First star formation in ultra-light particle dark matter cosmology
MMNRAS , 1–5 (2017) Preprint 26 September 2017 Compiled using MNRAS L A TEX style file v3.0
First star formation in ultra-light particle dark matter cosmology
Shingo Hirano, (cid:63) James M. Sullivan and Volker Bromm Department of Astronomy, University of Texas, Austin, TX 78712, USA
Accepted 2017 September 19. Received 2017 September 19; in original form 2017 May 25
ABSTRACT
The formation of the first stars in the high-redshift Universe is a sensitive probe ofthe small-scale, particle physics nature of dark matter (DM). We carry out cosmologicalsimulations of primordial star formation in ultra-light, axion-like particle DM cosmology,with masses of 10 − and 10 − eV, with de Broglie wavelengths approaching galactic scales( ∼ kpc). The onset of star formation is delayed, and shifted to more massive host structures.For the lightest DM particle mass explored here, first stars form at z ∼ ∼ M (cid:12) , compared to the standard minihalo environment within the Λ cold dark matter( Λ CDM) cosmology, where z ∼
20 – 30 and ∼ – 10 M (cid:12) . Despite this greatly alteredDM host environment, the thermodynamic behaviour of the metal-free gas as it collapses intothe DM potential well asymptotically approaches a very similar evolutionary track. Thus, thefragmentation properties are predicted to remain the same as in Λ CDM cosmology, implyinga similar mass scale for the first stars. These results predict intense starbursts in the axioncosmologies, which may be amenable to observations with the
James Webb Space Telescope . Key words: cosmology: theory – dark matter – dark ages, reionization, first stars – methods:numerical – stars: formation – stars: Population III
The particle physics nature of the dynamically dominant dark mat-ter component of the cosmic energy density is one of the crucialopen questions in modern science. Whereas the Λ cold dark matter( Λ CDM) model successfully explains the observed phenomenologyon scales larger than galaxies, its extrapolation to smaller scales islargely untested. Until recently, supersymmetric weakly interactingmassive particles (WIMPs) were considered the most promisingcandidates for dark matter, due to a number of extremely appeal-ing, seemingly ‘natural’ aspects, such as the WIMP miracle (e.g.Bertone 2010). However, in light of the failed experimental effortsto date to detect such WIMPs in the laboratory, alternative scenariosfor the nature of dark matter are explored with renewed vigour. Inguiding this theoretical exploration, astrophysical constraints are ofkey importance. The primordial power spectrum has been directlyprobed only down to length scales of (cid:39)
30 comoving Mpc (Hlozeket al. 2012), and we need to resort to non-linear probes to constrainthe structure formation model at even smaller scales. Specifically, ithas been realized for a while that high-redshift structure formation,and in particular the formation of the first stars, the so-called Pop-ulation III (Pop III), provides a sensitive probe of the small-scalenature of dark matter (e.g. Yoshida et al. 2003; Dayal et al. 2017).Pop III star formation has been investigated in great detailwithin standard Λ CDM, where minihaloes of virial mass ∼ – (cid:63) E-mail: [email protected] M (cid:12) at z ∼
20 – 30 are identified as host sites, resulting in a top-heavy distribution of stellar masses (e.g. Bromm 2013; Greif 2015).It is an open question how the character of Pop III star formationwill change with variations of the underlying dark matter cosmology.As an example, Hirano et al. (2015b) studied one possible effect byconsidering a primordial power spectrum with a blue tilt, enhancingpower on small scales, leading to a dramatic transformation of thefirst star formation process.
What, then, are possible alternatives to WIMP dark matter?
