Aggregate dust model to study the polarization properties of comet C/1996 B2 Hyakutake

In our present study, the observed linear polarization data of comet Hyakutake are studied at wavelengths $\lambda=0.365\mu m$, $\lambda=0.485\mu m$ and 0.684$\mu m$ through simulations using Ballistic Particle-Cluster Aggregate and Ballistic Cluster-Cluster Aggregate aggregates of 128 spherical monomers. We first investigated that the size parameter of the monomer, $x$ $\sim$ 1.56 -- 1.70, turned out to be most suitable which provides the best fits to the observed dust scattering properties at three wavelengths $\lambda = 0.365$$\mu m$, 0.485$\mu m$ and 0.684$\mu m$. Thus the effective radius of the aggregate (r) lies in the range $0.45 \mu m \le r \le 0.49 \mu m$ at $\lambda = 0.365$$\mu m$; $0.60 \mu m \le r \le 0.66 \mu m$ at $\lambda = 0.485$$\mu m$ and $0.88 \mu m \le r \le 0.94 \mu m$ at $\lambda = 0.684$$\mu m$. Now using superposition \textsc{t-matrix} code and the power-law size distribution, $n(r) \sim r^{-3}$, the best-fitting values of complex refractive indices are calculated which can best fit the observed polarization data at the above three wavelengths. The best-fitting complex refractive indices $(n,k)$ are found to be (1.745, 0.095) at $\lambda = 0.365$ $\mu m$, (1.743, 0.100) at $\lambda = 0.485$ $\mu m$ and (1.695, 0.100) at $\lambda = 0.684$ $\mu m$. The refractive indices coming out from the present analysis correspond to mixture of both silicates and organics, which are in good agreement with the \textit{in situ} measurement of comets by different spacecraft.Comment: 9 pages, 3 figure

Grain size limits derived from 3.6 {\mu}m and 4.5 {\mu}m coreshine

Recently discovered scattered light from molecular cloud cores in the wavelength range 3-5 {\mu}m (called "coreshine") seems to indicate the presence of grains with sizes above 0.5 {\mu}m. We aim to analyze 3.6 and 4.5 {\mu}m coreshine from molecular cloud cores to probe the largest grains in the size distribution. We analyzed dedicated deep Cycle 9 Spitzer IRAC observations in the 3.6 and 4.5 {\mu}m bands for a sample of 10 low-mass cores. We used a new modeling approach based on a combination of ratios of the two background- and foreground-subtracted surface brightnesses and observed limits of the optical depth. The dust grains were modeled as ice-coated silicate and carbonaceous spheres. We discuss the impact of local radiation fields with a spectral slope differing from what is seen in the DIRBE allsky maps. For the cores L260, ecc806, L1262, L1517A, L1512, and L1544, the model reproduces the data with maximum grain sizes around 0.9, 0.5, 0.65, 1.5, 0.6, and > 1.5 {\mu}m, respectively. The maximum coreshine intensities of L1506C, L1439, and L1498 in the individual bands require smaller maximum grain sizes than derived from the observed distribution of band ratios. Additional isotropic local radiation fields with a spectral shape differing from the DIRBE map shape do not remove this discrepancy. In the case of Rho Oph 9, we were unable to reliably disentangle the coreshine emission from background variations and the strong local PAH emission. Considering surface brightness ratios in the 3.6 and 4.5 {\mu}m bands across a molecular cloud core is an effective method of disentangling the complex interplay of structure and opacities when used in combination with observed limits of the optical depth.Comment: 23 pages, 18 figures, accepted for publication in A&

