arXiv:astro-ph/9903465v1 30 Mar 1999 raino ouaino od eeeaedaf with dwarfs degenerate cold, of the population namely masses possibility, a events. another of timescale address will short creation & I of (Kerins letter lack this functions the In mass explain varying to Paolis spatially 1998) De or Evans 1997, 1998) Kerins al 1987; Lacey et & dwarf of (Carr clusters brown dwarfs dark brown invoked the have salvage Some to worthwhile. hypothesis attempts & Hansen Gibson makes chemi- 1996; 1997) (e.g. the stages Freese Mould evolutionary with prior & associated from pollution Graff problems cal the sequence 1994; However main al 1998). than et more (Bahcall con- dwarfs observational stars white direct favours with short 1995) combined straints, al of limit, dwarfs. brown et mass lack than massive Aubourg This more the 1997; objects favour al particular, to appears et of In (Alcock nature events et the timescale matter. into Aubourg investigations dark 1993; stimulated baryonic al has et 1993) (Alcock al Cloud Magellanic Large rpittpstuigL using typeset Preprint 2018 30, April version Draft niiiiy h iiigln ewe hs ucmsi a is outcomes these of between to mass line rapidly becomes dividing cools it The and invisibility. 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T E ⊙ tl mltajv 04/03/99 v. emulateapj style X INTRODUCTION hc ontbr yrgnby hydrogen burn not do which , aais formation galaxies: crto tr:bondaf tr:frain–Glx:halo Galaxy: – formation stars: – dwarfs brown stars: – accretion rf eso pi 0 2018 30, April version Draft rdM .Hansen S. M. Brad ABSTRACT 1 rp.I rnil,ti rcdr slmtdol ythe to by limit raised burning only hydrogen be limited the could is and en- rate, procedure low burning this with pyconuclear dwarf principle, the In onto settles tropy. material the that rates hc a oetal ecntutdb h lwaccre- slow the by configurations dwarf constructed of be varying range potentially of the can dwarfs represents which parameter brown This of accommodate range mass. can the as determine which fades I space star enough Thus, the strong dwarf. and brown not luminosity a Be- is cooling the burning star. overwhelm nuclear burning to and hydrogen transition, runaway normal slow the a a low is becomes there dwarf point which the transition the above on a sequence is points the there various mass effect on each at the For burning consider sequence. nuclear cooling then on I switching burning. with- of star? sequence nuclear of a cooling into including dwarf a it constructed out a have turns I can burning mass, hot nuclear each For how before be ques- namely; mass the fashion, given address to another of prefer state in I the tion disk, in do a uncertainty by from the I done accreted Given as material dwarf (1992). 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1 −11 −9 −1 tion of low entropy material. must be in a narrow range ∼ 10 − 10 M⊙.yr to The first important point to note is that, for dwarfs yield both significant mass accretion while allowing the of primordial composition, the normal hydrogen burning accreted material to retain only low entropies (Lenzuni limit is raised to ∼ 0.1M⊙ as noted by Nelson (1989), a et al 1992). Furthermore, such rates are well above the −18 −1 consequence of the change in boundary condition result- ∼ 10 M⊙yr experienced in the local ISM, implying ing from the lower atmospheric opacity. As the mass in- that such rates must be related to the initial conditions creases, the transition temperature drops rapidly as we for the formation of such objects. pass through the range of masses 0.13-0.17M⊙. The effec- Let us assume that brown dwarfs form in small clusters. tive temperatures for models at the transition point are Unless the process is highly efficient, there will be a sub- ∼ 1500 K. At masses > 0.17M⊙, electron degeneracy in stantial amount of gas present as well. For a cluster of the centre leads to formation of an isothermal core where mass M and radius R, the ambient density ρ ∼ 0.25M/R3 energy transport by electron conduction dominates con- and velocity V 2 ∼ GM/R yield a Bondi-Hoyle accretion vection. This results in lower central temperatures than rate for a 0.01M⊙ brown dwarf of the adiabatic case and the effective temperature at the −1/2 −3/2 transition point remains essentially constant in the range ˙ −11 −1 M R ∼ − − M ∼ 6.4 × 10 M⊙yr 1200 1500 K for masses 0.17 0.3M⊙. Thus, if we 102M⊙  0.1pc allow material to be accreted with entropies appropri- (1) ∼ ate to Teff 1500 K atmospheres, the mass limit can Such an estimate lies within the acceptable range for trans- be raised considerably above the 0.15M⊙ estimated by formation of brown dwarfs into beige dwarfs. But we need Salpeter (1992). These stars represent a configuration con- to know what size clusters and collapsed objects do we taining elements of both brown dwarfs (in terms of com- expect from primordial star formation. position and lack of nuclear burning) and white dwarfs The formation of primordial stars is intricately tied to (in terms of mass and internal structure). Thus, for the the cooling mechanisms of primordial gas and thus to the purposes of clarity later, I shall refer to these (> 0.1M⊙) formation of molecular hydrogen, the dominant coolant in objects as ‘Beige dwarfs’. dense, metal-free media. In the traditional cosmological Once formed, these dwarfs will fade slowly, radiating scenario of hierarchical gravitational collapse, gas falls into what little thermal energy they possess, just as brown and the potential well of a cold, non-baryonic dark matter com- white dwarfs do. The cooling of the various models is ponent, is shock-heated to virial temperatures and cools shown in Figure 1. The watershed nature of the 0.15M⊙ to form the baryonic component of protogalaxies. Fall model is apparent. For smaller masses, the evolution is & Rees (1985) identified a thermal instability in such hot similar to that of a traditional brown dwarf, with a rapid gaseous halos, in which the gas fragments into cold clumps fading to insignificance within 5-6 Gyr. The 0.15M⊙ model surrounded by a hot, high pressure ambient medium. The retains a significant contribution from nuclear burning for isobaric collapse of the cold clumps was assumed to halt at several Gyr after birth, so that it takes longer to cool and ∼ 104 K where the Lyman edge leads to inefficient cooling. therefore is the brightest model after ∼ 15Gyr. For more The characteristic mass of such isobaric collapsing clumps 5 6 massive models, the central transition temperatures are was determined to be ∼ 10 −10 M⊙ and was thereby iden- low enough that the dwarfs essentially begin life in a cool, tified as a possible mechanism for forming globular clus- white dwarf-like configuration and do not cool significantly ters. However, non-equilibrium calculations of the cooling further within a Hubble time. Also shown is a 0.6 M⊙ of shock-heated gas (Shapiro & Kang 1987 and references Carbon/Oxygen white dwarf with hydrogen atmosphere therein) indicate that cooling progresses faster than re- from Hansen (1999). Thus, the larger radii of the beige combination, which leads to a residual electron fraction dwarfs mean they are ∼ 1 magnitude brighter (since they well above equilibrium levels, thereby promoting the for- have similar effective temperatures to the white dwarfs). mation of H2 and enhancing the cooling rate. The result For masses ∼ 0.3M⊙ the beige dwarfs will be superficially of this process is that the isobaric collapse is able to con- similar in appearance to white dwarfs. Figure 1 shows tinue down to temperatures ∼ 30−102 K. This conclusion the colours calculated for the HST WFPC bandpasses of is robust unless there is a strong, pre-existing source of Holtzmann et al (1995). Furthermore, a population of such ultra-violet radiation (such as an AGN) in the same proto- objects can be distinguished from a white dwarf popula- galaxy (Kang et al 1990), i.e. cooling below 104 K cannot tion by the very different cooling sequence. Beige dwarfs be stopped by a UV background alone. The Bonner-Ebert are born with effective temperatures ∼ 1500 − 3000 K, critical mass (Ebert 1955; Bonner 1956) for gravitational in which molecular hydrogen is already a strong source of instability in high pressure media is opacity (e.g. Borysow, Jorgensen & Zheng 1997), so that 2 they cannot populate a region equivalent to the upper part kbTcool −3/2 −1/2 of the white dwarf cooling sequence (i.e. the initial red- Mcrit =1.18 G p (2)  µmp  ward evolution of the white dwarf track), which occurs for temperatures > 4000 K. where p ∼ nhotkTvir is the pressure in the hot, virialised gas phase. The density of the hot phase is such that the 3. cooling time is comparable to the dynamical time (Fall COSMOLOGICAL CONSIDERATIONS & Rees 1985), so that the pressure is determined entirely This particular mode of star creation requires fairly by the virial temperature and cooling function. For virial special conditions to be important. The accretion rate temperatures appropriate to our galactic halo (∼ 106 K) 1Deuterium burning during construction may change the adiabat for a given object, but is not strong enough to change this bound (Salpeter 1992) 3