It is well known that Λ CDM is challenged on small scales by anumber of discrepancies between prediction and observation, suchas the ‘missing satellites’ problem (e.g. Bullock 2013), the ‘core-cusp’ problem (e.g. de Blok 2010), and the ‘too big to fail’ problem(e.g. Boylan-Kolchin et al. 2012). One class of proposed solutionsinvokes baryonic physics, such as star formation, supernovae, andblack hole feedback, acting to decouple the luminous componentof galaxies from their dark matter, or dynamically transformingtheir structure (e.g. Wetzel et al. 2016). On the other hand, thenature of DM itself can alleviate those problems, postulating lessmassive particles whose intrinsic motions can quench perturbationgrowth and structure formation below their free-streaming scale.An intriguing theoretical model involves ultra-light particles, likeaxions (e.g. Marsh 2016, and references therein), with masses about10 − eV. Their corresponding de Broglie wavelength is macroscop-ically large, ≈ fuzzy dark matter (FDM), because of the quantum mechanical origin of establishing © 2017 The Authors a r X i v : . [ a s t r o - ph . C O ] S e p Hirano et al. stability, similar to that in atoms and molecules (Hu et al. 2000). Insuch ultra-light DM particle universes, non-linear structure forma-tion can be prevented on small scales, with the suppression (Jeans)scale given by the de Broglie wavelength. This opens up the possi-bility to naturally solve the small-scale problems within the Λ CDMmodel, thus accommodating most observations, e.g. Lyman- α forestconstraints (Iršič et al. 2017; Zhang et al. 2017). In particular, anysuch suppression of small-scale structure can significantly affect theformation of the first objects in the Universe (e.g. Greif 2015). Dueto a lack of numerical simulations in a fully cosmological context,however, the exact impact of the FDM model on the early Uni-verse has not yet been established (e.g. Mocz et al. 2017, and theirupcoming paper II). Thus, remarkably the Heisenberg uncertaintyrelation may be manifest on galactic scales, stabilizing the dark mat-ter against gravitational instability on these scales. Such a ‘soliton’solution has been explored in-depth in the context of the core-cuspproblem, and is approximately consistent with an ultra-light axionmass range of ≈ − – 10 − eV (Marsh & Pop 2015).In this Letter , we investigate first object formation in suchultra-light dark matter cosmologies by performing a series of hy-drodynamic simulations. The suppression of small-scale structuredramatically alters the nature of the first star and galaxy forma-tion sites, rendering the DM host structures much more massive,with correspondingly higher virial temperatures. One consequenceis that the gaseous fuel available for Pop III star formation maybe greatly enhanced, thus possibly triggering luminous primordialstarbursts that in turn could be within reach of the
James WebbSpace Telescope (JWST) . The cooling of the metal-free gas, how-ever, still has to rely on molecular hydrogen (H ), and it is animportant question whether the characteristic thermodynamics thatimprints a fragmentation scale of a few ∼
100 M (cid:12) in the case ofstandard Λ CDM cosmology remains intact, or is critically different(e.g. Bromm 2013).The remainder of the paper is organized as follows. We beginby describing our numerical methodology in Section 2. Sections 3and 4 present simulation results, first regarding the DM host envi-ronment and then the physical properties of the collapsing cloud.Sections 5 summarizes the implications of adopting FDM cosmolo-gies. Throughout this study, we adopt cosmological parameters withmatter density Ω m = .
31, baryon density Ω b = . Ω Λ = .
69, a Hubble constant of h = .
68, a normalizationof the density fluctuations of σ = .
83, and a primordial powerspectral index of n s = .
96 (Planck Collaboration XVI 2014).
