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that radiative feedback will not prevent fragmentation, but will lower the final mass attainable by a Pop III star. Inclusion of feedback also led to a massive binary system instead of a higher-order multiple like that seen in, e.g., Stacy et al. (2010) and our ‘no-feedback’ case, since the feedback quenched disk growth and fragmentation early on. In agreement with Smith et al. (2011), we furthermore find that stellar N-body dynamics can also play a significant role in the growth of a Pop III star through stellar ejections and disk scattering. It is interesting to compare our results to that of recent work by Pe- ters et al. (2010). They similarly examine ionizing and non-ionizing radiative feedback on massive star formation, though they study the case of present-day star formation, and their initial configuration was different from ours in that they began with a 1000 M⊙ rotating molecular cloud core. They find H ii regions which fluctuate in size and shape as gas flows onto the stars, and that the final mass of the largest stars is set by ‘fragmentation-induced starvation,’ a process in which the smaller stars accrete mass flowing through the disk before it is able to reach the most massive star. This is in contrast to models in which the final stellar mass is set once ionizing radiation shuts off the disk accretion (e.g. McKee and Tan 2008). In our ‘with-feedback’ case we find that it is radiative feedback that shuts off accretion to both sinks, and that the smaller sink does not intercept any gas flow onto the main sink, simply because the infall rate is so low. A similar study of current-day star formation by Krumholz et al. (2009) found that a prestellar core would similarly collapse into a disk that would host a multiple system of massive stars, even under the effects of radiation pressure. However, they followed smaller average accretion rates over a longer period of time (50,000 yr) and found that gravitational and Rayleigh-Taylor instabilities would continue to feed mass onto the disk and 90
stars. We also note that, despite their very similar numerical setups, the disk evolution and accretion rate of our ‘no-feedback’ case differs somewhat from that described in Stacy et al. (2010). Several distinctions between the simulations, however, explain this. The high-density cooling and chemistry is updated from that used in Stacy et al. 2010 (see Chapter 3.2.2). We also use an adaptive softening length instead of a single softening length for all gas particles as in Stacy et al. (2010), and our criteria for sink accretion are slightly more stringent. The main contribution to the difference, however, is likely the stochastic nature of the sink particle dynamics. While no sink was ejected in Stacy et al. (2010), the sink ejection and subsequent rapid velocity of the main sink in our ‘no-feedback’ case altered the disk structure, and the main sink would likely have grown to a higher mass otherwise. Nevertheless, the final sink masses in both simulations were still the same to within a factor of two. The radiative feedback seen here is much stronger than the analytical prediction of McKee and Tan (2008). They found that a Pop III star could grow to over 100 M⊙ through disk accretion, as disk shadowing allowed mass to flow onto the star even while the polar regions became ionized. Our lack of resolution prevents this disk shadowing to be modeled properly on sub- sink scales, and the ionizing photon emission emanating from the sink edge is likely overestimated. McKee and Tan (2008) furthermore assumed disk axisymmetry, which does not describe the disk in either of our test cases. At various points in the ‘with-feedback’ simulation, the lack of axisymmetry allowed the sink to ionize the more diffuse parts of the disk, which would not have occured in the McKee and Tan (2008) model. Nevertheless, shielding does 91
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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
Page 53 and 54: actual final mass of the star is li
Page 55 and 56: the average temperature of all part
Page 57 and 58: 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: the discrete nature of the gas part
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 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
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Figure 5.4: Evolution of gas proper
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a much smaller contribution from <
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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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