2 3 the critical mass clusters will range from ∼ 10 − 10 M⊙, ∼ 0.01M⊙ objects is ∼ 10% then few objects will be able depending on the final cooled temperature (assuming a to grow by more than a factor of 10, providing a natural variation between 30-100 K). The appropriate accretion limiting mechanism. Furthermore, the formation of copi- rate is thus ous collapsed objects in a small cluster will result in two body relaxation on timescales 2 −5/2 − − Mbd Tcool ˙ ∼ × 11 1 −1 −3/2 M 1.6 10 M⊙yr − (3) 10 2M⊙  30 K ∼ 8 −1 Mbd 2 Tcool trel 10 yr ǫ − M2 (4) 10 2M⊙  30 K where we have assumed a velocity dispersion for the clump appropriate to the cooled gas temperature and Mbd is the where ǫ (in units of 0.1 here) is the efficiency of conversion mass of the accreting object. Note that the Bonner-Ebert of gas into 0.01M⊙ bound objects and M2 is cluster mass mass in this situation is an lower limit on the collapsed in units of 100 M⊙. In fact, ǫ and Mbd may be regarded as mass. Larger clumps with lower accretion rates can form dynamically evolving quantities as the characteristic col- also, depending on the spectrum of perturbations in the lapsed object mass grows through accretion. Although hot gas phase. Nevertheless, this is exactly the kind of cluster evaporation takes place on timescales ∼ 300trel accretion rate we require, low enough to allow accretion of (e.g. Spitzer 1987), as more gas mass is incorporated into low entropy material but high enough to allow significant dwarfs, the cluster potential becomes ‘lumpier’ and two- mass accretion on cosmological timescales. body relaxation accelerates, so that the cluster disruption Figure 2 shows the expected accretion rates in such cold time is ∼ 5trel as defined in (4) by the time all the gas clumps as a function of halo velocity dispersion (i.e. the mass has been accreted onto the original seeds. This is virial temperature of the hot confining medium). There also approximately equal to the timescale for Bondi-Hoyle is some variation allowed depending on the final temper- accretion runaway to infinite mass (this is not surpris- ature to which the clumps can cool and thus the fraction ing, given that both accretion and two-body relaxation of molecular hydrogen is important. The diagram may are intimately related to the gravitational focussing cross- be split into three parts, depending on the accretion rate. section). Thus there is a finely balanced competition be- −9 −1 For rates > 10 M⊙yr , the accreted material is too hot tween mass accretion and cluster evaporation that may for the dwarf to remain degenerate and normal hydrogen produce a very different mass spectrum than is usually burning stars in the mass range ∼ 0.1 − 0.2M⊙ are formed assumed for primordial objects. −11 −1 (Lenzuni et al 1992). For rates < 10 M⊙yr , brown 4. dwarfs will not accrete enough mass to change their char- CONCLUSION acter much in 109 yrs, and so any brown dwarfs formed In this paper I have considered the possibility that ther- in such clusters will remain true brown dwarfs. However, mal instabilities in primordial gas collapse favour the cre- 2 3 between those two extremes, the conditions are appropri- ation of small (∼ 10 − 10 M⊙) gaseous clusters, which ate for the transformation of brown dwarfs into the beige are ideal sites for the formation of massive brown (a.k.a. dwarfs described above in section 2. Furthermore, these beige) dwarfs by the process of Lenzuni, Chernoff & conditions are applicable in the range of 100 − 300km.s−1 Salpeter (1992). This offers a scenario for the formation that describe the dark matter haloes of galaxies. Such of baryonic dark matter which meets the requirements conditions may also apply in the case of pregalactic cool- of both the microlensing survey