We perform a series of cosmological simulations started from initialconditions representing different FDM models. The cosmologicalinitial conditions are generated using the publicly available codemusic (Hahn & Abel 2011). The linear power spectrum P FDM ( k ) for FDM cosmology, with the mass of the ultra-light dark matterparticle being m a , is given by assuming a transfer function T FDM ( k ) (Hu et al. 2000) as P FDM ( k ) = T ( k ) P CDM ( k ) , (1) T FDM ( k ) = cos x ( k )/( + x ( k )) , x J ( k ) = . ( m a / − eV / c ) / ( k / k J , eq ) , k J , eq = ( m a / − eV / c ) / Mpc − , (2)where P CDM ( k ) is the power-spectrum for CDM cosmology. Theadopted FDM cosmology only depends on the particle mass m a , and the transfer function has a sharp cut-off, exhibiting acoustic os-cillations on scales below k J , eq . In this study, we adopt two differentmasses, m a = − eV (Run-A) and 10 − eV (Run-B) to investi-gate the effect on first star formation. For comparison, we also carryout a simulation within standard Λ CDM cosmology (Run-Ref). Tocontrol for cosmic variance, we generate all initial conditions withthe same phases, assuming a Gaussian random process throughout.The cosmological simulations are performed by using theparallel N-body/Smoothed Particle Hydrodynamics (SPH) codegadget-2 (Springel 2005), suitably modified for the primordialstar formation case (Yoshida et al. 2006, 2007; Hirano et al. 2014,2015a). In order to achieve the numerical resolution required totreat the wide dynamic range from cosmological scales to thoseof the gravitationally unstable gas cloud, we employ hierarchi-cal zoom-in procedures. Within a parent computational box of10 comoving h − Mpc on a side, we insert a series of nested re-finement regions, reaching maximum resolution inside a volumewith linear size 1 ( . ) comoving h − Mpc for Run-A and B (Run-Ref). The corresponding DM (N-body) and baryonic (SPH) par-ticle masses in the maximally refined region are 119 ( . ) M (cid:12) and 21 . ( . ) M (cid:12) for Run-A and B (Run-Ref), which can wellresolve the halo structure. We follow structure formation from red-shift z =
99 until the maximum hydrogen number density reaches10 cm − . During the simulations, we use an on-the-fly particlesplitting technique (Kitsionas & Whitworth 2002), with the refine-ment criterion that the Jeans mass is always resolved by at least 50SPH particles, which is sufficient to examine the hydrodynamics offragmentation (Bate & Burkert 1997). The most refined baryonicparticle mass, as a result of splitting, thus reaches 1 . ( . ) M (cid:12) forRun-A and B (Run-Ref), able to resolve the gravitationally unstablegas cloud.In our simulations, we ignore the effect of FDM modified dy-namics which causes the quantum interference patterns and solitoniccores in the DM distribution (e.g. Woo & Chiueh 2009; Schive et al.2014a,b). The corresponding small-scale suppression may addition-ally delay the onset of star formation, but is likely sub-dominantcompared with the overall delay due to the modified initial condi-tions. Similarly, at the scale of the solitonic core the baryon densityis already larger than the DM one, such that the subsequent hydrody-namics is largely decoupled from the DM distribution. The currentuncertainty in the results is likely dominated by the unknown DMparticle mass, compared to any uncertainties due to the neglectedwave dynamics. Future, more complete simulations are needed tocheck these assumptions. The suppression of small-scale perturbations within FDM directlydelays structure formation in the early Universe. Star formation inthe cosmological volume first occurs at z = . .
9) in Run-A (B),which is significantly later than in Run-Ref at z = . m a ≈ − eV are consistent with results from priorFDM structure formation simulations (Schive et al. 2016). Suchtime delay results in a completely different morphology of the starformation site. In Λ CDM cosmology, the first star formation eventsoccur at the centre of almost spherically-symmetric dark matterminihaloes with 10 – 10 M (cid:12) at z ∼
20 – 30 (e.g. Hirano et al.2014). We compare the resulting star formation morphologies inFig. 1, where the near-spherical geometry is evident in Run-Ref
MNRAS , 1–5 (2017) irst star formation in FDM cosmology Run-A (a) Run-B (b) Run-Ref
100 kpc (c)
Figure 1.
Morphology of primordial star formation in different cosmologies. Cross-sectional views of gas density distribution around the collapse centre ofthe primordial star-forming cloud in Run-A with 5 kpc linear size ( panel a ), Run-B with 2 kpc ( panel b ), and Run-Ref with 100 pc on the side ( panel c ). Thetop and bottom panels show slices through the X - Y and X - Z planes, respectively. The blue, green, orange, and red colours represent density contours, with n H =
1, 10, 10 , and 10 cm − , respectively. The stark difference in morphology is evident, illustrating the shift from the near-spherical minihalo environmentin Λ CDM to the filaments, or even sheets, of the cosmic web within FDM. m a (eV) z R vir (pc) M vir ( M (cid:12) ) T vir (K) N cloud − (A) 6.5 4 . × . × . × − (B) 12.9 9 . × . × . × a fewCDM (Ref) 28.1 4 . × . × . × Table 1.
