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\@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces Image of the Universe when it first became transparent, 400 thousand years after the  Big Bang, taken over five years by the {\it  Wilkinson Microwave Anisotropy Probe} (WMAP) satellite (http://map.gsfc.nasa.gov/). Slight density  inhomogeneities at the level of one part in $\sim 10^5$ in the otherwise uniform early Universe imprinted hot and cold spots in the temperature map of the cosmic microwave background on the sky. The fluctuations are shown in units of $\mu $K, with the unperturbed temperature being 2.73 K. The same primordial  inhomogeneities seeded the  large-scale structure in the present-day Universe. The existence of background  anisotropies was predicted in a number of theoretical papers three decades before the technology for taking this image became available.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1.2}{\ignorespaces {\it  Top:} Schematic illustration of the growth of perturbations to collapsed halos through gravitational instability. Once the  overdense regions exceed a threshold density contrast above unity, they turn around and collapse to form halos. The material that makes the halos originated in the voids that separate them. {\it  Middle:} A simple model for the collapse of a spherical region. The dynamical fate of a rocket which is launched from the surface of the Earth depends on the sign of its energy per unit mass, $E={1\over 2} v^2 - GM_\oplus /r$. The behavior of a spherical shell of matter on the boundary of an  overdense region (embedded in a homogeneous and isotropic Universe) can be analyzed in a similar fashion. {\it  Bottom:} A collapsing region may end up as a galaxy, like NGC 4414, shown here (image credit: NASA and ESA). The halo gas cools and condenses to a compact disk surrounded by an extended  dark matter halo. }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  7}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1.3}{\ignorespaces  Cosmic archaeology of the observable volume of the Universe, in comoving coordinates (which factor out the cosmic expansion). The outermost observable boundary ($z=\infty $) marks the comoving distance that light has traveled since the Big Bang. Future observatories aim to map most of the observable volume of our Universe, and improve dramatically the statistical information we have about the density fluctuations within it. Existing data on the CMB probes mainly a very thin shell at the hydrogen  recombination epoch ($z\sim 10^3$, beyond which the Universe is opaque), and current large-scale galaxy surveys map only a small region near us at the center of the diagram. The formation epoch of the first galaxies that culminated with  hydrogen reionization at a redshift $z\sim 10$ is shaded grey. Note that the comoving volume out to any of these redshifts scales as the distance cubed.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  11}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1.4}{\ignorespaces Following inflation, the Universe went through several other milestones which left a detectable record. These include baryogenesis (which resulted in the observed asymmetry between matter and anti-matter), the electroweak phase transition (during which the symmetry between electromagnetic and weak interactions was broken), the QCD phase transition (during which  protons and  neutrons nucleated out of a soup of  quarks and gluons), the  dark matter decoupling epoch (during which the  dark matter decoupled thermally from the cosmic plasma),  neutrino decoupling,  electron-positron annihilation, light-element nucleosynthesis (during which  helium, deuterium and lithium were synthesized), and hydrogen  recombination. The cosmic time and CMB temperature of the various milestones are marked. Wavy lines and question marks indicate milestones with uncertain properties. The signatures that the same milestones left in the Universe are used to constrain its parameters.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  15}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1.5}{\ignorespaces Mass budgets of different components in the present day Universe and in the infant Universe when the first galaxies formed (redshifts $z=10$--50). The  CMB radiation (not shown) makes up a fraction $\sim 0.03\%$ of the budget today, but was dominant at redshifts $z>3,300$. The cosmological constant (vacuum) contribution was negligible at high redshifts ($z\gg 1$).