On the structure of radio pulsar magnetospheres

1. On the structure of radio pulsar magnetospheres Igor F. Malov, ЕlenaNikitina Pushchino Radio Astronomy Observatory, Astro Space Center of P.N. Lebedev Physical Institute, Russian Academy of Sciences YERAC 2011

2. This parameter allows us to understand the nature of the pulsar radiation and a distribution of the angles for the objects with different ages to make an assumption about their evolution. • The detection of the objects with small values of β and with the values near 90° gives us a possibility to predict an interpulse radiation. • The estimation of these angles on the different magnetosphere levels based on the observations in the different frequency ranges can be used for a check of the hypothesis on the dipole magnetic field. • There is a possibility to estimate the distribution of the emission levels based on these data, i.e. to make a mapping of these levels. • The analysis of all results on the estimation of the angles β in radio pulsars is one way to choice an adequate model for these objects and a mechanism of their radiation. YERAC 2011

3. P.Weltevrede, S.Johnston. “Profile and polarization characteristics of energetic pulsar”Mon. Not. Roy. Astron. Soc. V.391, P. 1210, 2008 • T.D. van Ommen et al. “Polarimetric observations of southern pulsars at 800 and 950 MHz”Mon. Not. Roy. Astron Soc., V.287, P.307, 1997. The first method: 80 pulsars from [2], 283 objects at 20 cm and 132 at 10 cm ones from [1] The second method: 34 pulsars form [2], 40 ones at 20 cm and 31 objects at 10 сm from [1] The third method: 34 pulsars from [2] Denote: 1 - the pulsars from [1], whose parameters were measured at 10 cm; 2 - the pulsars from [1], whose parameters were measured at 20 cm; 3 - the pulsars from [2], whose parameters were measured at near 30 cm YERAC 2011

4. to observer Fig.1 The model of a hollow cone The hollowcone model • μ – a direction of a magnetic moment vector • Ω – an axis of a pulsar rotation • L – a line of sightof an observer • ζ– an angle between the line of sightand the rotation axis • β – an angle between the direction of the magnetic moment vector (the axis of an emission cone) and the axis of the pulsar’s rotation • θ – the angular radius of an emission cone (the half-width of the cone of open field lines) YERAC 2011

5. The 1st method of the estimation of the angle β YERAC 2011

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7. The 2nd method of the estimation of the angle β lg W10 = (1,12±0,05) + (-0,25±0,09) lg Р for 1 lg W10 = (1,22±0,03) + (-0,24±0,05) lg Р for 2 lg W10 = (1,16±0,03) + (-0,27±0,08) lg Р for 3 C can be>0 and<0 in dependence on the sign ofdφ YERAC 2011

8. <β2> = 33°,9 for 1, <β2> = 33°,9 for 2 and <β2>=36°,4 for 3at С > 0; <β2> = 52°,1 for 1, <β2> = 54°,1 for 2 and <β2>=49°,1 for 3 at С < 0. YERAC 2011

9. Profiles n =∞ n = 4 n = 2 n = 3/2 n = 5/4 The 3nd method of the estimation of the angle β The general form of equations: YERAC 2011

10. The equations at various n n = 2 n = 3/2 YERAC 2011

11. n = 5/4 n = 4 YERAC 2011

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13. The slope of the straight lines, which characterize the width of the radiation cone,are differ from the expected slope with the index equals -0.5 in the model of polar cup appreciably. The similar dependencies are was made for different samples of radio pulsars at various frequencies. The straight lineslope versus the frequency YERAC 2011

14. Conclusions • The values of the angles β1 for three different samples of pulsars are calculated. These angles are low for all wavelengths. • The values of the angle β2 for dozens of pulsars are estimated. These values are equal to each other within experimental errors. The average angle between the magnetic dipole and the rotation axis is located approximately in the middle of the interval between 0° and 90° for all pulsars. The average value of this angle for all β2 is equal to 43°.5. • The difference between calculated W10(P) and the usually accepted in the model of the polar cap can be explained by the rate of development of plasma instabilities near the surface of a neutron star (in the generation area of high frequencies). • The role of the quadrupole component of the magnetic field is found to be unimportant. This is also in the agreement with the closeness of the calculated angles β at different frequencies. • The pulsars with β ≤ 10° are belong to the class of objects with possible interpulses and significant interpulse emission. They are PSR B1641-45, 1642-03 and 1944 +17. The pulsars with β> 80° may belong to orthogonal rotators with the possible interpulses at a distance of 180° from the main pulse. The candidate in such objects is PSR B2321-61. • We couldn’t find any dependence of the angle β of inclination of the axis on the pulsar age (z-distance, luminosity L and the characteristic age). YERAC 2011

15. ☺ Thank You! YERAC 2011

16. The first reason relates to the possible influence of the multipole components of magnetic field in the deep layers of the magnetosphere. A deviation from the dipole is assumed in many pulsar models, including the paper of the Ruderman and Sutherland, to ensure an ample production of the secondary electron-positron plasma. The angular width of the open field lines cone is equal to: The width of the radiation cone for the quadrupole field would be considerably less than in the case of the dipole structure and the dependence on the rotation period would have been stronger. But the dependence following from observations is weakly for high frequencies than in dipole field. That means observations data can not be explain by the deviation of the magnetic field structure from dipole. YERAC 2011

17. The second reason is connected with the growth of plasma instabilities in the magnetosphere of pulsars. The main instability is the two-stream instability, which leads to a marked increase in the amplitude of Langmuir waves. At a distance of about 10 radius of the stars the wave amplitude will increase by about two orders of magnitude. In these areas the radio emission at high frequencies is generated. The lowest frequencies (around 100 MHz) are generated at very large distances from the neutron star surface. Therefore, it is thought that at these levels the width of the cone is completely determined by the dipole dependence and a slope of 0.5, which corresponds to the universal proportionality, is reached. YERAC 2011