A New Weak Lensing Analysis of MS1224.7+2007

Galaxy cluster mass distributions are useful probes of Omega_0 and the nature of the dark matter. Large clusters will distort the observed shapes of background galaxies through gravitational lensing allowing the measurement of the cluster mass distributions. For most cases, the agreement between weak lensing and radial velocity mass measurements of clusters is reasonably good. There is, however, one significant exception, the z=0.32 cluster MS1224.7+2007, which has a lensing mass substantially larger than the virial mass and also a very high mass-to-light ratio. Since this controversial object might be an unusually dark mass a follow-up study is definitely warranted. In this paper we study the mass and light distributions of MS1224+2007 out to a projected radius of 800/h kpc by measuring the gravitationally-induced distortions of background galaxies. We detect a shear signal in the background galaxies in the radial range 27.5 arcsec < r < 275 arcsec at the 5.5 sigma level. The resultant mass map exhibits a peak centered on the dominant cluster galaxy and strong evidence for substructure which is even more strongly seen in the galaxy distribution. Assuming all the detected shear is due to mass at z=0.32 we find cluster mass-to-light ratio of M/L_R = 640 +/- 150. The mass profile is quite flat compared to other clusters, disagreeing with a pseudo-singular isothermal sphere at the 95% confidence level. Our mass and M/L estimates are consistent with the previous weak lensing result. The discrepancy between the lensing and virial mass remains although it might be partially explained by subclustering and infall perpendicular to the line-of-site. This cluster remains a candidate dark object deficient in baryons and as such severely tests cosmological models.Comment: AASTEX, 22 pages 9 figures. Also available at: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Fully Packed Loops in a triangle: matchings, paths and puzzles

Fully Packed Loop configurations in a triangle (TFPLs) first appeared in the study of ordinary Fully Packed Loop configurations (FPLs) on the square grid where they were used to show that the number of FPLs with a given link pattern that has m nested arches is a polynomial function in m. It soon turned out that TFPLs possess a number of other nice properties. For instance, they can be seen as a generalized model of Littlewood-Richardson coefficients. We start our article by introducing oriented versions of TFPLs; their main advantage in comparison with ordinary TFPLs is that they involve only local constraints. Three main contributions are provided. Firstly, we show that the number of ordinary TFPLs can be extracted from a weighted enumeration of oriented TFPLs and thus it suffices to consider the latter. Secondly, we decompose oriented TFPLs into two matchings and use a classical bijection to obtain two families of nonintersecting lattice paths (path tangles). This point of view turns out to be extremely useful for giving easy proofs of previously known conditions on the boundary of TFPLs necessary for them to exist. One example is the inequality d(u)+d(v)<=d(w) where u,v,w are 01-words that encode the boundary conditions of ordinary TFPLs and d(u) is the number of cells in the Ferrers diagram associated with u. In the third part we consider TFPLs with d(w)- d(u)-d(v)=0,1; in the first case their numbers are given by Littlewood-Richardson coefficients, but also in the second case we provide formulas that are in terms of Littlewood-Richardson coefficients. The proofs of these formulas are of a purely combinatorial nature.Comment: 40 pages, 31 figure

Optimal Addition of Images for Detection and Photometry

In this paper we describe weighting techniques used for the optimal coaddition of CCD frames with differing characteristics. Optimal means maximum signal-to-noise (s/n) for stellar objects. We derive formulae for four applications: 1) object detection via matched filter, 2) object detection identical to DAOFIND, 3) aperture photometry, and 4) ALLSTAR profile-fitting photometry. We have included examples involving 21 frames for which either the sky brightness or image resolution varied by a factor of three. The gains in s/n were modest for most of the examples, except for DAOFIND detection with varying image resolution which exhibited a substantial s/n increase. Even though the only consideration was maximizing s/n, the image resolution was seen to improve for most of the variable resolution examples. Also discussed are empirical fits for the weighting and the availability of the program, WEIGHT, used to generate the weighting for the individual frames. Finally, we include appendices describing the effects of clipping algorithms and a scheme for star/galaxy and cosmic ray/star discrimination.Comment: 27 pages (uuencoded compressed postscript), 199

The Mass distribution of the Cluster 0957+561 from Gravitational Lensing

Multiply gravitationally lensed objects with known time delays can lead to direct determinations of H$_0$ independent of the distance ladder if the mass distribution of the lens is known. Currently, the double QSO 0957+561 is the only lensed object with a precisely known time delay. The largest remaining source of systematic error in the H$_0$ determination results from uncertainty in the mass distribution of the lens which is comprised of a massive galaxy (G1) and the cluster in which it resides. We have obtained V-band CCD images from CFHT in order to measure the mass distribution in the cluster from its gravitional distorting effect on the appearance of background galaxes. We use this data to constuct a two-dimensional mass map of the field. A mass peak is detected at the $4.5\sigma$ level, offset from, but consistent with, the position of G1. Simple tests reveal no significant substructure and the mass distribution is consistent with a spherical cluster. The peak in the number density map of bright galaxies is offset from G1 similarly to the mass peak. We constructed an azimuthally averaged mass profile centered on G1 out to 2 \arcmin ($400 h^{-1}$ kpc). It is consistent with an isothermal mass distribution with a small core (r_c \approx 5 \arcsec = 17 h^{-1} kpc). The inferred mass within 1 Mpc is consistent with the dynamical mass estimate but $2\sigma$ higher than the upper limits from a ROSAT X-ray study. We discuss implications for H$_0$ in a future paper.Comment: LaTeX, aas version 4 macros. Calibration error in original led to overestimate of cluster mass. Seven out of twelve figures included. Complete paper is available at: http://www.astro.lsa.umich.edu:80/users/philf

