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Figure 4.3: Ratio of the energy of sink-accreted particles to the specific gravitational energy of the sinks (v 2 cent = GMsink/racc). Solid lines are for sink A, and dashed lines are for sink B. Upper (black) lines of each line type represent the energy of rotational motion, middle (green) lines represent the energy of radial motion, and lower (blue) lines represent thermal energy. For both sinks, the rotational energy component dominates for the majority of the accretion time, and a thin Keplerian disk is likely to develop on sub-sink scales. 110
steadily grows for the rest of the calculation. This relatively large amount of rotational energy and low amount of thermal and radial energy for both sinks implies that their sub-sink disks will become thin and Keplerian. A comparison of the cooling time, tcool, with the timescale for angular momentum loss, tam, of the gas around the sinks gives further supporting evidence for sub-sink, thin, Keplerian disks. We calculate tam directly from the simulation by recording the acceleration on each gas particle and determining the torque due to numerical viscosity (τvisc) as well as the torque exerted by gravity and pressure (τgrav and τpres). The total torque on a given particle within a gas cloud is given by where and τtot = τgrav + τpres + τvisc = mSPH d × (agrav + apres + avisc) , (4.4) tam JSPH/|τtot| , (4.5) tcool nkBT Λ , (4.6) with kB being the Boltzmann constant, T the gas temperature, and Λ the cooling rate (in erg cm −3 s −1 ). We find that τgrav and τpres dominate, accounting for 80% of the total. Fig. 4.4 shows the z-component, perpendicular to the disk plane, of the specific torque acting upon the gas within the large-scale disk, as measured from the location of sink A. The spiral structure indicates the dominance of gravitational torques which remove angular momentum from the center of the disk on timescales of 100 − 1000 years, enabling disk material to be accreted onto the sinks. 111
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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
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: through the disk, and the disk is e
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
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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
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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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