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  17}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.1}{\ignorespaces The root-mean-square amplitude of linearly-extrapolated density fluctuations $\sigma $ as a function of mass $M$ (in  solar masses $M_\odot $, within a spherical top-hat filter) at different redshifts $z$. Halos form in regions that exceed the background density by a factor of order unity. This threshold is only surpassed by rare (many-$\sigma $) peaks for high masses at high redshifts. When discussing the abundance of halos, we will factor out the linear growth of perturbations and use the function $\sigma (M)$ at $z=0$. The comoving radius of an unperturbed sphere containing a mass $M$ is $R=1.85\nobreakspace  {}{\rm  Mpc}(M/10^{12}M_\odot )^{1/3}$.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  25}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.1}{\ignorespaces Thermal history of the baryons, left over from the big bang, before the first galaxies formed. The residual fraction of free electrons couple the gas temperture $T_{\rm  gas}$ to the cosmic microwave background temperature [$T_\gamma \propto (1+z)$] until a redshift $z\sim 200$. Subsequently the gas temperature cools adiabatically at a faster rate [$T_{\rm  gas}\propto (1+z)^2$]. Also shown is the spin temperature of the 21cm transition of hydrogen $T_{\rm  s}$ which interpolates between the gas and radiation temperature and will be discussed in Chapter 10\hbox {}.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  30}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.2}{\ignorespaces {\it  Top:} The mass fraction incorporated into halos per logarithmic bin of halo mass $(M^2dn/dM)/\rho _m$, as a function of $M$ at different redshifts $z$. Here $\rho _m=\Omega _m\rho _c$ is the present-day matter density, and $n(M)dM$ is the comoving density of halos with masses between $M$ and $M+dM$. The halo mass distribution was calculated based on an improved version of the Press-Schechter formalism for ellipsoidal collapse [Sheth, R. K., \& Tormen, G. {\it  Mon. Not. R. Astron. Soc.} {\bf  329}, 61 (2002)] that fits better numerical  simulations. {\it  Bottom:} Number density of halos per logarithmic bin of halo mass, $Mdn/dM$ (in units of comoving Mpc$^{-3}$), at various redshifts. }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  38}}
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\@writefile{toc}{\contentsline {chapter}{Chapter\nobreakspace  {}{4.\kern .5em }The Intergalactic Medium}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  43}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.1}{\ignorespaces Cooling rates as a function of temperature for a primordial gas composed of atomic hydrogen and  helium, as well as  molecular hydrogen, in the absence of any external radiation. We assume a hydrogen number density $n_H=0.045\ {\rm  cm}^{-3}$, corresponding to the mean density of  virialized halos at $z=10$. The plotted quantity $\Lambda /n_H^2$ is roughly independent of density (unless $n_H >10\ {\rm  cm}^{-3}$), where $\Lambda $ is the volume cooling rate (in erg/sec/cm$^3$). The solid line shows the cooling curve for an atomic gas, with the characteristic peaks due to collisional excitation of hydrogen and  helium. The dashed line shows the additional contribution of  molecular  cooling, assuming a  molecular abundance equal to $1\%$ of $n_H$.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  46}}
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\@writefile{lot}{\contentsline {table}{\numberline {5.1}{\ignorespaces Important reaction rates for Hydrogen species as functions of temperature $T$ in K [with $T_\xi \equiv (T/10^\xi {\rm  K})$]. For a comprehensive list of additional relevant reactions, see Haiman, Z., Rees, M. J., \& Loeb, A. {\it  Astrophys. J.} {\bf  467}, 522 (1996); Haiman, Z., Thoul, A. A., \& Loeb, A., {\it  Astrophys. J.} {\bf  464}, 523 (1996); and Abel, T. Anninos, P., Zhang, Y., \& Norman, M. L. {\it  Astrophys. J.} {\bf  508}, 518 (1997).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  49}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.3}{\ignorespaces The average spectrum during the initial phase of the reionization epoch (arbitrary units). The upper panel shows that absorption by neutral hydrogen and helium suppresses the flux above 13.6eV up to the keV range. The lower panel shows a close-up of the sawtooth modulation due to line absorption below 13.6 eV. A constant comoving density of sources was assumed, with each source emitting a power-law continuum, which would result in the spectrum shown by the dashed lines if absorption were not taken into account. Figure credit: Haiman, Z., Rees, M. J., \& Loeb, A. {\it  Astrophys. J.} {\bf  476}, 458 (1997).