Galaxy Bulge Formation: Interplay with Dark Matter Halo and Central Supermassive Black Hole

0.17 MB·English

by  Bing-Xiao Xu

Draftversion February5,2008
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
GALAXY BULGE FORMATION: INTERPLAY WITH DARK MATTER HALO AND CENTRAL
SUPERMASSIVE BLACK HOLE
Bing-Xiao Xu1, Xue-Bing Wu1 and HongSheng Zhao2
1DepartmentofAstronomy,PekingUniversity,100871 Beijing,Chinaand
2SUPA,UniversityofStAndrews,KY169SS,Fife,UK
Draft versionFebruary 5, 2008
ABSTRACT
We present a simple scenario where the formation of galactic bulges was regulated by the dark
halo gravity and regulated the growth of the central supermassive black hole. Assuming the angular
7 momentum is low, we suggest that bulges form in a runaway collapse due to the ”gravothermal”
0 instability once the central gas density or pressure exceeds certain threshold (Xu & Zhao 2007). We
0
emphasize that the threshold is nearly universal, set by the background NFW dark matter gravity
2 g ∼ 1.2 × 10−8cm sec−2 in the central cusps of halos. Unlike known thresholds for gradual
DM
n formation of galaxy disks, we show that the universal ”halo-regulated” star formation threshold for
a spheroids matches the very high star formation rate and star formation efficiency shown in high-
J redshift observations of central starburst regions. The starburst feedback also builds up a pressure

9 shortlyafterthecollapse. Thislargepressurecouldbothactoutwardtohaltfurtherinfallofgasfrom
2 larger scale, and act inwardto counter the Compton-thick wind launched from the centralblack hole
inanEddingtonaccretion. Assumingthe feedbackbalancinginwardandoutwardforces,ourscenario
1 naturally gives rise to the black hole-bulge relationships observed in the local universe.
v
Subject headings: black hole physics – galaxies: formation – galaxies: nuclei – galaxies: starburst –
2
galaxies: structure
9
7
1
1. INTRODUCTION galactic bulges(Elmegreen 1999).
0
Many evidences also show that the growth of super-
7 It is now widely believed that the violent star forma-
massive black hole (SMBH) in galactic center is closely
0 tiontriggeredbythemergerofgas-richgalaxiesisrelated
/ to the formation of the galactic spheroidal component related to the star formation activity (Alexander et al.
h 2003; Heavens et al. 2004; Page et al. 2004). The simi-
in the early Universe. The observational counterpart of
p
larity in the comoving space density between the star-
- these formation events may be represented by some in-
o tense star formation activity such as the Lyman break forming galaxies and quasars offers strong proof for
r galaxies (LBGs) and submillimetre galaxies (SMGs) at such a causal connection (Cattaneo & Bernardi 2003;
t Page et al. 2004; Stevens et al. 2004). The tight
s z ≥3(Steidel et al. 1996;Smail et al. 1997),wherethe
:a star formation rate could be as high as ∼1000M⊙yr−1. rbeullagteionvsehloipcitoyf dtihseperbsliaocnk (hFoelrera(rBesHe)&mMaesrsritwtith20t0h0e;
v Theseobservedstar-forminggalaxiesarejusttheprogen-
Gebhardt et al. 2000; Tremaine et al. 2002) and the
i itorsofthespheroid-dominatedgalaxiesinthelocalUni-
X bulge mass (Magorrianet al. 1998; McLure & Dunlop
verse. Their extremely high star formation rate implies
r thatalargeamountofgasturnsintostarsinarelatively 2002; Marconi & Hunt 2003) also reveals such ap-
a parent association. On the other hand, observa-
short timescale, and the star formation efficiency (SFE)
tions of some starburst galaxies and bright quasars
associated with these extreme situations are also very
have shown clear evidences of outflows (Pettini et al.
high(30−100%),muchhigherthanthe SFE inferredby
2000; Adelberger et al. 2003; Pounds et al. 2003).
