On the Evolution of Supermassive Primordial Stars in Cosmological Flows
Tyrone E. Woods, Samuel Patrick, Jacob S. Elford, Daniel J. Whalen, Alexander Heger
DDraft version February 19, 2021
Typeset using L A TEX twocolumn style in AASTeX63
On the Evolution of Supermassive Primordial Stars in Cosmological Flows
Tyrone E. Woods ,
1, 2
Samuel Patrick , Jacob S. Elford , Daniel J. Whalen ,
3, 4 andAlexander Heger
2, 5, 6, 7 National Research Council of Canada, Herzberg Astronomy & Astrophysics Research Centre, 5071 West Saanich Road, Victoria, BCV9E 2E7, Canada Monash Centre for Astrophysics, School of Physics and Astronomy, Monash University, VIC 3800, Australia Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK Ida Pfeiffer Professor, University of Vienna, Department of Astrophysics, Tuerkenschanzstrasse 17, 1180, Vienna, Austria ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav), Melbourne, Australia ARC Centre of Excellence for Astrophysics in Three Dimensions (ASTRO-3D), Australia Joint Institute for Nuclear Astrophysics, 1 Cyclotron Laboratory, National Superconducting Cyclotron Laboratory, Michigan StateUniversity, East Lansing, MI 48824-1321, USA
Submitted to ApJABSTRACTPrimordial supermassive stars (SMSs) formed in atomic-cooling halos at z ∼
15 - 20 are leadingcandidates for the seeds of the first quasars. Past numerical studies of the evolution of SMSs havetypically assumed constant accretion rates rather than the highly variable flows in which they form.We model the evolution of SMSs in the cosmological flows that create them using the
Kepler stellarevolution and implicit hydrodynamics code. We find that they reach masses of 1 − × M (cid:12) beforeundergoing direct-collapse to black holes (DCBHs) during or at the end of their main-sequence hydrogenburning, at 1 - 1.5 Myr, regardless of halo mass, spin, or merger history. Our models confirm that theaccretion histories predicted for purely atomic-cooling halos impose a narrow spectrum of masses onthe seeds of the first massive quasars. Our results also indicate that multiple SMSs at disparate stagesof evolution can form in these halos, raising the possibility of SMS binaries and supermassive X-raybinaries (SMXBs), as well as DCBH mergers which could be detected by LISA. Keywords: quasars: general — black hole physics — early universe — dark ages, reionization, firststars — galaxies: formation — galaxies: high-redshift INTRODUCTIONSupermassive stars (SMS), as the progenitors of directcollapse black holes, are now one of the leading candi-dates for the seeds of the first massive quasars in theuniverse. Over 300 such objects have now been foundat z >
6, with 8 known quasars at z > - 10 M (cid:12) without everhaving formed stars, either because it is immersed in astrong Lyman-Werner background from nearby Popula- Corresponding author: Tyrone E. [email protected] tion III (Pop III) stars (e.g., Latif et al. 2015; Agarwalet al. 2016) and/or due to supersonic baryon streamingflows (Tanaka & Li 2014; Hirano et al. 2017; Schaueret al. 2017). At these masses, the virial temperatureof the halo reaches ∼ K and triggers rapid atomicH cooling, which causes gas to collapse at rates of upto ∼ M (cid:12) yr − (Bromm & Loeb 2003; Wise et al.2008). These flows flatten into an accretion disk thatbuilds up at least one SMS at its center (e.g. Lodato& Natarajan 2006; Regan & Haehnelt 2009; Latif et al.2013; Regan & Downes 2018a), although recent simula-tions suggest binaries or even small multiples of SMSsare possible (Latif et al. 2020; Patrick et al. 2020 – for re-cent reviews, see Valiante et al. 2017; Woods et al. 2019;Smith & Bromm 2019; Inayoshi et al. 2019; Haemmerl´eet al. 2020). a r X i v : . [ a s t r o - ph . GA ] F e b Woods et al.
