2010 (IPP)
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Item Quantitative measure of evolution of bright cluster galaxies at moderate redshifts(2010-01-01) Vikram, Vinu; et al.; Wadadekar, Yogesh; Kembhavi, A.K.Using archival data from the Hubble Space Telescope, we study the quantitative morphological evolution of spectroscopically confirmed bright galaxies in the core regions of nine clusters ranging in redshift from z = 0.31 to z = 0.84. We use morphological parameters derived from two dimensional bulge-disk decomposition to study the evolution. We find an increase in the mean bulge-to-total luminosity ratio B/T as the Universe evolves. We also find a corresponding increase in the fraction of early type galaxies and in the mean S´ersic index. We discuss these results and their implications to physical mechanisms for evolution of galaxy morphology.Item Interstellar extinction and polarization - A spheroidal dust grain approach perspective(2010-01-10) Das, H.K.; Voshchinnikov, N. V.; Il'in, V.B.We extend and investigate the spheroidal model of interstellar dust grains used to simultaneously interpret the observed interstellar extinction and polarization curves. We compare our model with similar models recently suggested by other authors, study its properties and apply it to fit the normalized extinction A(λ)/AV and the polarizing efficiency P(λ)/A(λ) measured in the near IR to far UV region for several stars seen through one large cloud. We conclude that the model parameter Ω being the angle between the line of sight and the magnetic field direction can be more or less reliably determined from comparison of the theory and observations. This opens a way to study the spatial structure of interstellar magnetic fields by using multi-wavelength photometric and polarimetric observations.Item Cosmic ray driven outflows from high redshift galaxies(2010-01-10) Samui, Saumyadip; Subramanian, Kandaswamy; Srianand, R.We study winds in high redshift galaxies driven by a relativistic cosmic ray (proton) component in addition to the hot thermal gas component. Cosmic rays (CRs) are likely to be efficiently generated in supernova(SNe)shocks inside galaxies. We obtain solutions of such CR driven free winds in a gravitational potential of the Navarro-Frenk-White (NFW) form, relevant to galaxies. Cosmic rays naturally provide the extra energy and/or momentum input to the system, needed for a transonic wind solution in a gas with adiabatic index = 5=3.We show that cosmic rays can effectively drive winds even when the thermal energy of the gas is lost due to radiative cooling. These wind solutions predict an asymptotic wind speed closely related to the circular velocity of the galaxy. Furthermore, the mass outflow rate per unit star formation rate ( w) is predicted to be ~ 0:2 0:5 for massive galaxies, with masses M ~ 1011 1012M .We show w to be inversely proportional to the square of the circular velocity. Magnetic fields at the G levels are also required in these galaxies to have a significant mass loss. A large w for small mass galaxies implies that cosmic ray driven outflows could provide a strong negative feedback to the star formation in dwarf galaxies. Further, our results will also have important implications to the metal enrichment of the intergalactic medium. These conclusions are applicable to the class of free wind models where the source region is confined to be within the sonic point.Item Time delay interferometry for LISA with one arm dysfunctional(2010-01-27) Dhurandhar, Sanjeev; Nayak, K. R.; Vinet, J-Y.In order to attain the requisite sensitivity for LISA - a joint space mission of the ESA and NASA- the laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. By combining six appropriately time-delayed data streams containing fractional Doppler shifts - a technique called time delay interferometry (TDI) - the laser frequency noise may be adequately suppressed. We consider the general model of LISA where the armlengths vary with time, so that second generation TDI are relevant. However, we must envisage the possibility, that not all the optical links of LISA will be operating at all times, and therefore, we here consider the case of LISA operating with two arms only. As shown earlier in the literature, obtaining even approximate solutions of TDI to the general problem is very difficult. Since here only four optical links are relevant, the algebraic problem simplifies considerably. We are then able to exhibit a large number of solutions (from mathematical point of view an infinite number) and further present an algorithm to generate these solutions.Item HD molecules at high redshift: The absorption system at z=2.3377 towards Q 1232+082(2010-02-10) Srianand, R.Item Detection of 21-cm, H2 and Deuterium absorption at z>3 along the line-of-sight to