Column 1: Mass of the ultra-light dark matter particle. Column2: Collapse redshift. Column 3: Virial radius. Column 4: Virial mass. Col-umn 5: Corresponding virial temperature. Column 6: Estimated number ofgravitationally unstable clumps. Virial properties are calculated from thesnapshots when the maximum gas density reaches 10 cm − . (Fig. 1c). In the FDM cosmologies, on the other hand, minihaloesdo not form, because the suppression scale of ∼ kpc is larger thanthe minihalo scale in Λ CDM. Pop III stars, therefore, do not form insuch spherical host regions, but instead in more massive DM sheets(Fig. 1a) or filaments (Fig. 1b) whose virial masses are 10 – 10 times the mass of a minihalo (Table 1). In FDM models, the firstobjects in the Universe finally appear after z ∼
15, when super-kpcscale structures begin to collapse from large-scale perturbations.Generically, the objects found in the simulations emerge ascomponents of the cosmic web, predicted by the standard model ofstructure formation (e.g. Zeldovich 1970; Shandarin & Zeldovich1989). A given perturbation on some scale in an almost uniformthree-dimensional density distribution in the early Universe firstcollapses along one dimension, forming two-dimensional sheets.Subsequently, these so-called ‘Zeldovich pancakes’ collapse in an-other dimension and form one-dimensional filaments, where theorder of collapse along the different axes is given by the eigenval-ues of the deformation tensor. Finally these filaments collapse inthe remaining dimension and form three-dimensional spheres (orhaloes). The large suppression scale of the FDM particle preventsthe later collapse at smaller scales, and our simulations demon-strate how first star formation consequently occurs during the initialphases of structure formation, inside the filaments, or even sheets,of the cosmic web. Such a shift in primordial star formation site from haloes to filaments was already found for warm dark matter(WDM) models (Gao & Theuns 2007), for similar reasons (dis-cussed in Section 5).To further elucidate the difference between Λ CDM and FDMmodels, Fig. 2 shows the radial distribution of mass and densityat the moment when the gas first undergoes runaway collapse. Theenclosed baryonic mass is significantly larger in the FDM runs com-pared to the Λ CDM one (Fig. 2a). Within the virial radius, there aremultiple density peaks in the FDM runs (Fig. 2b). In Run-B, in par-ticular, such secondary peaks are located along the dense filament(compare to Fig. 1b). Such morphology, where multiple regions arebecoming gravitationally unstable in a nearly synchronized fash-ion, is quite different from the Λ CDM case (Run-Ref). Here, onlyone gravitationally unstable cloud forms at the centre of the almostspherical dark matter minihalo (Figs. 1 and 2b).
The baryonic component is gravitationally dragged into the DMstructure and finally begins self-gravitational collapse, when thegravitational force overcomes the thermal pressure. This occurswhen the mass of the growing gas cloud exceeds the local Jeansmass (Abel et al. 2002) M J ≈ (cid:12) (cid:18) T
200 K (cid:19) / (cid:18) n H cm − (cid:19) − / , (3)where T is the gas temperature and n H the hydrogen number den-sity, normalized to the typical values encountered in primordialclouds. The latter defines what is termed the ‘loitering state’ ofPop III star formation (Bromm et al. 2002). The thermal evolutionof the collapsing gas cloud governs the final fate of the new-bornPop III protostars, because their mass accretion history, and thusthe resulting stellar mass, sensitively depends on temperature as (cid:219) M ≈ M J / t ff ∝ T / , where t ff is the free-fall time-scale. In Fig. 3(a),we show the thermal histories of the collapsing clouds within thedifferent DM models. In the standard Λ CDM case (Run-Ref), the
MNRAS000
MNRAS000 , 1–5 (2017)
Hirano et al. l og ( M en c [ M ⊙ ] ) FDM : m a =10 -22 [eV] FDM : m a =10 -21 [eV] CDMDM component (a)012345678-2 -1 0 1 2 3 4 l og ( n H [ c m - ] ) log (R [pc] ) (b) Figure 2.
