Study Of A Far Infrared Cavity At The Galactic Plane

A far infrared dust cavity nearby AGB star namely AGB19+26 found to be located, centered at R.A.(J2000)= 20h 02m 02.8s and Dec.(J2000)= 26° 52' 36.8".Distribution of Planck function, dust color temperature, dust mass and visual extinction of the far infrared cavity was studied. This cavity was found to have following properties: (a) it is located nearby AGB star named AGB19+26around far infrared loopG064-01 at 2000 pc, (b) it is close to the Galactic plane at galactic latitude -1.2° therefore the radiation field is strong and (c) the diameter of the cavity is greater than 0.2° on IRAS. The dust color temperatures are found to be in the range 21.48 ± 0.25 K to 22.03 ± 0.12 K. Planck function was found to be non-uniform along its extension and compression, suggesting that the dust and grains are not in the local thermodynamic equilibrium, possibly because of external cause. It is therefore, a deviation from the Gaussian distribution is noted in the histogram of dust color temperature. It is concluded that the cavity was formed due to the high pressure events occurred in the past.

EQUIVALENCE OF ELLIPTICITY AND THE FREDHOLM PROPERTY IN THE WEYL-HÖRMANDER CALCULUS

The main result is that the ellipticity and the Fredholm property of a $\Psi $ DO acting on Sobolev spaces in the Weyl-Hörmander calculus are equivalent when the Hörmander metric is geodesically temperate and its associated Planck function vanishes at infinity. The proof is essentially related to the following result that we prove for geodesically temperate Hörmander metrics: If $\lambda \mapsto a_{\lambda }\in S(1,g)$ is a $\mathcal {C}^N$ , $0\leq N\leq \infty $ , map such that each $a_{\lambda }^w$ is invertible on $L^2$ , then the mapping $\lambda \mapsto b_{\lambda }\in S(1,g)$ , where $b_{\lambda }^w$ is the inverse of $a_{\lambda }^w$ , is again of class $\mathcal {C}^N$ . Additionally, assuming also the strong uncertainty principle for the metric, we obtain a Fedosov-Hörmander formula for the index of an elliptic operator. At the very end, we give an example to illustrate our main result.

Study of Dust Properties of two Far Infrared Cavities near by Asymptotic Giant Branch stars under Infrared Astronomical Satellite Maps

The physical properties such as dust color temperature, dust mass, visual extinction, and Planck function with their distribution in the core region of two far-infrared cavities, namely FIC16-37 (size ~ 4.79 pc x 3.06 pc) located at R.A. (J2000): 16h 33m 57.25s & Dec. (J2000): -37d 47m 04.3s, and FIC12-58 (size ~ 22.54 pc x 14.84 pc) located at R.A. (J2000): 12h 52m 50.08s & Dec. (J2000): -58d 08m 55.02s, found within a galactic plane -10o to +10o nearby Asymptotic Giant Branch (AGB) stars namely AGB15-38 (R.A. (J2000): 15h 37m 40.74s & Dec. (J2000): -38d 20m 24.6s), and AGB12-57 (R.A (J2000): 12h 56m 38.50s & Dec. (J2000): -57d 54m 34.70s), respectively were studied using Infrared Astronomical Satellite (IRAS) survey. The dust color temperature was found to lie in the range of 23.95 ± 0.25 K to 23.44 ± 0.27 K with an offset about 0.5 K for FIC16-37, and 24.88 ± 0.27 K to 23.63 ± 0.98 K with an offset about 1 K for FIC12-58. The low offset in the dust color temperature indicated the symmetric distribution of density and temperature. The total mass of the cavities FIC16-37 and FIC12-58 were found to be 0.053 M☉ and 0.78 M☉, respectively. The contour plots of mass distribution of both of the cavities was found to follow the cosmological principle, suggesting the homogeneous and isotropic distribution of dust masses. The plot between temperature and visual extinction showed a negative correlation, suggesting that higher temperature has lower visual extinction and vice-versa. The distribution of Planck function along major and minor diameters of both of the cavities was found to be non-uniform, indicating oscillation of dust particles to get dynamical equilibrium. It further suggested the role of pressure-driven events nearby both cavities and suggested that dust particles are not in thermal equilibrium along the diameters.

