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of 10 −20 G, several orders of magnitude higher than what Ichiki et al. (2006) estimated for this length scale. When looking at CR propagation between minihaloes, the physical distance in question is much smaller, rL 1 kpc. This corresponds to a magnetic field strength of 5×10 −17 G, around an or- der of magnitude stronger than the magnetic field predicted by Ichiki et al. (2006). These seed fields from recombination are thus too small to affect CR propagation. It is therefore not implausible that at high redshift there existed suffi- cient magnetic fields in the DM haloes to accelerate CRs to relativistic energies while their propagation in the IGM and filaments was very close to rectilinear due to the weak magnetic fields in these regions. This unconfined propagation in the IGM would allow a universal isotropic CR background to build up, and this is what we assume in our analysis. 6.3 Evolution of Primordial Clouds 6.3.1 Idealized models We examine the evolution of primordial gas by adapting the one-zone models used in Johnson and Bromm (2006) (see also Mackey et al. 2003). In the z ∼ 20 collapsing minihalo case, typical halo masses are ∼ 10 6 M⊙. The minihaloes form during hierarchical mergers at velocities too low to cause any shock or ionization in the minihalo, so the electron-catalysed molecule formation and cooling is insufficient to allow stars less than around 100 M⊙ to form (e.g. Bromm et al. 1999, 2002; Abel et al. 2002). CR ionization and heating, however, can potentially alter the thermal and chemical evolution of primordial gas. In our model, the minihalo has an initial ionization fraction of xe = 10 −4 156
and undergoes free-fall collapse. Its density therefore evolves according to dn/dt = n/tff, with the free-fall time being tff = 1/2 3π 32Gρ , (6.18) where ρ = µmHn ≈ mHn and µ = 1.2 is the mean molecular weight for neutral primordial gas. The initial density was taken to be the density of baryons in DM haloes at the point of virialization (e.g. Clarke and Bromm 2003) n0 0.3 cm −3 3 1 + z . (6.19) 20 The initial temperature of the gas was taken to be 200 K, and the initial abundances were the primordial ones (e.g. Bromm et al. 2002). As our second case, we consider strong virialization shocks that arise in later stages of structure formation during the assembly of the first dwarf galaxies. The corresponding DM haloes virialize at z ∼ 10 − 15, and have masses ranging from ∼ 10 8 to ∼ 10 10 M⊙. The conditions during the assembly of the first dwarf galaxies show some key differences from the former case. The virial velocities of these DM haloes are much greater, implying merger velocites that are now high enough to create a shock that can partially ionize the primordial gas (Johnson and Bromm 2006 and references therein). The post-shock evolution is taken to be roughly isobaric (e.g. Shapiro and Kang 1987; Yamada and Nishi 1998). We use an initial post-shock temperature of Tps = mHu 2 sh 3kB . (6.20) For an initial density of nps, again found from Equ. (6.19), the temperature and density will follow the relation Tpsnps T n. 157
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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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the deaths of massive stars (see Wo
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It is apparent that the angular mom
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h = 0.7. To accelerate structure fo
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acc = Lres 50 AU, where: Lres 0.5
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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
Page 133 and 134: sink M∗(5000 yr) [M⊙] M∗(10 5
Page 135 and 136: present here, particularly if the s
Page 137 and 138: the stars grow to larger masses (se
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
Page 145 and 146: are initialized at high z with smal
Page 147 and 148: M⊙, where Nneigh 32 is the typic
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
Page 157 and 158: a much smaller contribution from <
Page 159 and 160: abundances of HD, which also acts a
Page 161 and 162: first stars had very short lifetime
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 virialization redshift zvir = 2
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
Page 195 and 196: to be part of an area of scientific
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
Page 211 and 212: Navarro, J. F. and White, S. D. M.
Page 213 and 214: Rollinde, E., Vangioni, E., and Oli
Page 215 and 216: Simon, M., Ghez, A. M., Leinert, C.
Page 217 and 218: Tanvir, N. R., Fox, D. B., Levan, A
Page 219 and 220: Rays, volume 576 of Lecture Notes i
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Zatsepin, G. T. and Kuz’min, V. A
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