The Microlensing and Halo Models of the Galaxy

We investigated the dependence of the optical depth $\tau$ of the microlensing events on model parameters of the Galactic halo. We only consider Galactic mass models in which the rotation curve inside the Sun is compatible with the observation and LMC is bound to the Galaxy. It is found that $\tau$ varies up to a factor 2.5 from the standard spherical and flat rotation halo model. This implies that only the most centrally concentrated halo model can be consistent with the observation if the halo consists of only MACHOs. We also calculate the power $x$ of IMF of MACHO consistent with Tyson's CCD survey as well as Bahcall \etal's observation by {\em HST}. It is found that $x$ is greater than 5.Comment: 17 pages (including 8 figures), uuencoded gz-compressed postscrip

Evolution of Primordial Protostellar Clouds --- Quasi-Static Analysis ---

The contraction processes of metal-free molecular clouds of starlike mass (or cloud cores) are investigated. We calculate radiative transfer of the H_2 lines and examine quasi-static contraction with radiative cooling. Comparing two time-scales, the free-fall time t_ff and the time-scale of quasi-static contraction t_qsc (nearly equal to t_cool, the cooling time) of these cores, we find that the ratio of the two time-scales t_ff/t_qsc, i.e., the efficiency of cooling, becomes larger with contraction even under the existence of cold and opaque envelopes. In particular, for fragments of primordial filamentary clouds, for which t_ff is nearly equal to t_qsc at the fragmentation epoch, they collapse dynamically in the free-fall time-scale. This efficiency of cooling is unique to line cooling.Comment: 13 pages, 8 Postscript figures, uses ptpte

The Thermal Evolution of the Postshock Layer in Pregalactic Clouds

We re-examine the thermal evolution of the postshock layer in primordial gas clouds. Comparing the time scales, we find that the evolutionary paths of postshock regions in primordial gas clouds can be basically understood in terms of the diagram drawn in the ionization degree vs temperature plane. The results obtained from the diagram are independent of the density in the case that we do not include photodissociation and photoionization. We also argue that the diagram is not only relevant to the case of the steady postshock flow, but also to the isochorically cooling gas.Comment: 15pages, tar gzipped, 5 figures, PTP TeX (PTP style files are in http://www2.yukawa.kyoto-u.ac.jp/~ptpwww/ptptex-eng.ptp.html). Progress of Theoretical Physics, in pres

Expected EAGLE event rate towards the Magellanic Clouds

We propose to search for MACHOs by observing EAGLE (Extremely Amplified Gravitational LEnsing) events of a majority of dim stars. This search is independent of the usual one. For the detection limit of EAGLE (about 20 mag), about 100 f (\tau^{LMC} / 3 \times 10^{-7}) (100 days / ) EAGLE events/y are expected to result from all the dim stars in LMC. Here \tau^{LMC} and are the optical depth and the average duration of microlensing events, respectively, while f (0 < f < 1) is a parameter depending on the unknown stellar luminosity function. The observed mean duration of EAGLE events also depends on the luminosity function and is (0.01 - 0.4) times the usual duration of microlensing events, which corresponds to (1 - 30) days. The follow-up observation using larger telescopes may enable us to determine the impact parameter and the true duration of the event. If f is determined by another independent method, we can also determine \tau^{LMC}. Even if f is undetermined, the detection of EAGLE events strongly suggest that MACHOs are not due to variable source stars, since EAGLE events are due to the dim main-sequence stars. Although for the SMC, the event rate is smaller by a factor of about 7, it is still a substantial number (about 13 f (\tau^{SMC} / 3 \times 10^{-7} (100 days / ) events/y).Comment: 8 pages, Prog. Theor. Phys. in pres

