The Formation of Supermassive Black Holes from Low-Mass Pop III Seeds
aa r X i v : . [ a s t r o - ph . C O ] J u l Draft version October 9, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE FORMATION OF SUPERMASSIVE BLACK HOLES FROM LOW-MASS POP III SEEDS
Daniel J. Whalen and Chris L. Fryer Draft version October 9, 2018
ABSTRACTThe existence of 10 M ⊙ black holes (BH) in massive galaxies by z sim z ∼
20 and then accrete at the Eddington limit down to the epochof reionization, which requires that they have constant access to rich supplies of fuel. Because earlynumerical simulations suggested that Pop III stars were &
100 M ⊙ , the supermassive black hole seedsconsidered up to now were 100 - 300 M ⊙ . However, there is a growing numerical and observationalconsensus that some Pop III stars were tens of solar masses, not hundreds, and that 20 - 40 M ⊙ blackholes may have been much more plentiful at high redshift. However, we find that natal kicks impartedto 20 - 40 M ⊙ Pop III BHs during formation eject them from their halos and hence their fuel supply,precluding them from Eddington-limit growth. Consequently, supermassive black holes are far lesslikely to form from low-mass Pop III stars than from very massive ones.
Subject headings: black hole physics - cosmology: early universe - theory - galaxies: formation INTRODUCTION
The existence of 10 M ⊙ black holes (BH) in massivegalaxies by z ∼
7, only a billion years after the Big Bang(e.g. Mortlock et al. 2011), poses one of the great un-solved problems in cosmological structure formation. Inthe ΛCDM paradigm, early structure formation is hierar-chical, with small objects at high redshifts evolving intoever more massive ones by accretion and mergers throughcosmic time. For this reason it is generally supposed thatthe supermassive black holes (SMBH) that power the z ∼ Sloan Digital Sky Survey ( SDSS ) quasars growfrom much smaller seeds at earlier epochs. The originof SMBH and how they reach such large masses in suchshort times is a subject of ongoing debate. Three modesof formation have been proposed for SMBH seeds: thecollapse of Pop III stars into 100 - 300 M ⊙ black holesat z ∼
20 (Alvarez et al. 2009), baryon collapse in 10 M ⊙ dark matter halos that have somehow bypassed pre-vious star formation into 10 - 10 M ⊙ BH at z ∼ - 10 M ⊙ BH (see section 3.3 of Djorgovski et al. 2008, for a recentreview).Stellar-mass SMBH seeds form at z ∼
20 when Pop IIIstars die in either core-collapse supernovae (SNe, 15 - 45M ⊙ ) or by direct collapse to a BH (45 - 100 M ⊙ , & ⊙ ) (Heger & Woosley 2002). This formation channelis favored by some because most dark matter halos willform a Pop III star at this epoch if they reach masses of ∼ M ⊙ (Abel et al. 2002; Bromm et al. 2002). However,these BH have such low initial masses that they mustcontinuously accrete at the Eddington limit to reach 10 M ⊙ by z ∼
7. This is problematic for several rea-sons. First, numerical simulations have shown that PopIII stars usually evaporate the halos that give birth to McWilliams Fellow, Department of Physics, Carnegie MellonUniversity, Pittsburgh, PA 15213 CCS-2, Los Alamos National Laboratory, Los Alamos, NM87545 them, so the BH are ’born starving’ (e.g. Whalen et al.2004; Kitayama et al. 2004; Whalen et al. 2008b). Fil-amentary inflows and mergers later restore baryons tothe halo but only after 50 - 100 Myr (Yoshida et al.2007), during which crucial e-foldings in mass are lost.Second, preliminary studies indicate that once accretioncommences, the BH itself emits ionizing radiation thatdisperses its own fuel supply, limiting its growth rateto a fraction of the Eddington limit (Milosavljevi´c et al.2009; Park & Ricotti 2011, 2012) (but see Li 2011). Fur-thermore, if the seed BH is not confined to the halo,its duty cycle as it meanders through cosmological den-sity fields is intermittent, which also curtails its growth(Alvarez et al. 2009).Until now, 20 - 40 M ⊙ Pop III BH (Zhang et al. 2008;Whalen et al. 2008a) have been overlooked as candidatesfor SMBH seeds because previous studies assume thatprimordial stars are &
