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Figure 6.5: Thermal evolution of primordial gas in a minihalo under the effect of a PISN explosion 100 pc away (left column) and 10 pc away (right column). The PISN is assumed to emit CRs for 2×10 5 yr with a minimum CR energy of 10 6 eV. We assume that the CR flux reaches the cloud during different stages in its collapse, characterized by the corresponding densities: nH = 1 cm −3 (top row) and nH = 10 2 cm −3 (bottom row). The dashed lines show the evolution without CR flux prsent. The dotted lines show the CMB temperature floor at z = 20. Notice that the cloud has to be extremely close to the explosion site (d ∼ 10 pc) to experience a significant effect. Such close proximity, however, is very unlikely due to the strong radiative feedback from the PISN progenitor. 170
2007). When considering realistic cases where the gas evolution in minihaloes could have been significantly impacted by CRs, one therefore needs to invoke a universal background that consists of the global contributions to the CR flux, as opposed to the burst-like emission from a single nearby PISN. However, at close distances the local CR feedback may still provide another source of ionization in nearby gas clouds, indirectly leading to increased molecular cooling, thus helping to facilitate collapse and possibly formation of lower-mass stars, as discussed below in Chapter 6.3.5. 6.3.4 Dependence on minimum CR energy One of the crucial uncertainties concerning high-redshift CRs is the minimum energy ɛmin of the CRs that impinge upon a primordial cloud. Our default value of ɛmin=10 6 eV derives from a simple estimate for the lowest possible energy that a CR proton could gain in a SN shock, though other processes may influence this value, possibly increasing or decreasing it. The minimum CR kinetic energy, however, is crucial, because the ionization cross section varies roughly as ɛ −1 CR for non-relativistic CRs with kinetic energies less than their rest mass energy but greater than ∼10 5 eV, the energy corresponding to a velocity of β0 0.01. Thus, higher-energy CRs will travel farther into the cloud before first ionizing a particle. Only lower-energy CRs will release a large portion of their energy into the cloud, and their absence can significantly lower the overall heating and ionization rate inside the cloud. This is espe- cially apparent when looking at how the thermal evolution of the minihalo (Fig. 6.2) changes when ɛmin is increased. For typical star formation rates and ɛmin = 10 8 eV, the impact of CRs becomes negligible. It is furthermore interesting to note that for a given UCR and low ɛmin values (∼ 10 6 eV), using a 171
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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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Figure 4.6: Evolution of stellar ro
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Page 151 and 152: Figure 5.2: Effect of relative stre
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Page 155 and 156: Figure 5.4: Evolution of gas proper
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Page 173 and 174: β = 1 − −2 1/2 ɛ + 1 mHc2
Page 175 and 176: and where ΓCR(D) = 5 × 10 −29 e
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
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Page 189 and 190: 2006). This decrease in fragmentati
Page 191 and 192: Chapter 7 Outlook Our understanding
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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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