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compared to the analytic predictions of Tan and McKee (2004). At a density and temperature of 10 8 cm −3 and 1000 K, respectively, we find a value of K ′ ∼ 1.33 from their equation (7), where K ′ is the entropy parameter, defined by K ′ = P/ργ 1.88 × 1012cgs = T 300 K nH 10 4 cm −3 −0.1 . (2.6) We estimate that the total star-disk system mass (red line in Fig. 2.7) is ∼ 100 M⊙ at the end of our simulation and set ɛ∗d equal to 1 for the no feedback case, where ɛ∗d is the fraction of infalling mass that is able to reach the star-disk system without being diverted by protostellar outflows, again in the terminology of Tan & McKee. From their equation (8), we then calculate an expected accretion rate onto the star-disk system of < ∼ 10 −2 M⊙ yr −1 . In our simulation we find that over the 5000 yr of sink accretion, mass flows onto the star-disk system very steadily at approximately the same rate of ∼ 10 −2 M⊙ yr −1 , which is also near the value for the average accretion rate onto the main sink particle (see Chapter 2.4.2.4). Fig. 2.7 further shows that once the first sink forms, the disk mass stays fairly constant at ∼ 35 M⊙ as mass falling from the outer regions onto the disk replaces the material accreted onto the sinks at similar rates. Tan and McKee (2004) furthermore predict the time needed to build up a given stellar mass in their equation (9). If we assume a value of 1 for fd, the ratio of disk to stellar mass, then the time to build up a 43 M⊙ star (the final mass of the main sink - see Chapter 2.4.2.4) is roughly 9000 yr. The simulation yields a similar though smaller value of 5000 yr, which reflects the slightly higher accretion rate of our simulation. Finally, if we estimate a value of 1 for fKep, the ratio of rotational to Keplerian velocity at the sonic point, then from equation (15) of Tan and McKee (2004) we find a predicted disk 30
Figure 2.7: Disk mass vs. time since the creation of the first sink particle (solid line). Disk particles are considered to be all gas particles, excluding sinks, with density greater than 10 8 cm −3 and a specific angular momentum within 50% of jKep. Once the first sink forms at t = 0 yr, the red line shows the total mass of the star-disk system. Also shown is the total mass of n > 10 8 cm −3 particles (sinks excluded) with temperatures less than 2500 K (dotted line) and temperatures greater than 2500 K (dashed line). 31
Page 1 and 2: Copyright by Athena Ranice Stacy 20
Page 3 and 4: New Insights into Primordial Star F
Page 5 and 6: Acknowledgments I first want to giv
Page 7 and 8: angular momentum to rotate at nearl
Page 9 and 10: 2.4.2.5 Thermodynamics of accretion
Page 11 and 12: Chapter 7. Outlook 177 Bibliography
Page 13 and 14: List of Figures 2.1 Density project
Page 15 and 16: 1.1 Motivation Chapter 1 Introducti
Page 17 and 18: leaving behind a neutron star or bl
Page 19 and 20: describe studies that have attempte
Page 21 and 22: CRs may therefore provide a pathway
Page 23 and 24: expected that some of the gas withi
Page 25 and 26: our numerical methodology in Chapte
Page 27 and 28: scattering is the major source of o
Page 29 and 30: portance. The reaction rates for an
Page 31 and 32: The size of the refinement levels h
Page 33 and 34: the sink a temperature and pressure
Page 35 and 36: same time, such as the fragments in
Page 37 and 38: Figure 2.2: Physical state of the c
Page 39 and 40: 2.4.2 Protostellar accretion 2.4.2.
Page 41 and 42: Despite some amount of rotational s
Page 43: Figure 2.6: Velocity field of the c
Page 47 and 48: Figure 2.8: Angular momentum struct
Page 49 and 50: sink tform [yr] Mfinal [M⊙] rinit
Page 51 and 52: sink (∼ 4 M⊙) that merged with
Page 53 and 54: actual final mass of the star is li
Page 55 and 56: the average temperature of all part
Page 57 and 58: disk accretion onto a primordial pr
Page 59 and 60: Figure 2.12: Impact of feedback on
Page 61 and 62: Figure 2.13: Comparison of specific
Page 63 and 64: the central core, eventually compri
Page 65 and 66: extending our simulation to later t
Page 67 and 68: that such a non-primordial origin t
Page 69 and 70: impose an upper mass limit to Pop I
Page 71 and 72: we use a ray-tracing scheme to foll
Page 73 and 74: 3.2.3 Sink Particle Method When an
Page 75 and 76: convenient way to directly measure
Page 77 and 78: where the sum now extends from the
Page 79 and 80: Figure 3.1: Evolution of various pr
Page 81 and 82: ased on the prescription of Omukai
Page 83 and 84: ate found at late times in our ‘n
Page 85 and 86: Figure 3.2: Evolution of various di
Page 87 and 88: Figure 3.3: Evolution of disk mass
Page 89 and 90: Figure 3.4: Temperature versus numb
Page 91 and 92: disk mass is able to level off in d
Page 93 and 94: Figure 3.6: Projected density and t
Page 95 and 96:
onto the disk. The numerical experi
Page 97 and 98:
that the I-front expands as an hour
Page 99 and 100:
Figure 3.8: Evolution of various H
Page 101 and 102:
˙ M∗ = 3πΣν, (3.18) where ν
Page 103 and 104:
the discrete nature of the gas part
Page 105 and 106:
stars. We also note that, despite t
Page 107 and 108:
current computational limits. If ra
Page 109 and 110:
the deaths of massive stars (see Wo
Page 111 and 112:
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
Page 137 and 138:
the stars grow to larger masses (se
Page 139 and 140:
Here, Σ is the disk surface densit
Page 141 and 142:
which has already detected GRBs at
Page 143 and 144:
M⊙. They find that the specific a
Page 145 and 146:
are initialized at high z with smal
Page 147 and 148:
M⊙, where Nneigh 32 is the typic
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
Page 157 and 158:
a much smaller contribution from <
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
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
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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