the Schmidt-Kennicutt star formation law in the nearby
This indicates that the mechanical feedback may
diskgalaxiesandstarburstgalaxies(Kennicutt 1998). It
play an important role in galaxy evolution and BH
has been proposed that there may be two different star
growth. Many previous discussions have emphasized
formation modes for the disk and the spheroidal com-
that the central BH can interact with the surround-
ponent respectively (Silk 2005). In the disk mode, the
ing environment in a self-regulated way (Silk & Rees
gravitationalinstability(Kennicutt 1989)andtheporos-
1998; Haehnelt, Natarajan,& Rees 1998; Blandford
ity (Silk 1997) regulated mechanisms can keep the disk
1999; Fabian 1999; King 2003; Wyithe & Loeb 2003;
star formation rate and SFE from raising too high; in
Murray et al. 2005;Begelman & Nath 2005). Allthese
the spheroid mode, the star formation may be triggered
models are basedon an ”outward”nuclear feedback sce-
by the bar instability in relatively less massive galax-
nario and are essentially similar; they differ only in
ies (Combes et al. 1990; Hasan, Pfenninger & Norman
whether the energy deposition or the momentum depo-
1993; Wyse 2004); however, there is a lack of detailed
sition dominates. All these models lead remarkably to
models for the star formation in the massive spheroid
theBH-bulgerelation. Nevertheless,fewofthesestudies
componentwhereaself-regulatedmechanismisprobably
carefully considered the star formation activity during
absent. So it has been suggestedthat the star formation
theformationofthespheroidcomponentanditsrelation
mayproceedinamaximumwayduringthe formationof
withtheBHgrowtheventhoughweknowitisimportant.
Electronicaddress: [email protected], [email protected], [email protected],c.iutkseems still worth to revisit more details of
2
this topic. halo in gaseous form. If we assume the angular momen-
The motivation of this paper is to link several physi- tumislow,anisothermalsphericalstructurewillbebuilt
cal phenomena mentioned above, and explain them co- in the core region of dark matter. Because there is large
herently. In this paper, we will present a simple ana- amounts of gas accumulating in the central region, the
lytical model to describe the star formation during the self-gravityof the gas sphere is not negligible. The com-
formation of the spheroidal component and the possible bined gravity from the gas sphere itself and the back-
connection between the central starburst and the BH’s grounddarkmatterpotentialbalanceswiththegaspres-
growth. We show that the isothermal gas sphere em- sure. Sowehavethe hydrostaticequilibriumequationin
beddedinaNFWdarkmatterhalobecomesunstableat the inner region
somecriticalradiusoncetheratioofthecentralgaspres- σ2dρ G(M +M ) G (ρ+Πr−1)4πr2dr
sure to the dark matter pressure exceeds certain thresh- =− gas DM =− ,
ρ dr r2 R r2
old value, and the gas within this critical radius (maxi-
(3)
mumstablegasmass)willcollapseandtriggerthecentral
where ρ(r) is the gas density and σ is the velocity dis-
starburst. Intense star formation accompanies strong
persion. The boundary conditions to be satisfied at the
star-forming feedback which plays an important role in
center r=0 are
resisting the gravity at large scale; while at small scale,
theinwardstarformingfeedbackisintroducedtoconnect ρ(0)=ρ , dρ =−2πΠGρ0, (4)
the starburst region and the nuclear region by virtue of 0 dr σ2
thetheoreticalandobservationalconsiderations. Wealso whereρ isthecentraldensity. Onceρ andσ aregiven,
0 0
show that the BH’s growth is confined and regulated by the gas density and mass profile under the hydrostatic
the inwardstar-formingfeedback. Basedonsuchinward equilibrium can be totally determined.
