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CR parameter values, Fig. 6.3 shows the minimum temperature Tmin reached by the minihalo gas versus UCR and spectral index x given a constant ɛmin = 10 6 eV. It is evident that the cloud can cool to temperatures near the CMB floor for UCR values ranging over nearly four orders of magnitude. At extremely high values of UCR that are near the upper limit set by the 6 Li measurements, CR-induced heating begins to overcome cooling effects, and the minihalo gas can no longer reach temperatures near the CMB floor. Also, for shallower spectral indices, much less of the CR energy density is distributed at low energies. For these shallower power laws, CRs thus cause only negligible change in the minimum gas temperature since they yield almost no heating or cooling of the gas. Examination of Fig. 6.2 and the corresponding ionization rates for each case show that CRs can facilitate cooling in the minihalo to nearly the CMB floor if the ionization rate is greater than approximately 10 −19 s −1 . Any rate below this yields negligible cooling. Considering the dependence of the ionization rate on ɛmin and UCR in Equ. (6.28) and Equ. (6.29) for the minihalo case, we can write ζCR ≈ 10 −19 s −1 UCR 2 × 10 −15 erg cm −3 ɛmin 107 −1.3 . (6.30) eV Recalling the dependence of UCR on redshift and Ψ∗ from Equ. (6.4), we find that there will be sufficient ionization, so that the CR-induced cooling will be significant in the minihalo, if the following condition is met: Ψ∗ 10 −2 M⊙ yr −1 Mpc −3 1 + z 21 164 3 2 ɛmin 107 −1.3 > eV ∼ 1 . (6.31)
Figure 6.3: Minimum temperature reached by the minihalo gas versus UCR (top panel) and spectral slope x (bottom panel). The dotted lines denote the CMB temperature, and the dashed line in the upper panel is the upper bound on UCR based on constraints from the 6 Li measurements. Here ɛmin is kept constant at 10 6 eV. Note that the cloud cools nearly to the CMB floor for UCR values ranging over almost four orders of magnitude. CR-induced heating starts to overcome cooling effects and the minimum temperature begins to rise only once UCR values are near the 6 Li constraint. For shallower spectral slopes, and thus smaller numbers of low-energy CRs for a given UCR, CRs cause little cooling or heating and do not change the minimum temperature of the minihalo gas. 165
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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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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 159 and 160: abundances of HD, which also acts a
Page 161 and 162: first stars had very short lifetime
Page 163 and 164: of star-forming material. Here we t
Page 165 and 166: star formation, they found CR energ
Page 167 and 168: The GZK cutoff applies only to thos
Page 169 and 170: and virialization redshift zvir = 2
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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: Figure 6.2: Thermal evolution of pr
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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