mass limits and those ing flows (Ashman & Carr 1988; Thomas & Fabian 1990). of limited chemical pollution of the interstellar medium If one wished to extend this picture to the case of cluster and production of extragalactic light (two stringent con- cooling flows (e.g. Fabian 1994), the larger virial temper- straints on the currently fashionable white dwarf scenario). atures and higher pressures suggest higher accretion rates The scenario predicts that baryonic dark matter lies pre- and thus low mass star formation rather than beige dwarfs. dominantly in beige dwarfs ∼ 0.1 − 0.3M⊙ with probably Thus, it appears that the formation of small gas clusters some contribution from low mass stars (∼ 0.2 − 0.3M⊙) of appropriate density is a generic feature of gas collapse as well. This mechanism is also peculiar to the early uni- in CDM haloes at moderate to high redshifts. However, verse because it will become less efficient at constructing there is also a requirement that brown dwarfs be the most beige dwarfs once the accreted material contains signifi- abundant initial collapsed object. Once again, the physics cant metallicity (since greater opacity means material is of H2 cooling in continued collapse provides the character- accreted with more entropy). Thus, any present day ana- istic mass scale, a Jeans mass < 0.1M⊙ (Palla, Salpeter logue is more likely to produce low mass stars. As such, & Stahler 1983). Although the complexity of star forma- this scenario may also naturally account for the red stel- tion prevents a conclusive answer, the preceding provide lar haloes of galaxies such as NGC 5907 (Sackett et al plausible conditions for our scenario, namely the copious 1994). Indeed, Rudy et al (1997) find that the peculiar production of brown dwarf mass objects in relatively dense colours of this halo requires a population rich in red dwarfs 9 media in which they may grow on timescales ∼ 10 yrs. (< 0.25M⊙), but of approximately solar metallicity (pri- How long will such accretion episodes last? This is an mordial metallicity stars are not red enough to explain ∝ 2 important question, because Bondi-Hoyle accretion Mbd these colours). and is thus a runaway process. An obvious concern is Given the many uncertainties inherent in discussing pri- that, if gas is too abundant, even accretion at rates ini- mordial star formation and galaxy evolution from first −9 −1 tially < 10 M⊙yr will eventually lead to sufficient ac- principles, I have also constructed preliminary models for cretion to create a star. The abundance of ambient gas the evolution and appearance of such objects. Hopefully, will depend on the efficiency with which one forms brown deep proper motion surveys will be able to constrain this dwarfs initially. If the efficiency of conversion of gas into scenario directly. In particular, such beige dwarfs will be 4 somewhat brighter than white dwarfs and should also oc- gram, i.e. they will not display a cooling track like a white cupy a restricted region of the Hertzsprung-Russell dia- dwarf population would.

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Fig. 1.— The solid line represents a 0.6 M⊙ white dwarf cooling track. The dotted lines are the cooling tracks of degenerate brown dwarfs of mass 0.13, 0.15, 0.17, 0.2, 0.25 and 0.3 M⊙. Each curve has three open circles plotted on it, at ages of 5 Gyr, 10 Gyr and 15 Gyr. The 0.13 M⊙ object cools to invisibility in less than 10 Gyr. Note that these represent the cooling of the hottest possible models only, i.e. cooler models are possible for each mass. Fig. 2.— Here we find the accretion rate we expect for brown dwarfs formed in clusters of cold gas resulting from the thermal instability of shock heated gas in dark matter haloes (Fall & Rees 1985) of varying velocity dispersion and for various final temperatures of the cold phase (which will depend on the amount of H2 that is formed). The dotted lines delineate the various outcomes, depending on the accretion rate. The two lower lines require significant accretion on timescales of 1 Gyr and 10 Gyr respectively. The dashed line indicates a velocity dispersion of 50 km/s. For smaller haloes, there is little non-equilibrium production of H2 behind virialisation shocks (Shapiro & Kang 1987), but the accretion rates are very low anyway for such small haloes.