Do pulsar radio fluxes violate the inverse-square law?

Original Article

Abstract

Singleton et al. (arXiv:0912.0350, 2009) have argued that the flux of pulsars measured at 1400 MHz shows an apparent violation of the inverse-square law with distance (\(r\)), and instead the flux scales as \(1/r\). They deduced this from the fact that the convergence error obtained in reconstructing the luminosity function of pulsars using an iterative maximum likelihood procedure is about \(10^{5}\) times larger for a distance exponent of two (corresponding to the inverse-square law) compared to an exponent of one. When we applied the same technique to this pulsar dataset with two different values for the trial luminosity function in the zeroth iteration, we find that neither of them can reproduce a value of \(10^{5}\) for the ratio of the convergence error between these distance exponents. We then reconstruct the differential pulsar luminosity function using Lynden-Bell’s \(C^{-}\) method after positing both inverse-linear and inverse-square scalings with distance. We show that this method cannot help in discerning between the two exponents. Finally, when we tried to estimate the power-law exponent with a Bayesian regression procedure, we do not get a best-fit value of one for the distance exponent. The model residuals obtained from our fitting procedure are larger for the inverse-linear law compared to the inverse-square law. Moreover, the observed pulsar flux cannot be parameterized only by power-law functions of distance, period, and period derivative. Therefore, we conclude from our analysis using multiple methods that there is no evidence that the pulsar radio flux at 1400 MHz violates the inverse-square law or that the flux scales inversely with distance.

