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Figure 4.1: Left: Growth of sink mass over time. Solid line is the growth of sink A, and dashed line is the growth of sink B. Dash-dot line is the result from Bromm & Loeb (2004). Red lines are power-law fit s to the mass curves. Though sink A grows rapidly for the first few hundred years, adding the accretion criterion of non-rotational support later causes its growth rate to be somewhat lower than that found in Br omm & Loeb (2004) until a large merger event at 3800 years. Right: Ratio ɛ = Jsink/Jcent as sinks grow over time. Representation of different sinks is the same as in the left panel. For sink B’s accretion and the first ∼ 1000 years of sink A’s accretion, note the similarity in how both mass and ɛ increase over time. This is due to the steadily growing rotational support of the mass that flows onto the sinks. Msink ∝ t 0.25 , and ˙ M ∝ t −0.75 . 4.3.1.2 Angular Momentum As the sinks grow in mass, the angular momentum of each particle accreted, JSPH = mSPHvrotd, is added to the total angular momentum of the sink, Jsink. Note that the scale of the sink, racc = 50 AU, is smaller than the radius corresponding to the sonic point: 104
sp = GM∗ c2 , (4.1) s where cs is the sound speed. A typical sink mass is 10 M⊙, and the highest- temperature, high-density (n > 10 8 cm −3 ) gas is approximately at 7000 K, or cs 7 km s −1 . This yields rsp 180 AU. For the cooler disk gas, T ∼ 500 K and cs 2 km s −1 , so that rsp is larger, ∼ 2000 AU, and similar to the size of the large-scale disk. The sinks therefore easily resolve the scale of the sonic point. Angular momentum transport from inside rsp to outside rsp will be difficult once the inflow becomes supersonic (Ulrich 1976; Tan and McKee 2004). In Chapter 4.3.2, we will show that the inflow onto the sinks does indeed quickly become supersonic, and in fact the total angular momentum within the sonic point steadily grows as more mass continues to fall in. However, the angular momentum inside rsp can still be redistributed through torques within the large-scale disk. Jsink stays at a fairly steady fraction, ɛ = Jsink/Jcent, of the angular momentum required for full centrifugal support at the accretion radius, Jcent = Msinkjcent. Figures 4.1 and 4.2 show this fraction to range from ɛ 0.45−0.5 for sink A and ɛ 0.25−0.35 for sink B. Thus, on the scale of the accretion radius the sinks never become fully rotationally supported. Rotational velocities of the accreted particles were also recorded, and the total rotational velocity of each sink, vsink, can be determined through a mass-weighted average of each accreted particle’s vrot (right panel of Fig. 4.2). Similar to the behavior of Jsink, vsink stays at the same fairly constant fraction of vcent = GMsink/racc. The specific angular momentum of the sinks does not stay perfectly constant, however. Comparing the mild evolution of ɛ with the sinks’ mass growth (Fig. 4.1) shows a general correspondence between them, similar to 105
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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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Page 69 and 70: impose an upper mass limit to Pop I
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Page 73 and 74: 3.2.3 Sink Particle Method When an
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Page 79 and 80: Figure 3.1: Evolution of various pr
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Page 83 and 84: ate found at late times in our ‘n
Page 85 and 86: Figure 3.2: Evolution of various di
Page 87 and 88: Figure 3.3: Evolution of disk mass
Page 89 and 90: Figure 3.4: Temperature versus numb
Page 91 and 92: disk mass is able to level off in d
Page 93 and 94: Figure 3.6: Projected density and t
Page 95 and 96: 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
Page 103 and 104: the discrete nature of the gas part
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: years, up to several dynamical time
Page 121 and 122: Figure 4.2: Left: Angular momentum
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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 139 and 140: Here, Σ is the disk surface densit
Page 141 and 142: which has already detected GRBs at
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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 and 160: abundances of HD, which also acts a
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Page 163 and 164: of star-forming material. Here we t
Page 165 and 166: star formation, they found CR energ
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and virialization redshift zvir = 2
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and undergoes free-fall collapse. I
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β = 1 − −2 1/2 ɛ + 1 mHc2
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and where ΓCR(D) = 5 × 10 −29 e
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Figure 6.2: Thermal evolution of pr
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Figure 6.3: Minimum temperature rea
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Figure 6.4: Thermal evolution of pr
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The CR energy density can now be es
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2007). When considering realistic c
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6.3.5 Fragmentation scale As is evi
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2006). This decrease in fragmentati
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Chapter 7 Outlook Our understanding
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that Pop III stars likely experienc
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to be part of an area of scientific
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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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