We present calculations on the formation of massive black holes with 10^5 Msun at z > 6 that can be the seeds of supermassive black holes at z > 6. Under the assumption of compact star cluster formation in merging galaxies, star clusters in haloes of
10^8 ~ 10^9 Msun can undergo rapid core-collapse leading to the formation of very massive stars (VMSs) with ~1000 Msun which directly collapse into black holes with similar masses. Star clusters in halos of > 10^9 Msun experience type-II supernovae before the formation of VMSs due to long core-collapse time scales. We also model the subsequent growth of black holes via accretion of residual stars in clusters. 2-body relaxation efficiently re-fills the loss cones of stellar orbits at larger radii and resonant relaxation at small radii is the main driver for accretion of stars onto black holes. As a result, more than ninety percent of stars in the initial cluster are swallowed by the central black holes before z=6. Using dark matter merger trees we derive black hole mass functions at z=6-20. The mass function ranges from 10^3 to 10^5 Msun at z <~ 15. Major merging of galaxies of >~ 4*10^8 Msun at z ~ 20 successfully leads to the formation of >~ 10^5 Msun BHs by z >~ 10 which can be the potential seeds of supermassive black holes seen today.
We give a condition under which the findings of the paper cited above work well and determine the surfaces that were not considered before. In this paper, we show that a parallel mean curvature surface of a general type in a complex two-dimensional c
omplex space form depends on one real-valued harmonic function on the surface and five real constants if the ambient space is not flat, the mean curvature vector does not vanish, and the Kaehler angle is not constant.
Using the very deep Subaru images of the GOODS-N region, from the MOIRCS Deep Survey and images from the HST/ACS, we have measured the Luminosity Ratio (LR) of the outer to the central regions of massive (M>10^{10.5}M_{Sun}) galaxies at fixed radii i
n a single rest-frame for z<3.5 as a new approach to the problem of size evolution. We didnt observe any evolution in the median LR. Had a significant size growth occurred, the outer to central luminosity ratios would have demonstrated a corresponding increase with a decrease in redshift.
We present chemical abundances of 57 metal-poor stars that are likely constituents of the outer stellar halo in the Milky Way. Almost all of the sample stars have an orbit reaching a maximum vertical distance (Z_max) of >5 kpc above and below the Gal
actic plane. High-resolution, high signal-to-noise spectra for the sample stars obtained with Subaru/HDS are used to derive chemical abundances of Na, Mg, Ca, Ti, Cr, Mn, Fe, Ni, Zn, Y and Ba with an LTE abundance analysis code. The resulting abundance data are combined with those presented in literature that mostly targeted at smaller Z_max stars, and both data are used to investigate any systematic trends in detailed abundance patterns depending on their kinematics. It is shown that, in the metallicity range of -2<[Fe/H]<-1, the [Mg/Fe] ratios for the stars with Z_max>5 kpc are systematically lower (~0.1 dex) than those with smaller Z_max. This result of the lower [alpha/Fe] for the assumed outer halo stars is consistent with previous studies that found a signature of lower [alpha/Fe] ratios for stars with extreme kinematics. A distribution of the [Mg/Fe] ratios for the outer halo stars partly overlaps with that for stars belonging to the Milky Way dwarf satellites in the metallicity interval of -2<[Fe/H]<-1 and spans a range intermediate between the distributions for the inner halo stars and the stars belonging to the satellites. Our results confirm inhomogeneous nature of chemical abundances within the Milky Way stellar halo depending on kinematic properties of constituent stars as suggested by earlier studies. Possible implications for the formation of the Milky Way halo and its relevance to the suggested dual nature of the halo are discussed.