J1337+3152(2010-02-24) Srianand, R.; Gupta, Neeraj; Petitjean, Patrick; et al.We report the detection of 21-cm and molecular hydrogen absorption lines in the same damped Lyman-α system (with log N(H i)=21.36±0.10) at zabs=3.17447 towards SDSS J133724.69+315254.55 (zem ∼3.174). We estimate the spin temperature of the gas to be, TS = 600+222−159 K, intermediate between the expected values for cold and warm neutral media. This suggests that the H i absorption originates from a mixture of different phases. The total molecular fraction is low, fH2=10−7, and H2 rotational level populations are not in equilibrium. The average abundance of the α- elements is, [S/H]=−1.45 ± 0.22. Nitrogen and iron are found underabundant with respect to α-elements by ∼1.0 dex and ∼0.5 dex respectively. Using photoionization models we conclude that the gas, of mean density, nH ∼2 cm−3, is located more than 270 kpc away from the QSO. While the position of 21-cm absorption line coincides with the H2 velocity profile, its centroid is shifted by ∼2.7±1.0 km s−1 with respect to the redshift measured from the H2 lines. However, the position of the strongest metal absorption component matches the position of the 21-cm absorption line within 0.5 km s−1. From this, we constrain the variation of the combination of fundamental constants x = α2Gp/µ, ∆x/x = −(1.7±1.7)×10−6. This system is unique as we can at the same time have an independent constrain on µ using H2 lines. However, as the H2 column density is low, only Werner band absorption lines are seen and, unfortunately, the range of sensitivity coefficients is too narrow to provide a stringent constraint: ∆µ/µ ≤ 4.0 × 10−4. The Ultraviolet and Visual Echelle Spectrograph (UVES) spectrum reveals another DLA at zabs= 3.16768 with log N(H i) = 20.41±0.15 and low metallicity, [Si/H] = −2.68 ± 0.11, in which [O/C] ∼ 0.18 ± 0.18 and [O/Si] ∼ 0. This shows that even in the very early stages of chemical evolution, the carbon or silicon to oxygen ratios can be close to solar. Using Voigt profile fitting we derive log(N(D i)/N(H i)) = −(4.93 ± 0.15) in this system. This is a factor of two smaller than the value expected from the best fitted value of Ωb from theWilkinson Microwave Anisotropy Probe (WMAP) 5 year data. This confirms the presence of astration of deuterium even at very low metallicity.Item Statistical isotropy violation of the CMB brightness fluctuations(2010-03-22) Aich, Moumita; Souradeep, TarunCertain anomalies at large angular scales in the cosmic microwave background measured by WMAP have been suggested as possible evidence of breakdown of statistical isotropy(SI). SI violation of cosmological perturbations is a generic feature of ultra large scale structure of the cosmos and breakdown of global symmetries. Most CMB photons free-stream to the present from the surface of last scattering. It is thus reasonable to expect statistical isotropy violation in the CMB photon distribution observed now to have originated from SI violation in the baryon-photon fluid at last scattering, in addition to anisotropy of the primordial power spectrum studied earlier in literature. We consider the generalized anisotropic brightness distribution fluctuations, ∆(~ k, ˆ n, τ ) (at con-formal time τ ) in contrast to the SI case where it is simply a function of |~ k| and ˆ k ˆ n. The brightness fluctuations expanded in Bipolar Spherical Harmonic (BipoSH) series, can then be written as ∆LM ℓ1ℓ2 (k, τ ) where L > 0 terms encode deviations from statistical isotropy. Violation of SI encoded in the present off-diagonal elements of the harmonic space correlation haℓmaℓ′m′ i, equivalently, the BipoSH coefficients ALM ℓℓ′ , are then related to the generalized BipoSH brightness fluctuation terms at present. We study the evolution of ∆LM ℓ1ℓ2 (k, τ ) from non-zero terms ∆LM ℓ3ℓ4 (k, τs) at last scattering, in the free streaming regime. We show that the terms with given BipoSH multipole, LM, evolve independently. Moreover, similar to the SI case, power at small spherical harmonic (SH) multipoles of ∆LM ℓ3ℓ4 (k, τs) at the last scattering, is transferred to ∆LM ℓ1ℓ2 (k, τ ) at larger SH multipoles. The structural similarity is more apparent in the asymptotic expression for large values of the final SH multipoles. This formalism allows an elegant identification of any SI violation observed today to a possible origin in SI violating physics present in the baryon-photon fluid. This is illustrated for the known result of SI violating angular correlations due to the presence of a homogeneous magnetic field in the baryon-photon fluid.Item Coherent versus coincidence detection of gravitational wave signals from compact inspiraling binaries(2010-03-30) Dhurandhar, Sanjeev; Mukhopadhyay, Himan; Tagoshi, H.; et al.We compare two multi-detector detection strategies, namely, the coincidence and