fromvelocity dispersions using the M − σ relation of Tremaine et al.(2002). Velocity dispersions were obtained from the HyperLEDAonline database. We obtained 2-10keV luminosities from the Tar-tarus database of ASCA observations, as it was not possible toextrapolate a 2-10keV luminosity from the SWIFT luminositiesprovided in Markwardt et al. (2005) without a value for the pho-ton index Γ . Finally, we convert to a bolometric luminosity us-ing the Eddington-ratio-dependent bolometric correction scheme ofVasudevan & Fabian (2007), using the black hole mass to estimatethe Eddington ratio λ , and assume that the emission is isotropic.We obtained velocity dispersions, and thus calculated masses, for23 objects in the composite sample. The results for this sample areshown in Fig. 3.In this Figure we see one object with a large column den-sity and high Eddington ratio in the unshaded region. This is NGC3783, and the absorption is part of an outflowing warm absorber(Kaspi et al. 2001). The 3 objects with > log N H > (justbelow the horizontal line) are, in order of increasing λ , IC 4329A,which has an outflow and is seen almost edge on so absorptionmay be from a distant dust lane (Markowitz et al. 2006); NGC3516,which has variable absorption and an outflow (Markowitz et al.2007); and 3C120, which has a soft excess in XMM spectra(Ballantyne et al. 2004) so may have N H overestimated in the valuetabulated by Markwardt et al (2005) used in Fig. 3.We then used deeper samples. First we use the Chandra DeepField South results of Tozzi et al. (2006). These authors providevalues for the column density N H for each AGN together withintrinsic X-ray luminosities. We calculate black hole mass esti-mates using K-band magnitudes from Szokoly et al. (2004) and the M BH − L K relation of Marconi & Hunt (2003). We impose a red-shift cut, requiring our objects to lie between redshifts . < z < . . We attempt to account for some evolution in the M BH − L K1 http://astro.ic.ac.uk/Research/Tartarus/ ABSORPTION LONG-LIVEDSTAR FORMATION?M arkwardt+/ D adina D U ST LANES?O U TFLO W S l og ( N H / c m - ) L B ol / L E dd -4 -3 Figure 3.
Objects from the samples taken from the work of Markwardt et al.(2005) and Dadina (2007) plotted on the N H − λ = L Bol /L Edd plane.An estimate of the uncertainty in λ = L Bol /L Edd is shown by the bar attop right. relation between that epoch and our own by incrementing the K-band magnitudes by unity before using the relation (i.e. account-ing for fainter bulge luminosities for the same central black holemass in the past). This is broadly consistent with the evolution ex-pected from van der Wel et al. (2006), assuming negligible evolu-tion in the ratio M stellar /M BH . This produces estimates for M BH in line with other measures. Using bolometric corrections as for thelocal sample, we estimate the Eddington ratios as before. This sam-ple yields 77 objects for which mass estimates could be obtained.The results are shown in Fig. 4 (top); objects with negligible col-umn density are marked nominally as having an upper limiting N H of cm − (downward arrows). The range of Eddington ratiosthat we find for the CDFS sources is comparable to that found in-dependently by Babi´c et al. (2007).Finally we used the Lockman Hole results of Mainieri et al.(2002) and Mateos et al. (2005). Mass estimates were calcu-lated using K-band magnitudes from Mainieri et al. (2002),whereas X-ray luminosities and column densities were taken fromMateos et al. (2005) and bolometric corrections as before. The red-shift range used was the same as for the CDFS sample. There were13 objects satisfying these criteria, and the results are shown inFig. 4 (bottom).The results from the deeper samples are qualitatively similarto the low redshift sample. For all three samples we find, as pre-dicted, that most objects lie within the shaded region. Note thatsince Chandra probes deeper than XMM, most of the CDFS ob-jects are at a lower value of λ than those in the Lockman Hole.We show relatively conservative estimates for the uncertain-tiess involved to provide some indication of the validity of our re-sults. In the local Seyfert sample (Fig. 3), we use published errorson velocity dispersions and assume errors of 10 per cent on the Tar-tarus X-ray fluxes and also on the values of N H provided. For thedistant samples, we assume errors of 20 per cent on both K-bandand 2–10 keV luminosities. In the case of the K-band, we note that c (cid:13) , 000–000 A.C. Fabian, R.V. Vasudevan & P. Gandhi
ABSORPTION LONG-LIVEDT ozzi+/Szokoly+ DUST LANES?OUTFLOWSSTAR FORMATION? l og ( N H / c m - ) L Bol /L Edd -4 -3 ABSORPTION LONG-LIVEDSTAR
FORMATION?M a inieri+/Mateos+ DUST LANES?OUTFLOWS l og ( N H / c m - ) L Bol /L Edd -4 -3 Figure 4.
