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of ∼ 7 × 10 7 and ∼ 5 × 10 8 years, respectively. In the accelerated collapse case these values are zcol = 23.6, 21.3, and 12.4, corresponding to delays of ∼ 2 × 10 7 and ∼ 2 × 10 8 years. Thus, this delay is noticeable only for high initial values of vs,i > ∼ 3 km s −1 , whereas at smaller values the delay is small compared to the Hubble time. We can understand the criterion for gas collapse in terms of the cosmo- logical Jeans mass. In the usual no-streaming case, the slow infall of gas into the halos will first begin when the gravitational potential well of the minihalo, characterized by its virial velocity Vvir, is large enough to assemble the gas, which occurs when Vvir > cs, where cs = kBT/µmH is the sound speed. Once this process begins, the sound speed cs will be coupled to Vvir through adiabatic heating (see top panels of Fig. 5.1), and the density will scale with sound speed approximately as c3 s . In Fig. 5.1, we determined the properties of the largest halo in our simulation using the HOP technique (Eisenstein and Hut 1998) to find the DM particle in the region of highest DM density. As- suming this particle marks the center of the halo, the extent of the halo was determined by finding the surrounding spherical region in which the average DM density is 200ρc, where ρc is the redshift-dependent critical density. The bottom panels of Fig. 5.1 illustrate that the adiabatic phase of evolution will continue until the virial mass of the minihalo is greater than the Jeans mass of the gas, Mvir > MJ. For the no-streaming case, we calculate MJ as MJ = π 6 c3 s G3/2 , (5.1) ρ1/2 Once the halo gains sufficient mass, and also provided that the H2-driven cooling time tcool of the gas is shorter than its free-fall time tff, the Jeans and 134
Figure 5.1: Top panels: Effective velocity veff = c2 s + v2 s of the gas (thin lines) and virial velocity Vvir of the simulated minihalo (thick red line). Top Left: ‘Standard collapse’ case. Dashed line: vs,i = 10 km s−1 , dotted line: vs,i = 3 km s−1 , solid black line: no-streaming case. At each redshift vs was found by taking an average over the entire gas within the simulation box. cs refers to the average sound speed of all particles within the virial radius of the minihalo. Top Right: Early collapse case. Note that for the streaming cases, the redshift at which veff first falls below vvir matches well with the point where the gas thermal evolution first follows that of Vvir. Bottom Panels: Evolution of the Jeans mass MJ with redshift, evaluated using veff in the role of the effective sound speed. Notation is the same as in the upper panels. Red line: virial mass Mvir of the minihalo. Green line: exponential fit to the growth of the ‘standard collapse’ case minihalo. Gas collapse occurs quickly after MJ drops below Mvir. The enhancement of veff due to the streaming velocity effectively increases MJ, causing the gas collapse to be delayed until Mvir can further grow. This alters the final gas collapse redshifts of each case (zcol = 14.4, 12.2, and 6.6 for the no streaming, moderate streaming, and fast streaming cases given ‘standard collapse’; zcol = 23.6, 21.3, and 12.4 for ‘early collapse’). 135
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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
Page 97 and 98: 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
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Page 141 and 142: which has already detected GRBs at
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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 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
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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
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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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