The Distance to M101 Hosting Type Ia SN 2011fe Based on the Tip of the Red Giant Branch

We present a new determination of the distance to M101, host of the type Ia SN 2011fe, based on the tip of the red giant branch method (TRGB). Our determination is based on {\it Hubble Space Telescope} archival $F555W$ and $F814W$ images of nine fields within the galaxy. Color-magnitude diagrams of arm-free regions in all fields show a prominent red giant branch (RGB). We measure the $I$-band magnitudes of the TRGB, obtaining a mean value of $I_{\rm TRGB}=25.28\pm0.01$ (where the error is a standard error), using an edge-detection method. We derive a weighted mean value of distance modulus $(m-M)_0=29.30\pm0.01 ({\rm random})\pm0.12 ({\rm systematic})$, corresponding to a linear distance of $7.24\pm0.03\pm0.40$ Mpc. While previous estimates for M101 show a large range (TRGB distances of $(m-M)_0=29.05$ to 29.42 and Cepheid distances of $(m-M)_0=29.04$ to 29.71), our measurements of the TRGB distances for nine fields show a small dispersion of only 0.02. We combine our distance estimate and photometry in the literature to derive absolute peak magnitudes in optical and near-infrared bands of SN 2011fe. Absolute maximum magnitudes of SN 2011fe are $\sim0.2$ mag brighter in the optical band and much more in the NIR than the current calibrations of SNe Ia in the literature. From the optical maximum magnitudes of SN 2011fe we obtain a value of the Hubble constant, $H_0=65.0\pm0.5({\rm random})\pm5.7({\rm systematic})$ \kmsMpc, slightly smaller than other recent determinations of $H_0$.Comment: 16 pages, 4 figures, 1 table, Accepted for publication in ApJ Letter

The Tip of the Red Giant Branch Distances to Type Ia Supernova Host Galaxies. III. NGC 4038/39 and NGC 5584

We present the tip of the red giant branch (TRGB) distances to Type Ia supernova (SNe Ia) host galaxies NGC 4038/39 and NGC 5584. Based on the deep images constructed using archival Hubble Space Telescope data, we detect red giant branch stars in each galaxy. VI photometry of the resolved stars and corresponding I-band luminosity functions show the TRGB to be at I_{TRGB} = 27.67 \pm 0.05 for NGC 4038/39 and I_{TRGB} = 27.77 \pm 0.04 for NGC 5584. From these estimates, we determine the distance modulus to NGC 4038/39 to be (m-M)_0 = 31.67 \pm 0.05 (random) \pm 0.12 (systematic) (corresponding to a linear distance of 21.58 \pm 0.50 \pm 1.19 Mpc) and the distance modulus to NGC 5584 to be (m-M)_0 = 31.76 \pm 0.04 (random) \pm 0.12 (systematic) (corresponding to a linear distance of 22.49 \pm 0.41 \pm 1.24 Mpc). We derive a mean absolute maximum magnitude of SNe Ia of M_V = -19.29 \pm 0.08 from the distance estimates of five SNe Ia (including two SNe in this study and three SNe Ia from our previous studies), and we derive a value of M_V = -19.19 \pm 0.10 using three low-reddened SNe Ia among the five SNe Ia. With these estimates, we derive a value of the Hubble constant, H_0 = 69.8 \pm 2.6 (random) \pm 3.9 (systematic) km/s/Mpc and 72.2 \pm 3.3 (random) \pm 4.0 (systematic) km/s/Mpc, respectively. The value from the five SNe is similar to those from the cosmic microwave background analysis, and not much different within errors, from those of recent Cepheid calibrations of SNe Ia. The value from the three SNe is between the values from the two methods.Comment: 12 pages, 9 figures, 6 tables, accepted for publication in Ap

A canonical decomposition of strong L2L^2-functions

The aim of this paper is to establish a canonical decomposition of operator-valued strong $L^2$-functions by the aid of the Beurling-Lax-Halmos Theorem which characterizes the shift-invariant subspaces of vector-valued Hardy space. This decomposition invites us to coin a new notion of the "Beurling degree" of the inner function. Eventually, we establish a deep connection between the spectral multiplicity of the model operator and the Beurling degree of the corresponding characteristic function.Comment: This paper was incorporated in a part of the new paper [The Beurling-Lax-Halmos Theorem for Infinite Multiplicity; arXiv:1910.09957] co-authored with Raul E. Curt