100 M ⊙ . However, there is a grow-ing numerical and observational consensus that somePop III stars are tens of solar masses, not hundreds.More recent, much larger ensembles of numerical simula-tions found many halos with central collapse rates con-sistent with 20 - 60 M ⊙ for the final mass of the star(O’Shea & Norman 2007) and that a fraction of the ha-los form binaries in this mass range (Turk et al. 2009).Furthermore, new simulations of the formation of Pop IIIprotostellar accretion disks suggest that they were proneto fragmentation into as many as a dozen smaller stars(Stacy et al. 2010; Clark et al. 2011; Smith et al. 2011;Greif et al. 2011). Very preliminary calculations of I-front breakout from these disks indicate that ionizing UVradiation may terminate accretion onto the nascent starat ∼
40 M ⊙ (Hosokawa et al. 2011; Stacy et al. 2012).On the observational side, recent attempts to recon-cile the nucleosynthetic yields of Pop III supernovae withthe chemical abundances found in ancient, dim extremelymetal-poor stars in the Galactic halo suggest that 15 -40 M ⊙ primordial stars may have been responsible formost of the heavy elements expelled into the primevalIGM (Joggerst et al. 2010). The failure to detect thedistinctive ’odd-even’ nucleosynthetic signature of 140 -260 M ⊙ pair-instability SNe in metal-poor stars to datereinforces the fact that some Pop III stars might not bevery massive, but this pattern may have been maskedby selection effects in the observations (Karlsson et al.2008).Low-mass Pop III BH are crucially different from moremassive BH because they are born in supernova explo-sions rather than by direct collapse. Asymmetries in thecore-collapse engine can impart kicks of 200 - 1000 km/sto 20 - 40 M ⊙ BH, ejecting them from the halos that gavebirth to them. In this Letter we examine the implicationsof natal kicks for low-mass Pop III black holes as candi-dates for SMBH seeds. In § § § LOW-MASS POP III BLACK HOLES
Three mechanisms can create Pop III black holes dur-ing stellar collapse. In order of increasing progeni-tor mass, they are fallback onto a neutron star (NS)during a supernova explosion, the direct collapse ofa proto-neutron star into a BH without an explosion,and enclosure of the core by an event horizon withoutever having attained nuclear densities (Fryer et al. 2001;O’Connor & Ott 2011).
Pop III BH Formation
It is generally believed that core-collapse supernova ex-plosion energies fall with increasing progenitor mass (seeFryer 2003, for a review). At some point, the explosionis too weak to fully overcome the binding energy of thestar and enough ejecta falls back onto the NS to collapseit to a black hole (Fryer et al. 1999; Zhang et al. 2008).In even more massive progenitors, the core of the starcollapses to a proto-neutron star without an explosion.About 1 s after the onset of collapse, it gains so muchadditional mass that it cannot support itself and it col-lapses to a black hole. In the most massive stars ( &
300 M ⊙ ) the entropy of the core becomes so high thatit never reaches nuclear densities. When enough mate-rial falls into the core it is suddenly engulfed by an eventhorizon, forming a BH of >
20 M ⊙ (Fryer et al. 2001).In general, the birth masses of Pop III BH vary from theminimum black hole mass ( ∼ − M ⊙ ) up to the massof the progenitor star. Pop III BH Kicks
The first two formation processes can impart kicks (ini-tial velocity pulses) to low-mass BH at birth. Kick mech-anisms generally fall into two categories: ejecta-drivenkicks (e.g. Scheck et al. 2006; Wongwathanarat et al.2010) and neutrino-driven kicks (see Fryer & Kusenko2006, and references therein). Ejecta kicks occur whenlow-mode instabilities erupt in the shock as it is drivenoutward by core bounce. They are likely seeded duringcollapse prior to bounce and result in explosion asymme-tries that impart a net linear momentum to the neutronstar (NS). Above 32 M ⊙ fallback is total, and no impulseis imparted to the BH. Neutrino kicks arise when mag-netic field lines through the center of the star are crushedto extremely high densities during collapse, polarizing Fig. 1.—