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  50}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.4}{\ignorespaces The large-scale distributions of dark matter (left) and gas (right) in the IGM show a network of filaments and sheets, known as the ``cosmic web''. Overall, the gas follows the dark matter on large scales but is more smoothly distributed on small scales owing to its pressure. The snapshots show the projected density contrast in a 7 Mpc thick slice at zero redshift from a numerical  simulation of a box measuring $140$ comoving Mpc on a side. Figure credit: Trac, H., \& Pen, U.-L. {\it  New Astron.} {\bf  9}, 443 (2004).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  52}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.5}{\ignorespaces Results from a numerical  simulation of the formation of a metal-free star [Yoshida, N., Omukai, K., \& Hernquist, L. {\it  Science} {\bf  321}, 669 (2008)] and its feedback on its environment [Bromm, V., Yoshida, N., Hernquist, L., \& McKee, C.\nobreakspace  {}F.\ {\it  Nature} {\bf  459}, 49 (2009)]. {\it  Top:} Projected gas distribution around a primordial protostar. Shown is the gas density (shaded so that dark grey denotes the highest density) of a single object on different spatial scales: {\it  (a)} the large-scale gas distribution around the cosmological mini-halo; {\it  (b)} the self-gravitating, star-forming cloud; {\it  (c)} the central part of the fully  molecular core; and {\it  (d)} the final protostar. {\it  Bottom:} Radiative feedback around the first star involves ionized  bubbles (light grey) and regions of high  molecule abundance (medium grey). The large residual free  electron fraction inside the relic  ionized regions, left behind after the central star has died, rapidly catalyzes the reformation of  molecules and a new generation of lower-mass stars. }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  54}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.6}{\ignorespaces Observed evolution of the mean half-light radius of galaxies across the redshift range $2<z<8$ in two bins of fixed intrinsic luminosity: (0.3-1)$L_*(z=3)$ (top) and (0.12-0.3)$L_*(z=3)$ (bottom), where $L_*(z=3)$ is the characteristic luminosity of a galaxy at $z=3$ (Eq. 12.6\hbox {}). Different point types correspond to different methods of analysing the data. The dashed lines indicate the scaling expected for a fixed halo mass ($\propto (1+z)^{-1}$; black) or at fixed halo circular velocity ($\propto (1+z)^{-3/2}$; gray). The central solid lines correspond to the best-fit to the observed evolution described by $\propto (1+z)^{-m}$, with $m=1.12\pm 0.17$ for the brighter luminosity bin, and $m=1.32\pm 0.52$ at fainter luminosities. Figure credit: Oesch, P. A., et al. {\it  Astrophys. J.} {\bf  709}, L21 (2010).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  60}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.7}{\ignorespaces Theoretically predicted distribution of galactic disk sizes in various redshift intervals. Each curve shows the fraction of the total number counts contributed by sources larger than an observed angle $\theta $ in arcseconds. The diameter $\theta $ is measured out to one scale length, $R_d$. The label next to each curve indicates the lower limit of the redshift interval; i.e. `0' indicates sources with $0<z<2$, and so forth for sources with $2<z<5$, $5<z<10$, and $z>10$. Figure credit: Barkana, R., \& Loeb, A. {\it  Astrophys. J.} {\bf  531}, 613 (2000). }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  61}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.8}{\ignorespaces Illustration of a long-duration gamma-ray burst in the popular ``collapsar'' model. The collapse of the core of a massive star (which lost its hydrogen envelope) to a  black hole generates two opposite jets moving out at a speed close to the speed of light. The jets drill a hole in the star and shine brightly towards an observer who happens to be located within the collimation cones of the jets. The jets emanating from a single massive star are so bright that they can be seen across the Universe out to the epoch when the first stars formed. Figure credit: NASA E/PO.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  64}}
