Drifting subpulse phenomenon in pulsars

Transcription

1 Drifting subpulse phenomenon in pulsars Lofar perspective Janusz Gil J. Kepler Astronomical Institute University of Zielona Góra, Poland Collaborators: G. Melikidze, B. Zhang, U. Geppert, F. Haberl, J. Kijak, M. Sendyk

2 LOFAR sensitivity for PSRs LOFAR sensitivity for PSRs

3 Broadening of the profile As frequency decreases Evidence of the radius-to-frequency mapping and dipolar nature of magentic field lines in the emission region Sensitive observations below 160 MHz would be highly desirable

4 40 years after discovery of pulsars the actual mechanism of their coherent radio emission is still a mystery. Drifting subpulses, which seem to be a common phenomenon in pulsar radiation, is also a puzzle. The mechanism for drifting subpulses cannot be very different from the mechanism of observed radio emission......intrinsic property of radiation mechanism (Weltevrede, Edwards & Stappers 2006, A&A 445,243)

5 LRFS longitude (deg) 2DFS f=ccp cycles per period ccp LRFS - Longitude Resolved Fluctuation Spectrum P2 = ± P / cpp 2DFS - Two Dimensional Fluctuation Spectrum calulated along various slopes

6 Unbiased search for drifting subpulses in 187 (191) pulsars About 55 % (more) of drifting subpulse pulsars Weltevrede, Edwards & Stappers et al. 2006, ATNF 20. S/N a= r a = rp / h At frequencies lower than 320 MHz (LOFAR range) the ratio of detected drifting subpulses should be even higher

7 m ρ D d h rem Ω γ 1 m γ 1 ρ NS - opening angle Subpulses (drifting) can be resolved if h rp ρ ρ > γ 1 d D rpc α at the emission altitude R rem P (γ 2 )3.76 P1.35

8 Unbiased search for drifting subpulses in 187 (191) pulsars About 55 % (more) of drifting subpulse pulsars Weltevrede et al. 2006, ATNF 20. P 15 = 52 (1.2)3.76 P a= r a = rp / h Lorentz factor γ = 120

9 Subpulse drift Carousel model Sub-beams of radio emission presumably related to sparks operating just above the Polar Cap circulate around the magnetic axis P 2 P3 Subpulses in subsequent pulses arrive in phases determined by the apparent drift rate D = P2 / P3 l of s P4 l of s l of s P4 Ω = Hot PC heated by sparks - circulational periodicity? 2π P Polar cap rpc = P 0.5 cm

10 150 PSR B Perhaps the best example of Drifting subpulses phenomenon in pulsars P2 Apparent subpulse drift-bands P3 11P Modulation of intensity along drift-bands consistent with carousel model that is Sub-beams continue to circulate beyond the observed pulse-window (after van Leuven, Stappers et al..)

11 B α = 175 β = 7

12 PSR B LRFS

13 P1, P2, P3, P4 Apparent drift rate P2 P4 P3 Intrinsic drift rate P1 = P N P4 = P3 N number of rotating sub-beams P4 P4 Ruderman & Sutherland 1975 distance between driftbands in longitude between P P3 distance 1 driftbands in D = P2 / P3 distance between the same driftbands time interval to complete one rotation around the pole very difficult to measure, only 8 cases known!!!

14 PSR B Deshpande&Rankin 1999 P=1.089 s P3 = 1.87 P ^ P4 = 37.35P Number of sub-beams circulating around B P ~37P 4 N = P4 / P3 = 20

15 PSR B MHz observations Asgekar & Deshpande MHz observations Deshpande & Rankin f4 f3 Phased-resolved fluctuation spectrum 1/37 f4 = 1/ 37P P4 = P = 41s. Spectral analysis fully consistent with carousel model. Sub-beams continue to circulate around the beam axis beyond the pulse-window and reapear after the period needed to complete one full circulation around the magnetic axis 1 / 2.f15 3 = 1 / P3 1/14 f4 1/37=0.027 N = P4 / P3 = =20 Low frequency observations (LOFAR range) are more sensitive to low frequency modulations possibly related to the carousel circulation times

16 Radius-to-frequency mapping PSR B Frequency dependent beam size 430 MHz 103 MHz 103 MHz 35 MHz Arecibo PRAO Gauribidanur

17 B Arecibo 327 MHz Rankin et al. 2007

18 B P = 1.19 s P 15 = MHz E = erg / s P3 = P P4 = P N = P4 / P3 = 22 Arecibo Observatory 327 MHz Rankin et al. 2007

19 B Cartographic map of 20 subpulse beams circulating around the pole in about 37 pulsar periods Deshpande & Rankin, 1999 P = s l-of-s P 15 = 3.52 E = 1032 erg / s 430 MHz P3 = 1.86 P P4 = P N = P4 / P3 = 20 α,β (Intensity; pulse longitude and pulse number) (Intensity; polar colatitude and azimuth) Clear manifestation of subpulse sub-beams circulating around the magnetic axis Pulsar geometry known

20 B MHz Q-mode Erratic No organized drift visible Cartographic map impossible to make

21 103 MHz 1/37=0.026 B Q-mode (erratic) Suleymanova & Rankin 2006 Clear feature at 37 P as in the B-mode

22 Spark plasma circulates around the local magnetic pole on the Polar Cap with a specific period P_4, regardless it is fragmented into equally spaced filaments or operates in much less organized manner. One cannot swich off the E x B drift, except when there is no E or B.

