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formalism (Lacey and Cole 1993) to model the abundance and merger history of cold dark matter (CDM) haloes. In a neutral medium, before the redshift of reionization, Bromm and Loeb (2006) assume star formation occurs only in haloes that have become massive enough to enable atomic line cooling with virial termparatures above approximately 10 4 K. Recent work (see Greif and Bromm 2006) suggests that these more massive haloes were indeed the dominant site for star formation. Greif and Bromm (2006) argue that about 90 percent of the mass involved in metal-free star formation initially cooled through atomic line transitions. At higher redshifts such as z ∼ 20, however, the first stars are thought to have formed inside of ∼ 10 6 M⊙ minihaloes through molecular cooling, and this mode of star formation is much more significant at this time. For the minihalo case at z ∼ 20, Yoshida et al. (2003) estimate the rate of star formation through H2 cooling to be Ψ∗ ∼ 10 −3 M⊙ yr −1 Mpc −3 . To account for such differences in these determinations of star formation rates, we examine a range of values spanning multiple orders of magnitude. The Pop III initial mass function (IMF) currently remains highly un- certain, so for this study we do not perform our calculations using a specific IMF. For simplicity, we instead assume that those Pop III stars whose masses lie in the pair instability SN (PISN) range (140-260 M⊙) have an average mass of 200 M⊙ (e.g. Heger et al. 2003). A Pop III initial mass function (IMF) that extends over a large range of masses would imply that only a fraction of these stars were in the PISN range. Thus, here we assume that only slightly less than half of Pop III stars are in this mass range, leading to a somewhat more conservative value for the CR energy density. Our estimate generally corresponds to an IMF peaked around 100 M⊙. Due to their high mass, the 146
first stars had very short lifetimes of about 3 Myr (e.g. Bond et al. 1984), and we therefore assume instantaneous recycling of the stellar material. As described below, this overall picture of Pop III star formation will be used to estimate the average CR energy density in the high-redshift Universe. 6.2.2 Cosmic ray production For this paper CRs are assumed to have been generated in the PISNe that may have marked the death of Pop III stars. The CRs are accelerated in the SN shock wave through the first-order Fermi process by which high-energy particles gain a small percentage increase in energy each time they diffuse back and forth across a shock wave. This yields a differential energy spectrum in terms of CR number density per energy (e.g. Longair 1994): dnCR dɛ = nnorm ɛmin ɛ ɛmin x , (6.1) where we will use x = −2 for definiteness, a typical value given by Fermi acceleration theory (e.g. Bell 1978a). Here, ɛ is the CR kinetic energy, ɛmin is the minimum kinetic energy, and nCR is the CR number density. Note that our results are somewhat sensitive to the choice of x. Choosing values for x that are closer to what is observed in the Milky Way, such as x = −2.5 or x = −3, or using a CR spectrum similar to that given in Rollinde et al. (2005, 2006) will increase CR heating and ionization, if the overall CR energy density is held constant. For these steeper power laws a higher fraction of the total CR energy resides in the lower-energy CRs, which are the ones that contribute the most to these CR effects, as discussed in Chapters 6.3.1 and 6.3.4 and in the discussion for Fig. 6.3. . Such steeper spectral slopes can in fact yield CR heating and ionization rates up to an order of magnitude higher than for 147
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Copyright by Athena Ranice Stacy 20
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New Insights into Primordial Star F
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Acknowledgments I first want to giv
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angular momentum to rotate at nearl
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2.4.2.5 Thermodynamics of accretion
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Chapter 7. Outlook 177 Bibliography
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List of Figures 2.1 Density project
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1.1 Motivation Chapter 1 Introducti
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leaving behind a neutron star or bl
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describe studies that have attempte
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CRs may therefore provide a pathway
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expected that some of the gas withi
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our numerical methodology in Chapte
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scattering is the major source of o
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portance. The reaction rates for an
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The size of the refinement levels h
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the sink a temperature and pressure
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same time, such as the fragments in
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Figure 2.2: Physical state of the c
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2.4.2 Protostellar accretion 2.4.2.