Keywords

Pulsars Luminosity function Malmquist bias Lynden-Bell C-method 

References

  1. Abdo, A.A., Ajello, M., Allafort, A., et al.: Astrophys. J. Suppl. Ser. 208, 17 (2013) ADSCrossRefGoogle Scholar
  2. Ardavan, H., Ardavan, A., Singleton, J., Perez, M.R.: Mon. Not. R. Astron. Soc. 388, 873 (2008a) ADSCrossRefGoogle Scholar
  3. Ardavan, H., Ardavan, A., Singleton, J., Perez, M.R.: Mon. Not. R. Astron. Soc. 388, 873 (2008b) ADSCrossRefGoogle Scholar
  4. Bagchi, M.: Int. J. Mod. Phys. D 22, 30021 (2013) ADSGoogle Scholar
  5. Baghram, S., Afshordi, N., Zurek, K.M.: Phys. Rev. D 84, 043511 (2011) ADSCrossRefGoogle Scholar
  6. Bhat, N.D.R., Cordes, J.M., Cox, P.J., et al.: Astrophys. J. 732, 14 (2011) ADSCrossRefGoogle Scholar
  7. Blandford, R.D.: Philos. Trans. R. Soc. Lond. Ser. A 341, 177 (1992) ADSCrossRefGoogle Scholar
  8. Bramante, J., Linden, T.: Phys. Rev. Lett. 113, 191301 (2014) ADSCrossRefGoogle Scholar
  9. Cordes, J.M., Lazio, T.J.W.: astro-ph/0207156 (2002)
  10. Deller, A.T., Tingay, S.J., Bailes, M., Reynolds, J.E.: Astrophys. J. 701, 1243 (2009) ADSCrossRefGoogle Scholar
  11. Desai, S., Kahya, E.O.: arXiv:1510.08228 (2015)
  12. Dexter, J., O’Leary, R.M.: Astrophys. J. Lett. 783, L7 (2014) ADSCrossRefGoogle Scholar
  13. Efstathiou, G., Ellis, R.S., Peterson, B.A.: Mon. Not. R. Astron. Soc. 232, 431 (1988) ADSCrossRefGoogle Scholar
  14. Foreman-Mackey, D., Hogg, D.W., Lang, D., Goodman, J.: Publ. Astron. Soc. Pac. 125, 306 (2013) ADSCrossRefGoogle Scholar
  15. Freire, P.C.C., Wex, N., Esposito-Farèse, G., et al.: Mon. Not. R. Astron. Soc. 423, 3328 (2012) ADSCrossRefGoogle Scholar
  16. Gonzalez, A.H., Faber, S.M.: Astrophys. J. 485, 80 (1997) ADSCrossRefGoogle Scholar
  17. Gunn, J.E., Ostriker, J.P.: Astrophys. J. 160, 979 (1970) ADSCrossRefGoogle Scholar
  18. Hankins, T.H., Rankin, J.M., Eilek, J.A.: In: The Astron. Astrophys. Decadal Survey. Astronomy, vol. 2010, p. 112 (2009) Google Scholar
  19. Hoekstra, H., Mahdavi, A., Babul, A., Bildfell, C.: Mon. Not. R. Astron. Soc. 427, 1298 (2012) ADSCrossRefGoogle Scholar
  20. Hogg, D.W., Bovy, J., Lang, D.: arXiv:1008.4686 (2010)
  21. Hui, C.Y., Cheng, K.S., Taam, R.E.: Astrophys. J. 714, 1149 (2010) ADSCrossRefGoogle Scholar
  22. Ivezić, Ż., Connolly, A., VanderPlas, J., Gray, A.: Statistics, Data Mining, and Machine Learning in Astronomy (2013) Google Scholar
  23. Jackson, J.C.: Mon. Not. R. Astron. Soc. 166, 281 (1974) ADSCrossRefGoogle Scholar
  24. Kramer, M., Stappers, B.: In: Advancing Astrophysics with the Square Kilometre Array (AASKA14), p. 36 (2015) Google Scholar
  25. Lee, K.J., Guillemot, L., Yue, Y.L., Kramer, M., Champion, D.J.: Mon. Not. R. Astron. Soc. 424, 2832 (2012) ADSCrossRefGoogle Scholar
  26. Lorimer, D.R.: In: Torres, D.F., Rea, N. (eds.) High-Energy Emission from Pulsars and their Systems, p. 21 (2011) CrossRefGoogle Scholar
  27. Lorimer, D.R., Bailes, M., Dewey, R.J., Harrison, P.A.: Mon. Not. R. Astron. Soc. 263, 403 (1993) ADSCrossRefGoogle Scholar
  28. Lucy, L.B.: arXiv:1511.02363 (2015)
  29. Lynden-Bell, D.: Mon. Not. R. Astron. Soc. 155, 95 (1971) ADSCrossRefGoogle Scholar
  30. Manchester, R.N., Lyne, A.G., Camilo, F., et al.: Mon. Not. R. Astron. Soc. 328, 17 (2001) ADSCrossRefGoogle Scholar
  31. Manchester, R.N., Hobbs, G.B., Teoh, A., Hobbs, M.: Astron. J. 129, 1993 (2005) ADSCrossRefGoogle Scholar
  32. McLaughlin, M.A., Cordes, J.M.: Astrophys. J. 596, 982 (2003) ADSCrossRefGoogle Scholar
  33. Narayan, R.: Astrophys. J. 319, 162 (1987) ADSCrossRefGoogle Scholar
  34. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C. The Art of Scientific Computing (1992) MATHGoogle Scholar
  35. Raja, R.: arXiv:physics/0509008 (2005)
  36. Rubio-Herrera, E., Stappers, B.W., Hessels, J.W.T., Braun, R.: Mon. Not. R. Astron. Soc. 428, 2857 (2013) ADSCrossRefGoogle Scholar
  37. Singleton, J., Sengupta, P., Middleditch, J., et al.: arXiv:0912.0350 (2009)
  38. Takeuchi, T.T., Yoshikawa, K., Ishii, T.T.: Astrophys. J. Suppl. Ser. 129, 1 (2000) ADSCrossRefGoogle Scholar
  39. Vanderplas, J., Connolly, A., Ivezić, Ž., Gray, A.: In: Conference on Intelligent Data Understanding (CIDU), pp. 47–54 (2012) Google Scholar
  40. Vivekanand, M., Narayan, R.: J. Astrophys. Astron. 2, 315 (1981) ADSCrossRefGoogle Scholar
  41. Weiner, B.J., Willmer, C.N.A., Faber, S.M., et al.: Astrophys. J. 653, 1049 (2006) ADSCrossRefGoogle Scholar
  42. Willmer, C.N.A.: Astron. J. 114, 898 (1997) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Ronin InstituteMontclairUSA

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