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within the first minihalos. More specifically, we aim to determine the final masses reached by the first stars, and whether the gas within a host minihalo forms a single star or fragments into a binary or small multiple system. To this end we perform a three-dimensional cosmological simulation that follows the formation of a minihalo with very high numerical resolution, allowing us to trace the evolution of its gas up to densities of 10 12 cm −3 . Unlike the study of Bromm and Loeb (2004), which employed a constrained initialization technique on scales of ∼ 150 pc, our simulation is initialized on cosmological scales. This allows the angular momentum of the minihalo to be found self- consistently, eliminating the need for an assumed spin parameter. In a fashion similar to Bromm and Loeb (2004), we represent high-density peaks that are undergoing gravitational runaway collapse using the sink particle method first introduced by Bate et al. (1995), allowing us to follow the mass flow onto the sinks well beyond the onset of collapse. The recent simulation by Turk et al. (2009), starting from cosmological initial conditions, has shown fragmentation and the formation of two high- density peaks, which are interpreted as seeds for a Pop III binary. These peaks are similar to the multiple sinks found in our simulation. Although Turk et al. employed even higher numerical resolution, they were able to follow the evolution of the high-density peaks for only ∼ 200 yr. Our sink particle method, on the other hand, enabled us to continue our calculation for several thousand years after initial runaway collapse. We could thus follow the subsequent disk evolution and further fragmentation in detail, rendering our study ideally complementary to their work. The structure of our paper is as follows. In Chapter 2.2, we discuss the basic physical ingredients determining the accretion flow, whereas we describe 10
our numerical methodology in Chapter 2.3. We proceed to present our results in Chapter 2.4, discuss the sensitivity of our results to variation in cosmological parameters (Chapter 2.5), and conclude in Chapter 2.6. 2.2 Physical Ingredients 2.2.1 Protostellar accretion Unlike the gas from which present-day stars are formed, which can typically cool to ∼ 10 K, primordial gas contained no metals and could only cool down to ∼ 100 K through H2 and HD line transitions. These elevated temperatures lead to a higher accretion rate, which can be estimated on dimensional grounds by assuming that the Jeans mass is infalling at the free-fall rate, resulting in ˙ M c3 s G ∝ T 3/2 , (2.1) where cs is the soundspeed. This is quite close to the Shu (1977) similarity solution for collapse of a singular isothermal sphere, which gives ˙ M = 0.975c 3 s /G. The Shu solution begins with an isothermal cloud with ρ ∝ r −2 and initially negligible infall velocities. The solution then describes the subsequent ‘inside- out’ collapse of the cloud, which physically corresponds to accretion of mass onto the central protostar. The earlier similarity solution of Larson (1969) and Penston (1969) described the collapse of an initially uniform cloud into a peaked structure with an r −2 density profile. This solution was later ex- panded by Hunter (1977) to capture the evolution after the initial formation of a hydrostatic core when it grows via accretion of the envelope. At the point of initial protostar formation, corresponding to when the central density be- comes infinite in the similarity solution, the infall velocity is already 3.3 times 11
Page 1 and 2: Copyright by Athena Ranice Stacy 20
Page 3 and 4: New Insights into Primordial Star F
Page 5 and 6: 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: expected that some of the gas withi
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 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
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where the sum now extends from the
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Figure 3.1: Evolution of various pr
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ased on the prescription of Omukai
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ate found at late times in our ‘n
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Figure 3.2: Evolution of various di
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Figure 3.3: Evolution of disk mass
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Figure 3.4: Temperature versus numb
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disk mass is able to level off in d
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Figure 3.6: Projected density and t
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onto the disk. The numerical experi
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that the I-front expands as an hour
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Figure 3.8: Evolution of various H
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˙ M∗ = 3πΣν, (3.18) where ν
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the discrete nature of the gas part
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stars. We also note that, despite t
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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
Page 199 and 200:
Bromm, V., Kudritzki, R. P., and Lo
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Daigne, F., Olive, K. A., Silk, J.,
Page 203 and 204:
Gao, L., White, S. D. M., Jenkins,
Page 205 and 206:
Heger, A., Woosley, S. E., and Spru
Page 207 and 208:
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.
Page 213 and 214:
Rollinde, E., Vangioni, E., and Oli
Page 215 and 216:
Simon, M., Ghez, A. M., Leinert, C.
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Tanvir, N. R., Fox, D. B., Levan, A
Page 219 and 220:
Rays, volume 576 of Lecture Notes i
Page 221 and 222:
Zatsepin, G. T. and Kuz’min, V. A
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