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energy conservation, ESN 1 2Meju2 sh , then indicates that the shock velocities of these different SNe will be similar. This also leads to similar estimates for ɛmin for both cases since the minimum CR energy is expected to depend on shock velocity. For a given star formation rate the results of our study would therefore change little if the source of CRs were CCSNe instead of PISNe. It should be pointed out that the explosion mechanism of the highest- mass CCSNe progenitors, ∼ 40 M⊙, is still somewhat uncertain and may be associated with very high explosion energies comparable to that of PISNe, though if most of the CCSNe derive from lower-mass progenitors they should still have lower explosion energies as argued above. Furthermore, we emphasize that the choice of PISNe versus CCSNe is not crucial for our study as long as there exists some source of sufficient CR production. These sources do not necessarily have to be only PISNe. Constraints on the number of PISNe in the early Universe, such as provided by the problem of overproduction of metals in the IGM by PISNe (e.g. Venkatesan and Truran 2003; Tumlinson et al. 2004; Daigne et al. 2006), will therefore not affect the relevance of this study. Finally, it is worth noting that the CR energy densities used in this paper are well-within upper limits placed by previous studies. For instance, one of the constraints that can be used to place an upper limit on UCR is the 6 Li plateau observed in metal-poor Galactic halo stars. While a number ratio of 6 Li/H 10 −11 is observed (Asplund et al. 2006), the much smaller ratio 6 Li/H 10 −14 is predicted by big bang nucleosynthesis (BBN). In Rollinde et al. (2005, 2006), the overabundance of 6 Li compared to predictions from BBN is assumed to have come from CRs generated by the first stars. In Rollinde et al. (2005) this assumption was used to derive an upper limit on the high-z CR energy density. Assuming a model with a single burst of Pop III 150
star formation, they found CR energy densities at the time of these bursts to range from approximately 10 −10 to 10 −12 erg cm −3 for burst times ranging from z = 100 to z = 10. Such limits are roughly three orders of magnitude larger than the UCR values used in our investigation, so that we do not violate any known constraints on CR production in the early Universe. 6.2.3 High-redshift GZK cutoff The Greisen-Zatsepin-Kuzmin (GZK) cutoff is an upper limit to the energy of a CR if it is extragalactic in origin and thus has traveled through the sea of CMB photons (Greisen 1966; Zatsepin and Kuz’min 1966). This limit exists because of interactions between CRs and CMB photons which lead to photo-pion and pair production, reducing the energy of the CR for each interaction. The reactions for pair production and photo-pion production, respectively, are (e.g. Berezinskii and Grigor’eva 1988) p + + γ → p + + e + + e − , (6.7) p + + γ → π + + n , (6.8) p + + γ → π 0 + p + . (6.9) Photo-pion production is the most important interaction for CR pro- tons (De Marco 2005). However, this reaction can only take place if the energy of a CMB photon is above the energy threshold of ɛt = 140 MeV, but this is possible in the rest frame of CRs with sufficiently large Lorentz factors (e.g. Longair 1994). The reaction will continue until the CR energy falls below the 151
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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
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
Page 129 and 130: sink B. Once on the MS, the sink A
Page 131 and 132: Figure 4.6: Evolution of stellar ro
Page 133 and 134: sink M∗(5000 yr) [M⊙] M∗(10 5
Page 135 and 136: present here, particularly if the s
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Page 139 and 140: Here, Σ is the disk surface densit
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Page 143 and 144: M⊙. They find that the specific a
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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 159 and 160: abundances of HD, which also acts a
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Page 163: of star-forming material. Here we t
Page 167 and 168: The GZK cutoff applies only to thos
Page 169 and 170: and virialization redshift zvir = 2
Page 171 and 172: and undergoes free-fall collapse. I
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
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
Page 195 and 196: to be part of an area of scientific
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
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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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