Stellar evolution models show that these supermas-sive objects do not immediately collapse, but surviveas core hydrogen-burning stars that can reach massesof several 10 M (cid:12) when accreting rapidly before dy-ing as direct-collapse black holes (DCBHs) via the gen-eral relativistic (GR) instability (e.g., Fuller et al. 1986and references therein; Umeda et al. 2016; Woods et al.2017; Haemmerl´e et al. 2018a,b; Herrington et al. 2021).Model calculations suggest that in some rare circum-stances SMSs may explode at the onset of core hydrogenburning in the case of monolithic collapse (see discussionin Woods et al. 2020) or during core helium burning(Johnson et al. 2013; Chen et al. 2014), although seeNagele et al. (2020). Most of the SMS evolution mod-els find that they evolve as cool, red supergiants alongthe Hayashi track because of H − opacity in their atmo-spheres, so they are not thought to be bright sourcesof ionizing UV radiation that could alter accretion ontothe star (Ardaneh et al. 2018; Luo et al. 2018), althoughLy α radiation pressure might affect flows on small scales(Smith et al. 2017). Pop III SMS, nevertheless, have ex-tremely large luminosities that could be detected in thenear infrared (NIR) by the James Webb Space Telescope ( JWST ) and large ground-based telescopes in the com-ing decade (Hosokawa et al. 2013; Surace et al. 2018,2019; Whalen et al. 2020b).Most studies of Pop III SMS to date, however haveonly considered constant accretion rates, not the rapidlyvarying flows in which the stars actually evolve. Saku-rai et al. (2015) examined the evolution of Pop III SMSin idealized, bursty accretion that approximated denseclumps in the disk due to fragmentation, and found thatthe star could exhibit temporary blue, hot phases beforesettling down onto cooler, redder evolutionary tracks.These hotter episodes occurred when quiescent timesbetween bursts were longer than ∼ NUMERICAL METHODWe extract accretion rates for the first disk to format the centers of eight halos in the enzo adaptive meshrefinement (AMR) cosmology code (Patrick et al. 2020).These rates were then used to evolve Pop III SMS in the
Kepler stellar evolution code, as described below.2.1.
Enzo Simulations
The eight halos for which we tallied central accretionrates were simulated in 1.5 h − Mpc boxes in enzo (Bryan et al. 2014), which self-consistently evolves gas,dark matter, and nonequilibrium primordial gas chem-istry and cooling. Each run had a (256) root grid withthree nested grids centered on the halo and up to 15 lev-els of refinement for a maximum resolution of 0.014 pc.To simulate isothermal collapse in high Lyman-WernerUV backgrounds, these simulations were limited to sixprimordial gas species (H, H + , He, He + , He ++ , and e − )with no H chemistry. Cooling due to collisional exci-tation and ionization of H and He, bremsstrahlung, andinverse Compton cooling by the cosmic microwave back-ground were all included.Each halo was evolved for 2 - 3 Myr after the on-set of collapse due to atomic cooling, which occurred at upermassive Stars in Cosmological Flows Figure 1.
SMS accretion rates from Patrick et al. (2020). The blue vertical lines indicate the times when the stars collapse inour
Kepler runs (see Section 3). Only the main disk in each halo is considered here.
