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Figure 3.9: Effect of radiative feedback on protostellar accretion. Black solid line shows mass growth with no radiative feedback, while black dotted line shows the ‘with-feedback’ case. The blue solid line is a double powerlaw fit to the sink growth rate for the ‘no-feedback’ case, and the red dotted line is a fit to the first 500 yr of the ‘with-feedback’ case. The red dashed line shows a conservative upper limit for continued sink growth in the ‘with-feedback’ case not seen in the simulation. Radiative feedback leads to a divergence in the accretion histories in less than 1000 yr, and in the ‘with-feedback’ case the sink does not grow beyond ∼ 20 M⊙ in the time of the simulation. 88
the discrete nature of the gas particles means that the average accretion rate after this point could be below ∼ 10 −5 M⊙ yr −1 over timescales on the order of 1000 yr without being resolved. Given the disruption of the disk in both cases at later times, let us estimate by how much the sink accretion rate should truly decline. In the ‘with-feedback’ case, by 3000 years of sink accretion the mass of gas in the disk has declined from 40 M⊙ to < ∼ 10 M⊙, over a factor of four. Σ thus decreases by the same amount. The disk temperature also decreases from 1000 to 600 K. Considering equations (18) and (19), this implies that the accretion rate should decrease by an order of magnitude, from 2 × 10 −2 M⊙ yr −1 over the first 1000 years to ∼ 10 −3 M⊙ yr −1 afterwards. A future simulation with improved resolution might thus show further sink growth, in this case to roughly 20 M⊙ after 5000 yr (see Fig. 3.9). In the ‘no-feedback’ case, at 1000 yr the disk mass has dropped to slightly more than half of its value at the time of initial sink formation, and the mass continues to decline further to one-fourth the intial value. If we also account for an increase in disk size due to angular momentum conservation, then Σ decreases by nearly an order of magnitude. The disk temperature has also dropped from 1000 to 500 K by the end of the simulation (see Figure 3.2), leading to a decrease in cs. From this we approximate that the sink accretion rate should again drop by over an order of magnitude after 1000 years, which indeed occurs for the ‘no-feedback’ case. 3.4 Summary and Discussion We have performed cosmological simulations of the build-up of a Pop III star to determine how LW and ionizing radiative feedback influences the mass growth of the star and the fragmentation of primordial gas. We find 89
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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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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
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Page 67 and 68: that such a non-primordial origin t
Page 69 and 70: impose an upper mass limit to Pop I
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Page 73 and 74: 3.2.3 Sink Particle Method When an
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Page 77 and 78: where the sum now extends from the
Page 79 and 80: Figure 3.1: Evolution of various pr
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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: ˙ M∗ = 3πΣν, (3.18) where ν
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
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Page 139 and 140: Here, Σ is the disk surface densit
Page 141 and 142: which has already detected GRBs at
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Page 145 and 146: are initialized at high z with smal
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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
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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
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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
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Chapter 7 Outlook Our understanding
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that Pop III stars likely experienc
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to be part of an area of scientific
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Barkana, R. and Loeb, A. (2001). In
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Bromm, V., Kudritzki, R. P., and Lo
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Daigne, F., Olive, K. A., Silk, J.,
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Gao, L., White, S. D. M., Jenkins,
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Heger, A., Woosley, S. E., and Spru
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Kratter, K. M. and Murray-Clay, R.
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Machida, M. N., Omukai, K., Matsumo
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Navarro, J. F. and White, S. D. M.
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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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