Drifting subpulse phenomenon in pulsars Lofar perspective

Janusz Gil

J. Kepler Astronomical InstituteUniversity of Zielona Góra, Poland

Collaborators:

G. Melikidze, B. Zhang, U. Geppert, F. Haberl, J. Kijak, M. Sendyk

LOFAR sensitivity for PSRs

LOFAR sensitivity for PSRs

Broadening of the profileAs frequency decreases

Evidence of the radius-to-frequency mappingand dipolar nature of magentic field linesin the emission region

Sensitive observations below 160 MHz would behighly desirable

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)

LRFS

2DFS

2DFS - Two Dimensional Fluctuation Spectrum – calulated along various slopes

LRFS - Longitude Resolved Fluctuation Spectrum

longitude (deg)

cycles per period

cppPP /2 ±=

f=ccp

ccp

13487

1990

23 138

S/N

Weltevrede, Edwards & Stappers et al. 2006, 2007

ra =

hra p /=

1.0

2.5

5.0

10.

20.

. ATNF

Unbiased search for drifting subpulses in 187 (191) pulsars

About 55 % (more) of drifting subpulse pulsars

At frequencies lower than 320 MHz (LOFAR range) the ratio of detected drifting subpulsesshould be even higher

pcr

pr

Ω m

m

NS

R

α

ρρ∆

ρ - opening angle

1−γ

1−γ

Subpulses (drifting) can be resolved if

emr

1−>∆ γρ

at the emission altitude

emr

h

hdD ≈≈

dD

35.176.3215 )(52 PP γ≤−

⋅

Weltevrede et al. 2006, 2007

ra =

hra p /=

1.0

2.5

5.0

10.

20.

. ATNF

Unbiased search for drifting subpulses in 187 (191) pulsars

About 55 % (more) of drifting subpulse pulsars

35.176.315 )2.1(52 PP =−⋅

120=γ

Lorentz factor

Subpulses in subsequentpulses arrive in phases determined by the apparent drift rate

32 / PPD =

Carousel model

sofl −−

sofl −−

sofl −−

3P2P

↔

Polar capcmPrpc

5.041045.1 −×=

Pπ2=Ω

4P

4P

Subpulse drift

Sub-beams of radio emissionpresumably related to sparksoperating just above the Polar Capcirculate around the magnetic axis

- circulational periodicity ?

Hot PCheated by sparks

PSR B0809+74

Perhaps the best example ofDrifting subpulsesphenomenon in pulsars

Modulation of intensity along drift-bands consistent with carousel model Sub-beams continue to circulate beyond the observed pulse-window

Apparent subpulse drift-bands

that is

PP 113 ≈

2P

−

↔

150

(after van Leuven, Stappers et al..)

B0818-41

°

°

=

=

7

175

β

α

PSR B 0818-41 LRFS

Ruderman & Sutherland 1975

32 / PPD =

PP =1

Apparent drift rate

4321 ,,, PPPP

Intrinsic drift rate NPP 34 =

2P distance between driftbands in longitude

N number of rotating sub-beams

time interval to complete onerotation around the pole

3P

4P

4P

distance between the same driftbands

↑

↓

4P

very difficult to measure, only 8 cases known !!!

↑

↓

distance between driftbands in3P 1P

PSR B0943+10

Deshpande&Rankin 1999

↑

↓

~37P

P=1.089 s

PP 87.13 =

^

4P PP 35.374 =

20/ 34 == PPN

Number of sub-beamscirculating around B

35 MHz observationsAsgekar & Deshpande 2001

1/37

1/14

s.4135.374 == PP

15.2/1

37.35 1.87

=20

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

Phased-resolved fluctuation spectrum

PSR B0943+10

== 34 / PPN

↑1/37=0.027

33 /1 Pf =

4f

Pf 37/14 =

430 MHz observationsDeshpande & Rankin

4f

3f

Low frequency observations (LOFAR range) are more sensitive to low frequency modulations possibly related to the „carousel” circulation times

103 MHz430 MHz

Radius-to-frequency mapping

Frequency dependent beam sizePSR B0943+10

Arecibo

PRAO

103 MHz 35 MHz

Gauribidanur

B1133+16

Rankin et al. 2007

Arecibo 327 MHz

327 MHz

Arecibo Observatory

22/44.28

237.1/109

7.3

19.1

34

4

31

15

3

===

=⋅=

=

=

⋅−

⋅

PPNPP

PPsergE

P

sP

Rankin et al. 2007

B1133+16

327 MHz

B0943+10 Cartographic map of 20 subpulse beams „circulating” around the pole in about 37 pulsar periods

s098.1=P

PP 86.13 =

PP 35.374 =

20/ 34 == PPN

Deshpande & Rankin, 1999

(Intensity; pulse longitude and pulse number) (Intensity; polar colatitude and azimuth)

Clear manifestation of subpulse sub-beams circulating around the magnetic axis

βα ,Pulsar geometry known

l-of-s

430 MHz sergE

P

/10

52.3

32

15

=

=⋅

−⋅

B0943+10 430 MHz

Q-modeErraticNo organized drift visible

Cartographic map impossible to make

B0943+10 Q-mode (erratic)

Suleymanova & Rankin 2006 Clear feature at 37 P as in the B-mode

↑

1/37=0.026

103 MHz

Spark plasma circulates around the local magneticpole on the Polar Cap with a specific period P_4,regardless it is fragmented into equally spaced filamentsor operates in much less organized manner.