Woods et al. redshifts z = 13.9 - 20.4 at masses of 1 . × M (cid:12) -8 . × M (cid:12) . These halos were chosen to bracket theirlikely range of spin parameters, λ , where λ = | J |√ GM R , (1)and J , R , and M are the angular momentum, virial ra-dius and virial mass of the halo, respectively. They werealso chosen to include a range of assembly histories rang-ing from growth primarily by accretion to growth bymajor mergers. Our ensemble thus yields SMS accre-tion rates for a variety of primordial environments. Weextracted these rates at 10 kyr intervals from the onsetof disk formation for all eight halos. At times, the ac-cretion rate as modelled in enzo can become negativeif turbulence drives gas out of the center of the disk.When this happens, we assume that accretion onto anycentral object formed is halted, setting the accretion rateto zero for our Kepler simulation. The resulting inputaccretion histories are plotted in Figure 1.Accretion begins with an initial surge, ranging from0.3 - 1 M (cid:12) yr − , that lasts for 200 - 300 kyr. The surgecoincides with the formation of the disk, which has aninitial diameter of ∼ in the upper right panel of Figure 2) or clumpy becauseof the fragmentation of the disk (as in Halo 12 in thelower left panel of Figure 2). The large jumps in ac-cretion rate at intermediate times are generally due tothe fragmentation of the disk and subsequent collisionof the clumps with its center, as at 0.7 Myr in Halo 02.The large peak at 1.0 Myr in Halo 01 (and at 1.4 Myrin halo 19) is due to the collision of a satellite disk thatalso hosts an SMS with the main disk, as shown in thelower right panel of Figure 2.2.2. Kepler
Models
We evolve each star in the one-dimensional lagrangianstellar evolution and hydrodynamics code
Kepler (Weaver et al. 1978; Woosley et al. 2002) using thepost-Newtonian approximation implemented by Fulleret al. (1986). Specifically,
Kepler solves the angularmomentum and energy equations with first-order (post-Newtonian) GR corrections to gravity: dvdt = 4 πr ∂P∂m r + 4 πr ∂Q∂m r − G rel m r r (2) dudt = − πP ∂∂m r ( vr ) + 4 πQ ∂∂m r (cid:16) vr (cid:17) − ∂L∂m r + (cid:15) (3)The terms on the right-hand side of Equation 2 are theacceleration due to pressure gradients, viscous drag and Figure 2.
Density projections of accretion disks in variousstates of flow in the atomically-cooled halos in Patrick et al.(2020). Top left: relatively smooth accretion in halo 10 at0.439 Myr. Top right: turbulent accretion flows in halo 20at 0.31 Myr. Bottom left: fragmentation of the disk in halo12 at 1.18 Myr. Bottom right: the onset of the collision ofa satellite disk with the main disk in halo 01 at 0.937 Myr.Each image is 6 pc on a side. gravity, respectively, while those on the right-hand sideof Equation 3 are the energy flux due to work, viscousdissipation, radiative flux, and nuclear burning. Thepost-Newtonian correction to gravity is implemented bymodifying the gravitational constant: G rel = G (cid:18) Pρc + 4 πP r m r c (cid:19) (cid:18) − Gm r rc (cid:19) − (4)The factor Q in the viscous term is Q = 43 η ν r ∂∂r (cid:16) vr (cid:17) , (5)where η ν is the dynamic viscosity from Weaver et al.(1978) and includes the real and artificial viscosity. Thelatter is used to dampen acoustic oscillations duringquiescent phases of the evolution of a star. Nuclear-burning is evolved with an adaptive network that is im-plicitly coupled to the hydrodynamics (Woosley et al.2004). We use a Helmholtz-like equation of state thatincludes electron-positron pair production, relativisticand non-relativistic degenerate and non-degenerate elec-trons, and radiation (Timmes & Swesty 2000). Time-dependent convection as described in Weaver et al.(1978) is included in our runs, as is convective heattransport when a zone satisfies the Ledoux criterion. upermassive Stars in Cosmological Flows M (cid:12) , n = 3 polytropeswith primordial compositions and central densities ρ c =10 − g cm − and temperatures T c = 1 . × K, whichare capable of sustaining deuterium burning. The ac-cretion flow onto the star is also primordial in compo-sition. We match its entropy to that of the surface ofthe star, which neglects the luminosity due to the ac-cretion shock, but at 1 M (cid:12) yr − this luminosity is onthe order of 10 L (cid:12) , which is negligible in comparisonto that of the star. Studies that include this luminos-ity at the base of the photosphere of the SMS find littlechange in its evolution above a few thousand M (cid:12) (e.g.,Hosokawa et al. 2013). We also do not include the ac-cretion of angular momentum, restricting our attentionto non-rotating models (though see Haemmerl´e et al.2018a; Haemmerl´e & Meynet 2019, for more on rotatingSMSs). Additional details on our treatment of accretioncan be found in Woosley et al. (2004) and Woods et al.