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et al. (2010), we represent gravitationally collapsing high-density peaks using the sink particle method first introduced by Bate et al. (1995). This allows us to follow the mass flow onto the sinks for many (∼ 100) dynamical times. As a sink particle grows in mass, the angular momentum of the accreted mass is recorded, allowing us to measure the total angular momentum of the sink and estimate the spin of the Pop III star represented by the sink. This is very similar to the method used in Jappsen and Klessen (2004) when they studied the angular momentum evolution of protostellar cores, though their calculation had lower resolution and was designed to study modern-day star formation as seen in the ISM. We give further details concerning our numerical methodology in Chapter 4.2, while in Chapter 4.3 we present our results, including estimates of the stellar rotation rate. In Chapter 4.4 we discuss the implications for the evolution and death of Pop III stars, and in Chapter 4.5 we address the possibility of sub-sink fragmentation. We summarize our main conclusions in Chapter 4.6. 4.2 Numerical Methodology 4.2.1 Initial Setup Similar to the method used in Stacy et al. (2010), we carry out our study using GADGET, a three-dimensional smoothed particle hydrodynamics (SPH) code (Springel et al. 2001; Springel and Hernquist 2002). We perform the final part of the simulation described in Stacy et al. (2010) again, starting from approximately 4000 years (∼ 100 free-fall times) before the first sink particle forms. This simulation was originally initialized at z = 99 in a periodic box of length 100 h −1 kpc using both SPH and DM particles. This was done in accordance with a ΛCDM cosmology with ΩΛ = 0.7, ΩM = 0.3, ΩB = 0.04, and 98
h = 0.7. To accelerate structure formation, we chose an artificially enhanced normalization of the power spectrum of σ8 = 1.4. We have verified that the density and velocity fields in the center of the minihalo are very similar to previous simulations. Even though we used an artificially high value of σ8, the angular momentum profile of our minihalo just before sink formation was still very similar to that of other cosmological simulations which used lower σ8 values. In particular, the cosmological simulation of Yoshida et al. (2006), which used σ8 = 0.9, and that of Abel et al. (2002), which used σ8 = 0.7, resulted in minihalo profiles which were especially similar to ours on the smaller scales from which the mass of the sinks is accreted. This demonstrates that our realization leads to conditions that are typical for primordial star formation (see the discussion in Stacy et al. 2010). To achieve high resolution we employed a standard hierarchical zoom-in procedure (see Stacy et al. 2010 for further details). This involved adding three additional nested refinement levels of length 40, 30, and 20 kpc (comoving) centered on the site where the first minihalo will form. Each level of higher refinement replaces particles from the lower level with eight child particles such that in the final simulation a parent particle is replaced by up to 512 child particles. The highest-resolution gas particles have a mass of mSPH = 0.015 M⊙. Therefore, the mass resolution of the refined simulation is: Mres 1.5NneighmSPH < ∼ 1 M⊙, where Nneigh 32 is the typical number of particles in the SPH smoothing kernel (e.g. Bate and Burkert 1997). The main difference between the current simulation and that described in Stacy et al. (2010) is that we now record the angular momenta and velocities of the sink-accreted particles before they become incorporated into the sinks. This allows us to track the total spin of the sink particles as they grow in mass. 99
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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
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 and 110: the deaths of massive stars (see Wo
Page 111: It is apparent that the angular mom
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
Page 161 and 162: 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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