The N H − λ = L Bol /L Edd plane with objects from theCDFS (top) using data from Tozzi et al. (2006) and Szokoly et al. (2004)),and the Lockman Hole (bottom) using data from Mainieri et al. (2002)and Mateos et al. (2005). There is one point missing from each plot with λ < − . Marconi and Hunt (2003) identify errors of ± . on K-band mag-nitudes, translating to ∼ per cent in luminosity; we suggest thatthe 20 per cent value used here is therefore a reasonably ‘safe’ esti-mate of the error. For the X-ray band, one may expect variability tointroduce significant uncertainties, but we suggest that 20 per centerror is again relatively conservative for most objects. Such errorestimates lead to uncertainties of around ∼ percent in the Ed-dington ratios; however, this is small enough to clearly differentiatethose lying within the shaded regions on Figs. 3 and 4 from thosewhich are not. The typical error in λ under these assumptions isshown in Figs. 3 and 4 by the bar in the top right. We see from the plots that most absorbed AGN with column den-sities N H > cm − have an Eddington ratio λ < . , as ex-pected if radiation pressure on dusty gas is important. The observedobjects are sub-Eddington in terms of radiation pressure on dustygas and so the absorbing gas may be long-lived. The line definingthe effective Eddington limit in the plots is determined for the massof the black hole only. It shifts to the right (higher values of λ ) iflarger masses associated with the stellar bulge are also involved.Since the lines drawn seem to apply to the samples, most of theabsorbing gas must be at small radii (much less than 100 pc). Theagreement between the expected location of absorbed AGN and theobserved locations provides support for the idea that radiation pres-sure acts to blow gas away from galaxy bulges. If the radiation isisotropic then it can stem the growth of both inner bulge and blackhole.The inner gas directly exposed to the radiation pressuremay be unstable to clumping (Blumenthal & Mathews 1979;H¨onig & Beckert 2007), the details of which will not be pur-sued here. Most of the long-lived gas at column densities above cm − is shielded by the inner gas and so need not beclumped.After blowing away the gas, AGN may decline in luminos-ity so creating unabsorbed sources at low Eddington ratios. Thereis also some uncertainty in the boundary between the various re-gions of the diagrams due to factors such as source variability andclumpiness in the absorption. The fact that most sources avoid theregion of our diagrams above N H ∼ × cm − and to theright of the radiation pressure line demonstrates that variabilitity isnot very important.Lower levels of absorption below cm − can be long-lived at large radii in a galaxy, since the relevant gravitating massthere is due to the black hole and the bulge. The radiation limit inour Figures shifts to the right by a factor of M bulge /M BH withall gas above the line bound to the bulge. The maximum boost A that can be obtained from radiation pressure on dusty gas is σ d /σ T ∼ which means that the black hole is above the effec-tive Eddington limit for the whole bulge if M BH /M bulge > / .Consequently we envisage a scenario where a black holesmothered in gas could grow in a bulge in stages. It pushes thegas out to a distance in the bulge where the mass within that ra-dius is 500 times the black hole mass. (The boost factor increasesas the column density decreases, so once gas starts to move out-ward it continues to do so, see Fig. 1 and Fabian et al. 2006) Afterthe accretion disk empties, the AGN switches off. If the bulge masswithin the radius to which the gas was pushed exceeds 500 timesthe mass of the black hole, then the gas falls back in and the cyclerepeats. Through accretion, the black hole mass and thus luminos-ity increases each cycle until is unable to retain the gas and it ispushed right out of the bulge. At this point M BH /M bulge ∼ σ T /σ d ∼ / , (4)similar to the value found by Marconi & Hunt (2004) from corre-lating the observed properties of galaxies.Star formation from the gas in the galaxy during these cyclespresumably leads to the bulge mass – velocity dispersion (Faber–Jackson) relation required such that equations (1), which acts lo-cally, and (2), which acts globally, agree.For much of the ‘cycling scenario’ envisaged above, theonly acceptable range for bright unabsorbed objects would be athigh Eddington ratios. From a large sample of AGN detected in c (cid:13) , 000–000 adiation pressure and absorption in AGN their AGN and Galaxy Evolution Survey (AGES), Kollmeier et al.(2006) find λ ∼ . . An important result from their survey is thatthey should have been sensitive to unabsorbed AGN with lowerEddington ratios, but found none. This could in part be a selectioneffect due to absorption since the Chandra X-ray observations usedare short, about 5 ks, which means that they are most sensitive tobright unabsorbed objects. The discussion of emission line strengthfor high and low Eddington ratio AGN from Vasudevan & Fabian(2007) could also be of particular relevance here, again implyingthat higher Eddington ratio AGN would be systematically favoured.The detected objects are in the unshaded part of our diagram, sohave high λ . Absorbed AGN are most commonly found at low Eddington ratiossuch that they are sub-Eddington for dusty gas. This agrees withthe hypothesis that radiation pressure acting on dust is important inremoving gas from galaxy bulges. In turn this leads to M BH − σ and M BH − M bulge relations similar to those observed.Studies seeking to examine the evolution of absorbed AGNwill need to include the dependence on Eddington ratio. We acknowledge Gary Ferland for the use of his code
CLOUDY andfor discussions. We thank Silvia Mateos and Vincenzo Mainierifor helpful suggestions and information on the data presented intheir papers. ACF thanks The Royal Society for support, RV ac-knowledges support from the UK Science and Technology Fund-ing Council (STFC) and PG acknowledges a Fellowship from theJapan Society for the Promotion of Science (JSPS). This researchhas made use of the Tartarus (Version 3.2) database, created byPaul O’Neill and Kirpal Nandra at Imperial College London, andJane Turner at NASA/GSFC. Tartarus is supported by funding fromSTFC (PPARC), and NASA grants NAG5-7385 and NAG5-7067.
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