(2017). Kepler partitions each star into a large number ofzones (here, up to ∼ ∼ g/zone) and outer layers( ∼ g/zone). In each model, the code makes an ar-bitrarily large initial guess for each time step, and theniterates to identify the largest step the code can takewithout exceeding preset limits on the change in frac-tional radius, temperature, luminosity, or density any-where on the grid, and while still following the emer-gence of shocks. This approach enables us to follow thelong-term evolution of the star over thermal and nu-clear timescales, dropping to short time steps to resolvehydrodynamic timescales only when instabilities ap-pear. This includes the onset of the post-Newtonian orGR instability (Chandrasekhar 1964). Recently, Haem-merl´e (2020) confirmed that Kepler predicts collapseat masses that are consistent with those expected fromcareful analytic estimates. We ignore mass loss due towinds, which are thought to be negligible in primor-dial stars (Vink et al. 2001) and in any event couldnot overcome the ram pressure of infall. We also donot consider pulsations and pulsational mass losses here(Baraffe et al. 2001). RESULTSThe evolution of the star in the main disk in eachhalo, along with its total mass and energy generationand transport within the star, are shown in the Kip-penhahn diagrams in Figure 3.1. We discuss the salientfeatures of each model in Section 3.1 and infer generalaspects of SMS formation and their connection to theproperties of their host halos in Section 3.2.3.1.
Individual Halos In Halo 01 , the initial surge in accretion rate due tothe formation of the disk peaks at ∼ M (cid:12) yr − in thefirst 100 kyr, before very gradually subsiding in a slow,somewhat oscillatory manner. Consequently, the SMSquickly develops a large, high-entropy radiative envelopesurrounding its convective, nuclear-burning core, muchas it would in the constant accretion rate case (e.g.,Hosokawa et al. 2013). This outer radiative envelopeis only very marginally stable against convection, andindeed, small transient convective cells do form withinthe upper envelope, as also seen in e.g., Umeda et al.(2016) and Woods et al. (2017). Accretion then nearlyhalts before three later dramatic bursts that are sep-arated by long quiescent phases. During each pause,the star thermally relaxes, and convective cells formedin the outer envelope in each accretion burst eventuallymerge with the central region as the star becomes almostwholly convective.The last of these bursts corresponds to the collision ofthe main accretion disk with a smaller, satellite disk thatlikely hosts another SMS. Our enzo simulations lack theresolution to determine if these two stars merge, so wesimply include the collision of the smaller disk in theaccretion rate of the main disk in our Kepler runs. Inthis halo, we find that the star reaches ∼
170 k M (cid:12) at ∼ X c ≈ .
29. We stress, however,that this merger event should be examined in greaterdetail, using e.g., a detailed three-dimensional smoothedparticle hydrodynamical simulation to follow the trajec-tories of the stars and their subsequent interaction. Wewill study such systems in future work. Notably, how-ever, we can confirm that the two massive stars in Halo01 will interact while both are on the main sequence,ultimately colliding in a supermassive stellar merger orforming a supermassive binary.The SMS in
Halo 02 initially only accretes at anaverage rate of about 0.07 M (cid:12) yr − for the first 500kyr. This leads to a (relatively) shallow radiative enve-lope (in keeping with previous calculations, e.g., Woodset al. 2017; Haemmerl´e et al. 2018b). Then the disk frag-ments, and accretion thereafter proceeds in an extremelyclumpy manner, with the first accretion spike at ∼ ∼ M (cid:12) over ∼
100 kyr ina marginally-convective, superadiabatic envelope beforeaccretion nearly halts. Over the next 200 kyr the starlargely thermally relaxes again, notably with a strong
Woods et al.
Halo 01 Halo 02Halo 08 Halo 10Halo 12 Halo 16Halo 19 Halo 20Figure 3.
