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Figure 4.4: Specific torque acting on the gas within the central 5000 AU of the simulation box, the region enclosing the large-scale star-forming disk. Torques are calculated at a representative time of 2500 years after the first sink forms. Shown is the z-component, perpendicular to disk plane, of all contributions to specific torque as measured from sink A. The asterisk denotes the location of sink A, the cross denotes the location of sink B, and the diamonds are the locations of the remaining lower-mass sinks. There is a total of six sinks, but this number will later be reduced through sink mergers. Note the spiral structure, where gravitational torques will remove angular momentum from the disk center on a timescale of approximately 100-1000 years. 112
Fig. 4.5 shows these timescales for the gas particles in radially averaged bins. From this we can see that for the gas surrounding each sink, tcool ∼ tam at distances greater than 1000 AU. However, at 1000 AU tcool falls below tam. This coincides well with the fact that this is the radius of the large-scale disk which embeds the whole stellar multiple system. At the sink edges, tcool is nearly an order of magnitude shorter than tam for both sinks. Thermal energy of the gas is radiated away quickly enough that rotational energy will likely remain dominant. Though torques are active, particularly gravitational ones from the spiral structure in the disk, they are unlikely to remove angular momentum quickly enough to prevent the formation of a sub-sink Keplerian disk once the central stellar mass has grown substantially. 4.3.2.2 Extrapolation to Stellar Surface If the entire extent of the sub-sink disks is indeed Keplerian and the disk self-gravity is negligible, then gas within the sinks will rotate at v(r) vKep(r) GM∗/r, where r is the distance from the star, M∗ = f∗Msink is the mass of the star, and f∗ is the sink mass fraction that ends up in the star while the remaining mass is stored in the disk. For f∗ < ∼ 1, we will have v(r) ∼ < GMsink/r. If the inneredge of the disk extends all the way to the stellar surface, which isexpected if magnetic fields are not important (see Chapter 4.6), then the gasacquired by the star from the accretion disk will be rotating at fullKeplerian velocity. a typical predicted size for a massive main- sequence (MS) Pop III star, and R∗ = 100 R⊙, a larger size expected for a Pop III protostar that has not yet begun Kelvin-Helmholtz contraction (Omukai and Palla 2003). For sink A, the protostar will have a rotational velocity up to > ∼ 200 km s −1 , while the corresponding velocity will be ∼ 100 km s −1 for 113
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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
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3.2.3 Sink Particle Method When an
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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 and 102: ˙ M∗ = 3πΣν, (3.18) where ν
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Page 105 and 106: stars. We also note that, despite t
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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
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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 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
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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
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Page 173 and 174: β = 1 − −2 1/2 ɛ + 1 mHc2
Page 175 and 176: 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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