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Woosley and Heger (2006) find through their stellar evolution models that very massive ∼ 20 M⊙ stars rapidly rotating at 400 km s −1 ( 40% of the break-up speed) can completely mix while on the MS, bypassing the red giant phase and becoming a Wolf-Rayet (WR) star. This evolutionary path may furthermore allow the star to retain enough angular momentum to become a GRB, particularly if the star has low-metallicity and thus experiences signif- icantly reduced mass loss compared to solar-metallicity WR stars. Yoon and Langer (2005) agree, using a different numerical methodology, that rotation- ally induced mixing will allow a low-metallicity massive star to evolve into a rapidly rotating WR star and potentially a GRB. Finally, Ekström et al. (2008a) studied the evolution of metal-free stars with a range of masses (15- 200 M⊙) and a high rotation rate of 800 km s −1 , corresponding to a fraction of 40-70% of their break-up speed. In contrast to the previous studies, in their models chemical mixing was usually not sufficient for the red giant phase to be avoided. In fact, they found that the rotating stars generally end their lives at a cooler location of the Hertzsprung-Russel diagram (HRD). In addition, rotating stars produced a higher amount of metals, compared to their non- rotating counterparts. Ekström et al. (2008a) attribute this difference to the fact that, unlike the earlier studies, they did not include the magnetic dynamo mechanism of Spruit (2002). With or without this mechanism, however, all studies conclude that stellar rotation altered the evolution and fate of low- metallicity and Pop III stars. We also point out that, though we sometimes refer to low-metallicity studies, Pop III evolution is distinct from that of low- metallicity, and results for one do not simply extrapolate to the other (e.g. Ekström et al. 2008b). This highlights the need for continued investigation of rotating metal-free stars. 96
It is apparent that the angular momentum of Pop III stars plays a key role in their evolution and death, as well as their subsequent impact on the IGM. Whereas the mass scale of the first stars has been investigated in numerous studies, their spin remains poorly understood. It is an open ques- tion whether Pop III stars can realistically attain the high spin needed for the above-mentioned processes to occur. Current observations of massive O and B-type stars in our Galaxy and the Large Magellanic Cloud show that they can indeed be rapid rotators, spinning at a significant percentage of break-up speed (a few tens of percent). They have a large range of spin, from several tens of km s −1 to well over 300 km s −1 , with an average of about 100–200 km s −1 (e.g. Huang and Gies 2008; Wolff et al. 2008). This does not necessarily apply to Pop III stars, however, which formed in a different environment. While Pop III stars formed in minihalos whose gravitational potential wells were dominated by dark matter (DM), massive stars today form within molecular clouds that are not DM dominated, and are embedded in much larger galaxies. The angular momentum in the latter case ultimately derives from galactic differential rotation on the largest scales, and turbulence in the interstellar medium (ISM) on smaller scales (see, e.g. Bodenheimer 1995). Wolff et al. (2008) argue that their measured stellar rotation rates reflect the initial conditions of the cores in which the stars formed, particularly the core turbulent speeds and resulting infall rates. To better determine the possible rotation rates of Pop III stars, it is thus necessary to study the environment specific to where they formed. To better understand the potential for the various spin-dependent evolutionary pathways of Pop III stars, we perform a three-dimensional cosmo- logical simulation that follows the evolution of primordial gas in a minihalo to densities of n > 10 12 cm −3 . Similar to Bromm and Loeb (2004) and Stacy 97
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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
Page 59 and 60: Figure 2.12: Impact of feedback on
Page 61 and 62: Figure 2.13: Comparison of specific
Page 63 and 64: the central core, eventually compri
Page 65 and 66: extending our simulation to later t
Page 67 and 68: that such a non-primordial origin t
Page 69 and 70: impose an upper mass limit to Pop I
Page 71 and 72: we use a ray-tracing scheme to foll
Page 73 and 74: 3.2.3 Sink Particle Method When an
Page 75 and 76: convenient way to directly measure
Page 77 and 78: where the sum now extends from the
Page 79 and 80: Figure 3.1: Evolution of various pr
Page 81 and 82: ased on the prescription of Omukai
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: the deaths of massive stars (see Wo
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 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
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first stars had very short lifetime
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of star-forming material. Here we t
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star formation, they found CR energ
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The GZK cutoff applies only to thos
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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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