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Figure 6.6: MBE as a function of hydrogen number density for freely-falling clouds inside minihalos at z ∼ 20. The curves correspond to the evolution shown in Fig. 6.2, and we adopt the same convention for the lines. Notice that the BE mass, which gives a rough indication for the final stellar mass, can decrease by up to a factor of 10, given that a sufficient flux of low-energy CRs is present. fragmentation occurs and the BE mass is relevant, at least to zeroth order, given that star formation is too complex to allow reliable predictions from simple one-zone models such as considered here (e.g. Larson 2003). Bearing this caveat in mind, we find that, with a sufficiently strong CR flux present, the gas density at which the ‘loitering phase’ occurs is increased by a factor of ∼ 10−100, and the corresponding temperature decreased by a factor of 2 to 3. Evaluating Equ. (6.37) shows that the BE mass thus decreases by an order of magnitude down to around 10 M⊙. This is the mass scale of what has been termed ‘Pop II.5’ stars (e.g. Mackey et al. 2003; Johnson and Bromm 174
2006). This decrease in fragmentation scale occurs for CR ionization rates greater than ∼ 10 −19 s −1 . A sufficiently large flux of low-energy CRs could thus have facilitated the fragmentation and collapse of primordial minihalo gas into Pop II.5 stars. Again, we emphasize the somewhat speculative nature of our argument regarding stellar mass scales. However, the general trend suggested here, that the presence of CRs in the early Universe tends to enable lower mass star formation, might well survive closer scrutiny with numerical simulations. 6.4 Summary and Discussion We have investigated the effect of CRs on the thermal and chemical evolution of primordial gas clouds in two important sites for Pop III star formation: minihaloes and higher-mass haloes undergoing strong virialization shocks. We show that the presence of CRs has a negligible impact on the evolution in the latter case, since the primordial gas is able to cool to the CMB floor even without the help of CR ionization, and the direct CR heating is also unimportant unless extremely high star formation rates are assumed. Thus, the thermal and chemical evolution of haloes corresponding to the first dwarf galaxies is rather robust, and the CR emission from the deaths of previously formed Pop III stars will not initiate any feedback in these star formation sites. The impact of CRs on gas in minihaloes, which would typically have formed before the more massive dwarf systems, could have been much more pronounced, given a sufficiently low ɛmin and Pop III star formation rates that are not too low. In each case, the effect of direct CR heating is weaker than the indirect molecular cooling that follows from the increased ionization due to CRs. The additional molecular cooling induced by the CRs allows the gas in a 175
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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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sink M∗(5000 yr) [M⊙] M∗(10 5
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present here, particularly if the s
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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
Page 165 and 166: star formation, they found CR energ
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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
Page 183 and 184: The CR energy density can now be es
Page 185 and 186: 2007). When considering realistic c
Page 187: 6.3.5 Fragmentation scale As is evi
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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