AR_final file_2018-19

remain more or less of the same order when they are evaluated at wavelengths equal to the width or radius of the macrospicule. It is worth noting that the excited MHD modes are super-Alfvenic. A change in the background magnetic field can lead to another MHD mode number, m, that ensures the required instability window. This study has been carried out in collaboration with I. Zhelyazkov. Suresh Chandra Suggestion for search of ethylene oxide ( c -C 2 H 4 O) in a cosmic object Because of their potential role in the formation of amino acids, ethylene oxide ( c -C 2 H 4 O) and its isomer acetaldehyde (CH 3 CHO) are important or- ganic molecules. The c -C 2 H 4 O is b -type asymmet- ric top molecule and due to half-spin of each of its four hydrogen atoms, it has two distinct ortho (nuclear spin one) and para (nuclear spin zero and two) species. It has been identified in the galac- tic source Sgr B2N. Using the spectroscopic infor- mation (rotational and centrifugal distortion con- stants, and the electric dipole moment), we have calculated energies of 100 rotational levels of each of the ortho and para species of molecule and the Einstein A -coefficients for radiative transitions be- tween the levels. Using scaled values for collisional rate coefficients along with the values of Einstein A - coefficients, we have solved a set of statistical equi- librium equations coupled with the equations of ra- diative transfer for each of the species. Brightness- temperatures of five rotational transitions of each of the ortho and para species of c -C 2 H 4 O are inves- tigated. Out of these ten transitions, three transi- tions are found to show the anomalous absorption and rest seven are found to show the emission fea- ture. We have also investigated seven transitions observed unblended in Sgr B2(N). It is found that the transitions 3 30 − 3 21 (23.139 GHz), 2 20 − 2 11 (15.605 GHz), and 3 31 − 3 22 (39.686 GHz) may play important role in the identification of ethylene ox- ide in a cosmic object. This work has been done in collaboration with Mohit K. Sharma, and Monika Sharma. Strengths of rotational lines from H 2 CC molecule: Addressing tentative detection Though H 2 C, H 2 CCC, H 2 CCCC, H 2 CCO, H 2 CO, H 2 CS molecules have been identified in cool in- terstellar clouds, identification of H 2 CC is still awaited. Formation of H 2 CC in the interstellar medium is quite probable as the cosmic abundance of carbon is 20 times larger than that of the sulpher, and the molecule H 2 CS has already been identi- fied in the interstellar medium. To our knowl- edge, no laboratory study for H 2 CC is available in literature. Physical conditions in the interstellar medium are quite different as compared to those in a terrestrial laboratory. Using the rotational and centrifugal distortion constants for H 2 CC, we have calculated the energies of rotational levels and the strengths of lines between the levels up to 270 cm − 1 . We have found that 88 and 87 lines of ortho- H 2 CC and para-H 2 CC, respectively have Einstein A -coefficient larger than 10 − 5 s − 1 . These lines may help in the identification of H 2 CC in the interstel- lar medium. Tentative detection of H 2 CC has been addressed. This work has been done in collabora- tion with Mohit K. Sharma, and Monika Sharma. Ayan Chatterjee Quasi-local first law of black hole dynamics from local Lorentz transformations Quasi-local formulations of black hole are of im- mense importance since they reveal the essential and minimal assumptions required for a consistent description of black hole horizon, without relying on the asymptotic boundary conditions on fields. Using the quasi-local formulation of Isolated Hori- zons, we construct the Hamiltonian charges cor- responding to local Lorentz transformations on a spacetime admitting isolated horizon as an internal boundary. From this construction, it arises quite generally that the area of the horizon of an iso- lated black hole is the Hamiltonian charge for local Lorentz boost on the horizon. Using this argument further, it is shown that observers at a fixed proper distance l 0 , very close to the horizon, may define a notion of horizon energy given by E = A/ 8 πGl 0 , the surface gravity is given by κ = 1 /l 0 , and con- sequently, the first law can be written in the quasi- local setting as δE = ( κ/ 8 πG ) δA . This study has been carried out in collaboration with Avirup Ghosh. Joining spacetimes on fractal hypersurfaces The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the ( 179 )