Search

In the hierarchical theory of galaxy formation, a galaxy overdensity is a hallmark of a massive cosmic structure. However, it is less well understood how different types of galaxies trace the underlying large-scale structure. Motivated by the discovery of a z=3.13 protocluster, we examine how the same structure is populated by Ly$\alpha$-emitting galaxies (LAEs). To this end, we have undertaken a deep narrow-band imaging survey sampling Ly$\alpha$ emission at this redshift. Of the 93 LAE candidates within a 36'x36'~(70x70~Mpc^2) field, 21 galaxies form a significant surface overdensity (delta_g=3.3+/-0.9), which is spatially segregated from the Lyman break galaxy (LBG) overdensity. One possible interpretation is that they trace two separate structures of comparable masses (~ 10^{15}M_sun) where the latter is hosted by a halo assembled at an earlier time. We speculate that the dearth of LAEs in the LBG overdensity region may signal the role of halo assembly bias in galaxy formation, which would suggest that different search techniques may be biased accordingly to the formation age or dynamical state of the host halo. The median Ly$\alpha$- and UV luminosity is 30--70\% higher for the protocluster LAEs relative to the field. This difference cannot be explained by the galaxy overdensity alone, and may require a top-heavy mass function, higher star formation efficiency for protocluster halos, or suppression of galaxy formation in low-mass halos. A luminous Ly$\alpha$ blob and an ultramassive galaxy found in this region paint a picture consistent with the expected early growth of galaxies in clusters., Comment: Accepted to ApJ

We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution kernel.\iffalse The order of fractional derivative, $\alpha$, is tied to finite difference methods and is of great interest.\fi We examine this new equation and utilize a numerical scheme that is derived in parallel to the L1-method for the time variable and a usual fourth order approximation in the spatial variable. The main method derived in this paper has a rate of convergence of $O(k^{2}+h^4)$ for $u(x,t) \in C^6(\Omega)\times C^2[0,T]$, which improves previous estimates by a factor of $k^{\alpha}$. We also present a novel alternative method for a first order approximation in time, which allows us to relax our regularity assumption to $u(x,t) \in C^6(\Omega)\times C^1[0,T]$, while exhibiting order of convergence slightly less than $O(k^{1+\alpha})$ in time. This allows for a much wider class of functions to be analyzed which was previously not possible under the L1-method. We present numerical examples demonstrating these results and discuss future improvements and implications by using these techniques., Comment: 22 pages, 3 tables, 1 appendix

We present a detailed census of galaxies in and around PC217.96+32.3, a spectroscopically confirmed Coma analog at z=3.78. Diverse galaxy types identified in the field include Lya emitters (LAEs), massive star-forming galaxies, and ultra-massive galaxies (log (Mstar/Msun)>= 11) which may have already halted their star formation. The sky distribution of the star-forming galaxies suggests the presence of a significant overdensity (delta_g=8+/-2), which is spatially offset from the previously confirmed members by 3-4 Mpc to the west. Candidate quiescent and post-starburst galaxies are also found in large excess (a factor of ~ 8-15 higher surface density than the field) although their redshifts are less certain. We estimate that the total enclosed mass traced by star-forming galaxy candidates is roughly comparable to that of PC217.96+32.3 traced by the LAEs. We speculate that the true extent of PC217.96+32.3 may be larger than previously known, a half of which is missed by our LAE selection. Alternatively, the newly discovered overdensity may belong to another Coma progenitor not associated with PC217.96+32.3. Expectations from theory suggest that both scenarios are equally unlikely (<1%), particularly in the cosmic volume probed in our survey. If confirmed as a single structure, its total mass will be well in excess of Coma, making this a singularly large cosmic structure rarely seen even in large cosmological simulations. Finally, we find that the protocluster galaxies follow the same SFR-M_star scaling relation as the field galaxies, suggesting that the environmental effect at z~4 is a subtle one at best for normal star-forming galaxies., Comment: 21 pages, 11 figures, accepted for publication in Astrophysical Journal