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educes the LW dissociation rate. This self-shielding factor depends upon the H2 column density NH2. With the above ray-tracing scheme, we determine NH2 along each ray by summing the contribution from each bin. We then use results from Draine and Bertoldi (1996) to determine the value for fshield. We note a recent update to their fshield fitting formula (Wolcott-Green et al. 2011; Wolcott-Green and Haiman 2011), but do not expect this to significantly affect the results for our particular case. Because of the unusually high column densities within the molecular disk (NH2 > ∼ 10 26 cm −2 ), we calculate fshield using equation 37 from Draine and Bertoldi (1996), which is more accurate for large NH2 than their simple power-law expression in their equation 36. These heating, ionization, and dissociation rates are accounted for at every timestep, while the ray-tracing procedure is performed every fifth timestep. The rates are updated every 10 yr as they evolve with the protostellar mass and accretion rate, because these determine the values of L∗ and Teff. 3.2.6 Protostellar evolution model Our ray-tracing algorithm requires an input of protostellar effective temperature Teff and luminosity L∗. This is the sum of Lacc, the accretion luminosity, and Lphoto, the luminosity generated at the protostellar surface: L∗ = Lacc + Lphoto = GM∗ ˙M R∗ + Lphoto, (3.9) where M∗ is the protostellar mass, ˙M the accretion rate, and R∗ the protostellar radius. The photospheric luminosity is either due to Kelvin Helmholtz 64
Figure 3.1: Evolution of various properties of the growing protostar according to our analytical model. Solid blue lines represent the protostellar values used in our ‘with-feedback’ simulation. Dashed lines represent the ZAMS stellar values for the current sink mass. Dotted lines represent the ‘slow contraction’ case in which the accretion rate initially evolves in the same fashion as in the ‘with-feedback’ simulation, but then holds steady at 10−3 M⊙. (a): Protostellar luminosity. Dash-dotted line is the estimate for LKH of a 15 M⊙ star of radius 10 R⊙. (b): Effective temperature. (c): Protostellar radius. (d): Ionizing luminosity, ˙Nion. Dashed-triple-dotted line represents the accretion rate of neutral particles onto the sink, extrapolated from the powerlaw fit to sink accretion rate over the first 500 years ( ˙ M ∝ t0.56 acc , see Chapter 3.3.4). Note how the ZAMS values used after 1000 years in our simulation yield a good approximation to the more physically realistic ‘slow-contraction’ case. Both also predict a break-out of ionizing radiation beyond the sink just before 1000 yr, when ˙ Nion exceeds the influx of neutral particles. 65
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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
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 and 76: convenient way to directly measure
Page 77: where the sum now extends from the
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
Page 127 and 128: 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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