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\@writefile{lof}{\contentsline {figure}{\numberline {9.1}{\ignorespaces Two important transitions of the Hydrogen atom. The  21-cm transition of hydrogen is between two slightly separated (hyperfine) states of the ground energy level (principal quantum number $n=1$). In the higher energy state, the spin of the  electron (e) is aligned with that of the  proton (p), and in the lower energy state the two are anti-aligned. A spin flip of the  electron results in the  emission of a  photon with a wavelength of  21-cm (or a  frequency of 1420 MHz). The second transition is between the $n=2$ and the $n=1$ levels, resulting in the  emission of a Lyman-$\alpha $  photon of wavelength $\lambda _{\alpha }=1.216\times 10^{-5}$ cm (or a  frequency of $2.468\times 10^{15}$ Hz).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  100}}
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\@writefile{lof}{\contentsline {figure}{\numberline {9.2}{\ignorespaces Observed spectra (flux per unit wavelength) of 19  quasars with redshifts $5.74<z<6.42$ from the {Sloan Digital Sky Survey}. For some of the highest-redshift  quasars, the spectrum shows no transmitted flux shortward of the Lyman-$\alpha $ wavelength at the  quasar redshift, providing a possible hint of the so-called `` Gunn-Peterson trough'' and indicating a slightly increased neutral fraction of the  IGM. It is evident from these spectra that broad-band  photometry is adequate for inferring the redshift of sources during the epoch of  reionization. Figure credit: Fan, X., et al. {\it  Astron. J.} {\bf  128}, 515 (2004). }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  101}}
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\@writefile{lof}{\contentsline {figure}{\numberline {9.4}{\ignorespaces Monochromatic photon luminosity of a Lyman-$\alpha $\nobreakspace  {}halo as a function of normalized frequency shift from the Lyman-$\alpha $\nobreakspace  {}resonance, ${\mathaccentV {tilde}07E\nu }\equiv (\nu _\alpha -\nu )/\nu _\star $. The observed spectral flux of photons $F(\nu )$ (in photons cm$^{-2}$ s$^{-1}$ Hz$^{-1}$) from the entire Lyman-$\alpha $\nobreakspace  {}halo is $F(\nu ) = ({{\mathaccentV {tilde}07EL}({\mathaccentV {tilde}07E\nu }) / 4 \pi d_{\rm  L}^2})({{\mathaccentV {dot}05FN_\alpha }/ \nu _\star }) (1+z_{s})^2$ where ${\mathaccentV {dot}05FN_\alpha }$ is the production rate of Lyman-$\alpha $\nobreakspace  {}photons by the source (in ${\rm  photons\nobreakspace  {}s^{-1}}$), $\nu ={\mathaccentV {tilde}07E\nu }\nu _\star /(1+z_{\rm  s})$, and $d_{\rm  L}$ is the luminosity distance to the source [from Loeb, A. \& Rybicki, G. B. {\it  Astrophys. J.} {\bf  524}, 527 (1999); see also {\bf  520}, L79 (1999)]. }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  107}}
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\@writefile{lof}{\contentsline {figure}{\numberline {9.5}{\ignorespaces  {\it  Top:} A false color image of a Lyman-$\alpha $ blob (LAB) at a redshift $z=2.656$. The hydrogen Lyman-$\alpha $ emission is shown in blue, and images in the optical V-band and the near-infrared J and H bands are shown in green and red, respectively. Note the compact galaxies lying near the northern (top) end of the LAB. The Lyman-$\alpha $ image was obtained using the SuprimeCam imaging camera on the Subaru Telescope, and the V, J, and H band images were obtained using the ACS and NICMOS cameras on the Hubble Space Telescope. This LAB was originally discovered by the Spitzer Space Telescope. Image credit: Prescott, M., \& Dey, A. (2010). {\it  Bottom:} A false color image of an LAB at a redshift $z=6.6$, obtained from a combination of images at different infrared wavelengths. Image credit: Ouchi, M. et al. {\it  Astrophys. J.} {\bf  696}, 1164 (2009). }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  108}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11.2}{\ignorespaces {\em  Top panel: }Evolution with redshift $z$ of the  CMB temperature $T_{\rm  CMB}$ (dotted curve), gas kinetic temperature $T_k$ (dashed curve), and  spin temperature $T_s$ (solid curve). Following cosmological  recombination at a redshift $z\sim 10^3$, the gas temperature tracks the  CMB temperature ($\propto (1+z)$) down to a redshift $z\sim 200$ and then declines below it ($\propto (1+z)^2$), until the first X-ray sources (accreting  black holes or exploding  supernovae) heat it up well above the  CMB temperature. The spin temperature of the  21-cm transition interpolates between the gas and  CMB temperatures; initially it tracks the gas temperature through atomic collisions, then it tracks the  CMB through radiative coupling, and eventually it tracks the gas temperature once again after the production of a cosmic background of UV  photons that redshift into the Lyman-$\alpha $ resonance. {\em  Middle panel:} Evolution of the gas fraction in  ionized regions $x_i$ (solid curve) and the ionized fraction outside these regions (due to diffuse X-rays) $x_e$ (dotted curve). {\em  Bottom panel: } Evolution of mean 21-cm brightness temperature $T_b$. The  horizontal axis at the top provides the observed  photon  frequency for the different redshifts shown at the bottom. Each panel shows curves for three models in which  reionization is completed at different redshifts: $z=6.47$ (thin lines), $z=9.76$ (medium thickness lines), and $z=11.76$ (thick lines). Figure credit: Pritchard, J. \& Loeb, A. {\it  Phys. Rev.