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Chapter 3 Mass Growth Under Protostellar Feedback 1 3.1 Introduction Previous work has found that Pop III stars begin as very small proto- stars of initial mass ∼ 5 × 10 −3 M⊙ (Omukai and Nishi 1998; Yoshida et al. 2008). Continued accretion onto the protostar over time ultimately leads to stars significantly larger than the initial seeds (e.g. Omukai and Palla 2003; Bromm and Loeb 2004). The final mass reached by Pop III stars therefore depends on the rate and duration of the accretion. Early numerical studies found that Pop III stars are likely to reach very high masses (> ∼ 100 M⊙; e.g. Abel et al. 2002; Bromm et al. 2002). The lack of metal and dust cooling in primordial gas leads to higher temperatures and greater accretion rates as compared to current star-forming regions such as the giant molecular clouds within the Milky Way. The accretion history of Pop III stars depends critically on the radiative feedback exerted during their growth phase, an effect not included in the earliest three-dimensional simulations. The strength of protostellar feedback in turn hinges upon the three-dimensional structure of the surrounding gas. For instance, Omukai and Inutsuka (2002) find that for spherically symmetric accretion onto an ionizing star, the formation of an H ii region in fact does not 1 Large portions of this chapter have been submitted for publication in MNRAS. Reproduced by permission of John Wiley and Sons. 54
impose an upper mass limit to Pop III stars. Similarly, the analytical study by McKee and Tan (2008) found that Pop III stars can grow to greater than 100 M⊙ even as a protostar’s own radiation ionizes its surroundings. Although the ionization front will expand along the polar regions perpendicular to the disk, mass from the disk itself can continue to accrete onto the star until this is halted through photoevaporation. Recent studies of present-day star formation also support the picture that stars can reach very high masses through disk accretion. For instance, numerical studies by Krumholz et al. (2009) and Kuiper et al. (2011) both find that strong feedback from radiation pressure will not halt mass flow through the stellar disk before the star has reached > ∼ 10 M⊙. The final stellar masses are likely even greater, though the simulations were not followed for sufficiently long to determine this. There is also growing observational evidence that massive star-forming regions exhibit disk structure and rotational motion (e.g. Cesaroni et al. 2007; Beuther et al. 2009). Meanwhile, the picture of a single massive Pop III star forming in a minihalo has been complicated by more recent work. Simulations by Clark et al. (2008, 2011a) employing idealized initial conditions found that primordial star-forming gas can undergo fragmentation to form Pop III multiple systems, while the simulations of Turk et al. (2009) and Stacy et al. (2010) established such fragmentation also when initialized on cosmological scales. Further work revealed that gas fragmentation can occur even on very small scales (∼ 10 AU) and in the majority of minihalos, if not nearly all (Clark et al. 2011b, Greif et al. 2011). These studies tentatively imply that the typical Pop III mass may be somewhat lower than ∼ 100 M⊙. Smith et al. (2011) recently found that, even under feedback from protostellar accretion luminosity, such fragmentation may be reduced but not halted. While Smith et al. (2011) included a heating 55
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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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Page 19 and 20: describe studies that have attempte
Page 21 and 22: CRs may therefore provide a pathway
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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
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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
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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 73 and 74: 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 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
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Page 93 and 94: Figure 3.6: Projected density and t
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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 115 and 116: acc = Lres 50 AU, where: Lres 0.5
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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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