A note on retracts of polynomial rings in three variables

In Costa's paper published in 1977, he asks us whether every retract of $k^{[n]}$ is also the polynomial ring or not, where $k$ is a field. In this paper, we give an affirmative answer in the case where $k$ is a field of characteristic zero and $n = 3$.Comment: 4 page

Tracing early structure formation with massive starburst galaxies and their implications for reionization

Cosmological hydrodynamic simulations have significantly improved over the past several years, and we have already shown that the observed properties of Lyman-break galaxies (LBGs) at z=3 can be explained well by the massive galaxies in the simulations. Here we extend our study to z=6 and show that we obtain good agreement for the LBGs at the bright-end of the luminosity function (LF). Our simulations also suggest that the cosmic star formation rate density has a peak at z= 5-6, and that the current LBG surveys at z=6 are missing a significant number of faint galaxies that are dimmer than the current magnitude limit. Together, our results suggest that the universe could be reionized at z=6 by the Pop II stars in ordinary galaxies. We also estimate the LF of Lyman-alpha emitters (LAEs) at z=6 by relating the star formation rate in the simulation to the Ly-alpha luminosity. We find that the simulated LAE LFs agree with the observed data provided that the net escape fraction of Ly-alpha photon is f_{Ly-alpha} <= 0.1. We investigate two possible scenarios for this effect: (1) all sources in the simulation are uniformly dimmer by a factor of 10 through attenuation, and (2) one out of ten LAEs randomly lights up at a given moment. We show that the correlation strength of the LAE spatial distribution can possibly distinguish the two scenarios.Comment: 9 pages, 4 figures. Summary of the talk given at the "First Light & Reionization" workshop at UC Irvine, May 2005. The published article is available from http://dx.doi.org/10.1016/j.newar.2005.11.00

Effects of metal enrichment and metal cooling in galaxy growth and cosmic star formation history

We present the results of a numerical study on the effects of metal enrichment and metal cooling on galaxy formation and cosmic star formation (SF) history using cosmological hydrodynamic simulations. We find following differences in the simulation with metal cooling when compared to the run without it: (1) the cosmic star formation rate (SFR) is enhanced by about 50 & 20% at z=1 & 3, respectively; (2) the gas mass fraction in galaxies is lower; (3) the total baryonic mass function (gas + star) at z=3 does not differ significantly, but shows an increase in the number of relatively massive galaxies at z=1; (4) the baryonic mass fraction of intergalactic medium (IGM) is reduced at z<3 due to more efficient cooling and gas accretion onto galaxies. Our results suggest that the metal cooling enhances the galaxy growth by two different mechanisms: (1) increase of SF efficiency in the local interstellar medium (ISM), and (2) increase of IGM accretion onto galaxies. The former process is effective throughout most of the cosmic history, while the latter is effective only at z<3 when the IGM is sufficiently enriched by metals owing to feedback.Comment: 16 pages, 11 figures, 1 table, accepted for publication in MNRAS. A full resolution version is available at http://www.physics.unlv.edu/~jhchoi/astro-ph/Metalcooling.pd

Incidence Rate of GRB-host-DLAs at High Redshift

We study the incidence rate of damped Ly-a systems associated with the host galaxies of gamma-ray bursts (GRB-host-DLAs) as functions of neutral hydrogen column density (N_HI) and projected star formation rate (SFR) using cosmological SPH simulations. Assuming that the occurrence of GRBs is correlated with the local SFR, we find that the median N_HI of GRB-host-DLAs progressively shifts to lower N_HI values with increasing redshift, and the incidence rate of GRB-host-DLAs with log N_HI > 21.0 decreases rapidly at z>=6. Our results suggest that the likelihood of observing the signature of IGM attenuation in GRB afterglows increases towards higher redshift, because it will not be blocked by the red damping wing of DLAs in the GRB host galaxies. This enhances the prospects of using high-redshift GRBs to probe the reionization history of the Universe. The overall incidence rate of GRB-host-DLAs decreases monotonically with increasing redshift, whereas that of QSO-DLAs increases up to z=6. A measurement of the difference between the two incidence rates would enable an estimation of the value of \eta_grb, which is the mass fraction of stars that become GRBs for a given amount of star formation. Our predictions can be tested by upcoming high-z GRB missions, including JANUS (Joint Astrophysics Nascent Universe Scout) and SVOM (Space multi-band Variable Object Monitor).Comment: 5 pages, 3 figures, ApJL, in pres

Future Evolution of the Intergalactic Medium in a Universe Dominated by a Cosmological Constant

We simulate the evolution of the intergalactic medium (IGM) in a universe dominated by a cosmological constant. We find that within a few Hubble times from the present epoch, the baryons will have two primary phases: one phase composed of low-density, low-temperature, diffuse, ionized gas which cools exponentially with cosmic time due to adiabatic expansion, and a second phase of high-density, high-temperature gas in virialized dark matter halos which cools much more slowly by atomic processes. The mass fraction of gas in halos converges to ~40% at late times, about twice its calculated value at the present epoch. We find that in a few Hubble times, the large scale filaments in the present-day IGM will rarefy and fade away into the low-temperature IGM, and only islands of virialized gas will maintain their physical structure. We do not find evidence for fragmentation of the diffuse IGM at later times. More than 99% of the gas mass will maintain a steady ionization fraction above 80% within a few Hubble times. The diffuse IGM will get extremely cold and dilute but remain highly ionized, as its recombination time will dramatically exceed the age of the universe.Comment: 22 pages, 10 figures. Accepted to New Astronomy. Movies and a higher resolution version of the paper are available at http://cfa-www.harvard.edu/~knagamine/FutureIG