the coherent, for the detection of spinless inspiraling compact binary gravitational wave (GW) signals. The coincident strategy treats the detectors as if they are isolated - com- pares individual detector statistics with their respective thresholds while the coherent strategy combines the detector network data phase coherently to obtain a single detection statistic which is then compared with a single threshold. In the case of geographically separated detectors, we also consider an enhanced coincidence strategy because the usual (naive) coincidence strategy yields poor results for misaligned detectors. For simplicity, we consider detector pairs having the same power spectral density of noise, as that of initial LIGO and also assume the noise to be stationary and Gaussian. We compare the performances of the methods by plotting the receiver operating characteristic (ROC) for the two strategies. A single astrophysical source as well as a distribution of sources is considered. We find that the coherent strategy performs better than the two coincident strategies under the assumptions of stationary Gaussian detector noise.Item Polarimetric observations of comet 67P/Churyumov-gerasimenko during its 2008-2009 apparition(2010-04-01) Hadamcik, E.; et al.; Sen, A.K.; Levasseur-Regourd, A. C.Remote observations of the light scattered by comet 67P/Churyumov-Gerasimenko dustcoma are of major importance to determine the physical properties of the particles and prepare the rendezvous with the ESA/Rosetta spacecraft in 2014. Aims. Light scattering and especially linear polarization observations allow a comparison between di erent coma regions and di erent comets, including comets that have been studied by space probes. Our aim is to retrieve physical properties of the dust particles and to characterize their evolution around perihelion passage. Methods. Recent imaging polarimetric observations have been conducted at Haute-Provence observatory (France) on 2009 March 17-19 at 35° phase angle and at IUCAA Girawali observatory (India) on 2008 December 25-27 at 36° phase angle and on 2009 April 30-May 1 at 29° phase angle. With the imaging technique, the intensity and linear polarization variations are studied through the various coma regions. These observations are compared to other cometary data (e.g.Jupiter family comets) and to numerical and experimental simulations. Results. The decrease in intensity as a function of the distance to nucleus in log-log scale is on average close to -1, although important variations with values down to -1.5 are noticed, in agreement with previous observations in 1982-83 and 1995-96. The intensity along the tailward direction decreases with a slope between -1.2 two months before perihelion (2009 February 28)to -1.0 two months after perihelion; the decrease is more pronounced in the sunward direction. Before perihelion, aperture polarization values are comparable to polarization values measured on other comets at similar phase angles. The sharp decrease in intensity and the feature in the tailward direction, without any di erence in polarization in the coma before perihelion, could suggest the presence of large dark particles. The post-perihelion increase in intensity and in polarization suggests that an outburst has occurred. The freshly ejected dust polarizes more the scattered light and is more sensitive to the solar radiation pressure, suggesting small micron- or submicron-sized grains. Conclusions. Polarization and intensity variations in the coma of 67P/Churyumov-Gerasimenko are reminiscent of those noticed for some comets such as comet 81P/Wild 2 and comet 9P/Tempel 1. The presence of rather large particles can thus be suggested before and just after perihelion and the ejection of smaller grains, eventually in flu y aggregates post-perihelion. An important sea-sonal e ect related to the obliquity of the comet suggests that the di erent grains originate from di erent hemispheres of the nucleus.Item CCD photometric study of the late type contact binary EK comae berenices(2010-04-26) Deb, Sukanta; Singh, Harinder P.; Seshadri, T. R.; et al.We present CCD photometric observations of the W UMa type contact binary EK Comae Berenices using the 2 metre telescope of IUCAA Girawali Observatory, India. The star was classified as a W UMa type binary of subtype-W by Samec et al. [20]. The new V band photometric observations of the star reveal that shape of the light curve has changed significantly from the one observed by Samec et al. [20]. A detailed analysis of the light curve obtained from the high-precision CCD photometric observations of the star indicates that EK Comae Berenices is not a W-type but an A-type totally eclipsing W UMa contact binary. The photometric mass ratio is determined to be 0.349 ± 0.005. A temperature difference of ∆T = 141 ± 