Polarization of high-energy emission in a pulsar striped wind

Transcription

1 Paris - 16/1/26 p.1/2 Polarization of high-energy emission in a pulsar striped wind Jérôme Pétri Max Planck Institut für Kernphysik - Heidelberg

2 Paris - 16/1/26 p.2/2 Outline 1. The models 2. The striped wind 3. Application to the Crab pulsar 4. Conclusions & Perspectives

3 Paris - 16/1/26 p.3/2 The existing models Light Cylinder null charge surface Ω. B = Ω α closed field region B polar cap two-pole caustic outer gap 1. the polar cap (Sturrock 1971, Ruderman & Sutherland 1975) ; particles acceleration and radiation close to the neutron star surface (at the magnetic poles). 2. the outer gap (Cheng et al. 1986) ; particles acceleration and radiation close to but inside the light cylinder. 3. the two-pole caustic (Dyks & Rudak 23) ; particles acceleration and radiation from the neutron star surface up to the light cylinder. 4. the striped wind (Coroniti 199, Michel 1994). radiation well outside the light cylinder.

4 Paris - 16/1/26 p.4/2 Aim of this work 1. to compute the polarization properties of the synchrotron emission in the relativistic striped wind. Relativistic beaming effect pulsed emission (Kirk et al. 22); 2. to make a quantitative comparison with the recent optical data from the Crab pulsar (Kanbach et al. 23). This will complete the work of Dyks et al. (24) who studied the synchrotron polarization for the outer/polar gap and two-pole caustic models.

5 Paris - 16/1/26 p.5/2 The striped wind Asymptotic MHD wind solution (Bogovalov 1999) Χ Ζ 1 5 y z r x assumes only a an exact analytical expression for component decreasing like is known ; independent of the magnetospheric structure inside the light cylinder ; discontinuous polarity reversal. ;

6 Paris - 16/1/26 p.6/2 Parameters of the model (1) Geometrical properties : the obliquity ( ) of the pulsar (angle between magnetic moment and rotation axis) ; the inclination ( ) of the line of sight ; Magnetic field configuration : no radial component, ; azimuthal and colatitudinal components follow the split monopole decay in radius, ; the current sheet (discontinuous (smooth polarity reversal) ; ) replaced by a transition layer of thickness the width of significant component : the maximum relative amplitude ( pulse. ) of the compared to defined in each

7 ! " % $ Paris - 16/1/26 p.7/2 Parameters of the model (2) Dynamical properties (emitting particles) : the Lorentz factor ( ) of the wind ; the power law index ( ) of the particle distribution ; the electron/positron number density ( (isotropic in momentum space ) is : ) such that the distribution function # " and chosen to mimic the total pressure balance between magnetic and gaseous component strong magnetic field associated with low density and conversely.

8 * + & ' ) Paris - 16/1/26 p.8/2 An example In the equatorial plane ( ( ) r BΘ, r Bφ Magnetic field φ Θ b 1, r r L Number density magnetic field sheet ; accompanied by a significant polarity reversal in the current component ; density non negligible in these transition layers ; asymmetry in the peak density to account for the pulse maximum intensity discrepancy. K r,t r r L

9 5 ( - 6 9= < ; 9: 2,,. -,, 34 >. Paris - 16/1/26 p.9/2 Polarization parameters With help on the aforementioned Stokes parameters ( the normalized intensity : ), we plot :, / 12 the polarization degree : 87 the polarization angle, defined as the position angle between the total electric field vector received by an observer and the projection of the pulsar s rotation axis on the plane of the sky is:?. -

10 B A C( ( Application to the Crab pulsar The geometrical parameters (Ng & Romani 24) : the obliquity ; the line of sight inclination angle ; the angle of the rotation axis of the pulsar on the plane of the sky. For the emitting particles : the power law index. Paris - 16/1/26 p.1/2