Good measures on locally compact Cantor sets

We study the set M(X) of full non-atomic Borel (finite or infinite) measures on a non-compact locally compact Cantor set X. For an infinite measure $\mu$ in M(X), the set $\mathfrak{M}_\mu = \{x \in X : {for any compact open set} U \ni x {we have} \mu(U) = \infty \}$ is called defective. We call $\mu$ non-defective if $\mu(\mathfrak{M}_\mu) = 0$. The class $M^0(X) \subset M(X)$ consists of probability measures and infinite non-defective measures. We classify measures $\mu$ from $M^0(X)$ with respect to a homeomorphism. The notions of goodness and compact open values set $S(\mu)$ are defined. A criterion when two good measures from $M^0(X)$ are homeomorphic is given. For any group-like $D \subset [0,1)$ we find a good probability measure $\mu$ on X such that $S(\mu) = D$. For any group-like $D \subset [0,\infty)$ and any locally compact, zero-dimensional, metric space A we find a good non-defective measure $\mu$ on X such that $S(\mu) = D$ and $\mathfrak{M}_\mu$ is homeomorphic to A. We consider compactifications cX of X and give a criterion when a good measure $\mu \in M^0(X)$ can be extended to a good measure on cX.Comment: 21 page

Far-Infrared Line Imaging of the Starburst Ring in NGC 1097 with the Herschel/PACS Spectrometer

NGC 1097 is a nearby SBb galaxy with a Seyfert nucleus and a bright starburst ring. We study the physical properties of the interstellar medium (ISM) in the ring using spatially resolved far-infrared spectral maps of the circumnuclear starburst ring of NGC 1097, obtained with the PACS spectrometer on board the Herschel Space Telescope. In particular, we map the important ISM cooling and diagnostic emission lines of [OI] 63 $\mu$m, [OIII] 88 $\mu$m, [NII] 122 $\mu$m, [CII] 158 $\mu$m and [NII] 205 $\mu$m. We observe that in the [OI] 63 $\mu$m, [OIII] 88 $\mu$m, and [NII] 122 $\mu$m line maps, the emission is enhanced in clumps along the NE part of the ring. We observe evidence of rapid rotation in the circumnuclear ring, with a rotation velocity of ~220$km s$^{-1}$(inclination uncorrected) measured in all lines. The [OI] 63$\mu$m/[CII] 158$\mu$m ratio varies smoothly throughout the central region, and is enhanced on the northeastern part of the ring, which may indicate a stronger radiation field. This enhancement coincides with peaks in the [OI] 63$\mu$m and [OIII] 88$\mu$m maps. Variations of the [NII] 122$\mu$m/[NII] 205$\mu$m ratio correspond to a range in the ionized gas density between 150 and 400 cm$^{-3}$.Comment: Accepted for publication on the A&A Herschel Special Issu

Anatomy of the Soft-Photon Approximation in Hadron-Hadron Bremsstrahlung

A modified Low procedure for constructing soft-photon amplitudes has been used to derive two general soft-photon amplitudes, a two-s-two-t special amplitude $M^{TsTts}_{\mu}$ and a two-u-two-t special amplitude $M^{TuTts}_{\mu}$, where s, t and u are the Mandelstam variables. $M^{TsTts}_{\mu}$ depends only on the elastic T-matrix evaluated at four sets of (s,t) fixed by the requirement that the amplitude be free of derivatives ($\partial$T/$\partial$s and /or $\partial$T/$\partial t$). Likewise $M^{TuTts}_{\mu}$ depends only on the elastic T-matrix evaluated at four sets of (u,t). In deriving these amplitudes, we impose the condition that $M^{TsTts}_{\mu}$ and $M^{TuTts}_{\mu}$ reduce to $\bar{M}^{TsTts}_{\mu}$ and $\bar{M}^{TuTts}_{\mu}$, respectively, their tree level approximations. The amplitude $\bar{M}^{TsTts}_{\mu}$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle s-channel exchange diagrams, while the amplitude $\bar{M}^{TuTts} _{\mu}$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle u-channel exchange diagrams. The precise expressions for $\bar{M}^{TsTts}_{\mu}$ and $\bar{M}^{TuTts}_{\mu}$ are determined by using the radiation decomposition identities of Brodsky and Brown. We point out that it is theoretically impossible to describe all bremsstrahlung processes by using only a single class of soft-photon amplitudes. At least two different classes are required: the amplitudes which depend on s and t or the amplitudes which depend on u and t. When resonance effects are important, the amplitude $M^{TsTts}_{\mu}$, not $M^{Low(st)}_{\mu}$, should be used. For processes with strong u-channel exchange effects, the amplitude $M^{TuTts}_{\mu}$ should be the first choice.Comment: 49 pages report # LA-UR-92-270