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Interstellar Scintillation of the Double Pulsar J0737-3039: Effects of Anisotropy

Interstellar Scintillation of the Double Pulsar J0737-3039: Effects of Anisotropy. Barney Rickett and Bill Coles (UC San Diego) Collaborators: Maura McLaughlin, Andrew Lyne (Jodrell Bank), Ingrid Stairs (UBC), Scott Ransom (NRAO).

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Interstellar Scintillation of the Double Pulsar J0737-3039: Effects of Anisotropy

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  1. Interstellar Scintillation of the Double Pulsar J0737-3039: Effects of Anisotropy Barney Rickett and Bill Coles (UC San Diego) Collaborators: Maura McLaughlin, Andrew Lyne (Jodrell Bank), Ingrid Stairs (UBC), Scott Ransom (NRAO) International Colloquium "Scattering and Scintillation in Radio Astronomy" Pushchino June 2006

  2. A yB0 B xB Pulsars J0737-3039A&B • Pulsars (neutron stars) A and B orbit around each other in 2.45 hours. • The orbit is small (0.003 AU); orbital speeds are fast ~300 km/s • The orbit is 9% eccentric and its plane is nearly aligned with the Earth • A is eclipsed by B for about 30sec each orbit • Center of mass moves at VCM, so A and B follow spiral paths relative to the ISM => Scintillation observations allow estimates of VCM • Scintillation of A shows strong orbital modulation due to changing transverse velocity VISS. The timescale is tISS = sISS/VISS , where sISS is the spatial scale of the scintillation pattern • Pulses from B are only visible for a narrow range of orbital phases

  3. PSR J0737-3039A ISS Dynamic spectrum from GBT using 1024 x 0.8 MHz channels (SPIGOT) 10 sec time averages: IA(t,n) Eclipses barely visible at Note fast and slow ISS timescales PSR J0737-3039B ISS Dynamic spectrum as above: IB(t,n) Note the two narrow time windows in each orbit where the B pulsar is visible

  4. We characterize the ISS by a timsescale - tiss • by auto-correlating the ISS spectra dIA(ta,n) [deviations from the meanIA(ta)] • r(ta,t) = Sn[dIA(ta,n) dIA(ta+t,n)]/{SndIA2(ta,n)} • We average over a range in ta and define r(ta,tiss) = 0.5 We plot 1/tiss2 versus ta (or orbit phase f):

  5. sD by bxparallel to orbit (1-s)D baseline bx,by PulsarA The ISS pattern has a spatial correlation function r(bx,by) = < dIA(x+bx,y+by) dIA(x,y) > ISS model - 1 q ISM screen • For diffractive Kolmogorov scattering: • r(bx,by) = exp[-(Q/siss2)5/6] • where Q is quadratic form of an ellipse • Q = a bx2 + b by2 + c bxby • a = cos2q/A+Asin2q; b = Acos2q+sin2q/A ; • c = sin2q(1/A-A) • for anisotropic turbulence with • Axial ratio A at orientation angle q • sissis the geometric mean spatial scale of the pattern. Intensity pattern IA(x,y,n)

  6. Orbital modulation of ISS Timescale for pulsar A • Observer samples the pattern due to velocity of the pattern (Viss at the pulsardue to velocities of Pulsar, Earth and ISM). • Characteristic timescale is where r=1/e : ie b=Visstiss Hence • 1/tiss2 = (aVax2 + bVay2 + cVaxVay)/siss2 • where A pulsar’s velocity is • Vax = Voax + Vcmx ; Vay = Voay + Vcmy(par and perp to orbit plane) • With Voax, Voay the known orbital velocities and unknown center of mass velocityVcm. From timing we know the orbital velocities Voax and Voay in terms of the orbital phase f relative to the line of nodes and find: 1/tiss2 = Ho + Hs sinf + Hc cosf + Hs2 sin2f + Hc2 cos2f In general these 5 coefficients describe the orbital modulation - including eccentricity terms.