One cannot swich off the E x B drift, except when there is no E or B.

Natural mechanism of subpulse drift

scsccor BcEBBEc //)( 2 =×=υ corotation

corc thenEEif υυ ≠≠ GJρρ ≠

Non-corotation plasma lags behind pulsar rotation anddrifts with respects the polar cap surface with velocity

BE ×

ssdr BEcBBEc //)( 2 ∆=×∆=υ

E∆ Electric field associated with charge depletion

Polar Gapcharge depletion

If plasma has transversal structure (spark filaments) then this inevitable

BE ×∆ drift should be observed in the form of drifting subpulses, and/or specific features in the intensity fluctuation spectrum

drυ

ρρρ −=∆ GJ

⇐

GJρρ =⇐

Natural state of the magnetospheric plasma frozen into electricand magnetic field is corotation with NS (global corotation)

sB -actual surface magnetic field-dipolar magnetic field at PC

( ) ]cm/s[2/2 hPB

hBcPcB

Ecs

s

sd

πηπηυ ==∆=

E∆ - component of electric field caused by charge depletion GJthGJ η ρρρρ =−=∆

hrP

hdPP p

ηη 224 ≤=

BE ×∆ spark plasma circulation drift rate

Gil, Melikidze & Geppert 2003

dB

Time interval to complete one circulation around periphery of PC

)/)(/2(/ dhPdd πηνω == Carusel angular speed

Linear velocity of the E x B drift (RS75)

Within the model of the inner acceleration region to surface of the PCis heated to high temperatures by the back-flow of particles producedin 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

and the observed heating rate (thermal X-ray luminosity from hot PC)

should be strongly correlated.

hrP

hdPdP p

d ηηυπ

22/24 ≤==

)/(44sdpcsbolsx BBATATL σσ ==

24

315

31 )/)(/(105.2 −•

−××= PPPPLx

2445 )/()/63.0(/ −•= PPIELx

erg/s

Thermal X-ray luminosity from spark-heated polar cap

Efficiency••

ΩΩ= IESpin-down power

. 15.0110

45

24545

±==

IcmgII

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

15.0145 ±=I

2445 )/()/63.0(/ −⋅= PPIELx

Further low frequency LOFAR observation using 2DFS techniques should result inDetection more drifting subpulse pulsars and pussible more determination of

4P

In nearby pulsars, in which thermal X-ray component from hot polar cap can be determined. Then the polar gap relationship can be tested further.2

4−∝ PLx

B0628-28 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..2006 P_3=(7+/-1) P P_4=P_3

Ruderman & Sutherland 1975

GJρρ =∆

Pure vacuum gap

Charge depletionmaximum possible

Very strong electric field

drift much too fastas compared with observations

Polar cap heating too intenseand subpulse drift was too fastas compared with observations

gap height

hVE /~ ∆∆E∆

BE ×∆

Within the acceleration region the sparkgenerated positrons are moving towards the magnetosphere while back-flow of electrons bombard the polar cap surface and heat it to MK temperatures

Modification needed

Strong non-dipolarSurface magnetic field

~MK

New XMM-Newton observations of PSR B0826-3450 Ks performed in November 2006 Zhang, Gil, Melikidze, Geppert, Haberl

Proposal for XMM-Newton observations ofPSR B0834+06 accepted – observation in summer 2006

Future work

114/4 ±=PP

115/4 ±=PP

(Gupta, Gil, Kijak, Sendyk 2004)

(Asgekar, Deshapande 2005)

Proposal for XMM-Newton observations of PSR B1702-19 will be submitted for the next cycle

110/4 ±=PP (Weltevrede 2006; GMRT planned)

Non-detected

Very promissing

Very promissing

(simultaneous radio observations with GMRT planned)

Co-rotating magnetosphere

sc BcrE ××Ω−= )/(0=⋅ sc BE

cPsBcsB

cdivEc

/)2/(

)2/1(

±=⋅Ω−=

==

π

πρ

sBccEBsBcEccor //)(2

=×=υ

Force-free magnetosphere

Linear co-rotation velocity

Co-rotating charge density

GJ69, RS750|| =∆ VNo acceleration along B

31077.0~/ −•

×ELxB1133+16 33~/3 PP

∧

B0943+103105.0~/ −

•×ELx 37~/3 PP

∧

The only two cases existing with both measurements

)/)(2/1( 3PPπη =

23 )/(63.0/ −

∧•= PPELx

23

315

31 )/)(/(109.2 −∧•

−××= PPPPLx

Screening factor ~(0.05-0.1)only few % of GJ plasma involved in acceleration

X-ray bolometric luminosity

Efficiency ~ 0.001

erg/s

serg /10 )2928( −

Gil, Melikidze & Zhang 2006

5.03

75.025.0

1525.0

46 )/()102.8( −

∧−

•

−−×= PPPPAKTs

1.0~)10/( 244 mAA bol= MKTs )32(~ −

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.

Pulsars are fast rotating and strongly magnetized Neutron Stars (NS)

Corotationwith NSE*B=0

1.4 GHz

1.4 GHz0.32 GHz

Weltevrede, Edwards & Stappers et al. 2006, 2007