} {\bf  D78}, 103511 (2008).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  120}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11.3}{\ignorespaces {\it  Top:} Artificial illustration of the expected MWA experiment with 512 tiles (white spots) of 16 dipole antennae each, spread across an area of 1.5 km in diameter in the desert of western Australia. With a collecting area of 8,000 square meters, the array will be sensitive to  21-cm  emission from cosmic hydrogen in the redshift range of $z=$6--15 by operating in the  radio  frequency range of 80--300 MHz. {\it  Bottom:} An actual image of one of the tiles. Image credits: Bowman, J. \& Lonsdale, C. (2009). }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  122}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11.4}{\ignorespaces Map of the fluctuations in the 21 cm brightness temperature on the sky, $\Delta T_b$ (mK), based on a numerical simulation which follows the dynamics of dark matter and gas in the IGM as well as the radiative transfer of ionizing photons from galaxies. The panels show the evolution of the signal in a slice of 140 comoving Mpc on a side, in three snapshots corresponding to the simulated volume being 25, 50, and 75 \% ionized. These snapshots correspond to the top three panels in Figure 7.1\hbox {}. Since neutral regions correspond to strong  emission (i.e., a high $T_b$), the 21-cm maps illustrate the global progress of  reionization and the substantial large-scale spatial fluctuations in  the reionization history.    Figure credit: Trac, H., Cen, R., \& Loeb, A. {\it  Astrophys. J.} {\bf  689}, L81 (2009). }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  123}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11.5}{\ignorespaces {\it  Top:} Predicted redshift evolution of the angle-averaged amplitude of the  21-cm  power spectrum ($|\mathaccentV {bar}016{\Delta }_{T_b}|=[k^3P_{\rm  21-cm}(k)/2\pi ^2]^{1/2}$) at comoving wavenumbers $k=0.01$ (solid curve), 0.1 (dotted curve), 1.0 (short dashed curve), 10.0 (long dashed curve), and 100.0${\rm  Mpc}^{-1}$ (dot-dashed curve). In the model shown,  reionization is completed at $z=9.76$. The  horizontal axis at the top shows the observed photon  frequency at the different redshifts. The diagonal straight lines show various factors of suppression for the synchrotron Galactic foreground, necessary to reveal the  21-cm signal. {\it  Bottom:} Redshift evolution of the angular scale on the sky corresponding different comoving wavenumbers, $\Theta =(2\pi /k)/d_{\rm  A}$. The labels on the right-hand side map angles to angular moments (often used to denote the multipole index of a spherical harmonics decomposition of the sky), using the approximate relation $\ell \approx \pi /\Theta $. Along the line of sight (the third dimension), an observed frequency bandwidth $\Delta \nu $ corresponds to a comoving distance of $\sim 1.8\nobreakspace  {}{\rm  Mpc}(\Delta \nu /0.1\nobreakspace  {}{\rm  MHz})[(1+z)/10]^{1/2}$. Figure credit: Pritchard, J. \& Loeb, A. {\it  Phys. Rev.} {\bf  D78}, 103511 (2008).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  125}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.2}{\ignorespaces The first Hubble Deep Field (HDF) image taken in 1995. The HDF covers an area 2.5 arcminute across and contains a few thousand galaxies (with a few candidates up to a redshift $z\sim 6$). The image was taken in four broadband filters centered on wavelengths of 3000, 4500, 6060, and 8140\r A, with an average exposure time of $\sim 0.127$ million seconds per filter. }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  132}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.3}{\ignorespaces The observed evolution in the cosmic mass density of stars (in solar masses per comoving Mpc$^{3}$) as a function of redshift [data compiled by Eyles, L. P., et al. {\it  Mon. Not. R. Astron. Soc.} {\bf  374}, 910 (2007); for additional recent data, see Labbe, I., et al. {\it  Astrophys. J.} {\bf  708}, L26 (2010).]. The estimates at $z>5$ should be regarded as lower limits due to the missing contribution of low-luminosity galaxies below the detection threshold [Stark, D., et al. {\it  Astrophys. J.