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with respect to the sink is denoted by rI. ˙Nion is the number of ionizing photons emitted per second, and αB is the case B recombination coefficient. We use αB = 1.3 × 10 −12 cm 3 s −1 for He iii recombinations to He ii, and αB = 2.6 × 10 −13 cm 3 s −1 for He ii and H ii recombinations to the ground state (Osterbrock and Ferland 2006). The emission rate of H i, He i and He ii ionizing photons is given by Nion ˙ = πL∗ σSBT 4 ∞ eff νmin Bν dν , (3.2) hν where h is Planck’s constant, σSB the Stefan-Boltzmann constant, and νmin the minimum frequency required for ionization of the relevant species (H i or He ii). For simplicity we do not distinguish between the H ii and He ii regions. We assume the sink emits a blackbody spectrum Bν with an effective temperature Teff, which depends upon the evolving stellar radius and luminosity. As described in Greif et al. (2009), the integral on the right-hand side of the ionization front equation is discretized by the following sum: rI 0 nen+r 2 dr i ne,in+,ir 2 i ∆ri , (3.3) where ∆ri is the radial extent of each bin i, and the sum ranges from the sink particle to the current position of the I-front. The left hand side of the ionization front equation is similarly discretized by: nnr 2 I drI dt 1 ∆t 62 i nn,ir 2 i ∆ri , (3.4)
where the sum now extends from the I-front position at the previous timestep t0 to its position at the current timestep t0 + ∆t. The above-described ray- tracing is performed separately for the H ii and He iii regions. 3.2.5 Photoionization and Heating Particles determined to be within the extent of the H ii and He iii regions are given additional ionization and heating rates in the chemistry solver: and Γ = nn kion = ∞ νmin ∞ νmin Fνσν Fνσν dν (3.5) hν 1 − νmin ν dν , (3.6) where Fν is the incoming specific flux and σν the photo-ionization cross section. For a blackbody, we have Fν = where r is the distance from the sink. by L∗ 4σT 4 eff r2 Bν , (3.7) Finally, H2 dissociation by LW radiation (11.2 to 13.6 eV) is described kH2 = 1.1 × 10 8 fshield FLW s −1 (3.8) (Abel et al. 1997), where FLW denotes the radiation flux, in units of erg s −1 cm −2 Hz −1 , at hν = 12.87eV, and fshield is the factor by which H2 self-shielding 63
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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
Page 25 and 26: our numerical methodology in Chapte
Page 27 and 28: scattering is the major source of o
Page 29 and 30: portance. The reaction rates for an
Page 31 and 32: The size of the refinement levels h
Page 33 and 34: the sink a temperature and pressure
Page 35 and 36: same time, such as the fragments in
Page 37 and 38: Figure 2.2: Physical state of the c
Page 39 and 40: 2.4.2 Protostellar accretion 2.4.2.
Page 41 and 42: Despite some amount of rotational s
Page 43 and 44: Figure 2.6: Velocity field of the c
Page 45 and 46: Figure 2.7: Disk mass vs. time sinc
Page 47 and 48: Figure 2.8: Angular momentum struct
Page 49 and 50: sink tform [yr] Mfinal [M⊙] rinit
Page 51 and 52: 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: convenient way to directly measure
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 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
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Fig. 4.5 shows these timescales for
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sink B. Once on the MS, the sink A
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Figure 4.6: Evolution of stellar ro
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sink M∗(5000 yr) [M⊙] M∗(10 5
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present here, particularly if the s
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the stars grow to larger masses (se
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Here, Σ is the disk surface densit
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which has already detected GRBs at
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M⊙. They find that the specific a
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are initialized at high z with smal
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M⊙, where Nneigh 32 is the typic
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Figure 5.1: Top panels: Effective v
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Figure 5.2: Effect of relative stre
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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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