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with mass and accretion rate is quite similar to the results of these more detailed previous studies, and here serves to highlight the relevant physics. During the next phase, the protostellar radius begins to shrink due to Kelvin-Helmholtz contraction. The major source of opacity in the interior of the protostar is electron scattering, which is independent of density and temperature. This along with hydrostatic equilibrium yields the mass-luminosity relation L∗ ∝ M 3 ∗ . Using figure 4 of Omukai and Palla (2003), we normalize this relation as follows: L∗II 10 4 L⊙ M∗ 10 M⊙ 3 , (2.13) where L∗II is the protostellar luminosity during the Kelvin-Helmholtz contraction phase. If we further assume that tKH tacc, we arrive at GM 2 ∗ R∗L∗ M∗ ˙M . (2.14) Using L∗ L∗II, we now find a relation for R∗II, the protostellar radius during the Kelvin-Helmholtz contraction phase: R∗II 140R⊙ M˙ M∗ −2 Mfid ˙ 10M⊙ . (2.15) In determining the evolution of Lacc, we set R∗ = R∗I at early times when the protostar is still experiencing adiabatic accretion. When M∗ ∼ 10 M⊙, after approximately 800 yr of accretion, the value of R∗II falls below that of R∗I. At this point, we estimate that Kelvin-Helmholtz contraction has com- menced and switch to setting R∗ = R∗II. The resulting transition in the 44
Figure 2.12: Impact of feedback on the accretion process. Solid red line is the accretion luminosity Lacc of the most massive sink versus time, calculated using R∗ = R∗I at early times and R∗ = R∗II at later times, as described in the text. In determining Lacc we use the power-law fit to the accretion rate ( ˙ M ∝ t−0.45 ). Dotted line is the prediction of Lacc by Tan & Mckee (2004) given fd = 1 and K ′ = 1.33. Dashed line is the Eddington luminosity LEdd due to electron scattering, calculated using the sink mass. The dash - doted line is LEdd due to H − bound-free opacity, calculated at a temperature of 6000 K. Note that the kink in the curves for the accretion luminosity is an artefact of our idealized modelling of protostellar structure. 45
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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
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 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: disk accretion onto a primordial pr
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
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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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the stars grow to larger masses (se
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Here, Σ is the disk surface densit
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which has already detected GRBs at
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M⊙. They find that the specific a
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are initialized at high z with smal
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M⊙, where Nneigh 32 is the typic
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Figure 5.1: Top panels: Effective v
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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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