} {\bf  659}, 84 (2007)]. Nevertheless, the data shows that less than a few percent of all present-day stars had formed at $z>5$, in the first 1.2 billion years after the Big Bang. A minimum density $\sim 1.7\times 10^6 f_{\rm  esc}^{-1} {\rm  M_\odot \nobreakspace  {}Mpc^{-3}}$ of Population II stars (corresponding to $\Omega _\star \sim 1.25\times 10^{-5}f_{\rm  esc}^{-1}$) is required to produce one ionizing photon per hydrogen atom in the Universe.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  133}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.4}{\ignorespaces Detectability of high-redshift GRB afterglows as a function of time since the GRB explosion as measured by the observer. The GRB afterglow flux (in Jy) is shown at the redshifted Lyman-$\alpha $ wavelength (solid curves). Also shown (dotted curves) is a crude estimate for the spectroscopic detection threshold of {\it  JWST}, assuming an exposure time equal to 20\% of the time since the GRB explosion. Each set of curves spans a sequence of redshifts: $z=5, 7, 9, 11, 13, 15$, respectively (from top to bottom). Figure credit: Barkana, R., \& Loeb, A. {\it  Astrophys. J.} {\bf  601}, 64 (2004). }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  135}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.5}{\ignorespaces Theoretically predicted rate of observable GRBs as a function of redshift (assuming that the GRB rate is proportional to the cosmic star formation rate at all redshifts). {\it  Dotted lines:} Contribution to the observed GRB rate from Pop\nobreakspace  {}I/II and Pop\nobreakspace  {}III for the case of slow metal enrichment of the IGM. {\it  Dashed lines:} Contribution to the GRB rate from Pop\nobreakspace  {}I/II and Pop\nobreakspace  {}III for the case of rapid metal enrichment of the IGM. {\it  Filled circle:} GRB rate from Pop\nobreakspace  {}III stars if these, in an extreme scenario, were responsible for reionizing the universe at $z\sim 17$. Figure credit: Bromm, V., \& Loeb, A. {\it  Astrophys. J.} {\bf  642}, 382 (2006).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  136}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.6}{\ignorespaces A full scale model of the {James Webb Space Telescope} (JWST), the successor to the {Hubble Space Telescope} (http://www.jwst.nasa.gov/).  JWST includes a primary mirror 6.5 meters in diameter, and offers instrument sensitivity across the infrared wavelength range of 0.6--28$\mu $m which will allow detection of the first galaxies. The size of the Sun shield (the large flat screen in the image) is 22 meters$\times $10 meters (72 ft$\times $29 ft). The telescope will orbit 1.5 million kilometers from Earth at the Lagrange L2 point.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  137}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.7}{\ignorespaces Artist's conception of the designs for three future giant telescopes that will be able to probe the first generation of galaxies from the ground: the {European Extremely Large Telescope} (EELT, top), the {Giant Magellan Telescope} (GMT, middle), and the {Thirty Meter Telescope} (TMT, bottom). Images credits: the European Southern Observatory (ESO), the GMT Partnership, and the TMT Observatory Corporation.}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  139}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.8}{\ignorespaces {\it  Upper panel:} The derived power-law index, $\Gamma $, of the IMF in nearby star forming regions, clusters and associations of stars within the Milky Way galaxy, as a function of sampled stellar mass (points are placed in the center of log\nobreakspace  {}m range used to derive each index, with the dashed lines indicating the full range of masses sampled). The colored solid lines represent three analytical IMFs. {\it  Bottom panel:} The present-day IMF in a sample of young star-forming regions, open clusters spanning a large age range, and old globular clusters. The dashed lines represent power-law fits to the data. The arrows show the characteristic mass of each fit, with the dotted line indicating the mean characteristic mass of the clusters in each panel, and the shaded region showing the standard deviation of the characteristic masses in that panel. The observations are consistent with a single underlying IMF. Figure credit: Bastian, N., Covey, K. R., \& Meyer, M. R., {\it  Ann. Rev. Astr. \& Astrophys.} {\bf  48} (2010).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  140}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.9}{\ignorespaces Comparison of the observed flux per unit frequency from a galaxy at a redshift $z_{s}=10$ for a Salpeter IMF ({\it  dotted line}; Tumlinson, J., \& Shull, M. J. {\it  Astrophys. J.