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cooling criteria will be satisfied and the gas will begin the next phase of rapid collapse to higher densities, quickly reaching nmax = 10 4 cm −3 . The cause for the delay in collapse of the streaming cases lies in the enhanced effective velocity of the gas, veff = c 2 s + v2 s , (5.2) where the streaming velocity decreases over time such that vs(z) = vs,i(1 + z)/(1 + zi). As shown in the top panels of Fig. 5.1, this delays the point at which the gas will begin falling into the halo. To accommodate the cases with streaming, we replace cs in Equ. (5.1) with veff, and the resulting increase of MJ is shown in the bottom panels of Fig. 5.1. For any given collapse redshift, a larger Mvir is therefore required to trigger the collapse of streaming gas compared to the non-streaming case. In Fig. 5.2, we estimate for different redshifts the mininum halo mass into which gas with various initial streaming velocities can collapse. We arrive at these estimates using the following simple prescription. We first determine for a range of redshifts the minihalo mass corresponding to a virial temperature of 1500 K, which serves as the minimum mass for collapse and cooling given no streaming. We fit a typical halo growth history using Mvir(z) = M0e αz (the green line shown in Fig. 5.1), with M0 = 2 × 10 7 M⊙ and α ranging from −0.2 to −0.5. We vary α depending on the no-streaming case minihalo mass and the desired collapse redshift. For every given collapse redshift and streaming velocity, we first determine the redshift zeq where Vvir(z) = veff(z). We assume that zeq is the point where the gas switches from having properties of the intergalactic medium (IGM) to properties determined by the halo. Thus, for 136
Figure 5.2: Effect of relative streaming on the minimum halo mass into which primordial gas can collapse. Each line represents the necessary halo masses for baryon collapse at a different redshift, marked in the plot. The diamonds represent the final halo masses found in ‘standard collapse’ simulations (zcol = 14 for no streaming), and the squares represent masses from the ‘early collapse simulations’ (zcol = 24 for no streaming). Note that the halo mass does not noticeably increase unless the initial streaming velocities are very high (greater than ∼ 3kms −1 ). Also note that halos collapsing at high redshift are more affected by relative streaming, as the physical streaming velocities are higher at these early times. 137
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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
Page 99 and 100: Figure 3.8: Evolution of various H
Page 101 and 102: ˙ M∗ = 3πΣν, (3.18) where ν
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Page 105 and 106: stars. We also note that, despite t
Page 107 and 108: current computational limits. If ra
Page 109 and 110: the deaths of massive stars (see Wo
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
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: Figure 5.1: Top panels: Effective v
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 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
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
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Daigne, F., Olive, K. A., Silk, J.,
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Gao, L., White, S. D. M., Jenkins,
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Heger, A., Woosley, S. E., and Spru
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Kratter, K. M. and Murray-Clay, R.
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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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