  7. Orbital modulation of ISS Timescale 3 The equations linking the five H-coefficients to the physical parameters are quadratic and so have two solutions. This was already noted by Ord et al. in their pioneering analysis of the orbital modulation of millisecond binary PSR J1141-65. • H-coeffs depend on pulsar parameters which are already known (through timing) • Vo mean orbital velocity, e orbit eccentricity, • w longitude of periastron, i inclination of orbit. • Unknown parameters : Vcmx,Vcmy velocity of center of mass of A&B • VEx,VEy Earth’s vel - known except for dependence on b angle of pulsar orbit in equatorial coords • a, b, c depend on axial ratio (A) and orientation of ISS pattern (q) • s fractional distance from pulsar to scattering region Ord et al assumed circular symmetry (A=1) and so had 2 fewer parameters and were able to constrain the inclination i to one of two solutions and to estimate Vcm. *** Allowing for A>1 changes conclusions about Vcm ***

  8. Orbital modulation of ISS Timescale 4 Since both Hc and Hs2 are proportional to cosi they are negligible for J0737, leaving 3 coefficients H0, Hs, Hc2 .

  9. Orbital modulation of ISS Timescale 5 The 3 coefficients depend on: Vcmx,Vcmy velocity of center of mass A axial ratio of ISS pattern q orientation of ellipse siss scale of ISS diffraction pattern (measured at the pulsar) We eliminate siss by dividing by Hc2 and have two observable coeffs: hs = Hs/Hc2 = [4Vcxe+ 2(c/a)Vcye]/Vo h0 = H0/Hc2 = -[1+ 2V2cxe+ 2{ab/c2}[(c/a)Vcye]2+ 2(c/a)VcyeVcxe]/V2o where Vo is the mean orbital velocity and Vcxe = Vcmx- eVo sinw Vcye = Vcmy where e is orbit eccentricity, w is longitude of periastron, Note offsets due to motion of Earth (VE) and ISM (Vism) Vcm = Vc + VEs/(1-s) - Vism/(1-s). Where Vc is the true system velocity Annual variation in VE provides extra information

  10. PSR J0737-3039A ISS Dynamic spectrum from GBT using 1024 x 0.8 MHz channels (SPIGOT) 10 sec time averages: IA(t,n) Eclipses barely visible at Dynamic Spectra PSR J0737-3039B ISS Dynamic spectrum as above: IB(t,n) Note the two narrow time windows in each orbit where the B pulsar is visible

  11. A-B correlation ISS of A and B are correlated near the time of the eclipse. Correlation averaged in frequency domain at times ta and tb relative to eclipse. r(ta,tb) = Sn[dIa(ta,n) dIb(tb,n)]/{SndIa(ta,n)2 SndIb(tb,n)2}0.5 Note normalization by each variance (over frequency) Next slide shows r(ta,tb) for Dec 2003 (data at 1.4 GHz Ransom et al, 2004)

  12. Rhoab all 52984 ta (10 sec units) tb (10 sec units)

  13. = Origin at position of A at eclipse J0737-3039A&B Correlated ISS B y b x A • At times ta and tb after the eclipse the transverse projected baseline vector from B to A is • bx = Vaxta - Vbxtb • by = ybo + Vayta -Vbytb • where Vax,Vay , Vbx,Vby are net velocities of A & B at eclipse. • Maximum correlation is at times tapk, tbpk which we can measure and give independent info: • yb0/Vcmy =tapk- tbpk where yb0 is the impact parameter at A's eclipse • Vcmx = hence we have one of the unknowns, but we introduced another yb0 .

  14. Model for A-B correlation • r(ta,tb) = r(bx,by) = exp[-(Q/siss2)5/6] • Where the baseline is bx = Vaxta-Vbxtb; and by = Vayta-Vbytb • Using the same model as before Q can be written as a quadratic form in • dta = ta-tapk and dtb = tb-tbpk: • r(ta,tb) = exp[-{(c1dta2 +c2dtb2 + c3dtadtb)}/siss2)5/6] • This definition of r(ta,tb) is properly normalized by the two variances, but it does not include the effect of a varying signal-to-noise ratio due A’s eclipse and B’s profile. So we explicitly corrected for this in our fit. Since Q describes the spatial structure of the ISS pattern its three coefficients depend on our unknown parameters in the same way as for the orbital harmonics h0 and hs . But tapk, tbpk give independent information from which we can estimate Vcmx , [(c/a)Vcye] and {ab/c2}.