Entropy versus enclosed mass for three 25 M ⊙ stars.Note that the differences due to the codes are greater than thosedue to metallicity. neutrinos created by the core during deleptonization andinducing anisotropies in emission that deliver an impulseto the NS. Consequently, neutrinos can impart momen-tum to the NS (and therefore the BH) even if there is noexplosion.Pop III core-collapse SNe imparted kicks to neutronstars and black holes in the same manner as in the Galaxytoday. Both kick mechanisms arise from asymmetries inthe explosion engine that are determined by the struc-ture of the inner core (inner 3-4 M ⊙ ) of the star. Weshow the entropy profile of this core for three 25 M ⊙ stars at collapse in Figure 1: a zero metallicity starmodeled by Chieffi & Limongi (2004) which collapsedwith a mass of 24.7 M ⊙ , a zero metallicity star mod-eled by Woosley & Heger (2007) which collapsed with amass of 24.9 M ⊙ and a solar metallicity star modeled byWoosley & Heger (2007) which collapsed with a mass of12.9 M ⊙ . Since metallicity has very little effect on thestructure below 6 M ⊙ , the engine will not differ signifi-cantly between a zero and solar metallicity star and theywill exhibit similar kick distributions. The structures ofthe cores of very massive stars do change with metallicitybut we do not expect kicks in their supernovae. POST-SUPERNOVA KINEMATICS OF LOW-MASS POPIII BH
Fully developed models for kick mechanisms do not yetexist, so neither the number of Pop III seed BH kicks northeir velocity distributions can be calculated from firstprinciples. However, natal kicks are commonly observedin compact remnants in the Galaxy today and there aremodels that infer reasonable relationships between BHand NS kick distributions, which have been measuredfor a large sample of pulsars. In our study we adoptthe pulsar velocity distribution of Arzoumanian et al.(2002). It is bimodal, with each mode being describedby a Maxwellian: 40% have a dispersion of 90 km/s and60% have a dispersion of 500 km s − . We derive velocitydistributions for low-mass Pop III BH by assuming thatin both mechanisms the black hole simply inherits the Fig. 2.—
Statistical properties of low-mass Pop III BH at birth. Left: black hole mass as a function of progenitor mass. Right: BHretention fraction in the halo as a function of progenitor mass. linear momentum of the NS: v BH = v NS m NS m BH , (1)where m NS is the Chandrasekar mass, 1.4 M ⊙ . Conse-quently, the BH kick velocity is inversely proportionalto its mass. We derive our BH mass distribution fromthe latest estimates of Fryer & Heger (2011) for zero-metallicity stars, assuming rapid explosions. We showthe distribution for these new fits in the left panel ofFigure 2. In reality, the BH could acquire more momen-tum than the NS intermediary because of the tendencyof weak explosions to be more delayed, which allows low-mode instabilities additional time to develop and creategreater asymmetry in the ejecta (Fryer & Heger 2011).With our black hole mass and pulsar velocity distribu-tions we can estimate the retention fraction of BH inhalos as a function of progenitor mass for a variety ofescape velocities from the halo, as we show in the rightpanel of Figure 2. Above ∼ M ⊙ , the kick velocitydrops to zero for the ejecta mechanism and we expect fullretention for stars above this mass limit in the absenceof neutrino kicks. If there are neutrino kicks, retentionfractions for BH below 40 M ⊙ are less than 10% in thehalos in which most Pop III stars form (those with v esc < ⊙ . DISCUSSION AND CONCLUSION
