Derived factorization categories of non-Thom–Sebastiani-type sums of potentials

We first prove semi-orthogonal decompositions of derived factorizationcategories arising from sums of potentials of gauged Landau-Ginzburg models,where the sums are not necessarily Thom--Sebastiani type. We then apply theresult to the category ${\rm HMF}^{L_f}(f)$ of maximally graded matrixfactorizations of an invertible polynomial $f$ of chain type, and explicitlyconstruct a full strong exceptional collection $E_1$,..., $E_{\mu}$ in {\rmHMF}^{L_f}(f) whose length $\mu$ is the Milnor number of theBerglund--H\"ubsch transpose $\widetilde{f}$ of $f$. This proves a conjecture,which postulates that for an invertible polynomial $f$ the category {\rmHMF}^{L_f}(f) admits a tilting object, in the case when $f$ is a chainpolynomial. Moreover, by careful analysis of morphisms between the exceptionalobjects $E_i$, we explicitly determine the quiver with relations $(Q,I)$ whichrepresents the endomorphism ring of the associated tilting object$\oplus_{i=1}^{\mu}E_i$ in ${\rm HMF}^{L_f}(f)$, and in particular we obtain anequivalence ${\rm HMF}^{L_f}(f)\cong {\rm D}^{\rm b}({\rm mod}\, kQ/I)$.<br

Characterization of the distribution of the Lly\alpha emitters in the 53W002 field at z = 2.4

We present the results of our wide-field narrow band imaging of the field around the radio galaxy 53W002 at z = 2.390 with Subaru/Suprime-Cam. A custom made filter NB413 centered at 4140 \AA\ with the width of 83 \AA\ is used to observe the 31' x 24' area around the radio galaxy. We detected 204 Ly\alpha emitters (LAEs) at z = 2.4 with a rest frame equivalent width larger than 25 \AA\ to the depth of 26 AB mag (in NB413). The entire LAE population in the 53W002 field has an average number density and distributions of equivalent width and size that are similar to those of other fields at z ~ 2. We identify a significant high density region (53W002F-HDR) that spreads over ~ 5' x 4' near 53W002 where the LAE number density is nearly four times as large as the average of the entire field. Using the probability distribution function of density fluctuation, we evaluate the rareness probability of the 53W002F-HDR to be 0.9^{+2.4}_{-0.62}%, which corresponds to a moderately rich structure. No notable environmental dependency at the comoving scale of 10 Mpc is found for the distributions of the Ly\alpha equivalent width and luminosity in the field. We also detected 4 Ly\alpha blobs (LABs), one of which is newly discovered. They are all found to be located in the rims of high density regions. The biased location and unique morphologies in Ly\alpha suggest that galaxy interaction play a key role in their formation.Comment: 26 pages, 12 figure

Large Cosmic Variance in the Clustering Properties of Lyman Alpha Emitters at z~5

We reported in a previous paper the discovery of large-scale structure of Lyman Alpha emitters (LAEs) at z=4.86+-0.03 with a projected size of 20 Mpc x 50 Mpc in narrow-band data of a 25' x 45' area of the Subaru Deep Field (Omega_0=0.3, lambda_0=0.7, H0=70 km/s/Mpc). However, the surveyed area, which corresponds to 55 Mpc x 100 Mpc, was not large enough that we can conclude that we are seeing a typical distribution of z~5 LAEs. In this Letter, we report the results of follow-up imaging of the same sky area using a new narrow-band filter (NB704, lambda_c=7046 A and FWHM=100 A) to detect LAEs at z=4.79, i.e., LAEs lying closer to us by 39 Mpc on average than the z=4.86 objects. We detect 51 LAEs at z=4.79+-0.04 down to NB704=25.7, and find that their sky distribution is quite different from the z=4.86 LAEs'. The clustering of z=4.79 LAEs is very weak on any scales and there is no large-scale high- contrast structure. The shape and the amplitude of the angular correlation function are thus largely different between the two samples. These results demonstrate a large cosmic variance in the clustering properties of LAEs on scales of ~ 50 Mpc.Comment: 4 pages (uses emulateapj5.sty), accepted for ApJ

Diffuse Lyman Alpha Haloes around Lyman Alpha Emitters at z=3: Do Dark Matter Distributions Determine the Lyman Alpha Spatial Extents?

Using stacks of Ly-a images of 2128 Ly-a emitters (LAEs) and 24 protocluster UV-selected galaxies (LBGs) at z=3.1, we examine the surface brightness profiles of Ly-a haloes around high-z galaxies as a function of environment and UV luminosity. We find that the slopes of the Ly-a radial profiles become flatter as the Mpc-scale LAE surface densities increase, but they are almost independent of the central UV luminosities. The characteristic exponential scale lengths of the Ly-a haloes appear to be proportional to the square of the LAE surface densities (r(Lya) \propto Sigma(LAE)^2). Including the diffuse, extended Ly-a haloes, the rest-frame Ly-a equivalent width of the LAEs in the densest regions approaches EW_0(Lya) ~ 200 A, the maximum value expected for young (< 10^7 yr) galaxies. This suggests that Ly-a photons formed via shock compression by gas outflows or cooling radiation by gravitational gas inflows may partly contribute to illuminate the Ly-a haloes; however, most of their Ly-a luminosity can be explained by photo-ionisation by ionising photons or scattering of Ly-a photons produced in HII regions in and around the central galaxies. Regardless of the source of Ly-a photons, if the Ly-a haloes trace the overall gaseous structure following the dark matter distributions, it is not surprising that the Ly-a spatial extents depend more strongly on the surrounding Mpc-scale environment than on the activities of the central galaxies.Comment: 7 pages, 4 figures, accepted for publication in MNRA

The Subaru Ly-alpha blob survey: A sample of 100 kpc Ly-alpha blobs at z=3

We present results of a survey for giant Ly-alpha nebulae (LABs) at z=3 with Subaru/Suprime-Cam. We obtained Ly-alpha imaging at z=3.09+-0.03 around the SSA22 protocluster and in several blank fields. The total survey area is 2.1 square degrees, corresponding to a comoving volume of 1.6 x 10^6 Mpc^3. Using a uniform detection threshold of 1.4 x 10^{-18} erg s^{-1} cm^{-2} arcsec^{-2} for the Ly-alpha images, we construct a sample of 14 LAB candidates with major-axis diameters larger than 100 kpc, including five previously known blobs and two known quasars. This survey triples the number of known LABs over 100 kpc. The giant LAB sample shows a possible "morphology-density relation": filamentary LABs reside in average density environments as derived from compact Ly-alpha emitters, while circular LABs reside in both average density and overdense environments. Although it is hard to examine the formation mechanisms of LABs only from the Ly-alpha morphologies, more filamentary LABs may relate to cold gas accretion from the surrounding inter-galactic medium (IGM) and more circular LABs may relate to large-scale gas outflows, which are driven by intense starbursts and/or by AGN activities. Our survey highlights the potential usefulness of giant LABs to investigate the interactions between galaxies and the surrounding IGM from the field to overdense environments at high-redshift.Comment: MNRAS Letters accepted (6 pages, 4 figures, 2 tables