Non-Parametric Dynamical Analysis of Globular Clusters: M15, 47~Tuc, NGC~362, and NGC~3201

We use radial velocities of member stars and cluster surface brightness profiles to non-parametrically determine the mass density profiles and isotropic phase-space distribution functions $f(E)$ for the globular clusters M15 (NGC7078), 47~Tuc (NGC104), NGC~362, and NGC~3201. Assuming isotropy and using the velocity dispersion and surface brightness profiles, the Jeans equation uniquely determines the mass density profile. In the two centrally-concentrated clusters, M15 and 47~Tuc, we find that the mass-to-light ratios (M/L's) reach minima around 1\arcmin, and increase by more than a factor of four towards the cluster centers. For the two less centrally concentrated clusters, the M/L decreases monotonically all the way into the center. All four clusters exhibit an increase in the M/L's in their outer parts. If the variations in the M/L's are due to equipartition of energy between different mass stars, then we attribute the central increases to massive remnants and the outer increases to low-mass stars (m$<0.3$M$_\odot$). By applying the crude approximation of local thermodynamic equilibrium, we derive the present-day mass function for each cluster. In the central 2--3 parsecs, 0.7--1.5 M$_\odot$ objects provide the bulk of the cluster mass. The paper is in a uuencoded compressed tar file (260kb)

Improved Parameters and New Lensed Features for Q0957+561 from WFPC2 Imaging

New HST WFPC2 observations of the lensed double QSO 0957+561 will allow improved constraints on the lens mass distribution and hence will improve the derived value of H$_0$. We first present improved optical positions and photometry for the known components of this lens. The optical separation between the A and B quasar images agrees with VLBI data at the 10 mas level, and the optical center of the primary lensing galaxy G1 coincides with the VLBI source G' to within 10 mas. The best previous model for this lens (Grogin and Narayan 1996) is excluded by these data and must be reevaluated. Several new resolved features are found within 10\arcsec of G1, including an apparent fold arc with two bright knots. Several other small galaxies are detected, including two which may be multiple images of each other. We present positions and crude photometry of these objects.Comment: 7 pages including 2 postscript figures, LaTeX, emulateapj style. Also available at http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

The Mass distribution of the Most Luminous X-ray Cluster RXJ1347.5-1145 from Gravitational Lensing

Galaxy cluster mass distribution are potentially useful probes of $\Omega_0$ and the nature of the dark matter. Large clusters will distort the observed shapes of background galaxies through gravitational lensing allowing the measurement of the cluster mass distributions. In this paper we describe weak statistical lensing measurements of the most luminous X-ray cluster known, RXJ1347.5-1145 at z=0.45. We detect a shear signal in the background galaxies at a signal-to-noise ratio of 7.5 in the radial range $120 \le r \le 1360 h^{-1}$ kpc. A mass map of the cluster reveals an 11$\sigma$ peak in the cluster mass distribution consistent with the position of the central dominant galaxy and 3 $\sigma$ evidence for the presence of a subcluster at a projected radius of 1.3 - 1.7 h^{-1} Mpc from the cluster center. In the range $120 \le r \le 1360 h^{-1}$ kpc mass traces light, and the azimuthally averaged cluster mass and light profiles are consistent with singular isothermal spheres with M(r<1 Mpc) = $1.7 \pm 0.4 \times 10^{15} M_\odot$. Assuming an isotropic velocity distribution function, the implied velocity dispersion is $\sigma = 1500 \pm 160 km s^{-1}$. The rest-frame mass-to-light ratio is $M/L_B = 200 \pm 50 h M_\odot/L_{B\odot}$. The lensing mass estimate is almost twice as high as a previously determined X-ray mass estimate.Comment: 21 Pages LaTeX, AASTEX version 4 macros, Accepted for publication in the AJ. 8 of 12 figures included, full paper at http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Discovery of a New Quadruple Lens HST 1411+5211

Gravitational lensing is an important tool for probing the mass distribution of galaxies. In this letter we report the discovery of a new quadruple lens HST 1411+5211 found in archived WFPC2 images of the galaxy cluster CL140933+5226. If the galaxy is a cluster member then its redshift is $z=0.46$. The images of the source appear unresolved in the WFC implying that the source is a quasar. We have modeled the lens as both a single galaxy and a galaxy plus a cluster. The latter model yields excellent fits to the image positions along with reasonable parameters for the galaxy and cluster making HST 1411+5211 a likely gravitational lens. Determination of the source redshift and confirmation of the lens redshift would allow us to put strong constraints on the mass distribution of the lensing galaxy.Comment: 11 pages including 1 postscript figure, aastex. Accepted to the ApJL. Also available from: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Dynamics of the Intermediate-Age Elliptical LMC Cluster NGC 1978

In this paper we investigate the internal dynamics of the LMC cluster NGC 1978 through the use of Photometric (CCD images) and kinematic (stellar radial velocities) data. We apply a variety of dynamical models to this data, including multi-mass King-Michie models and rotating and non-rotating oblate spheroid models. We discuss the cluster mass-to-light ratio and place constraints on the cluster mass function.Comment: 36 pages (plus 8 figures available through anonymous FTP, see below