11 D ( Polarization properties of the pulsed emission Models with Observations (Kanbach et al. 23) 1 Intensity 1 Intensity I.4.2 I.4.2 in % Polarisation degree in % Polarisation degree 18 Polarisation angle 18 Polarisation angle ΧCrabe in degrees Χ in degrees (Pétri & Kirk, ApJL 25) Paris - 16/1/26 p.11/2

12 E 7 34 FC 7 Q R@ ( 34 Q D F C Influence of Model with ( C I Intensity Polarisation degree light curves and polarization angle unchanged by varying ; average polarization degree correlated with indeed, in the most favorable case (straight magnetic field lines), the maximum degree of polarization is : ; 4 in % ΧCrabe in degrees Polarisation angle For instance, 5 2 GIHJHJK HLHJM GIHJHJK HLHJM N HJHJO HLHJP N HJHJO HLHJP Paris - 16/1/26 p.12/2

13 S U ' C ' T ' A V ( ' Influence of Model with ( 1 Intensity.8.6 I.4 in % Polarisation degree Polarisation angle peak separation and correlated quantities (degree of polarization and angle sweep) depending on the inclination of the line of sight : but relative peak intensity preserved ; degree of polarization weakly disturbed ; sweep angle reaches case. in the symmetric ΧCrabe in degrees Paris - 16/1/26 p.13/2

14 W D D ( X A V Influence of Model with 1 Intensity.8.6 I.4.2 in % Polarisation degree In the ultrarelativistic regime the polarization degree reaches a constant limit for high Lorentz factors ; sweep angle of ; : 18 Polarisation angle ΧCrabe in degrees Paris - 16/1/26 p.14/2

15 Conclusions pulsed high-energy emission of pulsars arises from well outside the light cylinder ; electric vector of the off-pulse emission is aligned with the projection of the pulsar s rotation axis on the plane of the sky : computations are in agreement with recent observations of the Crab pulsar ; the striped wind scenario naturally incorporates features of the phase-dependent properties of the polarization angle, degree of polarization and intensity. Perspectives : the manner in which magnetic energy is released into particles in the current sheet remains poorly understood ; the link between the asymptotic magnetic field structure and the pulsar magnetosphere is obscure. Paris - 16/1/26 p.15/2

16 Y. -, hi g ^ % ^ % b ) f e 1 ) & c d kj; c a k 7 f e 1 s ) & Stokes parameters (1) Stokes parameters ( ) as measured by an observer at time : Z\[ &n n &n m = k N HJHJO HLHJP l ( GIHJHJK HLHJM l ( m = b c ^`_ Z\[ N HJHJO HLHJP, ] - ]. ] GIHJHJK HLHJM emission starts for o ;c p Z\[ #pq r is the retarded time : is a unit vector along the line of sight from the pulsar to the observer ; is the angular frequency of the emitted radiation ; is the local polarization angle at a given point l aberration of light causing a rotation in the polarization angle (relativistic cinematics effect, included in the definition of ). l. Paris - 16/1/26 p.16/2

17 c d z u? > {z u y $ s t x ) & c d t ~ y y Stokes parameters (2) The function is defined by the synchrotron emissivity: w x #pq y } w x uv is a constant factor that depends only on the nature of the radiating particles (charge and mass ) and the power law index of their distribution; the Doppler boosting factor: #p q } is a unit vector along the magnetic field line ; Paris - 16/1/26 p.17/2

18 ? ˆ ~ ˆ iˆ ~ ˆ?? F ƒ 7 t Š r i U ( ( U ' w x uv >C Paris - 16/1/26 p.18/2 function > C > C C ( r c ' with the Euler gamma function

19 Aberration of light Χ in degrees Χ in degrees Polarisation angle Α Π Ξ Polarisation angle Α Π 3 Β Paris - 16/1/26 p.19/2

20 Polar/outer gap and two-pole caustic model 3 Crab Pulsar 3 Polar cap model α=7, ζ=12 Two-pole caustic model α=7, ζ=5 Outer gap model α=65, ζ=82 Intensity Position angle Degree of polarization phase phase phase phase (Dyks et al. 24) Paris - 16/1/26 p.2/2