10 K between the components and an orbital inclination of i[°] = 89.800 ± 0.075 were obtained for the binary system. Absolute values of masses, radii and luminosities are estimated by means of the standard mass-luminosity relation for zero age main-sequence stars. The star shows O’Connell effect, asymmetries in the light curve shape around the primary and secondary maximum. The observed O’Connell effect is explained by the presence of a hot spot on the primary component.Item Primordial features due to a step in the inflaton potential(2010-05-12) Hazra, Dhiraj Kumar; et al.; Aich, Moumita; Jain, Rajeev KumarCertain oscillatory features in the primordial scalar power spectrum are known to provide a better fit to the outliers in the cosmic microwave background data near the multipole moments of ℓ = 22 and 40. These features are usually generated by introducing a step in the popular, quadratic potential describing the canonical scalar field. Such a model will be ruled out, if the tensors remain undetected at a level corresponding to a tensor-to-scalar ratio of, say, r ≃ 0.1. In this work, in addition to the popular quadratic potential, we investigate the effects of the step in a small field model and a tachyon model. With possible applications to future datasets (such as PLANCK) in mind, we evaluate the tensor power spectrum exactly, and include its contribution in our analysis. We compare the models with the WMAP (five as well as seven-year), the QUaD and the ACBAR data. As expected, a step at a particular location and of a suitable magnitude and width is found to improve the fit to the outliers (near ℓ = 22 and 40) in all these cases. We point out that, if the tensors prove to be small (say, r . 0.01), the quadratic potential and the tachyon model will cease to be viable, and more attention will need to be paid to examples such as the small field models.Item Associated spectral and temporal state transition of the bright ULX NGC 1313 X-1(2010-05-21) Dewangan, Gulab Chand; et al.Stellar mass black hole X-ray binaries exhibit X-ray spectral states which also have distinct and characteristic temporal properties. These states are believed to correspond to different accretion disc geometries. We present analysis of two XMM-Newton observations of the Ultra-Luminous X-ray source (ULX) NGC 1313 X-1, which reveal that the system was in two different spectral states. While spectral variations have been observed in this source before, this data provides clear evidence that the spectral states also have distinct temporal properties. With a count rate of ~ 1.5 counts/s and a fractional variability amplitude of ~ 15%, the ULX was in a high flux and strongly variable state in March 2006. In October 2006, the count rate of the ULX had reduced by a factor of ~ 2 and the spectral shape was distinctly different with the presence of a soft component. No strong variability was detected during this low flux state with an upper limit on the amplitude < 3%. Moreover, the spectral properties of the two states implies that the accretion disc geometry was different for them. The low flux state is consistent with a model where a standard accretion disc is truncated at a ra- dius of ~ 17 Schwarzschild radius around a ~ 200M⊙ black hole. The inner hot region Comptonizes photons from the outer disc to give the primary spectral component. The spectrum of the high flux state is not compatible with such a geometry. Instead, it is consistent with a model where a hot corona covers a cold accretion disc and Comptonizes the disc photons. The variability as a function of energy is also shown to be consistent with the corona model. Despite these broad analogies with Galactic black hole systems, the spectral nature of the ULX is distinct in having a lower temperature (~ 2 keV) of the hot Comptonizing plasma and higher optical depth (~ 15) than what is observed for the Galactic ones.Item Non-adiabatic gravitational collapse of a superdense star(2010-06-01) Sarwe, S. B.; Tikekar, R.The relativistic equations governing the non-adiabatic shear-free collapse of massive superdense stars in the presence of dissipative forces producing heat flow in the background of space–times of the Vaidya–Tikekar ansatz with associated physical three-spaces that have the three-spheroidal geometry are formulated. It is shown how the system can be used to examine the development and progress of the collapse during subsequent epochs until the radiating star becomes a black hole.Item GMRT mini-survey to search for 21-cm absorption in quasar-galaxy pairs at z~0.1(2010-07-05) Gupta, N.; et al.; Srianand, R.We present the results from our 21-cm absorption survey of a sample of 5 quasar-galaxy pairs (QGPs), with the redshift of the galaxies in the range 0.03≤ zg ≤ 0.18, selected from the Sloan Digital Sky Survey (SDSS). The H i 21-cm absorption was searched towards the 9 sight lines with impact parameters ranging from ∼10 to ∼55 kpc using Giant Metrewave Radio Telescope (GMRT). 