Gaussian and q-Gaussian Functions for the Decomposition of J1022+1001 Pulsar Profiles

Gaussian and q-Gaussian Functions for the Decomposition of J1022+1001 Pulsar Profiles

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Author(s)

Author(s): Amelia Carolina Sparavigna

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DOI: 10.18483/ijSci.2772 10 11 18-27 Volume 13 - Jun 2024

Abstract

The pulsar profiles are profiles obtained by pulse sequences averaged on several cycles. The mean profiles are usually decomposed in Gaussian components, but decompositions in von Mises functions have been proposed too. The Gaussian decompositions can be based on the central limit theorem (CLT), so that a Gaussian component can be regarded as an attractor in the space of distributions with finite variance. Well-known non-Gaussian attractors exist and are the Lévy distributions. Other proposed attractors are the q-Gaussian functions, which are generalizing the Gaussians in the Tsallis q-statistics. These functions have power-law tails. For parameter q equal to 1, the q-Gaussians become the standard Gaussian distributions. In this framework of Gaussian and non-Gaussian attractors, we propose decompositions of pulsar profiles both in Gaussian and q-Gaussian functions. Our investigation is aiming to compare the decompositions to highlight possible differences and dependences on q-parameters. Here we consider, in particular, the intensity profiles given by the EPN Database of Pulsar Profiles, of J1022+1001 at several frequencies. Power-law behaviors of the leading edges have been observed.

Keywords

Pulsar Profiles, Profile Decomposition, q-Gaussian Tsallis Lines, Central Limit Theorem