Radially averaged profiles of the enclosed gas mass ( panel a )and density ( panel b ), at the moment when the maximum density reaches10 cm − . The red, blue, and black lines represent results at the end ofthe simulation for Run-A, Run-B, and Run-Ref, respectively. The solid anddashed lines in panel (a) show baryonic and DM components, respectively.The structural differences between the models are readily apparent, in par-ticular regarding the more distributed nature of gravitational instability inthe FDM models. gas is adiabatically heated to the virial temperature of the minihalo(Barkana & Loeb 2001), T vir (cid:39) (cid:18) M vir × M (cid:12) (cid:19) / (cid:18) + z (cid:19) . (4)Subsequently, the cloud cools via H -cooling and finally becomesgravitationally unstable, when M enc ≥ M J at n H ∼ cm − , at theloitering state (see Fig. 3b).Within FDM, the first structures to virialize are more massivecompared to Λ CDM, such that the primordial gas collapses intodeeper potential wells with correspondingly larger virial tempera-tures. During the collapse, the gas temperature initially increasesthrough adiabatic compression, until it reaches T ∼ . × Kfor Run-A, and 3 . × K for Run-B. The massive gas clouds canbe supported until H -cooling becomes effective (Fig. 3c), whenthe gas temperature finally declines, and the Jeans mass decreases(Eq. 3).The massive gas clouds with 10 – 10 M (cid:12) are initially heatedup to 8,000 K, but finally cool to 200 K, which is below the minimumtemperature in Run-Ref, via enhanced H -cooling. This boost incooling results from the increased free electron fraction which inturn catalyses additional H formation. In such low-temperatureand H -rich gas, additional cooling via the HD molecule couldbecome efficient and cool the gas even further (e.g. Nakamura & [ M ⊙ ] [ M ⊙ ] [ M ⊙ ] [ M ⊙ ] l og ( T e m p [ K ] ) (a)-1012 l og ( M en c / M J ) (b)-2-10123-2 -1 0 1 2 3 4 5 6 l og ( U / | Γ - Λ | [ M y r ] ) log (n H [cm -3 ] ) Γ - Λ <0 Γ - Λ >0t ff (c) Figure 3.
Profiles of collapsing cloud properties as a function of hy-drogen number density: gas temperature ( panel a ), ratio of enclosed toJeans mass ( panel b ), and thermal time-scale where U , Γ , and Λ arethe internal energy, heating rate, and cooling rate, respectively ( panel c ).For the red, blue, and black lines, we adopt the same convention as inFig. 2. The grey lines in panel (a) show the density-temperature relationfor a given Jeans mass (Eq. 3; 10 – 10 M (cid:12) ). The grey line in panel (c)represents the corresponding free-fall time-scale as a function of density, t ff = (cid:112) π / G ρ = . × ( n H / cm − ) − / yr. It is evident that the ther-mal histories of the primordial gas approach a very similar behaviour at highdensities, implying similar fragmentation properties ( panel a ). The ‘Jeansnumber’ M enc / M J , on the other hand, is greatly enhanced in the FDM cases,implying a possibly larger star formation efficiency in turn. Umemura 2002; Gao & Theuns 2007). In the FDM cases studiedhere, however, the HD fraction remains below the critical valuerequired for cooling to affect the cloud’s thermal evolution. This isbecause the gravitationally unstable gas clouds (Fig. 3b) collapsetoo rapidly for sufficient HD molecule formation (see fig. 23 inHirano et al. 2014).Due to the delayed collapse and the corresponding increase invirial mass scale, more massive gas clouds become gravitationallyunstable in the FDM universe. The temperatures encountered bythose clouds, on the other hand, are similar to the standard Λ CDMcase (Run-Ref), such that the corresponding Jeans masses approachsimilar values as well. In Run-Ref, the mass of the collapsing cloudfirst exceeds the local Jeans mass with about 10 M (cid:12) at the loiter-ing point, whereas a gas cloud with more than 10 M (cid:12) becomesJeans unstable during the temperature decline phase in Run-A andB. These differences may result in a qualitatively altered star forma-tion process, where star formation efficiencies could be much higher,and a massive cluster of Pop III stars could arise. Such a primordialstarburst would