star forming feedback scenario, the BH-bulge relations The stability of gas sphere embedded in a background
are naturally derived, which well match with the obser- potential was first investigated by Spitzer (1942), who
vations. We alsoshowthatthe narrowrangeofthe star- pointed out that there is a maximum stable gas mass
burstdurationandthedust-torusstructureinAGNscan for a given temperature with a background potential of
be explained under the same scenario. stars. A more recent sophisticated calculation was pro-
The paper is organized as follows. In §2 we first dis- vided by Elmegreen (1999). He directly integrated the
cuss the density profile of the background dark matter hydrostatic equilibrium equations for a mixture of the
potentialandtheisothermalgassphere,thendiscussthe coldgasanddarkmatter. Theequilibriumequationsare
stabilitycriterionoftheisothermalgassphereembedded dP /dr =ρ gforgasanddP /dr=ρ gfordark
gas gas DM DM
in the dark matter background in detail. In §3 we de- matter. The gravitationalaccelerationg comes from the
scribe the effects of the star-forming feedback and make both components and can be determined by the Poisson
adetaildescriptionoftheso-called”halo-regulated”star equation: ∇·g = −4πG(ρ +ρ ). He used various
gas DM
formationmode. Wediscusstheeffectoftheinwardstar density profile for gas and dark matter in his calcula-
forming feedback and the obscured BH’s growth in §4, tions, involving different central gas density. He found
andeventuallyobtainthe BH-bulge relationsinthis sec- that there is no solution satisfying the equations if the
tion. We present some discussions in §5 and the main ratio of the central gas density to the central dark mat-
conclusions in §6. ter density is largerthan certainthreshold value. Above
such threshold value, any additional mass added to the
2. GRAVOTHERMALINSTABILITYANDPROTOGALAXY combined components of gas and dark matter will make
COLLAPSE thewholesystemunstable. Thesetwostudiessharecom-
Following (Xu & Zhao 2007, hereafter XZ), we model mon feature of finding a maximum gas mass from the
the protogalaxy as an isothermal gas sphere embedded hydrostaticor virialequilibrium equations. If the cumu-
in the central r−1 cusp region of the dark matter po- lated gas mass is larger than the maximum one, the gas
tential, adopting the NFW density distribution for the pressure can not support the combined gravity from the
dark matter (Navarro, Frenk & White 1997). The dark sphereitselfandthebackgrounddarkmatter,thesphere
matter density profile is given by will inevitably collapse. So such instability is mainly af-
fected by the ”external” fluctuations. In another words,
ρNFW(r)≈Πr−1, Π≡130M⊙pc−2Mv0,.1027ζc(z), the equilibrious sphere will always keep in equilibrium
(1) unless there is additional mass from the outside added
where Mv,12 = Mvir/1012M⊙ and Mvir is the virial into the system.
mass of the halo, ζ (z) ≈ [0.3 + 0.7(1 + z)−3]2/3 × The idea of XZ is similar but they emphasize the
c
0.58[ln(1+c)−c/(1+c)]wherec≈13.4M−0.13(1+z)−1 role of the so-call ”gravothermal” instability: consider
v,12
an isothermal gas sphere with fixed enclosed mass. A
isthe concentrationparameter(Bryan & Norman 1998;
tiny compression of the sphere will decrease the volume
Barkana & Loeb 2001; Bullock et al. 2001). Such a
andincreasethedensityeverywhere. Theisothermalgas
dark matter distribution produces almost a constant
sphere would be stable with the density increasing ev-
gravity
erywhere at the same time, because the pressure will in-
GM (r) crease everywhere to push back the decreasing volume,
g (r)= DM =2πGΠ∼1.2×10−8cmsec−2.
DM r2 balancing the increased gravity. However, if the den-
(2) sity increasesat the center, but is reduced at some large
After the baryons entering the dark matter halo, they radii, the isothermal gas in the reduced pressure region
will be shock-heated to the virial temperature. Then can not support the gravity, and the region is unstable.
