YERAC 2011 1 On the structure of radio pulsar magnetospheres On the structure of radio pulsar...

YERAC 2011YERAC 2011 11

On the structure On the structure of radio pulsar of radio pulsar

magnetospheresmagnetospheres

Igor F. Malov, Еlena Nikitina

Pushchino Radio Astronomy Observatory,

Astro Space Center of P.N. Lebedev Physical Institute, Russian Academy of Sciences


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.


1. P.Weltevrede, S.Johnston. “Profile and polarization characteristics of

energetic pulsar”Mon. Not. Roy. Astron. Soc. V.391, P. 1210, 2008

2. 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.

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

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]


The hollow cone model

μ – a direction of a magnetic moment vector

Ω – an axis of a pulsar rotation

L – a line of sight of an observer

ζ – an angle between the line of sight and 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)

to observer

Fig.1 The model of a hollow cone


The 1st method of the estimation of the angle β

2cossinsincoscoscos 10W

4

Wsin

2sin

arcsin10

2min10W


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

cosy

BcosCd

dmax)(

DW

2

cos 10

cossincoscossin

sinsin

tg

Cy

yCtg

1

1 2

)sin(

sin

max

d

d

C can be >0 and <0 in dependence on the sign of dφ

0)1()(2)]1(21[)1(2)1( 22222223422 CBCDyBDCyDDCyDCyDC

The 2nd method of the estimation of the angle β


<β2> = 33°,9 for 1, <β2> = 33°,9 for 2 and <β2>=36°,4 for 3 at С > 0;

<β2> = 52°,1 for 1, <β2> = 54°,1 for 2 and <β2>=49°,1 for 3 at С < 0.


The general form of equations:

)sin(sin C

sinsincoscoscos D

)( n

n = 2

n = 5/4

n = 3/2

n = 4

n = ∞

Profiles

The 3nd method of the estimation of the angle β


The equations at various n

0)1(2

121

]12)(2[ 22

2

CDyDCyCyC

yC

CyCCy

32242224523 ]2)21([2]4)56()1([)1(2 yDDDCCyDDCDCyDC

yCCDDCCyDDCDDC )]1(2)1([2]5)762()1(2[ 22222224

0)1()1( 22222 CCDC

n = 2n = 2

n = 3/2n = 3/2


n = 5/4

012

)1(

22

121

1)

121(2

12

)(21

2

2

2

22

CyC

CDyDCyCyC

yC

CyC

yC

CyC

Cy

n = 4

34322 168)12()1( CyyCyCDCyyCD

016)3(4)23(4 24222 CCyCCyC


ν (ν (MHzMHz)) bb

111111 0,45 ± 0,080,45 ± 0,08

408408 0,36 ± 0,05 0,36 ± 0,05

800-950800-950 0,27 ± 0,08 0,27 ± 0,08

15001500 0,24 ± 0,05 0,24 ± 0,05

30003000 0,25 ± 0,090,25 ± 0,09

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.

bPaPW )(10

The straight line slope versus the frequency


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).


Thank YouThank You!!

☺


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.

PRr

радrr

LC

4103,1)(62,0


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 1 On the structure of radio pulsar magnetospheres On the structure of radio pulsar...

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