be markedly different from the standard predictionfor minihaloes, where small groups of Pop III stars, including bina-ries and small multiples, are expected to form (e.g. Bromm 2013).As a simple estimation of the number of gravitationally-unstableclumps in the FDM runs, we could consider that the 10 M (cid:12) cloudfragments at the final Jeans scale of 10 M (cid:12) , resulting in about 100star-forming clumps. Slightly more precise, we can measure the MNRAS , 1–5 (2017) irst star formation in FDM cosmology mass of the gas which actually reaches the minimum temperature,giving about ten (a few) times the Jeans mass in Run-A (Run-B).In fact, a number of independent clumps can be discerned in thedensity distribution (Figs. 1 and 2). We present a series of cosmological simulations with ultra-lightparticle dark matter, suggesting an entirely different process of firststar formation in the early Universe. Multiple star-forming clouds,formed within sheet-like or filamentary massive structures, becomegravitationally unstable at the same time. Although their detailedsubsequent evolution is beyond the scope of the current work, thefurther fate of such primordial proto-clusters is clearly of greatinterest in terms of the effect on the chemical and radiative evolutionat early epochs, possibly shaping the assembly of the first galaxiesand the reionization process. Standard theory posits that massivestar clusters can only form in metal-enriched gas (e.g. Safranek-Shrader et al. 2014). Intriguingly, within FDM cosmologies, suchmassive starbursts could already occur at the very onset of cosmicstar formation. The extreme time delay of the first objects in theFDM vs. Λ CDM models, with collapse occurring at z = . . JWST , and beyond that with the suiteof extremely large telescopes on the ground (the GMT, TMT, andE-ELT), will conduct searches for the timing and intensity of suchprimordial (Pop III) starbursts, as predicted for FDM cosmologies.There are alternative origins which can reproduce similar en-vironmental conditions for massively-clustered first star formation.One such scenario is adopting warm dark matter (WDM) particleswith masses of ≈ M (cid:12) . Gao & Theuns (2007)also discuss the possibility of filament fragmentation and subse-quent coalescence. We find similar filamentary structure in Run-B,and also multiple gravitational collapse events along the filament.Furthermore, in Run-A for the lower-mass axion, a sheet-like struc-ture initially forms and fragments into multiple clumps. Additional,qualitatively very different physical origins exist to realize a similarthermal history of the primordial gas. Among them are the collapsewithin standard Λ CDM, but exposed to a strong external soft ultra-violet radiation field which photo-dissociates the H molecule untilthe gas cloud becomes sufficiently dense to self-shield (e.g. Latif &Volonteri 2015), or gas collapse subject to the impeding effect ofrelative baryon-DM streaming (e.g. Tseliakhovich & Hirata 2010;Latif et al. 2014; Schauer et al. 2017). In these cases, however,the small-scale DM perturbations still exist, leading to dynamicaldifferences to the FDM (or WDM) models.In the possible post-WIMP era of dark matter physics, astro-physical constraints will have to play a unique role in guiding particlephysics theory. This is in particular the case for high-redshift struc-ture formation, encompassing the epochs of first star formation andreionization, as there we encounter the small-scale consequencesof any DM models which have hitherto been largely beyond reachfor empirical testing. The imminent arrival of the next generationof telescopes may thus herald exciting new discoveries not only forastronomy, but also for fundamental physics. ACKNOWLEDGEMENTS
The simulations were carried out on XC30 at CfCA, National Astro-nomical Observatory of Japan, XC40 at YITP, Kyoto University, andStampede at TACC, University of Texas at Austin. This work wasfinancially supported by Grant-in-Aid for JSPS Overseas ResearchFellowships (S.H.) and NSF grant AST-1413501 (V.B.).
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