they will cool and settle into the core region of the dark In another words,the onset of instability is still possible
3
even if there is no additional mass added to the system. Actually,observationshaveshowenthattherearealarge
Actually, this is a thermodynamic type of instability amountofdusts inthe localanddistantstarburstgalax-
which originates from the negative specific heat brought ies(Lehnert & Heckman1996;Sanders & Mirabel 1996;
by the self-gravity of the sphere. The gravothermal Adelberger & Steidel 2000). They should be produced
instability of the pressure-bounded isothermal sphere by the supernovae rather than the AGB stars because
has been investigated by many authors (Bonnor 1956; of the relatively short duration of the starbursts. For a
Lynden-Bell & Wood 1968; Lombardi & Bertin 2001). large star formation rate, the timescale for supernovae
It is suggested that there is a threshold density contrast to reach τ ≈ 1 can be very short in comparing with
Dust
between the center and the edge, above which the sys- the starburst duration (Murray et al. 2005). The mo-
tem will become unstable. For the isothermal sphere mentum deposition rate of radiation pressure can be ex-
embedded in a background potential, the background pressed as P˙ = ǫM˙ c, where M˙ is the star formation
rp ⋆ ⋆
potential provides an additional inward force which is rate,ǫ is the efficiency of converting mass to energy in
much like the external pressure in the pressure-bounded starbursts, and ǫ ≈ 10−3 for a Salpeter IMF according
isothermal sphere. However, it has not been seriously to some starburst models (Leitherer et al. 1999). Here
considered. Using the variation method to investigate we assume that the star formation rate is proportional
the problem, XZ have derived the exact stability crite- tothegasmassM andinverselyproportionaltothe
c,max
rion for the isothermal sphere with a background NFW dynamical time scale t ,
dyn
potential. Thecriterionforthe gasspheretokeepstable
M
is M˙ =η g,max, (8)
p0 ≡ρ0σ2 ≤31pDM,0 (5) ⋆ tdyn
where p0 is the central gas pressure and where η is the star formation efficiency and tdyn ≈
σ/(3.5πGΠ) is the dynamical time scale.
p =4πGΠ2 (6)
DM,0 On the other hand, the supernova remnants (SNRs)
is the central dark matter pressure. XZ find that the willquicklyradiatetheirthermalenergywhentheyprop-
instability starts at a critical radius r ≈ σ2/2.2πΠG, agate in the dense environment such as the central gas
c
inside which the enclosed gas mass is reserviorforstarbursts,andenter the momentumdriven
phase (Monaco 2004). For a typical value, the net mo-
Mg,max =1.78×1011σ2400Mv−,102.07ζc(z)−1M⊙. (7) mentum depositedby supernovaehas approximatelythe
same order as that deposited by the radiation pressure
XZ suggest that there is a threshold of the gas mass
(Murray et al. 2005). Thewholemomentumdeposition
M to collapse and trigger rapid star formation. It
g,max rate can be written as
is reasonable to consider that the bulge formation just
originates from such a gas collapse when the stability P˙ =P˙ +P˙ =ξ ǫM˙ c, (9)
rp sn m ⋆
criterion Eq. (5) is violated. The gas that collapsed due
to self-gravity is the direct material source for the bulge where ξm = 1+P˙sn/P˙rp is assumed of order of unity in
formation. our model.
3. THEOUTWARDSTARFORMINGFEEDBACKDURING 3.2. The halo-regulated star formation
THEBULGEFORMATION
Gas in the inner regionhas higher density and shorter
In this section we will discuss the effects of the star- dynamical time, so the star formation feedback should
forming feedback. First, we will give a brief description be stronger there than in the outer region. The total
to the star-forming feedback in starburst galaxies; Then netstar-formingfeedbackisoutwardatlargescale(how-
wedescribetheso-called”halo-regulated”starformation ever, we must bear in mind that it may not be the case
modebyconsideringtheeffectsofstar-formingfeedback. at very small scale, see discussions in §4), and the out-
We note that many conclusions inferred from such star ward star-forming feedback can be regardedas the anti-
formation mode are consistent with recent observations. gravitationalsource. Becausethegasdensityinthestar-
We point out that such mode is not only expected the- burstregionis extremely highandthe coolingofthe gas
oretically, but also actually exists in some extreme star- isveryefficient,theheatingeffectisneglected. Thestar-
burst regions. forming feedback could increase the potential energy of
the whole system so as to help the system back to the
3.1. The effects of star-forming feedback
virialequilibrium. We assume that the whole system re-
Whenthecentralgasdensityexceedsthecriticalvalue, virialize at radius r′. According to the above argument,
thecollapsewillcompressthegassphereandenhancethe we expect that the additional inward drag provided by
gas density. The squeezed gas is capable to form molec- thebackgrounddarkmatterpotentialiscompensatedby
ular clouds and eventually form stars inside the clouds, the outward star-forming feedback. Namely, we should
and a large amount of the gas accumulating in the cen- have
tral region will trigger the central starburst. Vigorous
star formation activities will inevitably lead to strong Z ξmǫM˙⋆cdr′ =ξmǫM˙⋆cr′ =πΠGMc,maxr′, (10)
star forming feedback. Here we mainly focus on two pri-
mary sources of star forming feedback: radiation pres- where the left side and right side of Eq. (10) denote
sure and supernovae. We know that the UV radiation the equivalent potential energy of the star forming feed-
can be absorbed by the dust efficiently, so the radiation backandthepotentialenergyfromthedarkmatterback-
pressureof the newly formedstars becomes important if ground. Here we use the fact that the quantity ξ ǫM˙ c
m ⋆
the optical depth to the dust τ can reach the unity. is independent on the radius r′ and we assume that the
Dust
4
stars form deeply inside the molecular cloud and don’t main growth phase of the BH should be obscured (so-
appear optically bright during the main epoch of star called ”pre-quasar” phase), which is consistent with the
formation. Eq. (10) can also be directly written as SMG observations (Alexander et al. 2005).
