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

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
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Pulsars J0737-3039AB

• 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 30 sec each orbit
• Center of mass moves at VCM, so A and B follow
  spiral paths relative to the ISM gt
  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 mean IA(ta) r(ta,t)
SndIA(ta,n) dIA(tat,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)
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ISS model - 1
baseline bx,by
Pulsar A
The ISS pattern has a spatial correlation
function r(bx,by) lt dIA(xbx,yby) dIA(x,y) gt
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/AAsin2q b Acos2qsin2q/A
c sin2q(1/A-A) for anisotropic turbulence
with Axial ratio A at orientation angle q siss
is 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 pulsar due to
velocities of Pulsar, Earth and ISM).
Characteristic timescale is where r1/e ie
bVisstiss Hence 1/tiss2 (aVax2 bVay2
cVaxVay)/siss2 where A pulsars 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
velocity Vcm.
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.
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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 AB
• VEx,VEy Earths 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 (A1) 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 Agt1 changes
conclusions about Vcm
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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 .
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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 2ab/c2(c/a)Vcye2 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
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Dynamic Spectra
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
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
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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) SndIa(ta,n) dIb(tb,n)/SndIa(ta,n)2
SndIb(tb,n)20.5 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)
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Rhoab all 52984
ta (10 sec units)
tb (10 sec units)
13
(No Transcript)
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J0737-3039AB 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 .

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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-(c1 dta2 c2 dtb2 c3
  dtadtb)/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 As eclipse and Bs 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.

16
rab fit Mjd 52984 (Dec 2003)
Observation Model
Residual
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Evolution in the on-windows for 0737BBurgay et
al 2005
6/03 9/03 1/04 4/04 7/04 11/04
f270 deg is near where the orbits cross and we
can see correlations in ISS from A and B
B profile
Orbital Longitude f
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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-(c1 dta2 c2 dtb2 c3
  dtadtb)/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 Earths
  velocity and so vary with epoch.
• But ab/c2 should be a constant.

The AB correlation is only possible while B is
visible during As 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
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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.
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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 40002000 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.
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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 (1R)/(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)/(A21)
2q
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Refractive shifts
23
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
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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 Earths 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 AB 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.
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ISS Timescale (full equations skip at AAS!)

• 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 Earths 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

H0 a(0.5V2o V2cxe) b(0.5cos2i V2oV2cye)
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)
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r(ta,tb) inclination
Shapiro delay gives sin(i) 0.9995.0004
(Kramer et al. Texas Symp.)
ybo 2a cos(i) (for a circular orbit of radius
a)
i (deg) sin(i) ybo (km) tA (sec)
90 1.0 0 0
89.7 0.999986 4,712 56
89.19 0.9999 12,700 150
88.19 0.9995 28,400 340
87.57 0.9991 38,159 460
tapk apparent was 33 sec !
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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)(VcxVob)/(VoaVob) 0.6(ybo/Vcy) tbpk
(ybo/Vcy)(Vcx-Voa)/(VoaVob)
-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)
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Orbital modulation in the ISS Arcs
from J0737-3039A 2GHz July 17 2004 GBT04B11 16
x 10 min panels Eclipse in 8
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rab fit Mjd 53560 (July 2005)
ta (sec)
tb (sec)
tb (sec)
tb (sec)
Observation model
residual
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ISS model - AB
baseline bx,by
Pulsar A
Pulsar B
The ISS pattern has a spatial correlation
function r(bx,by) lt dIB(xbx,yby) dIA(x,y) gt
q
ISM screen
Intensity pattern IB(x,y,n)
Intensity pattern IA(x,y,n)
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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.
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mjd53203
GBT 2 GHz A-B cross correlation MJD 53203
eclipse of A
tapk has changed sign! not yet corrected for B
profile
B profile
10 sec time units
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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)