Discovery of "Warm Dust" galaxies in clusters at z ~ 0.3: evidence for stripping of cool dust in the dense environment?

Using far-infrared imaging from the "Herschel Lensing Survey," we derive dust properties of spectroscopically confirmed cluster member galaxies within two massive systems at z ~ 0.3: the merging Bullet Cluster and the more relaxed MS2137.3-2353. Most star-forming cluster sources (~90%) have characteristic dust temperatures similar to local field galaxies of comparable infrared (IR) luminosity (T_dust ~ 30 K). Several sub-luminous infrared galaxy (LIRG; L_IR < 10^11 L_☉) Bullet Cluster members are much warmer (T_dust > 37 K) with far-infrared spectral energy distribution (SED) shapes resembling LIRG-type local templates. X-ray and mid-infrared data suggest that obscured active galactic nuclei do not contribute significantly to the infrared flux of these "warm dust" galaxies. Sources of comparable IR luminosity and dust temperature are not observed in the relaxed cluster MS2137, although the significance is too low to speculate on an origin involving recent cluster merging. "Warm dust" galaxies are, however, statistically rarer in field samples (>3σ), indicating that the responsible mechanism may relate to the dense environment. The spatial distribution of these sources is similar to the whole far-infrared bright population, i.e., preferentially located in the cluster periphery, although the galaxy hosts tend toward lower stellar masses (M_* < 10^10 M_☉). We propose dust stripping and heating processes which could be responsible for the unusually warm characteristic dust temperatures. A normal star-forming galaxy would need 30%-50% of its dust removed (preferentially stripped from the outer reaches, where dust is typically cooler) to recover an SED similar to a "warm dust" galaxy. These progenitors would not require a higher IR luminosity or dust mass than the currently observed normal star-forming population.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.