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Figure 6.1: Penetration depth as a function of CR energy. We here assume a neutral hydrogen number density of nH = 1 cm −3 . Only clouds with radii larger than about a few hundred pc will entirely attenuate the lowest-energy CRs through ionization losses. This also implies that low-energy CRs are necessary to contribute significant ionization and heating, as those are the ones that will release most of their energy into gas clouds of size ∼ 0.1−1 kpc. their energy into the gas. In contrast, higher energy CRs will quickly travel through a minihalo without transferring much of their energy into the gas. They instead lose energy more slowly over much longer distances. Accounting for the attenuation yields CR ionization and heating rates of and ΓCR(D) = Eheat ɛmax 50 eV ɛmin These rates can also be written as ζCR(D) = ΓCR 160 dɛ dnCR dt ion dɛ e−D/Dpdɛ (6.25) nH 0Eheat . (6.26)
and where ΓCR(D) = 5 × 10 −29 erg cm −3 s −1 × Eheat nH0 6 eV 1 cm3 ɛmin 106 eV ζCR(D) = 5 × 10 −18 s −1 I(ɛ) = UCR 2 × 10−15 erg cm−3 −1 UCR 2 × 10 −15 erg cm −3 I(ɛ) (6.27) ɛmin × 106 −1 I(ɛ), (6.28) eV ɛmax ɛmin f(ɛ) x ɛ e ɛmin −D/Dpdɛ x+1 ɛmax ɛ dɛ ɛmin ɛmin . (6.29) The factor Eheat is equal to 6 eV for the minihalo case because, though CRs lose about 50 eV of energy after each ionization, only about 6 eV of that energy goes toward heating in a neutral medium (see Spitzer and Scott 1969; Shull and van Steenberg 1985). The value of Eheat increases for media with larger ionization fractions due to an increase in Coulomb interactions between the newly freed electrons and the medium, and for the ionization fractions typical of the virialization shock case, one has Eheat 26 eV. The minimum kinetic energy, ɛmin, with which the CRs impinge upon the gas clouds can be roughly estimated by assuming that during Fermi ac- celeration a particle will acquire the velocity of the shock wave itself after crossing it a single time (see Bell 1978b). This gives a minimum energy 161
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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
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Figure 2.13: Comparison of specific
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the central core, eventually compri
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extending our simulation to later t
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that such a non-primordial origin t
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impose an upper mass limit to Pop I
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we use a ray-tracing scheme to foll
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3.2.3 Sink Particle Method When an
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convenient way to directly measure
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where the sum now extends from the
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Figure 3.1: Evolution of various pr
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ased on the prescription of Omukai
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ate found at late times in our ‘n
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Figure 3.2: Evolution of various di
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Figure 3.3: Evolution of disk mass
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Figure 3.4: Temperature versus numb
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disk mass is able to level off in d
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Figure 3.6: Projected density and t
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onto the disk. The numerical experi
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that the I-front expands as an hour
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Figure 3.8: Evolution of various H
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˙ M∗ = 3πΣν, (3.18) where ν
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the discrete nature of the gas part
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stars. We also note that, despite t
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current computational limits. If ra
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the deaths of massive stars (see Wo
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It is apparent that the angular mom
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h = 0.7. To accelerate structure fo
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acc = Lres 50 AU, where: Lres 0.5
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years, up to several dynamical time
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sp = GM∗ c2 , (4.1) s where cs is
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Figure 4.2: Left: Angular momentum
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Page 127 and 128: Fig. 4.5 shows these timescales for
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Page 131 and 132: Figure 4.6: Evolution of stellar ro
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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
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Page 163 and 164: of star-forming material. Here we t
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Page 173: β = 1 − −2 1/2 ɛ + 1 mHc2
Page 177 and 178: Figure 6.2: Thermal evolution of pr
Page 179 and 180: Figure 6.3: Minimum temperature rea
Page 181 and 182: Figure 6.4: Thermal evolution of pr
Page 183 and 184: The CR energy density can now be es
Page 185 and 186: 2007). When considering realistic c
Page 187 and 188: 6.3.5 Fragmentation scale As is evi
Page 189 and 190: 2006). This decrease in fragmentati
Page 191 and 192: Chapter 7 Outlook Our understanding
Page 193 and 194: that Pop III stars likely experienc
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Page 197 and 198: Barkana, R. and Loeb, A. (2001). In
Page 199 and 200: Bromm, V., Kudritzki, R. P., and Lo
Page 201 and 202: Daigne, F., Olive, K. A., Silk, J.,
Page 203 and 204: Gao, L., White, S. D. M., Jenkins,
Page 205 and 206: Heger, A., Woosley, S. E., and Spru
Page 207 and 208: Kratter, K. M. and Murray-Clay, R.
Page 209 and 210: Machida, M. N., Omukai, K., Matsumo
Page 211 and 212: Navarro, J. F. and White, S. D. M.
Page 213 and 214: Rollinde, E., Vangioni, E., and Oli
Page 215 and 216: Simon, M., Ghez, A. M., Leinert, C.
Page 217 and 218: Tanvir, N. R., Fox, D. B., Levan, A
Page 219 and 220: Rays, volume 576 of Lecture Notes i
Page 221 and 222: Zatsepin, G. T. and Kuz’min, V. A
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