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Figure 4.7: Angular momentum relative to the center of the stars, assuming they have grown to a mass of 100 M⊙ and have an approximate radius of 5 R⊙. Thick black solid line represents the situation of Keplerian rotation where J(r) = JKep(r). The thin diagonal lines represent the case of J(r) = ɛ JKep(r). For sink A (solid line), ɛ = 0.45 was used. For sink B (dashed line), we used a smaller value of ɛ = 0.35. Blue line (labeled as “collapsar”) shows JISCO. Red line (labeled as “mixing”) shows 0.4 ∗ Jbreak−up, the approximate minimum angular momentum necessary for a low-metallicity star to undergo rotational mixing and chemically homogeneous evolution, as determined by Yoon and Langer (2005) and Woosley and Heger (2006). The angular momentum requirement for the collapsar engine, J > JISCO, is easily met on sub-sink scales. Rotational mixing will readily occur as well as the stars approach their break-up speed. 120
present here, particularly if the stars do indeed rotate at nearly full break- up speed (see Fig. 4.7). This will have important implications for Pop III feedback. Effective temperatures of stars that undergo such rotational mixing can reach up to an order of magnitude higher than corresponding non-rotating stars, while luminosities may be two to three times as high (see, e.g. Yoon and Langer 2005). This will lead to an increased emission of ionizing radiation at harder wavelengths, so the HII regions will be larger than expected from non-rotating models of stars of the same mass (e.g. Greif et al. 2009). It is important to note that these results do vary depending upon metallicity and details of the stellar model. For instance, in contrast to earlier studies, Ekström et al. (2008a) find that even rotational speeds of up to 70% of break-up speed will not be sufficient to drive chemically homogeneous evolution. However, they do find rotation to increase the MS lifetime by 10-25%, which again would increase the total amount of ionizing radiation from rotating massive Pop III stars. A final distinction between rotating and non-rotating Pop III evolution is that rotating models generally yield higher total amounts of metals by the end of their nucleosynthesis (Ekström et al. 2008a). De- pending on how this metallicity gets spread to the star’s surroundings through stellar winds and SN explosions, higher metallicity will enhance the later cool- ing and collapse of gas when subsequent generations of stars form, most likely lowering their average mass (e.g. Omukai 2000; Bromm et al. 2001b; Schneider et al. 2006; Frebel et al. 2007, 2009; Greif et al. 2010) 4.4.2 GRBs and Hypernovae The final fate of the stars in our simulation will depend on the mass they reach through accretion, though computational limitations prevent us 121
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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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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
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Page 93 and 94: Figure 3.6: Projected density and t
Page 95 and 96: onto the disk. The numerical experi
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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
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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
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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
Page 161 and 162: first stars had very short lifetime
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Page 165 and 166: star formation, they found CR energ
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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
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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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