  15. rab fit Mjd 52984 (Dec 2003) Observation Model Residual

  16. Evolution in the “on-windows” for 0737BBurgay et al 2005 6/03 9/03 1/04 4/04 7/04 11/04 f=270 deg is near where the orbits cross and we can see correlations in ISS from A and B B profile Orbital Longitude f

  17. Model for A-B correlation 2 • Using the same model as before Q can be written as a quadratic form in • dta = ta - tapk and dtb = tb - tbpk: • r(ta,tb) = exp[-{(c1dta2 +c2dtb2 + c3dtadtb)}/siss2)5/6] • Since Q describes the spatial structure of the ISS pattern its three coefficients depend on our unknown parameters in the same way as for the orbital harmonics h0 and hs . But tapk, tbpk give independent information from which we can estimate Vcmx , [(c/a)Vcye] and {ab/c2}. • The velocities include the changing Earth’s velocity and so vary with epoch. • But {ab/c2} should be a constant. The AB correlation is only possible while B is visible during A’s eclipse. Unfortunately, this occurred during only 3 out of 11 observations. So we take the measured {ab/c2} and apply it to the remaining 8 epochs in which the tiss data were fitted by three harmonic coefficients. This gave 11 epochs with an estimate of Vcmx as shown next

  18. Annual change in Vcmx Vcmx derived from AB correlation estimate ab/c2 = 0.384 There are two solutions at each epoch the slower velocities are chosen, since the faster ones are inconsistent with VLBI limits on the system proper motion.

  19. Annual change in Vcmx (2) The annual fit Vcmx gives estimates of Vcx, Vcy The transverse center of mass velocity relative to the scattering region in the ISM , which is at fractional distance s from the pulsar. It also give the absolute orientation of the pulsar orbital plane projected onto the sky. With Vcy known we will be able to go back to the tapk,tbpk measurements and refine our estimate of the orbital inclination. Our earlier analysis yielded yb0 = 4000±2000 km/s which is about 3s smaller than the value obtained by Kramer et al. from the observed Shapiro delay in the timing of pular A.

  20. The Poincaré circle We find 4ab/c2 = 1.54 which gives an ellipse in the Poincare circle: [1-R2 cos2(2q)]/R2 sin2(2q) =1.54 where A = [(1+R)/(1-R)]0.5 Constraint on axial ratio: Rmin = c/(2ab)0.5 = 0.81 Hence Amin = 3.1 (2.6 - 4.4) R=(A2-1)/(A2+1) 2q

  21. Refractive shifts

  22. siss Estimated spatial ISS scale over one year. It should be constant. The changes may be due to refractive modulations? Evidently there is more to learn! Date mjd x1e-4

  23. Conclusions The ISS timescale for PSR J0737-3039A has been measured near 2 GHz versus orbital phase at 8 epochs over a year. With the Earth lying in the orbit plane there are 3 harmonic coefficients which have been estimated at each epoch. We present theoretical analysis of the harmonic coefficients in the presence of anisotropic ISS and how they vary with the Earth’s velocity. Anisotropy has a strong influence on the derived center of mass velocity. Fits to these annual changes in the coefficients are not fully consistent with the model and so do not yet improve the estimate of the center of mass velocity of the pulsars nor of the anisotropy in the interstellar scattering. Correlation in the ISS between the A&B pulsars provides strong independent evidence for the axial ratio and orientation. It also provides an independent estimate for the orbital inclination which is very close to 90 deg. However, the drift in the on-times for B have reduced the A-B correlation after Dec 2003. We are working to dig the correlation out when B is weak.

