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6.3.3 Local CR Feedback Our study thus far has assumed that the CRs possibly created in the early Universe all become part of a homogeneous and isotropic background. However, if a particular minihalo is within sufficiently close range to a CR- accelerating PISN, the flux of CRs from the nearby PISN may have a greater effect on the evolution of the minihalo than that from the CR background. The average CR luminosity associated with the PISN is given by LCR = 2 × 10 38 erg s −1 pCR 0.1 ESN × 1052 ∆tSN erg 2 × 105 yr −1 , (6.32) where ∆tSN is the time over which the PISN emits CRs, here assumed to be approximately the time that passes from the beginning of the PISN to the end of its Sedov-Taylor phase of expansion (see Lagage and Cesarsky 1983). We can then estimate the CR flux, fCR, and energy density, UCR, emitted by the PISN using fCR = LCR , (6.33) 4πd2 where d is the distance between the CR source and the minihalo. This can also be expressed as fCR 10 −4 erg cm −2 s −1 pCR × 0.1 ESN 1052 ∆tSN erg 2 × 105 −1 −2 d . (6.34) yr 100 pc 168
The CR energy density can now be estimated to be UCR fCR < βc > . (6.35) For pCR = 0.1, ESN = 10 52 erg, and ∆tSN = 2×10 5 yr, UCR can then be written as UCR 5 × 10 −15 erg cm −3 −2 ɛmax d ɛmin 100 pc ɛxdɛ ɛmax ɛmin βɛxdɛ . (6.36) This energy density is now used in Equ. (6.27) and Equ. (6.28) to determine the CR heating and ionization rates due to the CR emission from a single nearby PISN. Fig. 6.5 shows the thermal evolution of a minihalo under the influence of the CR flux from a 10 52 erg PISN at 10 and 100 pc away. The PISN was assumed to emit CRs for 2 × 10 5 yr with a minimum CR energy of 10 6 eV. The resulting CR flux begins to impinge on the minihalo at times that correspond to two different stages during the collapse, when the gas cloud reaches a density of nH = 1 cm −3 and when it reaches nH = 100 cm −3 . At 10 pc, the CR emission allows the gas cloud to cool nearly to the CMB floor, while at 100 pc distance, it causes only a slight change in the thermal evolution of the gas. We also examined the evolution at a distance of 1 kpc from the PISN, but the CR effects were negligible. For such a local burst of CR emission to have a noticeable impact on the evolution of the primordial gas, a PISN in very close proximity would be required. However, such a scenario is not very likely. In effect, a cloud at 10 pc distance from the explosion would be part of the same minihalo, and the strong UV radiation from the PISN progenitor would have evaporated any gas in its vicinity by photoionization-heating (e.g. Alvarez et al. 2006; Greif et al. 169
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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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through the disk, and the disk is e
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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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Page 155 and 156: Figure 5.4: Evolution of gas proper
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Page 177 and 178: Figure 6.2: Thermal evolution of pr
Page 179 and 180: Figure 6.3: Minimum temperature rea
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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
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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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