Abstract
The Square Kilometre Array (SKA), when it becomes functional, is expected to enrich Neutron Star (NS) catalogues by at least an order of magnitude over their current state. This includes the discovery of new NS objects leading to better sampling of under-represented NS categories, precision measurements of intrinsic properties such as spin period and magnetic field, as also data on related phenomena such as microstructure, nulling, glitching, etc. This will present a unique opportunity to seek answers to interesting and fundamental questions about the extreme physics underlying these exotic objects in the Universe. In this paper, we first present a meta-analysis (from a methodological viewpoint) of statistical analyses performed using existing NS data, with a two-fold goal. First, this should bring out how statistical models and methods are shaped and dictated by the science problem being addressed. Second, it is hoped that these analyses will provide useful starting points for deeper analyses involving richer data from SKA whenever it becomes available. We also describe a few other areas of NS science which we believe will benefit from SKA which are of interest to the Indian NS community.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Airoldi, E. M., Blei, D. M., Erosheva, E. A. Fienberg, S. E. 2014, Introduction to mixed membership models and methods, in: E. M. Airoldi, D. M. Blei, E. A. Erosheva and S. E. Fienberg, editors, Handbook of Mixed Membership Models and their Applications, pages 3–13, CRC Press.
Arjunwadkar, M., Rajwade, K. Gupta, Y. 2016, Inferring pulsar null fraction using Gaussian mixtures, under preparation.
Aschwanden, M. 2011, Self-Organized Criticality in Astrophysics: The Statistics of Nonlinear Processes in the Universe, Springer.
Backer, D. C. 1970, Pulsar nulling phenomena, Nature, 228, 42–43.
Bagchi, M. 2013, Luminosities of radio pulsars, Int. J. Mod. Phys. D, 22 (10), 1330021.
Bagchi, M., Lorimer, D. R. Chennamangalam, J. 2011, Luminosities of recycled radio pulsars in globular clusters, Mon. Not. R. Astron. Soc., 418 (1), 477–489.
Bates, S. D., Lorimer, D. R. Verbiest, J. P. W. 2013, The pulsar spectral index distribution, Mon. Not. R. Astron. Soc., 431 (2), 1352–1358.
Burnham, K. Anderson, D. 2002, Model Selection and Multimodel Inference, Springer , New York.
Chennamangalam, J. Lorimer, D. R. 2014, The galactic centre pulsar population, Mon. Not. R. Astron. Soc.: Letters, 440 (1), L86–L90.
Chennamangalam, J., Lorimer, D. R., Mandel, I. Bagchi, M. 2013, Constraining the luminosity function parameters and population size of radio pulsars in globular clusters, Mon. Not. R. Astron. Soc., 431 (1), 874–881.
Craft, H. D., Comella, J. M. Drake, F. D. 1968, Submillisecond radio intensity variations in pulsars, Nature, 218, 1122–1124.
Efron, B. 2011, Foreword, in: International Encyclopedia of Statistical Science, edited by M. Lovric, pages vii–x, Springer-Verlag.
Ellis, J. A. 2013, A Bayesian analysis pipeline for continuous GW sources in the PTA band, Class. Quantum Gravit., 30 (22), 224004.
Espinoza, C. M., Lyne, A. G., Stappers, B. W. Kramer, M. 2011, A study of 315 glitches in the rotation of 102 pulsars, Mon. Not. R. Astron. Soc., 414, 1679–1704.
Faucher-Giguère, C. -A. Kaspi, V. M. 2006, Birth and evolution of isolated radio pulsars, Astrophys. J., 643 (1), 332.
Fraley, C. Raftery, A. E. 2002, Model-based clustering, discriminant analysis, and density estimation, J. Amer. Stat. Assoc., 97, 611–631.
Gregory, P. C. 2005, Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica Support, Cambridge University Press.
Hall, P. York, M. 2001, On the calibration of silverman’s test for multimodality, Statistica Sinica, 11, 515–536.
Hartigan, J. Hartigan, P. 1985, The dip test of unimodality, Ann. Statistics, 13, 70–84.
Hastie, T., Tibshirani, R. Friedman, J. 2009, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, second edition.
Holzmann, H. Vollmer, S. 2008, A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU, Advances in Statistical Analysis, 92 (1), 57–69.
Kashikar, A., Konar, S. Arjunwadkar, M. 2016, Agnostic clustering of neutron star data suggests multiple populations, in progress.
Keane, E., Bhattacharyya, B., Kramer, M., Stappers, B., Keane, E. F., Bhattacharyya, B., Kramer, M., Stappers, B. W., Bates, S. D., Burgay, M., Chatterjee, S., Champion, D. J., Eatough, R. P., Hessels, J. W. T., Janssen, G., Lee, K. J., van Leeuwen, J., Margueron, J., Oertel, M., Possenti, A., Ransom, S., Theureau, G. Torne, P. 2015, A Cosmic Census of Radio Pulsars with the SKA, Advancing Astrophysics with the Square Kilometre Array (AASKA14), 40.
Kijak, J., Gupta, Y. Krzeszowski, K. 2007, Turn-over in pulsar spectra around 1 Ghz, Astron. Astrophys., 462, 699–702.