Kippenhahn diagrams illustrating energy generation, energy transport, and stellar structure as a function of time andmass coordinate for the stars in our study. Figure captions: “conv” denotes convective regions, “semi” denotes semi-convectiveregions, and “neut” denotes neutral regions Regions without hashing are radiative, and the specific energy generation rate (blueshading) at each mass coordinate in the star is indicated by the color axis (see, e.g., the description in Woods et al. 2017). upermassive Stars in Cosmological Flows X c ≈ .
34) at the onset of a third accretionburst at 1.46 Myr at a final mass of ∼
155 k M (cid:12) . This isextremely close to the upper boundary mass for avoidingdirect collapse for fully thermally relaxed SMSs (Woodset al. 2020).In Halo 08 , after a brief initial burst that peaks at0.37 M (cid:12) yr − , accretion proceeds at rates of 0.1 - 0.3 M (cid:12) yr − for the first ∼
700 kyr of the star’s evolution.During this time, the SMS very closely resembles starsaccreting at uniform rates with similar average values(e.g., Hosokawa et al. 2013; Woods et al. 2017; Haem-merl´e et al. 2018b). This is only somewhat interruptedby a minor accretion episode at ∼ M (cid:12) yr − before subsiding. Al-though convective cells form in the outer envelope, thesupermassive star remains far from being thermally re-laxed up to its collapse at 0.954 Myr and ∼
186 k M (cid:12) ,when it is still burning hydrogen (X c ≈ . Halo 10 grows by nearly 0.4 M (cid:12) yr − for the first 100 kyr of evolution, with the accreted massmostly remaining in the high-entropy envelope. Accre-tion then begins to slow, allowing the star to thermallyrelax somewhat and the central, nuclear-burning convec-tive region to grow both in absolute mass and in totalmass fraction of the star. The star continues to growat a more modest pace over the next 1.6 Myr, which al-lows its convective hydrogen- and helium-burning “core”mass fraction to grow as it continues to thermally re-lax. The mean accretion rate over the life of the SMSis ∼ M (cid:12) yr − . During this latter accretion phase,transient convective regions within the high-entropy en-velope arise and disappear or merge with the centralconvective region before accretion nearly halts at 1.7Myr. A little over 100 kyr later, the star is almost fullyconvective. Shortly after the onset of a final accretionburst at ∼ . c ≈ .
06) at a final mass of132 k M (cid:12) .As in halos 01 and 02, the disk in Halo 12 is stronglyturbulent and begins to fragment soon after formation,which leads to large accretion bursts at the beginning ofour
Kepler run and at 0.5 Myr and 0.65 Myr. Unlikethose in the other halos, the SMS in Halo 12 producessomewhat more substantial, transient semi-convectiveregions at the interface between the convective core andthe high-entropy envelope, the reason for which remainsunclear. Ultimately, the precise treatment of convectionin extremely radiation-dominated SMSs remains highlyuncertain, a problem which we will revisit in futurework. The star collapses at 1.22 Myr at a final mass of 178 k M (cid:12) while burning hydrogen (X c ≈ . Halo 16 is somewhat of anoutlier in our sample because the initial peak associatedwith the formation of the disk is particularly strong andpersistent, depositing nearly 80 k M (cid:12) onto the star inits first 200 kyr. Accretion then almost entirely haltsbefore resuming at ∼
700 kyr. Infall rates at the centerof the disk fall to low values because Halo 16 collideswith three other halos just before cooling and collaps-ing. These mergers spin gas up at the center of the haloand make the disk very rotationally supported, reducingaccretion onto the star. The initial accretion peak pro-duces an enormous, high-entropy envelope surroundingthe convective hydrogen-burning region of the star. Thelatter grows in mass much more slowly, following thethermal relaxation of the SMS, only nearly catching upwith the total mass of the star at ∼
400 kyr, well afterthe initial accretion burst has ended. After accretion re-sumes at 0.7 Myr, the SMS slowly accumulates another30 k M (cid:12) before collapsing at a mass of 110 k M (cid:12) at 1.68Myr. This is the only star in our sample that reachescore hydrogen exhaustion (X c ≈ × − , with a cen-tral helium fraction of ≈ Halo 19 is similar to that in Halo 01: af-ter the initial peak, accretion falls to modest rates withoccasional and brief bursts prior to the appearance ofa large burst due to the merger of the main disk witha satellite disk, in this case at 1.4 Myr. Here again,although the satellite disk may also host an SMS wemake no attempt to model its mass or follow its mergerwith the star in the main disk. Because of the lowerinfall rates up to 1.4 Myr the SMS in the main diskhas mostly thermally relaxed and become almost fullyconvective by the time the disks collide, and it remainslargely convective during the collision. Given its rela-tively modest prior accretion rate, the SMS within themost massive disk in Halo 19 is largely thermally relaxedand almost fully convective by the time of the merger,remaining largely convective as it survives the resultingburst of accretion. After another much smaller spike in
Woods et al.