  24. In general the 5 harmonic coefficients are related to the physical parameters by: • Vcxe = Vcmx- eVo sinw + VExs/(1-s) -Vismx/(1-s) • Vcye = Vcmy- eVo sinw cos i + VEys/(1-s) -Vismy/(1-s) • Known parameters (from pulsar timing): • Vo is the mean orbital velocity, e is orbit eccentricity, • w is longitude of periastron, i is the inclination of orbit. Vcmx,Vcmy velocity of center of mass • VEx,Vey Earth’s vel - known except for dependence on b angle of pulsar orbit in equatorial coords • a, b, c depend on axial ratio (A) and orientation of ISS pattern (q) • Vismx, Vism is velocity of ISM at distance s ISS Timescale (full equations skip at AAS!) H0= [a(0.5V2o+ V2cxe)+ b(0.5cos2i V2o+V2cye) + cVcxeVcye]/s2iss Hs = -Vo (2aVcxe+ cVcye)/s2iss Hc = Vocosi (2bVcye+ cVcxe)/s2iss Hs2 = 0.5cV2o cosi /s2iss Hc2 = V2o(b cos2i - a)/s2iss siss scale of ISS diffraction pattern (not so interesting)

  25. Shapiro delay gives sin(i) = 0.9995±.0004 (Kramer et al. Texas Symp.) r(ta,tb) inclination ybo = 2a cos(i) (for a circular orbit of radius a) : tapk apparent was 33 sec !

  26. r(ta,tb) model - 2 • We can fit for the 3 coefficients c1, c2 and c3 and 2 times of peak correlation, which • depend on the known orbital velocities and the 6 unknown model parameters: • Vcx,Vcy velocity of center of mass (inc terms in VE and VISM/(1-s) ) • A axial ratio • q orientation of ellipse (relative to line of nodes) • siss diffractive scintillation scale at J0737 • i inclination of orbit • In particular the inclination is determined by ybo (projected separation at eclipse) through: • tapk = (ybo/Vcy)(Vcx+Vob)/(Voa+Vob) ~ 0.6(ybo/Vcy) • tbpk = (ybo/Vcy)(Vcx-Voa)/(Voa+Vob) ~ -0.4(ybo/Vcy) • Since Voa and Vob are larger than Vcx, the values of tapk tbpk are largely determined by (ybo/Vcy) and so can change as VEy changes: • Vcx = Vcmx+ VExs/(1-s) - VISMx/(1-s) • Vcy = Vcmy + VEys/(1-s) -VISMy/(1-s)

  27. Orbital modulation in the ISS Arcs from J0737-3039A 2GHz July 17 2004 GBT04B11 16 x 10 min panels Eclipse in #8

  28. rab fit Mjd 53560 (July 2005) ta (sec) tb (sec) tb (sec) tb (sec) Observation model residual

  29. sD by bxparallel to orbit (1-s)D baseline bx,by PulsarA PulsarB The ISS pattern has a spatial correlation function r(bx,by) = < dIB(x+bx,y+by) dIA(x,y) > ISS model - AB q ISM screen Intensity pattern IB(x,y,n) Intensity pattern IA(x,y,n)

  30. Annual plot We observed J0737 every 2 months in 2004-5 with GBT at 1.7-2.2 GHz. tiss vs orbit were estimated for each epoch and the two harmonic coefficients are shown together with a model fit. The fit is reasonable - not excellent. But the 2nd harmonic coefficient Hc2 varies with epoch, which is not consistent with the model. So we are not satisfied with the result. We are attempting to resolve this via the correlation of the ISS between A & B pulsars.

  31. GBT 2 GHz A-B cross correlation MJD 53203 mjd53203 eclipse of A tapk has changed sign! not yet corrected for B profile B profile 10 sec time units

  32. We fit Vcmx, Vcmy and siss. If we change A and  we get equally good fits but with different Vcmx, Vcmy and siss. Trade-Off for Center of mass velocity vs Anisotropy angle q with fixed A = 4 tiss data: J0737-3039A 820 MHz (Ransom 2005)

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