H_2 Line Emission Associated with the Formation of the First Stars

Molecular hydrogen line radiation emitted in formation events of first-generation stars are evaluated in a discussion of its detectability by future observational facilities. H_2 luminosity evolution from the onset of prestellar collapse until the formation of a \sim 100 M_{\odot} protostar is followed. Calculations are extended not only to the early phase of the runaway collapse but also to the later phase of accretion, whose observational features have not been studied before. Contrary to the runaway collapse phase, where the pure-rotational lines are always dominant, in the accretion phase rovibrational line emission becomes prominent. The maximum luminosity is also attained in the accretion phase for strong emission lines. The peak intensity of the strongest rovibrational line reaches \sim 10^{-29} (W/m^2), corresponding to the flux density of 10^{-5} (\mu Jy), for a source at the typical redshift of first-generation star formation, 1+z=20. Although the redshifted rovibrational H_2 emission from such an epoch falls in the wavelength range of the next-generation infrared satellite, Space Infrared Telescope for Cosmology and Astrophysics, for exceeding the detection threshold 10^7 such protostars are required to reach the maximum luminosity simultaneously in a pregalactic cloud. It is improbable that this condition is satisfied in a realistic scenario of early structure formation.Comment: 16 pages, 5 figures, accepted by PAS

Formation and Disruption of Cosmological Low Mass Objects

We investigate the evolution of cosmological low mass (low virial temperature) objects and the formation of the first luminous objects. First, the `cooling diagram' for low mass objects is shown. We assess the cooling rate taking into account the contribution of H_2, which is not in chemical equilibrium generally, with a simple argument of time scales. The reaction rates and the cooling rate of H_2 are taken from the recent results by Galli & Palla (1998). Using this cooling diagram, we also estimate the formation condition of luminous objects taking into account the supernova (SN) disruption of virialized clouds. We find that the mass of the first luminous object is several times 10^7 solar mass, because smaller objects may be disrupted by the SNe before they become luminous. Metal pollution of low mass (Ly-alpha) clouds also discussed. The resultant metallicity of the clouds is about 1/1000 of the solar metallicity.Comment: 11 pages, 2 figures, To appear in ApJ

Back Reaction to the Spectrum of Magnetic Field in the Kinetic Dynamo Theory --- Modified Kulsrud and Anderson Equation ---

We take account of the lowest order back reaction on the fluid and modify the Kulsrud and Anderson equation $\partial_t{\cal E}_M= 2 \gamma {\cal E}_M$ obtained in the kinetic dynamo theory, where ${\cal E}_M$ is the energy density of the magnetic field. Furthermore, we apply our present result to some astrophysical stages where the magnetic field is expected to be amplified by the dynamo mechanism.Comment: 9 pages, LaTex, to appear in Prog. Theor. Phy

The Minimum Total Mass of MACHOs and Halo Models of the Galaxy

If the density distribution \rho (r) of MACHOs is spherically symmetric with respect to the Galactic center, it is shown that the minimal total mass M_{min}^{{ MACHO}} of the MACHOs is 1.7\times 10^{10}\sol \tau_{-6.7}^{{ LMC}} where \tau_{-6.7}^{{ LMC}} is the optical depth (\tau^{{ LMC}}) toward the Large Magellanic Cloud (LMC) in the unit of 2\times 10^{-7}. If \rho (r) is a decreasing function of r, it is proved that M_{min}^{{ MACHO}} is 5.6\times 10^{10}\sol \tau_{-6.7}^{{ LMC}}. Several spherical and axially symmetric halo models of the Galaxy with a few free parameters are also considered. It is found that M_{min}^{{ MACHO}} ranges from 5.6\times 10^{10}\sol \tau_{-6.7}^{{ LMC}} to \sim 3 \times 10^{11}\sol \tau_{-6.7}^{{ LMC}}. For general case, the minimal column density \Sigma_{min}^{{ MACHO}} of MACHOs is obtained as \Sigma_{min}^{{ MACHO}} =25 \sol { pc}^{-2}\tau_{-6.7}^{{ LMC}}. If the clump of MACHOs exist only halfway between LMC and the sun, M_{min}^{{ MACHO}} is 1.5\times 10^9\sol. This shows that the total mass of MACHOs is smaller than 5 \times 10^{10}\sol , i.e. \sim 10\% of the mass of the halo inside LMC, either if the density distribution of MACHOs is unusual or \tau^{{ LMC}}\ll 2\times 10^{-7}.Comment: 5 pages, 5 Encapsulated PostScript figures, Latex, Accepted for publication in Apj. Letter