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Interstellar Scintillation of Pulsar B0809+74
B. J. Rickett 1 , Wm. A. Coles 2
Department of Electrical and Computer Engineering, University of California, San Diego, CA
92093
Jussi Markkanen 3
EISCAT­Geophysical Observatory, SF­99600 Sodankyl¨a, Finland
ABSTRACT
To Appear in Astrophysical Journal April 10, 2000.
Weak interstellar scintillations of pulsar B0809+74 were observed at two epochs
using a 30m EISCAT antenna at 933 MHz. These have been used to constrain
the spectrum, the distribution and the transverse velocity of the scattering plasma
with respect to the local standard of rest (LSR). The Kolmogorov power law is a
satisfactory model for the electron density spectrum at scales between 2 \Theta 10 7 m
and 10 9 m. We compare the observations with model calculations from weak
scintillation theory and the known transverse velocities of the pulsar and the Earth.
The simplest model is that the scattering is uniformly distributed along the 310 pc
line of sight (l = 140 ffi , b = 32 ffi ) and is stationary in the LSR. With the scattering
measure as the only free parameter, this model fits the data within the errors and
a range of about \Sigma10 km s \Gamma1 in velocity is also allowed. The integrated level of
turbulence is low, being comparable to that found toward PSR B0950+08, and
suggests a region of low local turbulence over as much as 90 ffi in longitude including
the galactic anti­center. If, on the other hand, the scattering occurs in a compact
region, the observed time scales require a specific velocity­distance relation. In
particular, enhanced scattering in a shell at the edge of the local bubble, proposed
by Bhat et al. (1998), near 72 pc toward the pulsar, must be moving at about ¸ 17
km s \Gamma1 ; however, the low scattering measure argues against a shell of enhanced
scattering in this direction. The analysis also excludes scattering in the termination
shock of the solar wind or in a nebula associated with the pulsar.
1 e­mail: rickett@ece.ucsd.edu
2 e­mail: coles@ece.ucsd.edu
3 e­mail: jussi@eiscat.sgo.fi

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1. Introduction
The use of pulsar scintillation to probe the interstellar medium has been complicated by
the fact that most observations below about 1 GHz are in the strong scintillation regime. In
this regime there are both refractive and diffractive components in the intensity scintillation
pattern, and neither spatial scale is known a priori. Furthermore the contributions from various
locations along the path of propagation do not add in a simple linear fashion (see Rickett,
1990 and Narayan, 1992 for reviews). Weak scintillation is much simpler to interpret since
contributions from various locations add linearly and the spatial scale of each contribution
depends only weakly on unknown parameters such as the spectral exponent and the inner
scale. The temporal scale of each contribution depends primarily on its distance and its
velocity. In principle, it is feasible to ``invert'' the observations to estimate the spatial spectrum
of the electron density and, by exploiting the variable velocity of the Earth, to investigate
distribution of the scattering plasma and its velocity.
Observations can be made in weak scintillation by using higher frequencies and/or nearby
pulsars. However it is difficult to obtain a stable estimate of the covariance function because
the time scale of the scintillation is of the order of an hour. Thus a given observation will
typically contain only a few time scales. Earlier observations by Backer (1975) at 3 GHz and
Malofeev et al (1996) at 3, 5 and 8 GHz have confirmed that weak scattering occurs more or
less as expected, but have not been long enough to provide the statistical accuracy necessary
for detailed model fitting.
In this paper we report two longer measurements of a circumpolar pulsar in weak
scintillation. The temporal statistics of these data sets are adequate to estimate the spectrum
over a decade in wavenumber and put constraints on the distribution and velocity of scattering
plasma. We have developed a procedure for the analysis that may be more generally useful.
2. Conclusions
We have developed a method for observing multiple epochs of weak scintillation of nearby
pulsars whose proper motion has been measured. Our observations for pulsar B0809+74 can
be explained by a uniform distribution of plasma ``turbulence'' which is stationary in the LSR.
The density spectrum follows Kolmogorov law for scales between 2 \Theta 10 7 m and 10 9 m, i.e. the
turbulence may have an inner scale ! ¸ 2 \Theta 10 7 m. This bound is consistent with the hypothesis
that the inner scale is the ion inertial scale, which would be about 4 \Theta 10 6 m for an electron
density of 0.03 cm \Gamma3 . The velocity of the scattering medium that best fits the observations is
in the range \Gamma12 Ÿ V ff Ÿ 5 km s \Gamma1 and \Gamma16 Ÿ V ffi Ÿ 7 km s \Gamma1 . The error bounds, which are
dominated by error in the pulsar proper motion, include the LSR.

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Fig. 1.--- Observations of the total pulse flux of B0809+74 at 933 MHz, normalized to the mean
flux over the observing period. The samples plotted are 10 minute averages. The lower traces
are computed from an off­pulse window to provide a noise estimate. (a) Data from April 1996.
(b) data from October 1998.
The scintillation is also consistent with scattering from a localized region which is not
stationary in the LSR, but this appears to be less likely for two reasons. First the scattering
is considerably weaker than predicted by models of the distribution of turbulence in the local
neighbourhood, so it is unlikely that the line of sight to B0809+74 is dominated by a local
intensely scattering region. Second, if the scattering is dominated by a local region, it must
be moving at a substantial velocity with respect to the LSR as shown in Figure ??. While
this is possible, it appears to be somewhat less likely. The scintillation is not consistent with
scattering in a ``nebula'' associated with the pulsar because the time scale of the scintillation
is too short by several orders of magnitude.

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Fig. 2.--- Power spectra of the pulse flux time series shown in Figure 1 corrected for receiver
noise and intrinsic variation, (a) 1996 and (b) 1998. The data are marked by \Sigmaoe error bars
and the resolution is indicated by the horizontal bar. The off­pulse noise spectrum is marked
by a dotted horizonal line. The sum of the off­pulse noise and the intrinsic noise is marked
by a dashed horizontal line. The frequency range from which the intrinsic contribution was
estimated is marked with a heavy horizontal line. The best fit theoretical models for a thin
screen are shown by solid lines. The best fit theoretical models for a uniform medium which is
stationary in the LSR are shown by dashed lines. The best fit models in 1996 have zero inner
scale, but in 1998 they have s i
= 2 \Theta 10 7 m. A best­fit theoretical model for a uniform medium
with zero inner scale is also drawn over the 1998 data as a dotted line for comparison.

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Fig. 3.--- Dependence of weak scintillation parameters on screen distance: (a) contribution to
variance; (b) effective velocity V eff
with respect to the LSR (solid line 1996, dashed 1998); (c)
Fresnel scale; and (d) time scale (solid line 1996, dashed 1998). The time scales have been
reduced by a factor 1.20 from the Born theory to account for incipient strong scattering. The
thin lines show the envelope of time scales corresponding to errors in the pulsar proper motion.
The confidence intervals for the observed time scale are shown as horizonal line pairs near 2
hrs (solid line 1996, dashed 1998). The bars indicate allowed distances to the screen at each
epoch assuming the nominal pulsar velocity. The rectangle indicates the distance to the shell
of enhanced scattering proposed by Bhat et al. (1998).

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Fig. 4.--- Scintillation time scale for observation in April 1996 (solid lines) and in October 1998
(dashed lines), calculated for a uniform scattering medium with a uniform velocity (V ff ; V ffi )
relative to the LSR. The time scales have been reduced by the factor 1.20 to account for the
incipient strong scattering, as described in the text. The hashed region is where the computed
time scales agree with the observations within \Sigmaoe in both years.