Time

Photon luminosity emitted by a single OB association (solid line) and the luminosity of photons escaping each side of the HI disk (dashed line) for coeval star formation. Also shown is the fraction of photons emitted that escape, Ve.sc (Nt,t) Sesc (t) S(t). Here, Ztr , the cavity height is Zcy and ft 1. The I-front is trapped within the shell during the time interval where nesc 0. After blowout, nesc suddenly increases even though the photon luminosity of the association is...

Mm

Provides the average distribution of progenitor masses M1 at a higher red-shift z1, dP dM(M1,z1 M0,z0). It might appear that it would be a simple matter to construct a merger tree by simply choosing the masses of the progenitors of our parent halo at some earlier redshift z1 from the expression for dP dM(M1, z1 M0, z0) given by Equation (3.16) above, then repeating this process starting from each progenitor in turn for the next step back in time. Two difficulties immediately arise in...

Redshift

The linear growth function for three cosmologies (see text). 3.1.3 Linear Growth of Perturbations The little lumps are amplified by gravity as time progresses overdensities get more overdense and underdensities get more underdense. It is straightforward to write down the differential equations describing the evolution of an overdensity 6 as a function of time. This is done in the standard texts and I will not reproduce these calculations here (e.g., Peacock 1998, p. 460). In the...

Integrated Stellar Dynamics

Historically, modeling the kinematics of stars in galactic nuclei has been the method of choice to constrain the central potential, and for good reason stars are always present, and their motion is always gravitational. But, as with every method, there are downsides. Stellar absorption lines are faint, and the central surface brightness, especially in bright ellipticals, is low (Crane et al. 1993 Ferrarese et al. 1994 Lauer et al. 1995 Rest et al. 2001). Acquiring stellar kinematical data...

Log f [Hz

A selected sample of binaries in the gravitational wave strain and frequency domain with the LISA and LIGO noise curves over-plotted. We assumed a distance to the source of 10 kpc. The lower solid curve to the right is for a 2 Mg donor, the dashes for a 5 Mg donor, the dotted curves are for a 10 Mg donor with a 100 Mg black hole (lower dotted curve) and 1000 Mg black hole (upper dotted curve). The upper solid curve is for a 15 Mg donor. Except for the lower dotted curve all are...

Chemistry

Since molecules play such an important role in the formation of the first luminous objects, it is important to include a proper treatment of their abundance evolution. However, a full treatment should take into account 20 different species and 100 different reactions. For instance, GP98 give a chemical network of 87 reactions, which includes e-, H, H+, H-, D, D+, He, He+, He++, Li, Li+, Li-, H2, H+, HD, HD+, HeH+, LiH, LiH+, H+, and H2D+ even their minimal model is too complicated to be...

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1011 1012 1013 1014 1015 1011 1012 1013 1014 1015 Mhalo M0 Mhalo M0 Figure 3.23. Fraction of baryons in cold gas, hot gas, and stars as a function of halo mass, in a semi-analytic model with cooling, star formation, photo-ionization squelching, and SN feedback. peak in time redshift depends (apparently, fairly weakly) on the details of the gastrophysical recipes included in the models. To understand the origin of this rise and decline of star formation, let us examine a few more of the...

Mono Dimensional Models

5.5.2.1 The Formation of the Protostellar Core A less simplified approach relies on 1D studies, such as those of Omukai & Nishi (1998) and Ripamonti et al. (2002) in such studies the heavy price of assuming that the collapsing object always remains spherical (which makes it impossible to investigate the effects of angular momentum, and prevents fragmentation) is compensated by the ability to properly treat Figure 5.19. Protostellar collapse, formation of an hydrostatic core, and start of the...

Summary of SMBH Mass Densities

Local Quiescent Galaxies (z < 0.025) 2.3-4.5 x 105 Wyithe & Loeb (2003) 2.4 0.8 x 105 Aller & Richstone (2002) 2.5 x 105 Yu & Tremaine (2002) 2.8 0.4 x 105 McLure & Dunlop (2004) 4.2 1.0 x 105 Shankar et al. (2004) 4.5 x 105 Ferrarese (2002a) 4.6-1 9 x 105 Marconi et al. (2004) 5 x 105 Merritt & Ferrarese (2001a) QSOs Optical Counts (0.3 < z < 5.0) 1.4 x 105 Shankar et al. (2004) 2.1 x 105 Yu & Tremaine (2004) 2.2 x 105 Marconi et al. (2004) AGN X-Ray Counts (z(peak)...

Black Hole Demographics

Tracing the mass function of SMBHs from the quasar era to the present day can yield important clues about the formation and growth of SMBHs. It is, however, a road that can prove treacherous, unless we are fully aware of the uncertainties associated with this process. For instance, in 1998, a widely cited study by Magorrian et al. led to a cumulative mass density recovered in local SMBHs in excess, by a factor five, relative to the one required to power quasars during the optically bright phase...

Molecular Cooling

In the current scenario for the formation of primordial objects, the most relevant molecule is H2. The only reason for this is the high abundance of H2 when compared with all other molecules. In fact, the radiating properties of an H2 molecule are very poor because of the absence of a dipole moment, radiation is emitted only through weak quadrupole transitions. In addition, the energy difference between the H2 ground state and the lowest H2 excited roto-vibrational levels is relatively large...

K r T

Pcool 3.52 x 107-f- , (3.24) where kBT is in degrees Kelvin, Tcool is in Gyr, and A23(T) A(T) (10-23 ergs s-1 cm3). The virial temperature is approximated as kBT 71.8 , where < yvir is the virial velocity dispersion of the halo. Assuming a form for the gas density profile pg (r), one can now invert this expression to obtain the cooling radius, defined as the radius within which the gas has had time to cool during the timescale Tcooi. Assuming p(r) < r-2 (a singular isothermal sphere), this...

Post Recombination Universe

The CMB plays a key role in the early evolution of structures. First, it sets the epoch of decoupling, when matter becomes free to move through the radiation field to form the first generation of gravitationally bound systems. Second, CMB fixes the matter temperature that in turn determines the Jeans scale of the minimum size of the first bound objects. The net drag force acting on an electron moving at speed v c through the CMB is where aT is the Thomson cross-section, and aB the...

Spatial Clustering and Bias

Generally, the term bias represents the possibility that galaxies do not exactly trace the dark matter. The concept of bias was first discussed in the early days of the CDM model, before the results from the COBE satellite told us how to normalize the overall amplitude of the matter power spectrum, and at a time when at least theorists were strongly predisposed to believe that we live in a universe with critical density fim 1. The concept of biased galaxy formation was discussed by Kaiser...