Resolving the Discrepancy of Distance to M60, a Giant Elliptical Galaxy in Virgo

There is a well-known discrepancy in the distance estimation for M60, a giant elliptical galaxy in Virgo: the planetary nebula luminosity function (PNLF) distance moduli for this galaxy are, on average, $~0.4$ mag smaller than the values based on the surface brightness fluctuation (SBF) in the literature. We present photometry of the resolved stars in an outer field of M60 based on deep F775W and F850LP images in the Hubble Space Telescope obtained as part of the Pure Parallel Program in the archive. Detected stars are mostly old red giants in the halo of M60. With this photometry we determine a distance to M60 using the tip of the red giant branch (TRGB). A TRGB is detected at $F850LP_{\rm TRGB}=26.70\pm0.06$ mag, in the luminosity function of the red giants. This value corresponds to $F814W_{0,\rm TRGB}=27.13\pm0.06$ mag and $QT_{\rm TRGB}=27.04\pm0.07$ mag, where $QT$ is a color-corrected F814W magnitude. From this we derive a distance modulus, $(m-M)_0=31.05\pm0.07{\rm(ran)}\pm0.06{\rm (sys)}$ ($d=16.23\pm0.50{\rm (ran)}\pm0.42{\rm (sys)}$ Mpc). This value is $0.3$ mag larger than the PNLF distances and $0.1$ mag smaller than the SBF distances in the previous studies, indicating that the PNLF distances to M60 in the literature have larger uncertainties than the suggested values.Comment: 8 pages, 7 figures, 3 tables, ApJ in pres

Discovery of an Ultra-Faint Dwarf Galaxy in the Intracluster Field of the Virgo Center : A fossil of the First Galaxies?

Ultra-faint dwarf galaxies (UFDs) are newcomers among galaxies, and are the faintest galaxies in the observed universe. To date, they have only been found around the Milky Way Galaxy and M31 in the Local Group. We present the discovery of an UFD in the intracluster field in the core of the Virgo cluster (Virgo UFD1), which is far from any massive galaxies. The color-magnitude diagram of the resolved stars in this galaxy shows a narrow red giant branch, similar to those of metal-poor globular clusters in the Milky Way. We estimate its distance by comparing the red giant branch with isochrones, and we obtain a value 16.4 +/- 0.4 Mpc. This shows that it is indeed a member of the Virgo cluster. From the color of the red giants we estimate its mean metallicity to be very low, [Fe/H]= -2.4 +/- 0.4. Its absolute V-band magnitude and effective radius are derived to be M_V = -6.5 +/- 0.2 and r_eff = 81 +/- 7 pc, much fainter and smaller than the classical dwarf spheroidal galaxies. Its central surface brightness is estimated to be as low as u_V,0 = 26.37 +/- 0.05 mag arcsec^-2. Its properties are similar to those of the Local Group analogs. No evidence of tidal features are found in this galaxy. Considering its narrow red giant branch with no asymptotic giant branch stars, low metallicity, and location, it may be a fossil remnant of the first galaxies.Comment: 6 pages, 4 figures, 1 table, published in the Astrophysical Journal Letters, minor changes to agree with published versio

The Tip of the Red Giant Branch Distances to Type Ia Supernova Host Galaxies. II. M66 and M96 in the Leo I Group

M66 and M96 in the Leo I Group are nearby spiral galaxies hosting Type Ia Supernovae (SNe Ia). We estimate the distances to these galaxies from the luminosity of the tip of the red giant branch (TRGB). We obtain $VI$ photometry of resolved stars in these galaxies from $F555W$ and $F814W$ images in the {\it Hubble Space Telescope} archive. From the luminosity function of these red giants we find the TRGB $I$-band magnitude to be $I_{\rm TRGB}=26.20\pm0.03$ for M66 and $26.21\pm0.03$ for M96. These values yield distance modulus $(m-M)_0=30.12\pm0.03 ({\rm random})\pm0.12 ({\rm systematic})$ for M66 and $(m-M)_0=30.15\pm0.03 ({\rm random})\pm0.12 ({\rm systematic})$ for M96. These results show that they are indeed the members of the same group. With these results we derive absolute maximum magnitudes of two SNe (SN 1989B in M66 and SN 1998bu in M96). $V$-band magnitudes of these SNe Ia are $\sim$0.2 mag fainter than SN 2011fe in M101, the nearest recent SN Ia. We also derive near-infrared magnitudes for SN 1998bu. Optical magnitudes of three SNe Ia (SN 1989B, SN 1998bu, and SN 2011fe) based on TRGB analysis yield a Hubble constant, $H_0=67.6\pm1.5 ({\rm random})\pm 3.7({\rm systematic})$ \kmsMpc. This value is similar to the values derived from recent WMAP9 results, $H_0=69.32\pm0.80$ \kmsMpc. % and from Planck results, $H_0=67.3\pm1.2$ \kmsMpc, but smaller than other recent determinations based on Cepheid calibration for SNe Ia luminosity, $H_0 = 74 \pm3$ km s$^{-1}$ Mpc$^{-1}$.Comment: 10 pages, 4 figures, 8 tables, accepted for publication in Ap

Dual Stellar Halos in the Standard Elliptical Galaxy M105 and Formation of Massive Early-Type Galaxies