23 Natural mechanism of subpulse drift E B Natural state of the magnetospheric plasma frozen into electric and magnetic field is corotation with NS (global corotation) υ cor = c( Ec Bs ) / B 2 = cec / Bs if E Ec then υ υ cor ρ = ρ GJ ρ ρ GJ corotation Polar Gap charge depletion Non-corotation plasma lags behind pulsar rotation and drifts with respects the polar cap surface with velocity υ dr υ dr = c( E Bs ) / B 2 = c E / Bs E Electric field associated with charge depletion ρ = ρ GJ ρ If plasma has transversal structure (spark filaments) then this inevitable E B drift should be observed in the form of drifting subpulses, and/or specific features in the intensity fluctuation spectrum

24 E B spark plasma circulation drift rate Linear velocity of the E x B drift (RS75) υd = c E cη ( 2π / cp ) Bs h 2π = =η h [cm/s] Bs Bs P Bs -actual surface magnetic field Bd -dipolar magnetic field at PC E - component of electric field caused by charge depletion ρ = ρ GJ ρ th = η ρ GJ ω = ν d / d = η (2π / P)(h / d ) Carusel angular speed Time interval to complete one circulation around periphery of PC P d P rp P4 = 2η h 2η h Gil, Melikidze & Geppert 2003

25 Within the model of the inner acceleration region to surface of the PC is heated to high temperatures by the back-flow of particles produced in sparking discharges. The heating rate is determined by the same value of the electric field that is involved in the E x B drifting phenomenon. thus, the observed drifting rate P d P rp P 4 = 2π d / υ d = 2η h 2η h and the observed heating rate (thermal X-ray luminosity from hot PC) Lx = σ Ts4 Abol = σ Ts4 Apc ( Bd / Bs ) should be strongly correlated.

26 Thermal X-ray luminosity from spark-heated polar cap Lx = ( P 15 / P )( P 4 / P ) 31 Efficiency 3 2 erg/s E = IΩ Ω Lx / E = (0.63 / I 45 ) ( P 4 / P) 2. Spin-down power I = I g cm 2 I 45 = 1 ± 0.15

27 X-ray Multi Mirror (XMM) Newton satelite telescope One revolution on an excentric orbit around the Earth takes 48 hours observations are not performed close to the Earth due to strong noise contamination

28 I 45 = 1 ± 0.15 Lx / E = (0.63 / I 45 ) ( P 4 / P) 2

29 Further low frequency LOFAR observation using 2DFS techniques should result P4 in Detection drifting subpulse pulsars and pussible more of be In nearbymore pulsars, in which thermal X-ray component fromdetermination hot polar cap can determined. Then the polar gap relationship Lx P4 2 can be tested further.

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31 B L_x=2.78 x 10^30 erg/s E_dot=1.5 x 10^32 erg/s P_4=6 P Weltevrede et al P_3=(7+/-1) P P_4=P_3

32 Ruderman & Sutherland 1975 Strong non-dipolar Surface magnetic field Charge depletion maximum possible gap height ~MK Pure vacuum gap ρ = ρ GJ E ~ V /h Very strong electric field E E B drift much too fast as compared with observations Within the acceleration region the spark generated positrons are moving towards the magnetosphere while back-flow of electrons bombard the polar cap surface and heat it to MK temperatures Polar cap heating too intense and subpulse drift was too fast as compared with observations Modification needed

33 Future work New XMM-Newton observations of PSR B Ks performed in November 2006 Zhang, Gil, Melikidze, Geppert, Haberl Non-detected P4 / P = 14 ± 1 (Gupta, Gil, Kijak, Sendyk 2004) Proposal for XMM-Newton observations of PSR B accepted observation in summer 2006 (simultaneous radio observations with GMRT planned) Very promissing P4 / P = 15 ± 1 (Asgekar, Deshapande 2005) Proposal for XMM-Newton observations of PSR B will be submitted for the next cycle Very promissing P4 / P = 10 ± 1 (Weltevrede 2006; GMRT planned)

34 Co-rotating magnetosphere Ec = (Ω r / c) Bs Ec Bs = 0 V = 0 Force-free magnetosphere GJ69, RS75 No acceleration along B ρ c = (1 / 2π ) dive c = = Ω B s /( 2π c ) = ± B s / cp 2 υ cor = c ( Ec Bs ) / B = cec / Bs Co-rotating charge density Linear co-rotation velocity

35 The only two cases existing with both measurements B Lx / E ~ B Lx / E ~ P 3 / P ~ 33 P 3/ P ~ 37

36 Gil, Melikidze & Zhang 2006 η = (1 / 2π )( P / P3 ) Screening factor ~( ) only few % of GJ plasma involved in acceleration Lx = ( P 15 / P )( P 3 / P ) X-ray bolometric luminosity erg/s 10( 28 29) erg / s Lx / E = 0.63 ( P 3 / P) 2 Ts = ( K ) A4 6 A4 = Abol /(10 4 m 2 ) ~ P 15 Efficiency ~ P 0.75 ( P3 / P ) 0.5 Ts ~ (2 3) MK

37 Pulsars are fast rotating and strongly magnetized Neutron Stars (NS) Corotation with NS E*B=0 Polar Cap (PC) region of NS surface connected to ISM via open magnetic field lines penetrating the Light Cylinder Charged particles will leave through LC due to inertia and create charge depletion just above the PC. If this charge cannot be re-supplied by the PC surface (strong binding) then huge accelerating potential drop will occur along the open magnetic field lines close to the PC surface.

38 1.4 GHz 0.32 GHz 1.4 GHz Weltevrede, Edwards & Stappers et al. 2006, 2007