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the sound speed, and the accretion rate grows to 48 times higher than that found in Shu collapse (Hunter 1977). In our simulation, the collapse of the gas from initially more uniform densities can be expected to behave similarly to a Larson-Penston-type solu- tion (e.g. Omukai and Nishi 1998). The following accretion of this gas onto the central hydrostatic core should proceed from the ‘inside-out’ at rates similar to those found in the Shu and Larson-Penston-Hunter solutions. 2.2.2 Protostellar feedback effects As the protostellar mass grows through accretion, feedback from photoionization, heating, and radiation pressure will begin to have important effects on the accretion flow and may set the upper mass limit for both present- day and primordial stars. One important difference between feedback in primordial and present-day massive star formation is due to the existence of dust grains in the latter case. For instance, Ripamonti et al. (2002) found with their one-dimensional calculations that Pop III protostellar radiation pressure will not affect the initial collapse and early stages of accretion due to the low opacity of the infalling gas. In contrast, for present-day star formation the in- creased opacity from dust enhances the radiation pressure and can halt infall onto stars of more than a few tens of solar masses without further mechanisms to alleviate the radiative force (see summary in McKee and Ostriker 2007). On the other hand, later in the life of a present-day star, dust absorption of ionizing photons will alter the evolution of the H II region around the star, thus reducing the photoionization feedback. Omukai and Palla (2003) performed a detailed study of spherical accretion of metal-free gas onto a growing hydrostatic core. In this case, electron 12
scattering is the major source of opacity determining the Eddington luminosity LEDD and the critical accretion rate ˙ Mcrit, above which the protostellar luminosity exceeds LEDD before the protostar reaches the zero-age main se- quence (ZAMS), disrupting further accretion. As estimated in Bromm and Loeb (2004), if we assume the protostellar luminosity before the onset of hy- drogen burning is approximately the accretion luminosity, Lacc GM∗ ˙ M/R∗, and set this luminosity equal to LEDD, we find that ˙ Mcrit LEDDR∗ GM∗ ∼ 5 × 10 −3 M⊙yr −1 , (2.2) where R∗ ∼ 5 R⊙ (Bromm et al. 2001c). This approximation is quite close to that found in the calculations of Omukai and Palla (2003). It should be noted that initial accretion rates higher than ˙ Mcrit are possible since protostars begin with much larger radii and only gradually shrink during Kelvin-Helmholtz contraction. Other types of feedback also have the potential to halt protostellar accretion and set the upper mass limit of Pop III stars. McKee and Tan (2008) consider several feedback mechanisms operating during Pop III star formation, including H2 photodissociation and Lyα radiation pressure. They find, however, that the accretion rate is not significantly reduced through feedback until HII region breakout beyond the gravitational escape radius, generally occuring once the star has reached 50-100 M⊙. Omukai and Inutsuka (2002), on the other hand, find that for spherically symmetric accretion onto an ionizing star, the formation of an HII region in fact does not impose an upper mass limit to Pop III stars. As McKee and Tan (2008) determine, however, this does not remain the case for rotating inflow. 13
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: our numerical methodology in Chapte
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 and 44: Figure 2.6: Velocity field of the c
Page 45 and 46: Figure 2.7: Disk mass vs. time sinc
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
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onto the disk. The numerical experi
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that the I-front expands as an hour
Page 99 and 100:
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
Page 105 and 106:
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
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
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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
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sink B. Once on the MS, the sink A
Page 131 and 132:
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
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
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Figure 5.2: Effect of relative stre
Page 153 and 154:
Using cs ∝ T 1/2 results in ρ
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Figure 5.4: Evolution of gas proper
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a much smaller contribution from <
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abundances of HD, which also acts a
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first stars had very short lifetime
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of star-forming material. Here we t
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star formation, they found CR energ
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The GZK cutoff applies only to thos
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and virialization redshift zvir = 2
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and undergoes free-fall collapse. I
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β = 1 − −2 1/2 ɛ + 1 mHc2
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and where ΓCR(D) = 5 × 10 −29 e
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Figure 6.2: Thermal evolution of pr
Page 179 and 180:
Figure 6.3: Minimum temperature rea
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Figure 6.4: Thermal evolution of pr
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The CR energy density can now be es
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2007). When considering realistic c
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6.3.5 Fragmentation scale As is evi
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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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