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hierarchical zoom-in procedure (see Stacy et al. 2010 for more details). We added three additional nested refinement levels of 40, 30, and 20 kpc (comov- ing), centered on the location where the first minihalo will form. At each level of refinement, we replaced every ‘parent’ particle with eight ‘child’ particles, such that at the highest refinement level each parent particle has been replaced with 512 child particles. The highest-resolution gas particles have a mass mSPH = 0.015 M⊙, so that the mass resolution is Mres 1.5NneighmSPH < ∼ 1 M⊙, where Nneigh 32 is the typical number of particles in the SPH smoothing kernel (e.g. Bate and Burkert 1997). 3.2.2 Chemistry, Heating, and Cooling We use the same chemistry and cooling network as described in Greif et al. (2009). The code follows the abundance evolution of H, H + , H − , H2, H + 2 , He, He + , He ++ , and e − , as well as the three deuterium species D, D + , and HD. All relevant cooling mechanisms are accounted for, including H2 cooling through collisions with He and H atoms and other H2 molecules. Also included are cooling through H and He collisional excitation and ionization, recombi- nation, bremsstrahlung, and inverse Compton scattering. We finally note that H2 cooling through collisions with protons and electrons is included, as they play an important role within H ii regions (Glover and Abel 2008). One important difference we note between the high density (n > ∼ 10 9 cm −3 ) evolution in the current simulation and that of Stacy et al. (2010) is that we here account for the optical thickness of the H2 ro-vibrational lines, which reduces the effectiveness of these lines in cooling the gas. We include this effect using the Sobolev approximation (see Yoshida et al. 2006; Greif et al. 2011 for more details). 58
3.2.3 Sink Particle Method When an SPH particle reaches a density of nmax = 10 12 cm −3 , we convert it to a sink particle. If a gas particle is within the accretion radius racc of the sink, and if it is not rotationally supported against infall onto the sink, the sink accretes the particle. The sink thus accretes the particles within its smoothing kernel immediately after it first forms. We check for rotational support by comparing the angular momentum of the nearby gas particle, jSPH = vrotd, with the angular momentum required for centrifugal support, jcent = √ GMsinkracc, where vrot and d are the rotational velocity and distance of the particle relative to the sink. If a gas particle satisfies both d < racc and jSPH < jcent, it is removed from the simulation, and the mass of the accreted particle is added to that of the sink. Our sink accretion algorithm furthermore allows for the merging of two sink particles. We use similar criteria for sink particle merging as for sink accretion. If the smaller, secondary sink is within racc of the more massive sink and has specific angular momentum less than jcent of the larger sink, the sinks are merged. After an accretion or merger event, the position of the sink is set to the mass-weighted average of the sink’s former position and that of the accreted gas or secondary sink. The same is done for the sink velocity. We note that, as discussed in Greif et al. (2011), modifications to the sink merging alogorithm can significantly alter the sink accretion history. Future work will include studies of how a different technique for sink merging would modify our results. We set the accretion radius equal to the resolution length of the simulation, racc = Lres 50 AU, where 59
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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
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 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: we use a ray-tracing scheme to foll
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
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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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