The number of stars that 10 - 10 M ⊙ halos typicallyform is not well constrained. The studies of Pop III pro-tostellar disk fragmentation performed thus far do notfollow the evolution of the disk for enough dynamicaltimes to determine the ultimate fate of the fragments,which may later merge with the central object or be de-stroyed by gravitational torques before becoming distinctstars. Ionizing UV radiation from one star-forming frag- ment or even from a nearby halo can also prematurelyhalt the collapse of other fragments in the disk, loweringthe number of stars that eventually form in the halo (e.g.Susa & Umemura 2006; Whalen et al. 2008a; Susa et al.2009; Whalen et al. 2010). We also note that while theevolution of the fragments in the disk is expected to beroughly coeval, their 5 - 10 Myr quasistatic collapse timesraise the possibility that the first star to form in the halomay explode and pre-empt the collapse of other frag-ments (e.g. Sakuma & Susa 2009). Consequently, thenumber of low-mass Pop III stars that occupy the halolikely ranges from one to at most ten.Ejecta-driven natal kicks will evict most 20 - 32 M ⊙ BH from their host halos, neutrino-driven kicks can drivemore than 90% of 32 - 40 M ⊙ BH from their halos, aswe show in the right panel of Figure 2. This guaranteesthat on average all the BH will vacate the halo even if tenstars originally formed in it. Post-supernova kinematicsthus strongly discourages 20 - 40 M ⊙ Pop III BH frombecoming supermassive because they are ejected fromtheir fuel supply and deprived of crucial early e-foldingsin mass. This process greatly reduces the parameterspace in stellar mass from which SMBH can originate(e.g. Tanaka & Haiman 2009; Lippai et al. 2009), espe-cially if Pop III stars were mostly less than 50 M ⊙ . Also,if a given halo is capable of supporting early continuousEddington rate accretion, a 20 - 40 M ⊙ BH is much lesslikely to become supermassive than a 100 M ⊙ BH, eitherbecause it is ejected from the halo at birth or becauseit must undergo additional e-folding times to reach largemasses.If most low-mass Pop III black holes were ejected fromtheir halos at z ∼
20, where are they today? If on av-erage they depart their host halos at ∼
500 km/s, theyare unlikely to encounter another halo capable of cap-turing them in less than a Hubble time, and so manyof these BH were exiled to the voids between galaxies.Over time, they may have gradually gained mass as theyencountered high-density regions. In contrast, Pop IIIBH above 40 M ⊙ are unlikely to be born with kicks andremain in the halo, intermittently accreting and growingover cosmic time. These black holes are much more likelyto reside in the galaxies into which their host halos weretaken, a few of which may have become the supermassiveblack holes found in the SDSS quasars today. We thank the anonymous referee for comments thatimproved the quality of this paper and Jarrett John-son and Brian O’Shea for valuable comments. DJW wassupported by the Bruce and Astrid McWilliams Centerfor Cosmology at Carnegie Mellon University. Work atLANL was done under the auspices of the National Nu-clear Security Administration of the U.S. Department ofEnergy at Los Alamos National Laboratory under Con-tract No. DE-AC52-06NA25396.are unlikely to be born with kicks andremain in the halo, intermittently accreting and growingover cosmic time. These black holes are much more likelyto reside in the galaxies into which their host halos weretaken, a few of which may have become the supermassiveblack holes found in the SDSS quasars today. We thank the anonymous referee for comments thatimproved the quality of this paper and Jarrett John-son and Brian O’Shea for valuable comments. DJW wassupported by the Bruce and Astrid McWilliams Centerfor Cosmology at Carnegie Mellon University. Work atLANL was done under the auspices of the National Nu-clear Security Administration of the U.S. Department ofEnergy at Los Alamos National Laboratory under Con-tract No. DE-AC52-06NA25396.