References

  1. Bassa, C.G., Janssen, G.H., Karuppusamy, R., Kramer, M., Lee, K.J., Liu, K., McKee, J., Perrodin, D.E.L.P.H.I.N.E., Purver, M., Sanidas, S. and Smits, R., 2016. LEAP: the large European array for pulsars. Monthly Notices of the Royal Astronomical Society, 456(2), pp.2196-2209.
  2. Bianucci, M. (2021). Operators central limit theorem. Chaos, Solitons & Fractals, 148, 110961.
  3. Breitenberger, E. (1963). Analogues of the normal distribution on the circle and the sphere. Biometrika, 50(1/2), 81-88.
  4. Camilo, F., Nice, D. J., Shrauner, J. A., & Taylor, J. H. (1996). Princeton-Arecibo Declination-Strip Survey for Millisecond Pulsars. I. Astrophysical Journal v. 469, p. 819, 469, 819.
  5. Condon, J. J., & Ransom, S. M. (2016). Essential radio astronomy (Vol. 2). Princeton University Press.
  6. Dai, S., Hobbs, G., Manchester, R.N., Kerr, M., Shannon, R.M., van Straten, W., Mata, A., Bailes, M., Bhat, N.D.R., Burke-Spolaor, S. and Coles, W.A., 2015. A study of multifrequency polarization pulse profiles of millisecond pulsars. Monthly Notices of the Royal Astronomical Society, 449(3), pp.3223-3262.
  7. Deng, J. (2010, June). Relationship between Lévy Distribution and Tsallis Distribution. In ICEIS (2) (pp. 360-367).
  8. Fano, U. (1961). Effects of configuration interaction on intensities and phase shifts. Physical review, 124(6), 1866.
  9. Ferrari, A. C., & Robertson, J. (2000). Interpretation of Raman spectra of disordered and amorphous carbon. Physical Review B 61: 14095–14107.
  10. Gardner, F. F., & Whiteoak, J. B. (1969). The linear polarization of radio sources between 11 and 20 cm wavelength. II. Polarization and related properties of extragalactic sources. Australian Journal of Physics, 22(1), 107-120.
  11. Hanel, R., Thurner, S., & Tsallis, C. (2009). Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example. The European Physical Journal B, 72(2), 263.
  12. Helfand, D. J., Manchester, R. N., & Taylor, J. H. (1975). Observations of pulsar radio emission. III-Stability of integrated profiles. Astrophysical Journal, vol. 198, June 15, 1975, pt. 1, p. 661-670., 198, 661-670.
  13. Hilhorst, H. J. (2009). Central limit theorems for correlated variables: some critical remarks. Brazilian Journal of Physics, 39, 371-379.
  14. Hilhorst, H. J. (2010). Note on a q-modified central limit theorem. Journal of Statistical Mechanics: Theory and Experiment, 2010(10), P10023.
  15. Hotan, A. W., Bailes, M., & Ord, S. M. (2005). PSR J0737-3039A: baseband timing and polarimetry. Monthly Notices of the Royal Astronomical Society, 362(4), 1267-1272.
  16. Keane, E. F. (2010). The transient radio sky. The University of Manchester (United Kingdom).
  17. Kijak, J., Kramer, M., Wielebinski, R., & Jessner, A. (1997). Observations of millisecond pulsars at 4.85 GHz. Astronomy and Astrophysics, v. 318, p. L63-L66, 318, L63-L66.
  18. Kramer, M., Wielebinski, R., Jessner, A., Gil, J. A., & Seiradakis, J. H. (1994). Geometrical analysis of average pulsar profiles using multi-component Gaussian FITS at several frequencies. I. Method and analysis. Astronomy and Astrophysics Suppl., Vol. 107, p. 515-526 (1994), 107, 515-526.
  19. Kramer, M. (1994). Geometrical analysis of average pulsar profiles using multi-component Gaussian FITS at several frequencies. II. Individual results. Astronomy and Astrophysics Suppl., Vol. 107, p. 527-539 (1994), 107, 527-539.
  20. Kramer, M., Xilouris, K.M., Lorimer, D.R., Doroshenko, O., Jessner, A., Wielebinski, R., Wolszczan, A. and Camilo, F., 1998. The characteristics of millisecond pulsar emission. I. Spectra, pulse shapes, and the beaming fraction. The Astrophysical Journal, 501(1), p.270.
  21. Krishnamohan, S., & Downs, G. S. (1983). Intensity dependence of the pulse profile and polarization of the VELA pulsar. Astrophysical Journal, Part 1, vol. 265, Feb. 1, 1983, p. 372-388., 265, 372-388.
  22. Lundgren, S. C., Foster, R. S., & Camilo, F. (1996, January). Hubble Space Telescope Observations of Millisecond Pulsar Companions: Constraints on Evolution. In International Astronomical Union Colloquium (Vol. 160, pp. 497-500). Cambridge University Press.
  23. Mantegna, R. N., & Stanley, H. E. (1999). Introduction to econophysics: correlations and complexity in finance. Cambridge university press.
  24. Marsh, J. A., Fuentes, M. A., Moyano, L. G., & Tsallis, C. (2006). Influence of global correlations on central limit theorems and entropic extensivity. Physica A: Statistical Mechanics and its Applications, 372(2), 183-202.
  25. Meier, R. J. (2005). On art and science in curve-fitting vibrational spectra. Vibrational spectroscopy, 2(39), 266-269
  26. Naudts, J. (2009). The q-exponential family in statistical physics. Central European Journal of Physics, 7, 405-413.
  27. Osłowski, S., van Straten, W., Hobbs, G. B., Bailes, M., & Demorest, P. (2011). High signal-to-noise ratio observations and the ultimate limits of precision pulsar timing. Monthly Notices of the Royal Astronomical Society, 418(2), 1258-1271.
  28. Padmanabh, P. V., Barr, E. D., Champion, D. J., Karuppusamy, R., Kramer, M., Jessner, A., & Lazarus, P. (2021). Revisiting profile instability of PSR J1022+ 1001. Monthly Notices of the Royal Astronomical Society, 500(1), 1178-1187.
  29. Sayer, R. W., Nice, D. J., & Taylor, J. H. (1997). The Green Bank northern sky survey for fast pulsars. The Astrophysical Journal, 474(1), 426.
  30. Sparavigna, A. C. (2024). q-Gaussian and q-BWF Functions Applied to the Decomposition of Pulsar Profiles: Preliminary Results, International Journal of Sciences 06(2024):1-9 DOI: 10.18483/ijSci.2768
  31. Sparavigna, A. C. (2023). Convolution and Fourier Transform: from Gaussian and Lorentzian Functions to q-Gaussian Tsallis Functions. Int. J. Sciences, 11, 7-11.
  32. Stairs, I. H., Thorsett, S. E., & Camilo, F. (1999). Coherently dedispersed polarimetry of millisecond pulsars. The Astrophysical Journal Supplement Series, 123(2), 627.
  33. Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of statistical physics, 52, 479-487.
  34. Tsallis, C. (2011). The nonadditive entropy Sq and its applications in physics and elsewhere: Some remarks. Entropy, 13(10), 1765-1804.
  35. Umarov, S., Tsallis, C., Steinberg, S. (2008). On a q-Central Limit Theorem Consistent with Nonextensive Statistical Mechanics. Milan J. Math. Birkhauser Verlag. 76: 307–328. doi:10.1007/s00032-008-0087-y. S2CID 55967725.
  36. Van der Wateren, E., Bassa, C.G., Cooper, S., Grießmeier, J.M., Stappers, B.W., Hessels, J.W.T., Kondratiev, V.I., Michilli, D., Tan, C.M., Tiburzi, C., & Weltevrede, P. (2023). The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the properties of the LOFAR pulsar discoveries. Astronomy & Astrophysics, 669, p.A160.
  37. Wahl, H., Rankin, J., Venkataraman, A., & Olszanski, T. (2023). Radio pulsar emission-beam geometry at low frequency: LOFAR High-Band Survey sources studied using Arecibo at 1.4 GHz and 327 MHz. Monthly Notices of the Royal Astronomical Society, 520(1), 314-321.
  38. Wojdyr, M. (2010). Fityk: a general‐purpose peak fitting program. Journal of Applied Crystallography, 43(5‐1), 1126-1128.

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