M105 is a standard elliptical galaxy, located in the Leo I Group. We present photometry of the resolved stars in its inner region at R ~ 4' ~ 4Reff, obtained from F606W and F814W images in the Hubble Space Telescope archive. We combine this with photometry of the outer region at R ~ 12' ~ 12Reff from archival imaging data. Color-magnitude diagrams of the resolved stars in the inner region show a prominent red giant branch (RGB) with a large color range, while those of the outer region show better a narrow blue RGB. The metallicity distribution function (MDF) of the RGB stars shows the existence of two distinct subpopulations: a dominant metal-rich population (with a peak at [M/H] ~ 0.0) and a much weaker metal-poor population (with a peak at [M/H] ~ -1.1). The radial number density profiles of the metal-rich and metal-poor RGB stars are fit well by a Sersic law with n=2.75+-0.10 and n=6.89+-0.94, and by a single power law, respectively. The MDFs of the inner and outer regions can be described well by accretion gas models of chemical evolution with two components. These provide strong evidence that there are two distinct stellar halos in this galaxy, metal-poor and red metal-rich halos, consistent with the results based on globular cluster systems in bright early-type galaxies (Park & Lee 2013). We discuss the implications of these results with regard to the formation of massive early-type galaxies in the dual halo mode formation scenario.Comment: 17 pages, 13 figures, and 7 tables ; Accepted for publication in Ap

Star Clusters in the Elliptical Galaxy NGC 4589 Hosting a Calcium-rich SN Ib (SN 2005CZ)

_NGC 4589, a bright E2 merger-remnant galaxy, hosts the peculiar fast and faint calcium-rich Type Ib supernova (SN) SN 2005cz. The progenitor of Ca-rich SNe Ib has been controversial: it could be a) a young massive star with 6-12 M$\odot$ in a binary system, or b) an old low-mass star in a binary system that was kicked out from the galaxy center. Moreover, previous distance estimates for this galaxy have shown a large spread, ranging from 20 Mpc to 60 Mpc. Thus, using archival $Hubble$ $Space$ $Telescope$/ACS $F435W$, $F555W$, and $F814W$ images, we search for star clusters in NGC 4589 in order to help resolve these issues. We find a small population of young star clusters with $25<V\leq27$ ($-7.1<M_V\leq-5.1$) mag and age $< 1$ Gyr in the central region at $R<0.5'$ ($<3.8$ kpc), thus supporting the massive-star progenitor scenario for SN 2005cz. In addition to young star clusters, we also find a large population of old globular clusters. In contrast to previous results in the literature, we find that the color distribution of the globular clusters is clearly bimodal. The turnover (Vega) magnitude in the $V$-band luminosity functions of the blue (metal-poor) globular clusters is determined to be $V_0{(\rm max)}=24.40\pm0.10$ mag. We derive the total number of globular clusters, $N_{\rm GC} =640\pm50$, and the specific frequency, $S_N =1.7\pm0.2$. Adopting a calibration for the metal-poor globular clusters, $M_V({\rm max})=-7.66\pm0.14$ mag, we derive a distance to this galaxy: $(m-M)_0=32.06\pm0.10({\rm ran})\pm0.15({\rm sys})$ ($d=25.8\pm2.2$ Mpc).Comment: 27 pages, 12 figures, 6 tables, accepted for publication in Ap

Indexing by Latent Dirichlet Allocation and Ensemble Model

The contribution of this paper is two-fold. First, we present Indexing by Latent Dirichlet Allocation (LDI), an automatic document indexing method. The probability distributions in LDI utilize those in Latent Dirichlet Allocation (LDA), a generative topic model that has been previously used in applications for document retrieval tasks. However, the ad hoc applications, or their variants with smoothing techniques as prompted by previous studies in LDA-based language modeling, result in unsatisfactory performance as the document representations do not accurately reflect concept space. To improve performance, we introduce a new definition of document probability vectors in the context of LDA and present a novel scheme for automatic document indexing based on LDA. Second, we propose an Ensemble Model (EnM) for document retrieval. The EnM combines basis indexing models by assigning different weights and attempts to uncover the optimal weights to maximize the Mean Average Precision (MAP). To solve the optimization problem, we propose an algorithm, EnM.B, which is derived based on the boosting method. The results of our computational experiments on benchmark data sets indicate that both the proposed approaches are viable options for document retrieval.Comment: Accepted by the Journal of American Society for Information Science and Technology (JASIST

A new superconducting open-framework allotrope of silicon at ambient pressure

Diamond Si is a semiconductor with an indirect band gap that is the basis of modern semiconductor technology. Although many metastable forms of Si were observed using diamond anvil cells for compression and chemical precursors for synthesis, no metallic phase at ambient conditions has been reported thus far. Here we report the prediction of pure metallic Si allotropes with open channels at ambient pressure, unlike a cubic diamond structure in covalent bonding networks. The metallic phase termed P6/m-Si6 can be obtained by removing Na after pressure release from a novel Na-Si clathrate called P6/m-NaSi6, which is discovered through first-principles study at high pressure. We confirm that both P6/m-NaSi6 and P6/m-Si6 are stable and superconducting with the critical temperatures of about 13 and 12 K at ambient pressure, respectively. The discovery of new Na-Si and Si clathrate structures presents the possibility of exploring new exotic allotropes useful for Si-based devices