Chaotic dynamics of off-equatorial orbits around pseudo-Newtonian compact objects with dipolar halos

In this paper, we implement a generalised pseudo-Newtonian potential and prescribe a numerical fitting formalism to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around both Schwarzschild and Kerr-like compact object primaries surrounded by a dipolar halo of matter. The chaotic dynamics of the orbits are detailed for both non-relativistic and special-relativistic test particles. The dependence of the degree of chaos on the rotation parameter $a$ and the inclination angle $i$ is established individually using widely used indicators, such as the Poincar\'e Map and the Lyapunov Characteristic Number. We find that although the chaoticity of the orbits has a positive correlation with $i$, the growth in the chaotic behaviour is not systematic. There exists a threshold value of the inclination angle $i_{\text{c}}$, after which the degree of chaos shows a sharp increase. On the other hand, the chaoticity of the inclined orbits anti-correlates with $a$ throughout its entire range. However, the negative correlation is systematic at lower values of the inclination angle. At higher values of $i$, the degree of chaos is maximum for the maximally counter-rotating compact objects, the Kerr parameter of which is below a threshold value $a_{\text{c}}$. Above this threshold value, the correlation becomes weak. Furthermore, we establish a qualitative correlation between the threshold values and the overall chaoticity. The studies performed with different orbital parameters and several initial conditions reveal the intricate nature of the system.Comment: 27 pages, 13 figure

Implications of the Universal Temperature Profile for Galaxy Clusters

We study the X-ray cluster gas density distribution in hydrostatic equilibrium using the universal temperature profile obtained from recent simulations involving only gravitational processes. If this temperature profile is an indicator of the influence of gravitational processes alone on the intracluster medium, then the comparison of various X-ray parameters expected from this profile and the observed data would point towards any additional physics that may be required. We compare the entropy at 0.1 R_{200} and R_{500}, the scaled entropy profile, the gas fraction at 0.3 R_{200} and the gas fraction profile with recent observations and discuss the implications of this temperature profile in light of these data. We find that the entropy imparted to the gas from gravitational processes alone is larger than previously thought. The entropy at R_{500} for rich clusters is consistent with data, whereas the entropy at 0.1R_{200} is still less than the observed values. We also find that the gas fraction in the inner region of clusters, expected from gravitational processes alone, is smaller than previously thought but larger than the observed data. It does show a trend with the emission-weighted temperature () as shown by data. We therefore find that the role of any additional non-gravitational process influencing the physical state of ICM would have to be revised in light of these findings.Comment: 11 pages including 11 figures, accepted for publication in MNRAS, uses mn.sty (included

Model dependence of the multi-transonic behavior, stability properties and corresponding acoustic geometry for accretion onto a spinning black hole

Multi-transonic accretion for a spinning black hole has been compared among different disc geometries within post Newtonian pseudo potential framework. The variation of stationary shock characteristics with black hole spin has been studied in details for all the disc models and compared for adiabatic as well as for isothermal scenario. The variations of surface gravity with spin for all these cases have also been investigated.Comment: 18 pages. 19 figure

Gender-Based Comparative Study of Type 2 Diabetes Risk Factors in Kolkata, India: A Machine Learning Approach

Type 2 diabetes mellitus represents a prevalent and widespread global health concern, necessitating a comprehensive assessment of its risk factors. This study aimed towards learning whether there is any differential impact of age, Lifestyle, BMI and Waist to height ratio on the risk of Type 2 diabetes mellitus in males and females in Kolkata, West Bengal, India based on a sample observed from the out-patient consultation department of Belle Vue Clinic in Kolkata. Various machine learning models like Logistic Regression, Random Forest, and Support Vector Classifier, were used to predict the risk of diabetes, and performance was compared based on different predictors. Our findings indicate a significant age-related increase in risk of diabetes for both males and females. Although exercising and BMI was found to have significant impact on the risk of Type 2 diabetes in males, in females both turned out to be statistically insignificant. For both males and females, predictive models based on WhtR demonstrated superior performance in risk assessment compared to those based on BMI. This study sheds light on the gender-specific differences in the risk factors for Type 2 diabetes, offering valuable insights that can be used towards more targeted healthcare interventions and public health strategies.Comment: 10 pages, 7 tables,3 figures, submitted to a conferenc

Solving relativistic hydrodynamic equation in presence of magnetic field for phase transition in a neutron star

Hadronic to quark matter phase transition may occur inside neutron stars (NS) having central densities of the order of 3-10 times normal nuclear matter saturation density ($n_0$). The transition is expected to be a two-step process; transition from hadronic to 2-flavour matter and two-flavour to $\beta$ equilibrated charge neutral three-flavour matter. In this paper we concentrate on the first step process and solve the relativistic hydrodynamic equations for the conversion front in presence of high magnetic field. Lorentz force due to magnetic field is included in the energy momentum tensor by averaging over the polar angles. We find that for an initial dipole configuration of the magnetic field with a sufficiently high value at the surface, velocity of the front increases considerably.Comment: 16 pages, 4 figures, same as published version of JPG, J. Phys. G: Nucl. Part. Phys. 39 (2012) 09520

Magnetic fields and Sunyaev-Zel'dovich effect in galaxy clusters

In this work we study the contribution of magnetic fields to the Sunyaev Zeldovich (SZ) effect in the intracluster medium. In particular we calculate the SZ angular power spectrum and the central temperature decrement. The effect of magnetic fields is included in the hydrostatic equilibrium equation by splitting the Lorentz force into two terms one being the force due to magnetic pressure which acts outwards and the other being magnetic tension which acts inwards. A perturbative approach is adopted to solve for the gas density profile for weak magnetic fields (< 4 micro G}). This leads to an enhancement of the gas density in the central regions for nearly radial magnetic field configurations. Previous works had considered the force due to magnetic pressure alone which is the case only for a special set of field configurations. However, we see that there exists possible sets of configurations of ICM magnetic fields where the force due to magnetic tension will dominate. Subsequently, this effect is extrapolated for typical field strengths (~ 10 micro G) and scaling arguments are used to estimate the angular power due to secondary anisotropies at cluster scales. In particular we find that it is possible to explain the excess power reported by CMB experiments like CBI, BIMA, ACBAR at l > 2000 with sigma_8 ~ 0.8 (WMAP 5 year data) for typical cluster magnetic fields. In addition we also see that the magnetic field effect on the SZ temperature decrement is more pronounced for low mass clusters ( ~ 2 keV). Future SZ detections of low mass clusters at few arc second resolution will be able to probe this effect more precisely. Thus, it will be instructive to explore the implications of this model in greater detail in future works.Comment: 20 pages, 8 figure

Heating of the intracluster medium by quasar outflows

We study the possibility of quasar outflows in clusters and groups of galaxies heating the intracluster gas in order to explain the recent observation of excess entropy in this gas. We use the extended Press-Schechter formalism to estimate the number of quasars that become members of a group of cluster of a given mass and formation epoch. We also estimate the fraction of mechanical energy in the outflows that is imparted to the surrounding medium as a function of the density and temperature of this gas. We finally calculate the total amount of non-gravitational heating from such outflows as a function of the cluster potential and formation epoch. We show that outflows from broad absorption line (BAL) and radio loud quasars can provide the required amount of heating of the intracluster gas. We find that in this scenario most of the heating takes place at $z \sim 1\hbox{--}4$, and that this ``preheating'' epoch is at lower redshift for lower mass clusters.Comment: Latex (mn.sty), 8 figures, accepted for publication in the MNRA