Lower limit on the entropy of black holes as inferred from gravitational wave observations

Black hole (BH) thermodynamics was established by Bekenstein and Hawking, who made abstract theoretical arguments about the second law of thermodynamics and quantum theory in curved spacetime respectively. Testing these ideas experimentally has, so far, been impractical because the putative flux of Hawking radiation from astrophysical BHs is too small to be distinguished from the rest of the hot environment. Here, it is proposed that the spectrum of emitted gravitational waves (GWs) after the merger of two BHs, in particular the spectrum of GW150914, can be used to infer a lower limit on the magnitude of the entropy of the post-merger BH. This lower bound is potentially significant as it could be of the same order as the Bekenstein-Hawking entropy. To infer this limit, we first assume that the result of the merger is an ultracompact object with an external geometry which is Schwarzschild or Kerr, but with an outer surface which is capable of reflecting in-falling GWs rather than fully absorbing them. If the absence of deviations from the predictions of general relativity in detected GW signals will be verified, we will then obtain a bound on the minimal redshift factor of GWs that emerge from the vicinity of the object's surface. This lack of deviations would also mean that the remnant of the merger has to have a strongly absorbing surface and must then be a BH for all practical purposes. We conclude that a relationship between the minimal redshift factor and the BH entropy, which was first proposed by 't Hooft, could then be used to set a lower bound on the entropy of the post-merger BH.Comment: Corrected error in estimation of current bounds on the entropy. Improved discussion of energy stored in echoes, V3 replaced to match published version, clarifications and explanations adde

Star Clusters in the Magellanic Clouds-1: Parameterisation and Classification of 1072 Clusters in the LMC

We have introduced a semi-automated quantitative method to estimate the age and reddening of 1072 star clusters in the Large Magellanic Cloud (LMC) using the Optical Gravitational Lensing Experiment (OGLE) III survey data. This study brings out 308 newly parameterised clusters. In a first of its kind, the LMC clusters are classified into groups based on richness/mass as very poor, poor, moderate and rich clusters, similar to the classification scheme of open clusters in the Galaxy. A major cluster formation episode is found to happen at 125 +- 25 Myr in the inner LMC. The bar region of the LMC appears prominently in the age range 60 - 250 Myr and is found to have a relatively higher concentration of poor and moderate clusters. The eastern and the western ends of the bar are found to form clusters initially, which later propagates to the central part. We demonstrate that there is a significant difference in the distribution of clusters as a function of mass, using a movie based on the propagation (in space and time) of cluster formation in various groups. The importance of including the low mass clusters in the cluster formation history is demonstrated. The catalog with parameters, classification, and cleaned and isochrone fitted CMDs of 1072 clusters, which are available as online material, can be further used to understand the hierarchical formation of clusters in selected regions of the LMC.Comment: 19 pages, 19figures, published in MNRAS on August 16, 2016 Supplementary material is available in the MNRAS websit

Further evidence for intra-night optical variability of radio-quiet quasars

Although well established for BL Lac objects and radio-loud quasars, the occurrence of intra-night optical variability (INOV) in radio-quiet quasars is still debated, primarily since only a handful of INOV events with good statistical significance, albeit small amplitude, have been reported so far. This has motivated us to continue intra-night optical monitoring of bona-fide radio-quiet quasars (RQQs). Here we present the results for a sample of 11 RQQs monitored by us on 19 nights. On 5 of these nights a given RQQ was monitored simultaneously from two well separated observatories. In all, two clear cases and two probable case of INOV were detected. From these data, we estimate an INOV duty cycle of $\sim$8% for RQQs which would increase to 19% if the `probable variable' cases are also included. Such comparatively small INOV duty cycles for RQQs, together with the small INOV amplitudes ($\sim$1%), are in accord with the previously deduced characteristics of this phenomenon.Comment: 15 Pages, 4 Tables, 24 Figures; Accepted in BAS