Kim, C., Perera, B. B. P. McLaughlin, M. A. 2015, Implications of PSR j0737–3039b for the galactic NS–NS binary merger rate, Mon. Not. R. Astron. Soc., 448 (1), 928–938.
Konar, S. Arjunwadkar, M. 2014, Glitch statistics of radio pulsars: Multiple populations, arXiv:1402.1594.
Konar, S. Arjunwadkar, M. 2015, Radio pulsars glitches: A statistical study, in preparation.
Lentati, L., Alexander, P., Hobson, M. P., Feroz, F., van Haasteren, R., Lee, K. J. Shannon, R. M. 2014, TEMPONEST: a Bayesian approach to pulsar timing analysis, Mon. Not. R. Astron. Soc., 437, 3004–3023.
Lorimer, D. R., Bailes, M., Dewey, R. J. Harrison, P. A. 1993, Pulsar statistics: the birthrate and initial spin periods of radio pulsars, Mon. Not. R. Astron. Soc., 263 (2), 403–415.
Malofeev, V. M., Gil, J. A., Jessner, A., Malov, I. F., Seiradakis, J. H., Sieber, W. Wielebinski, R. 1994, Spectra of 45 pulsars, Astron. Astrophys., 285.
Manchester, R., Hobbs, G., Teoh, A. Hobbs, M. 2005, The Australia telescope national facility pulsar catalogue, Astrophys. J., 129 (4), 1993–2006.
McLachlan, G. Peel, D. 2000, Finite Mixture Models, Wiley, New York.
Mitra, D., Arjunwadkar, M. Rankin, J. M. 2015, Polarized quasiperiodic structures in pulsar radio emission reflect temporal modulations of non-stationary plasma flow, Astrophys. J., 806 (2), 236.
Mitra, D., Rankin, J. M. Arjunwadkar, M. 2016, Core and conal component analysis of pulsar B1933+16 — Investigation of the segregated modes, Mon. Not. R. Astron. Soc., to be published.
Rajwade, K., Arjunwadkar, M., Gupta, Y. Kumar, U. 2016, Probing nulling in millisecond pulsars, under preparation.
Ridley, J. P., Crawford, F., Lorimer, D. R., Bailey, S. R., Madden, J. H., Anella, R. Chennamangalam, J. 2013, Eight new radio pulsars in the large magellanic cloud, Mon. Not. R. Astron. Soc., 433 (1), 138–146.
Ritchings, R. 1976, Pulsar single pulse energy measurements and pulse nulling, Mon. Not. R. Astron. Soc., 176, 249–263.
Silverman, B. 1981, Using kernel density estimates to investigate multimodality, J. R. Statistical Soc., Series B, 43, 97–99.
Swarup, G., Ananthakrishnan, S., Kapahi, V. K., Rao, A. P., Subrahmanya, C. R. Kulkarni, V. K. 1991, The giant metre-wave radio telescope, Current Science, 60 (2), 95–105.
Taylor, S., Ellis, J. Gair, J. 2014, Accelerated Bayesian model-selection and parameter-estimation in continuous gravitational-wave searches with pulsar-timing arrays, Phys. Rev. D, 90 (10), 104028.
Toscano, M., Bailes, M., Manchester, R. N. Sandhu, J. S. 1998, Spectra of southern pulsars, Astrophys. J., 506 (2), 863.
Verbiest, J. P. W., Lorimer, D. R. McLaughlin, M. A. 2010, Lutz-kelker bias in pulsar parallax measurements, Mon. Not. R. Astron. Soc., 405, 564–572.
Verbiest, J. P. W., Weisberg, J. M., Chael, A. A., Lee, K. J. Lorimer, D. R. 2012, On pulsar distance measurements and their uncertainties, Astrophys. J., 755, 39.
Wall, J. V. Jenkins, C. R. 2003, Practical Statistics for Astronomers, Cambridge University Press.
Wasserman, L. 2004, All of Statistics, Springer, New York.
Wasserman, L. 2006, All of Nonparametric Statistics, Springer, New York.
Woodbury, M. A., Clive, J. Garson, A. 1978, Mathematical typology: A grade of membership technique for obtaining disease definition, Computers and Biomedical Res., 11 (3), 277–298.
Acknowledgements
The first author, MA would like to thank Sushan Konar and Dipanjan Mitra for discussions, encouragement and critical comments. We would like to thank the anonymous referee for a thorough and meticulous review and for useful suggestions that have helped improve this paper. We would like to thank Cristóbal Espinoza for drawing our attention to the fact that no plan for regular monitoring of young glitching pulsars using SKA is specified at present. Such a plan is desirable for obtaining more and better glitch data, which will in turn enable researchers to apply and improve upon the methods discussed in this paper. This will also help understand many other properties of young pulsars; see Watts et al. (arXiv:1501.00042) for details.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Arjunwadkar, M., Kashikar, A. & Bagchi, M. Neutron Stars in the Light of Square Kilometre Array: Data, Statistics and Science. J Astrophys Astron 37, 28 (2016). https://doi.org/10.1007/s12036-016-9410-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12036-016-9410-0