Halo z col M halo spin N mergers M SMS X c t GR ˙ M avg M (cid:12) M (cid:12) Myr M (cid:12) yr − Table 1.
Properties of the halos at collapse (redshifts, masses, spin parameters, and number of major mergers prior to collapse)and their stars (final masses and central hydrogen fractions, times at which they reach the post-Newtonian instability, andaverage accretion rates). accretion at ∼ M (cid:12) while still burning hydrogen(X c ≈ . Halo 20 is accom-panied by a particularly strong accretion peak, similarto that in Halo 16. In Halo 20, however, accretion neversubsides, in spite of the formation of another disk thatsoon rivals the original in mass. A close encounter withthis companion disk at 1.36 Myr produces a second pow-erful surge in accretion (see Patrick et al. 2020, for moredetails). After this burst, accretion falls off and the SMScollapses at 1.48 Myr at a final mass of 178 k M (cid:12) whilestill burning hydrogen (X c ≈ . General Properties
We find that the object at the center of the diskin each halo survives initial thermal contraction andreaches pp-chain hydrogen-burning without first collaps-ing to a BH. Eventually, the central temperature ex-ceeds T c ∼ K, permitting the onset of of the triple-alpha reaction, quickly producing the CNO abundancesneeded to reach sufficient hydrogen-burning to stabiliz-ing the star against further contraction, and producinga long-lived SMS. The subsequent evolution of the stardepends on the halo’s accretion and merger history buta number of general trends are evident.All of the stars in our sample undergo collapse at somepoint during the hydrogen-burning main sequence withthe nominal exception of the SMS in Halo 16, which col-lapses at the exhaustion of its central hydrogen. Thisis in keeping with the large masses deposited onto theseSMSs by rapid accretion, which in almost all cases bringthe SMS up to the post-Newtonian limit and the onsetof the GR instability before the end of their main se-quence lifetimes (as also found in, e.g., Woods et al.2017; Haemmerl´e et al. 2018a). The SMS in halo 16accretes almost all its mass in its first 200,000 yr and then lives for very nearly the main sequence lifetimepredicted for an Eddington-limited star, before collaps-ing at the age expected for a wholly thermally-relaxedSMS (Woods et al. 2020). Note that some stars, likethose in Halos 10 and 19, live somewhat longer than theEddington-limited main sequence lifetime because of theingestion of additional hydrogen at later times in theiraccretion histories.The properties of each SMS and its host halo are listedin Table 1. Note that these eight halos were chosen byPatrick et al. (2020) to span their likely range of spin pa-rameters and assembly histories, i.e., growth primarilyby accretion, by major mergers, or both. Here, a majormerger is defined to be the collision of two halos withmass ratios of 1/5 or more. We show scatter plots ofmean accretion rate and final stellar mass, core hydro-gen fraction and age versus halo mass, collapse redshift,spin parameter and number of major mergers prior tocollapse in Figure 4. Although our sample is small, it isclear that some properties of SMS populations at highredshift can be inferred from those of the halos in whichthey form.First, a history of major mergers limits the maximummass of the SMS and therefore produces the least mas-sive DCBHs. These halos form the smallest and mostrotationally-supported disks, and thus have the lowestaccretion rates. Lower rates create more thermally-relaxed, compact SMSs with less opportunity for growthbefore significant nuclear evolution, as in Halo 16 wherethe star collapses after reaching the