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Despite some amount of rotational s
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Figure 2.6: Velocity field of the c
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Figure 2.7: Disk mass vs. time sinc
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Figure 2.8: Angular momentum struct
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sink tform [yr] Mfinal [M⊙] rinit
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sink (∼ 4 M⊙) that merged with
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actual final mass of the star is li
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the average temperature of all part
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disk accretion onto a primordial pr
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Figure 2.12: Impact of feedback on
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Figure 2.13: Comparison of specific
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the central core, eventually compri
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extending our simulation to later t
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that such a non-primordial origin t
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impose an upper mass limit to Pop I
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we use a ray-tracing scheme to foll
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3.2.3 Sink Particle Method When an
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convenient way to directly measure
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where the sum now extends from the
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Figure 3.1: Evolution of various pr
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ased on the prescription of Omukai
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ate found at late times in our ‘n
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Figure 3.2: Evolution of various di
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Figure 3.3: Evolution of disk mass
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Figure 3.4: Temperature versus numb
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disk mass is able to level off in d
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Figure 3.6: Projected density and t
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onto the disk. The numerical experi
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that the I-front expands as an hour
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Figure 3.8: Evolution of various H
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˙ M∗ = 3πΣν, (3.18) where ν
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the discrete nature of the gas part
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stars. We also note that, despite t
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current computational limits. If ra
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Page 111 and 112: It is apparent that the angular mom
Page 113 and 114: h = 0.7. To accelerate structure fo
Page 115 and 116: acc = Lres 50 AU, where: Lres 0.5
Page 117 and 118: years, up to several dynamical time
Page 119 and 120: sp = GM∗ c2 , (4.1) s where cs is
Page 121 and 122: Figure 4.2: Left: Angular momentum
Page 123 and 124: through the disk, and the disk is e
Page 125 and 126: steadily grows for the rest of the
Page 127 and 128: Fig. 4.5 shows these timescales for
Page 129 and 130: sink B. Once on the MS, the sink A
Page 131 and 132: Figure 4.6: Evolution of stellar ro
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Page 135 and 136: present here, particularly if the s
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Page 139 and 140: Here, Σ is the disk surface densit
Page 141 and 142: which has already detected GRBs at
Page 143 and 144: M⊙. They find that the specific a
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Page 149 and 150: Figure 5.1: Top panels: Effective v
Page 151 and 152: Figure 5.2: Effect of relative stre
Page 153 and 154: Using cs ∝ T 1/2 results in ρ
Page 155 and 156: Figure 5.4: Evolution of gas proper
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Page 159: abundances of HD, which also acts a
Page 163 and 164: of star-forming material. Here we t
Page 165 and 166: star formation, they found CR energ
Page 167 and 168: The GZK cutoff applies only to thos
Page 169 and 170: and virialization redshift zvir = 2
Page 171 and 172: and undergoes free-fall collapse. I
Page 173 and 174: β = 1 − −2 1/2 ɛ + 1 mHc2
Page 175 and 176: and where ΓCR(D) = 5 × 10 −29 e
Page 177 and 178: Figure 6.2: Thermal evolution of pr
Page 179 and 180: Figure 6.3: Minimum temperature rea
Page 181 and 182: Figure 6.4: Thermal evolution of pr
Page 183 and 184: The CR energy density can now be es
Page 185 and 186: 2007). When considering realistic c
Page 187 and 188: 6.3.5 Fragmentation scale As is evi
Page 189 and 190: 2006). This decrease in fragmentati
Page 191 and 192: Chapter 7 Outlook Our understanding
Page 193 and 194: that Pop III stars likely experienc
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Page 197 and 198: Barkana, R. and Loeb, A. (2001). In
Page 199 and 200: Bromm, V., Kudritzki, R. P., and Lo
Page 201 and 202: Daigne, F., Olive, K. A., Silk, J.,
Page 203 and 204: Gao, L., White, S. D. M., Jenkins,
Page 205 and 206: Heger, A., Woosley, S. E., and Spru
Page 207 and 208: Kratter, K. M. and Murray-Clay, R.
Page 209 and 210: Machida, M. N., Omukai, K., Matsumo
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Navarro, J. F. and White, S. D. M.
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Rollinde, E., Vangioni, E., and Oli
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Simon, M., Ghez, A. M., Leinert, C.
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Tanvir, N. R., Fox, D. B., Levan, A
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Rays, volume 576 of Lecture Notes i
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Zatsepin, G. T. and Kuz’min, V. A
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