21-cm absorption was detected only in one case i.e. towards the Quasar (zq = 2.625SDSS J124157.54+633241.6) − galaxy (zg = 0.143 SDSS J124157.26+633237.6) pair with the impact parameter ∼11 kpc. The quasar sight line in this case pierces through the stellar disk of a galaxy having near solar metallicity (i.e (O/H)+12 = 8.7) and star formation rate uncorrected for dust attenuation of 0.1M⊙ yr−1. The quasar spectrum reddened by the foreground galaxy is well fitted with the Milky Way extinction curve (with an AV of 0.44) and the estimated H i column density is similar to the value obtained from 21-cm absorption assuming spin temperature (TS) of 100K. In the remaining cases, our GMRT spectra provide upper limit on N(H i) in the range, (1017 −1018)×TS cm−2. Combining our sample with the z ≤ 0.1 data available in the literature, we find the detectability of 21-cm absorption with integrated optical depth greater than 0.1 kms−1 to be 50% for the impact parameter less than 20 kpc. Using the surface brightness profiles and well established relationship between the optical size and extent of the H i disk known for nearby galaxies, we conclude that in most of the cases of 21-cm absorption non-detection, the sight lines may not be passing through the H i gas (1σ column density of few times 1019 cm−2). We also find that in comparison to the absorption systems associated with these QGPs, z < 1 DLAs with 21-cm absorption detections have lower Ca ii equivalent widths despite having higher 21-cm optical depths and smaller impact parameters. This suggests that the current sample of DLAs may be a biased population that avoids sight lines through dusty star-forming galaxies. A systematic survey of QGPs over a wider redshift range using a large sample is needed to confirm these findings and understand the nature of 21-cm absorbers.Item Turbulence modeling and the physics of the Intra-cluster medium(2010-07-11) Niemeyer, Jens C.; Paul, Surajit; et al.; Iapichino, L.The effective modeling of the stirring and development of turbulent flows in grid-based hydrodynamical simulations is computationally challenging. Here we present two possible ways to tackle the problem: first, we consider the use of the adaptive mesh refinement (AMR), applying novel refinement criteria which are optimized to follow the evolution of a turbulent flow. In a second step, the AMR is combined with a subgrid scale (SGS) model for the unresolved turbulence, thus resulting in a new numerical technique called FEARLESS (Fluid mEchanics with Adaptively Refined Large Eddy SimulationS). FEARLESS performs both the adaptive refinement of the regions where turbulent flows develop and a consistent coupling of the SGS turbulence with the resolved scales, and is argued to be a suitable tool in simulations of turbulent clumped flows. The results of galaxy cluster simulations, performed with the new tool, give rise to several interesting implications with regard to the physics of these objects, and to the numerical methods employed for their exploration in computational cosmology.Item PyMorph: Automated galaxy structural parameter rstimation using python(2010-07-20) Vikram, Vinu; et al.; Wadadekar, Yogesh; Kembhavi, A.K.We present a new software pipeline – PyMorph – for automated estimation of structural parameters of galaxies. Both parametric fits through a two dimensional bulge disk decomposition as well as structural parameter measurements like concentration, asymmetry etc. are supported. The pipeline is designed to be easy to use yet flexible; individual software modules can be replaced with ease. A find-and-fit mode is available so that all galaxies in a image can be measured with a simple command. A parallel version of the Pymorph pipeline runs on computer clusters and a Virtual Observatory compatible web enabled interface is under development.Item Photopolarimetric study of the star-forming clouds CB3,CB25,and CB39(2010-07-22) Sen, A.K.; et al.; Polcaro, V. F.; Dey, I.The small compact isolated dark clouds also known as ’Bok globules’ are believed to be ideal sites for low-mass star formation. Some of these clouds are undergoing gravitational collapse, and the ambient magnetic field plays a key role in collapse dynamics. The background star polarimetry is generally accepted as a good tool to map the magnetic field, which is responsible for the alignment of dichroic grains that produce polarization. Aims. The background star polarization when studied together with extinction is expected to help us to understand various grain properties and the role of polarimetry as a tracer of magnetic field in these star-forming clouds. With this idea, polarization and colour excess E(B − V ) values for a set of background stars have been studied together to understand various astrophysical process in some star-forming dark clouds. Methods. Optical photometric observations of the three clouds CB3, CB25, and CB39 were carried out at the 2m H.C. Telescope, India, to determine the colour excess E(B −V ) of the background stars by following a technique adopted by Barnei and Polacaro (2001). These three clouds were selected from a set of eight clouds previously observed by us in optical polarimetry ( Sen et al. 2000). Further independent spectroscopic measurements of a few selected sample stars were recently carried out during February and March 2010 from 1.52m Cassini Telescope, Loinao, Italy, to confirm the correctness of estimated E(B − V ) values obtained by this photometric technique. Results. The colour excess E(B−V ) values so obtained were compared with optical polarization values obtained for the same set of stars. It was found that the measured extinction values increase with the increase in percentage polarization for the cloud CB39 and to some extent for CB25. However, for cloud CB31 no such correlation was observed. It is normally expected that the grains causing extinction should also cause polarization of the light from background stars. Any possible deviation from this under different circumstances here has been discussed in the light of the ongoing physical processes in the star-forming clouds.Item Coude-feed stellar spectral library - atmospheric parameters(2010-09-09) Wu, Yue; et al.; Singh, Harinder P.; Prugniel, PhilippeEmpirical libraries of stellar spectra play an important role in different fields. For example, they are used as reference for the automatic determination of atmospheric parameters, or for building synthetic stellar populations to study galaxies. The CFLIB (Coud´e-feed library, Indo-US) database is at present one of the most complete libraries, in terms of its coverage of the atmospheric parameters space (Teff, log g and [Fe/H]) and wavelength coverage 3460 - 9464 ˚ A at a resolution of ∼1 ˚ A FWHM. Although the atmospheric parameters of most of the stars were determined from detailed analyses of high-resolution spectra, for nearly 300 of the 1273 stars of the library at least one of the three parameters is missing. For the others, the measurements, compiled from the literature, are inhomogeneous. Aims. In this paper, we re-determine the atmospheric parameters, directly using the CFLIB spectra, and compare them to the previous studies. Methods. We use the ULySS program to derive the atmospheric parameters, using the ELODIE library as a reference. Results. Based on comparisons with several previous studies we conclude that our determinations are unbiased. For the 958 F,G, and K type stars the precision on Teff, log g, and [Fe/H] is respectively 43 K, 0.13 dex and 0.05 dex. For the 53 M stars they are 82 K, 0.22 dex and 0.28 dex. And for the 260 OBA type stars the relative precision on Teff is 5.1%, and on log g, and [Fe/H] the precision is respectively 0.19 dex and 0.16 dex. These parameters will be used to re-calibrate the CFLIB fluxes and to produce synthetic spectra of stellar populations.Item Size of the longest filament in the luminous red galaxy distribution(2010-09-12) Souradeep, TarunFilaments are one of the most prominent features visible in the galaxy distribution. Considering the Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey Data Release Seven (SDSS DR7), we have analyzed the filamentarity in 11 nearly two dimensional (2D) sections through a volume limited subsample of this data. The galaxy distribution, we find, has excess filamentarity in comparison to a random distribution of points. We use a statistical technique “Shuffle” to determine LMAX, the largest length-scale at which we have statistically significant filaments. We find that LMAX varies in the range 100−130 h−1Mpc across the 11 slices, with a mean value LMAX = 110 ± 12 h−1Mpc. Longer filaments, though possibly present in our data, are not statistically significant and are the outcome of chance alignments.Item Group theoretic approach to detecting gravitational waves from asymmetric rotating neutron stars(2010-10-12) Dhurandhar, Sanjeev; Krishnan, B.The era of advanced ground based interferometric detectors of gravitational waves (GW) has arrived. These detectors are expected to go line in six years or so from now and which will have requisite sensitivity for detecting and observing astrophysical gravitational wave sources. In this article we will focus on a specific GW source, the GWs emitted by an isolated rotating neutron star/pulsar, and describe a novel approach to address this highly com- putationally intensive problem. We will describe how the symmetries in the model can be potentially used to reduce the computational effort.