end of the mainsequence. Second, if we exclude the two halos with ma-jor mergers prior to collapse, we see that there is alsoa tentative correlation between redshift and accretionrate, and thus an anti-correlation between redshift andSMS lifetime, because more rapidly-accreting SMS haveshorter lives (Woods et al. 2017). In the six halos thatgrew primarily by accretion, we also see a tentative anti- upermassive Stars in Cosmological Flows enzo sim-ulations, well before the gas in the disk is exhausted.Accretion onto the nascent BH from its natal disk ora companion star will release X-rays that will alter thecourse of the evolution of the halo by, for example, cat-alyzing H formation and triggering new star formationin the vicinity of the BH (e.g., Aykutalp et al. 2014; In-ayoshi & Tanaka 2015). Stellar evolution calculationswith accretion rates from cosmological simulations willbe required to predict when X-rays are turned on in ahalo after the death of its SMS in future studies of itslater evolution. CONCLUSIONStars evolving in cosmological flows taken from nu-merical simulations of the collapse of atomically-coolinghalos become supermassive before collapsing to BHs af-ter 1 - 1.5 Myr. Accounting for the nuclear evolutionand the short- and long-term response of SMSs to accre-tion, we find that all objects within our sample collapseduring or at the end of the hydrogen-burning main se-quence. In particular, halos that cool purely by atomiccooling produce DCBHs with a narrow range of masses( ∼ × M (cid:12) ) for a wide range of collapse redshifts,spin parameters and merger histories. These masses are similar to the final masses of stars in Woods et al. (2017),whose uniform accretion rates were comparable to ouraverage ones.Patrick et al. (2020) do not bridge all the spatial scalesof accretion onto the star because they are limited toresolutions of ∼ James Webb Space Telescope ( JWST ) and large ground-based telescopes in the com-ing decade (Hosokawa et al. 2013; Surace et al. 2018,2019; Whalen et al. 2020b). Their BHs could also befound in the NIR at z ∼ −
20 by
JWST (Pacucciet al. 2015; Natarajan et al. 2017; Barrow et al. 2018;Whalen et al. 2020a) and at z ∼ Euclid andthe
Roman Space Telescope (although lensing by galaxyclusters and massive galaxies in their wide fields couldextend these detections up to z (cid:46)
10 - 15; Vikaeus et al.2021). DCBHs will only be marginally visible to theSquare Kilometre Array or next-generation Very LargeArray in the radio at z (cid:38) z ∼
10 by future X-ray missions such as the
AdvancedTelescope for High-Energy Astrophysics ( ATHENA ) and
Lynx (Aird et al. 2013; The Lynx Team 2018).Here, we have focused on the first disk to form in eachhalo, but Patrick et al. (2020) found that other diskscan appear and exchange mass or even merge with theoriginal disk. Although we do not model such mergershere, we find that they can occur at any time from whenthe SMS in the main disk is early in its evolution to wellafter it has collapsed to a black hole. This suggests anumber of possible interactions between SMSs and theirprogeny in the early Universe, from supermassive stellarmergers to stable mass exchange in supermassive X-raybinaries (“SMBXs”) to DCBH–DCBH mergers, the lat-ter being detectable by LISA out to redshifts of ∼ Woods et al.
Figure 4.
Scatter plots of mean accretion rates and final SMS masses, core hydrogen fractions and ages from our
Kepler models vs. key properties of the host halos from Patrick et al. (2020). Individual halos are each identified by a unique colourand shape for all plots, as described in the figure legend. upermassive Stars in Cosmological Flows