} {\bf  528}, L65 (2000)) and a purely massive IMF ({\it  solid line}; Bromm, V. Kudritzki, R. P. \& Loeb, A. {\it  Astrophys. J.} {\bf  552}, 464 (2001)). The flux in units of $\unhbox \voidb@x \hbox {nJy}$ per $10^{6}M_{\odot }$ of stars is plotted as a function of observed wavelength in $\mu $m. The cutoff below an observed wavelength of $1216\unhbox \voidb@x \hbox {\tmspace  +\thinmuskip {.1667em}\r A\tmspace  +\thinmuskip {.1667em}} (1+z_{s})=1.34\mu $m is due to hydrogen Lyman-$\alpha $ absorption in the IGM (the so-called Gunn-Peterson effect; see \S  {GPT}). For the same total stellar mass, the observable flux is larger by an order of magnitude for stars biased towards having masses $>100M_\odot $. }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  141}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.10}{\ignorespaces {\it  Top panel:} The $i^\prime $ and $z^\prime $ bands of HST (shaded regions) on top of the generic spectrum from a galaxy at a redshift $z=6$ (solid line). The Lyman-$\alpha $ wavelength at various redshifts is also shown. {\it  Bottom panel:} Models of the color-redshift tracks for different types of galaxies with non-evolving stellar populations. The bump at $z\sim 1$--2 arises when the Balmer break or the 4000\r A\nobreakspace  {}break redshift beyond the $i^\prime $-filter. Synthetic models indicate that that the Balmer break takes $\sim 10^8$ years to establish, providing a measure of the galaxy age. Figure credit: Bunker, A. et al., preprint arXiv:0909.1565, (2009).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  144}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.11}{\ignorespaces The Lyman-$\alpha $ emission line of a typical $i^\prime $-dropout galaxy SBM03\# at $z=5.83$. Figure credit: Stanway, E., et al. {\it  Astrophys. J.} {\bf  607}, 704 (2004). }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  145}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.12}{\ignorespaces The star formation rate density as functions of redshift (lower horizontal axis) and cosmic time (upper axis), for galaxies brighter than -18.3 AB magnitude (corresponding to $0.07L_\star $ at $z=3$). The conversion from observed UV luminosity to star formation rate assumed a Salpeter IMF for the stars. The upper curves includes dust correction based on estimated spectral slopes of the observed UV continuum. Figure credit: Bouwens, R., et al., preprint http://arxiv.org/pdf/0912.4263v2 (2009).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  149}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.13}{\ignorespaces  The theoretically predicted contributions to the total variance (equation 12.25\hbox {}; solid lines) in LBG dropout surveys as a sum of cosmic variance (dashed lines) and Poisson shot noise (dotted lines) contributions (i.e. the first and second terms, respectively, on the right-hand-side of equation 12.25\hbox {}). The top and bottom panels show results for surveys extending from z=6-8 and z=8-10, respectively. Thin lines assume a luminosity threshold of $z_{850,{\rm  AB}}$=29, while for thick ones, the cut is at $z_{850,{\rm  AB}}$=27. Figure credit: Munoz, J., Trac, H., \& Loeb, A. {\it  Mon. Not. R. Astron. Soc.}, in press (2010).}}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  153}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12.14}{\ignorespaces  {\bf  Upper panel:} predicted relative contributions to the fractional variance in the number counts of galaxies as a function of UV luminosity at an emission wavelength of 1500\r A, z-band AB magnitude, or host halo mass in counts of LBGs within a dropout survey spanning the redshift interval $z=6$--$8$ with a $3.4'\times 3.4'$ field-of-view (matching HUDF and approximately that of JWST). Solid lines show the total variance, while long-dashed and dotted lines show the contributions from sample variance and Poisson noise, respectively. Upper curves show the results from numerical simulations, while lower curves were calculated analytically based on linear perturbation theory. Vertical lines brackett the region where the variance is higher than expected due to the skewness of the full count probability distribution but is not Poisson-dominated. {\bf  Lower panel:} the skewness of the full galaxy count probability distribution calculated from a numerical simulation based on equation\nobreakspace  {}(12.28\hbox {}). Figure credit: Munoz, J., Trac, H., \& Loeb, A. {\it  Mon. Not. R. Astron. Soc.}, in press (2010). }}{\fontsize  {8.75}{11pt}\selectfont  \sffamily  155}}
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