The feedback from BH will be stronger as the BH
ξmǫM˙⋆c=πΠGMc,max. (11) grows bigger. Because of the obscured growth environ-
ment and the possible high accretion rate, the momen-
Theaboveequationsuggeststhatthestarformationrate
tum flux may transport outwards via a Compton-thick
of the central starburst region, being directly related to
wind launched from the BH’s accretion disk. If we as-
thetotalcollapsegasmassM ,isconstantifM
c,max c,max sumethatthecoveringfactorofthewindislargeenough,
is fixed. If the star formation rate increases slightly, the
thenetmomentumfluxratedepositedinthewinddriven
leftsideofEq. (11)willbelargerthantherightside,and
by the radiation pressure from BH can be expressed as
thesystemispuffedupduetothestar-formingfeedback,
(King & Pounds 2003)
and the star formationrate will therefore decreaseagain
tomakethewholesystemreturntotheequilibriumstate. P˙ =M˙ v = 2LEDD = 8πGMBH, (15)
So Eq. (11) requires that the star formation activity in wind out out c κ
the central starburst region is regulated by the gravity
where M˙ is the outflow rate and v is the outflow
fromthedarkmatterbackground. Such”halo-regulated” out out
velocity. Once the balancebetween the inwardstarburst
star formation mode is very different from that in the
feedback and outwardBH feedback is achieved, we have
nearbydiskgalaxies. Herewecalculatesomeparameters
based on this mode in order to compare them with the P˙ =ξ ǫM˙ c, (16)
wind m ⋆
observations.
Using Eq. (8) to eliminate M˙ /M in Eq. (11), then the BH’s feedback is large enough to halt the fur-
⋆ c,max ther gas supply, so we can say that a BH will end its
from the expression of t in §3.1 we obtain the star
dyn main growth phase after Eq. (16) is satisfied. Based on
formation efficiency as
the argument in §2, the bulge mass is approximated as
η = σπ =0.68σ ξ−1ǫ−1, (12) Mc,max. Using Eqs. (11), (15) and (16), the ratio of BH
3.11ξ ǫc 200 m 3 mass to bulge mass can be expressed as
m
where ǫ3 = ǫ/10−3. Substituting Eq. (7) into Eq. (8) MBH = κΠ ≈1.4×10−3M0.07ζ (z). (17)
and using Eq. (12), we obtain the threshold star forma- M 8 v,12 c
bulge
tion rate in the central starburst region as
Combining Eq. (17) with (7), we can also derive the
M˙⋆ = 1.1Gσξ4 ǫc ≈1000σ2400ξm−1ǫ−31M⊙yr−1, (13) MBH −σ relation κσ4
m MBH ≈ 10πG2 =1.8×108σ2400M⊙. (18)
and the star formation timescale
The above results are surprisingly consistent
t ξ ǫc
t = dyn = m with the local observations (Magorrianet al. 1998;
⋆
η πΠG McLure & Dunlop 2002; Marconi & Hunt 2003;
≈1.0×108ξ ǫ M−0.07ζ−1(z)yr. (14) Tremaine et al. 2002).