Planck Function Distribution in the Far Infrared Cavity Nearby AGB Star at Galactic Latitude 0.6º

A far infrared cavity nearby AGB star namely AGB2308+6058 was found to be located centered at R. A. (J2000)= 23h 06m 54.6s and Dec. (J2000)= 61° 16' 09.8". Distribution of dust color temperature, dust mass and visual extinction of the far infrared cavity have studied. In addition, the distribution of Planck function along the compression and extension of the cavity also has studied. This cavity has found to be located nearby the AGB star around far infrared loop G110+00 at 730 pc. It is close to the Galactic plane at galactic latitude 0.6° therefore the radiation field is strong and the diameter of the cavity is found to be greater than 0.2°. The dust color temperatures was found to be in the range 22.76 ± 0.14 K to 23.55 ± 0.29 K with offset 0.79 K. The contour maps of dust color temperature and dust mass showed that the low temperature region have greater mass density. Planck function showed non-uniform distribution along its extension and compression, suggesting that the dust and grains are not in the local thermodynamic equilibrium, possibly due to nearby AGB star. A clearly noted result is from counter map of dust mass and visual extinction that they showed consistent nature in their distribution.

Study of a Far Infrared Cavity Around a Post-Asymptotic Giant Branch Star at Galactic Latitude -0.1º

We present dust color temperature, Planck function and visual extinction distributions of a far infrared cavity FIC19+30 found to be located around post-AGB star namely AGB20+29 at the galactic plane. Minimum and maximum dust color temperature of the core region of the cavity was found to be (22.17±0.23) K and (22.41±0.29) K respectively with offset value 0.24 K which suggests that the cavity is isolated and stable. The product of dust color temperature and visual extinction was found to be in the order of 10-4 K mag. The distribution of Planck function along the extension (major diameter) and compression (minor diameter) was found to be non-uniform distribution. Specifically dust particles are oscillating in order to get dynamical equilibrium which may be the cause of grain temperature. It further suggests that the dust particles in the cavities might not be in the thermal equilibrium possibly due to pressure driven events of nearby AGB stars. There is continuous increase in flux density with increase in wavelength as in case of nebula which suggests that number density of dust particles increase according to the increase in wavelength and vice-versa.

Study of a Far Infrared Cavity at 60 μm and 100 μm IRAS Map around the Carbon-Rich AGB Star at Galactic Latitude 8.6°

In this paper, we discussed about the dusty environment of the far infrared cavity around the AGB star located at R.A. (J2000) =01h41m 01s and Dec (J2000) = 71° 04’ 00 9, lying within far infrared loop G125+09 6 in the far infrared IRAS maps. A cavity like structure (major diameter ∼2.55pc & minor diameter ∼0.77pc) is found to lie at R.A. (J2000) = 01h46m57.2s and DEC (J2000) = 71°24’57.1”, located at a distance ∼ 220pc from the star. We studied the distribution of flux density, dust color temperature, dust mass, visual extinction in the cavity. We further studied the distribution Planck function along extension and compression, distribution of dust color temperature along square of the major and minor diameters. The dust color temperature is found to lie in the range (19.7±1.25) K to (21.1±0.55)K which shows the cavity is isolated and stable. A possible explanation of the results will be discussed.

Study of Two Far Infrared Cavities Nearby Asymptotic Giant Branch Stars Under Infrared Astronomical Satellite Maps

Dust colour temperature, dust mass, visual extinction and Planck function with their distributions in the core region of two far infrared cavities (named FIC04+61 and FIC11-54) found within 3° of AGB stars namely AGB0409+6105 and AGB1105-5451 were studied. Dust colour temperature of the core region of the cavities was found to be (19.4 ± 0.93) K to (20.6 ± 0.65) K and (21.4 ± 0.51) K to (22.6 ± 0.23) K, respectively. The product of dust colour temperature and visual extinction was consistent in the order of 10-4. The contour maps showed that the low-temperature region has greater mass density and suggests that the distribution of dust mass is homogeneous and isotropic. The distribution of Planck function along with the extension (major diameter) and compression (minor diameter) found to be non-uniform distribution means dust particles were oscillating to get dynamical equilibrium. It further suggests that the dust particles in the cavities might not be in the thermal equilibrium possibly due to pressure-driven events of nearby AGB stars. A negative slope in the transition from 25 μm to 60 μm was our finding regarding far infrared spectral distribution in the cavities. It suggests that the number density of dust particles was less than expected in 60 μm regions.