m 3 v,12 c
It is interesting to note that the star formation effi- 5. DISCUSSIONS
ciency (SFE) as well as the star formation rate (SFR) Theso-called”halo-regulated”starformationmodere-
are closely related to the velocity dispersion. The large quires the additional gravity from dark matter to regu-
the velocity dispersion is, the higher SFR and SFE are. latetheSFRandSFEtoaveryhighlevel(althoughthey
The result implies that there is higher fraction of gas may drop at the late stage). It means that a large frac-
convertinginto stars in more massive galaxies (eg. giant tion of gas is converted into stars in a relatively short
elliptical)andthe highredshiftSMGs observationsshow timescale without being dispersed or blown out. The
that it may be just the case (Alexander et al. 2005). SFR is much higher than that in normal disk galax-
ies inferred from the Kennicutt Law, but is consistent
4. THEINWARD STARFORMINGFEEDBACKANDTHE with the observations of high-redshift starburst galaxies
OBSCUREDBLACKHOLEGROWTH (Solomon & Vanden Bout 2005) and some small scale
Because the star formation is unlikely to proceed ef- star formation phenomena (e.g. SFE during the forma-
ficiently at very small scales (e.g. galactic nuclei), the tion of the bound cluster (Lada, Margulis & Dearborn
starburst region can not be regarded as a point source 1985)). Thisconvincesusthatsuchstarformationmode
comparingwiththecentralBH,andthemomentumfeed- actuallyworksinextremeenvironments,suchasthecen-
back from starbursts should transport in two directions: tral starburst region at high redshift, which is very dif-
the outwardone to resistthe gravityandthe inwardone ferent from that of local universe. We also note that
to drive some part of gas to feed the BH. If the initial the star formation timescale only has weak dependence
BH mass is not very large (≤ 106M⊙), the inflow gas is with the redshift (see Eq. (14)), and is independent on
sufficient for the BH to accrete at Eddington accretion the mass of the galaxy roughly keeping the same over a
rate for a long time. Initially, the feedback exerting on large redshift range. It may explain the narrow range
the surrounding gas of the BH can’t balance the inward (100∼300Myr) of the starburst duration inferred from
feedback from the starburst region, the BH will hide in Faber-Jacksonrelation (Murray et al. 2005).
agasshell(see Figure 1for acartoonview)andbe opti- Many previous momentum driven models argue that
cally thick to the optical and UV radiations. Hence the when the BH grows big enough it can blow most of the
5
gas away to end its growth (King 2003; Murray et al. 1993). We also predict that the dust in the dust-torus
2005;Begelman & Nath 2005). The maindifference be- ofAGNmayoriginatefromthe outsidestarburstregion,
tween our model and these previous models is that in and the covering angle of the dust torus may closely re-
our model the inward star forming feedback plays im- late to the BH mass. This tentative result needs to be
portant role in regulating the BH mass. Simulation confirmed by the future observations.
shows that the inward star forming feedback transports
most momentum but little gas into the nuclear region
6. CONCLUSIONS
(Mori, Ferrara & Madau 2002). Hence, the gas obscur-
ing the BH is much less than the total amount of gas Hereweitemizetheconclusionswhichwehavederived
in the starburst region. According to Eq. (11), we find in this paper:
that the gravity of the gas in the nuclear region is much 1. We suggest that bulges form in a ”monolithic” col-
smaller than the inward star forming feedback. So it is lapse and subsequent rapid star formation. We argue
reasonable to reckon that the BH is confined by the in- that such runaway collapse is due to the gravothermal
ward star forming feedback rather than to drive large instability. The isothermal sphere with a NFW dark
scaleoutflow. The BH willend its growthoncethe feed- matter background becomes unstable when the central
back from BH is big enough to balance the inward star gas pressure is about 30 times larger than the central
formingfeedback,andtheBH-bulgerelationisnaturally dark matter pressure. The collapsed gas will result in
derived from the final balance condition (see Eq.(16)). vigorousstarformationactivitiesandisthe directmate-
There are two interesting points to note: first, our de- rial source of the bulge formation.
rived M −σ relation (see Eq.(18)) is independent of 2. The squeeze and compression help the gas to form
BH
theparameterofthedetailedstarformationprocess;sec- molecular clouds, then many stars form in those clouds
ond,the derivedmassratiobetweenthe BHandbulgeis during a relatively short timescale and the central star-
only related to some properties of the background dark burst is triggered. Intense starburst brings strong star
matter density profile Π, independent of the progeni- formingfeedback,havingtheMg,min andrc inhandand
tor’s gas fraction or the total gas mass in the nuclear assuming the momentum driven mechanism dominates,
region. We think that it is all because that the ”halo- we calculate the star formation rate and the related star
regulated”starformationmodemakesthestarformation forming feedback. We argue that the star forming feed-
activity as an equivalent effect as the dark matter grav- back serves as the source to resist the gravity and will
itational effect. We also find that our derived M −σ finallyhelpthesystemreturntoequilibriumandhaltthe
BH
relation(see Eq.(17))hasno evolutionwiththe redshift, gascollapse. Hence, the ”halo-regulated”star formation
which is consistent with many previous models and the mode is required and we find such star formation mode
observations out to the median redshift (Shields et al. can well match the high redshift starburst observations.
2003; Wu 2007), while the M −M relation has 3. We reckon that the inward star forming feedback
BH bulge
weakdependenceontheredshift. Athighredshiftz ∼3, shouldexisttoconservethelocalmomentumandtocon-
M0.07ζ (z)changebyafactor100.14×0.52/3×1.4∼1.3; necttheoutsidestarburstregionandnuclearregion. The
v,12 c
inwardstar forming feedback can push large amounts of
assuming M was ten times smaller at high redshift.
vir
gas to the central regionto obscure and confine the cen-
From Eq. (17) we can see that the total effect is: the
tral BH (if the BH mass is not so large) and the BH
M /M ratio is roughly the same, only with small
BH bulge
scatters(atz ≤3). Theresultimpliesthatatleastsome system may appear as a ”pre-quasar”. We suggest that
part of the scatter of the M −M is intrinsic. theBHgrowthisjustregulatedbytheinwardstarform-
BH bulge
ingfeedback. WegivetheconditionfortheBHtoendits
Furthermore,theremainingangularmomentumofthe
growthis thatthe compton-thickdisk windbalancesthe
dustygassurroundingtheBHduringitsobscuredgrowth
inward star forming feedback. Based on this we derive
phasemaynotbenegligibleatverysmallscale. Thisan-
theBH-bulgerelationswhicharewellconsistentwiththe
gular momentum could make the configuration of the
local observations.
shrouded gas deviate from the ideal sphere, and dis-
tributemorelikea”hamburger”. Therefore,oncetheBH
growslargeenough,thewindfromthedirectionofangu-
larmomentumwillfirst”crushthe cocoon”andshowan TheauthorsthankFukunLiuandShudeMaoforhelp-
optically bright phase (see Figure 2 for a cartoon view). ful discussions and the anonymous referee for helpful
Suchascenariooffersanaturalexplanationtotheforma- suggestions. XBW acknowledges the support of NSFC
tionofthedust-torusinAGNs,whichisconsideredasan Grant (No.10473001 and No.10525313) and the RFDP
importantpartintheAGNunificationmodel(Antonucci Grant (No.20050001026).
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central BH feedback
outward star-
burst feedback starburst
region
inward star-
burst feedback thick surrounding gas
central growing super-
massive black hole
Fig. 1.— A cartoon which describes the obscured growth of the central BH at the early growth stage. The shaded part is starburst
region, which generates momentum feedback in two directions if there are enough dusts. The outward one resists the gravity while the
inwardoneregulatesthegrowthoftheBH.BecausethemassofBHissmallatearlystage,thefeedbackfromBHcan’tbalancetheinward
feedbackfromthestarburst. Thepushoftheinwardstarburstfeedbackcombiningwiththeremainedangularmomentumforcethegasto
formtheaboveshape. TheBHwillhideinthethickgasshellandcannotbeseeninopticalband.
outward star-
burst feedback starburst
region
inward star-
burst feedback dust torus
Fig. 2.— A cartoon which describes the stage after the main (obscured) growth stage of the central BH. Till the feedback from the
BH balances the inwardfeedback from the starburst, compton-thick wind from BH can easily”crush the cocoon” in the direction of the
angularmomentumandformthetorus-shape. Itmayexplaintheformationofthedust-torusinmanyAGNs.