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scattering by density inhomogeneities in the ionized interstellar medium causes multiple rays to interfere , producing frequency structure in the spectra of spatially coherent sources such as pulsars @xcite .
the relatively high transverse velocities of most pulsars cause the spectra to change significantly on timescales of minutes to hours .
when the spectrum is monitored over time , the resulting two - dimensional array or `` dynamic spectrum '' is often dominated by a random pattern of scintillation maxima with characteristic bandwidth and timescale @xcite . on occasion , however , more organized features are present .
the best studied of these are periodic fringe patterns in the dynamic spectra due to the interference between two or more discrete bundles of rays or , equivalently , rays arriving from multiple images on the sky ( * ? ? ?
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* hereafter rlg ) .    a less well - studied pattern in pulsar dynamic spectra consists of a crisscross of intensity maxima that are variably spaced perpendicular to the ridge lines of the maxima .
cordes and wolszczan ( 1986 ) drew attention to these `` multiple drift rates '' in dynamic spectra , building on earlier work ( hewish 1980 ; roberts & ables 1982 ; hewish , wolszczan , & graham 1985 ; cordes , weisberg , & boriakoff 1985 ) .
numerous examples of the phenomenon are evident in the dynamic spectra presented by gupta , rickett , & lyne ( 1994 ) in their multi - year study of 8 pulsars , but the autocorrelation analysis that they employed is not well suited to its full elucidation
. the remarkable episode of `` fringing '' in the dynamic spectra of psr  b0834 + 06 that rlg explore is also accompanied at all epochs by this phenomenon .
the central result of our study is to show that this crisscross pattern has a much clearer representation in transform space , where it is seen to be a high - q phenomenon with a characteristic parabolic curvature .
we discuss the constraints that the presence of this pattern places on the image geometry and speculate on the physical structures that might give rise to this scattering geometry .
our observations were made at the arecibo observatory at 430  mhz .
spectra across a 10  mhz band centered on this frequency were produced by a fourier - transform - based spectrometer ( aoftm ) .
rcp and lcp signals were summed in hardware , and spectra with 1024 frequency channels ( i.e. 10  khz frequency resolution ) were produced every @xmath2  1.6  ms . during later analysis
the spectra were synchronously averaged at the pulsar period , calculated using tempo @xcite , and summed over 10  s time intervals , creating a cube with axes of time , frequency , and pulsar rotational phase .
we used 512 phase bins across the pulsar period .
dynamic spectra were created by producing an on - pulse spectrum from a window of phase bins centered on the pulse and subtracting an off - pulse spectrum to remove the baseline .
we observed 19 pulsars during 1999 january and 11 pulsars during 2000 january .
a typical observation lasted one hour ; we made 46 and 43 separate observations at the two observing epochs , respectively .
following several previous studies ( e.g.  cordes & wolszczan 1986 ; rlg ) we produced two - dimensional power spectra from the dynamic spectra .
these `` secondary spectra '' form the basis for most of the further analysis reported here .
we normalized each secondary spectrum by its maximum and converted the relative power levels into a decibel scale .
figure  [ fig : dynsec ] shows dynamic and secondary spectra for psr  b0834 + 06 .
the crisscross pattern in the dynamic spectrum shows up in the secondary spectrum as two parabolic features , curving away from the conjugate time axis , that we call `` arcs '' .
these arcs are remarkable for their narrowness and extent . in figure
[ fig : coadded ] we present secondary spectra , averaged over multiple days to improve dynamic range .
psr  b0823 + 26 and psr  b0834 + 06 showed a persistent arc pattern over both the 1999 and 2000 observing runs . in 2000 , psr  b0919 + 06 showed arcs that were relatively broad and faint and , hence , showed up only upon averaging of @xmath3 secondary spectra .
however , we did not see arcs in two high - quality 1999 observations .
psr  b1133 + 16 showed arcs during most of the 1999 and 2000 observations , but several high - quality 2000 observations failed to show them , even though they were made on days adjacent to those on which they were present .
psr  b1933 + 16 did not show the arc pattern in either of two high - quality observations in 1999 or 2000 .
time variability of the arcs will be the subject of a separate study .
we detected arcs in the secondary spectra of pulsars b0823 + 26 , b0834 + 06 , b0919 + 06 , and b1133 + 16 . by using the relationship between fringe frequencies in the secondary spectrum and scattering parameters ( e.g.  cordes & wolszczan 1986 ; rlg ; gupta , bhat , & rao 1999 )
, we can analyze the arcs more quantitatively . here
we summarize a more detailed study that will be reported elsewhere ( cordes 2001 ) . to simplify calculations
, these treatments assume that the scattering takes place in a thin screen a distance @xmath4 from the pulsar , with the pulsar - observer distance @xmath5 .
they show that the interference between two points @xmath6 on the image plane ( i.e. as seen by an observer ) will lead to two - dimensional fringing in the dynamic spectrum with fringe frequencies f_t & = & ( ) ( _ 2 - _ 1 ) , [ eq : ft ] + f _ & = & ( ) ( d- ) ( _ 2 ^ 2 - _ 1 ^ 2 ) .
[ eq : fnu ] here @xmath7 is the conjugate time axis , @xmath8 is the conjugate frequency axis , and the effective velocity ( cordes & rickett 1998 ) is a weighted sum of the velocities of the source , screen and observer , = ( 1 - /d)+ ( /d ) -
. we can introduce the dimensionless variables p & = & ( _ 2 ^ 2 - _ 1 ^ 2 ) = f _ , [ eq : pbar ] + q & = & ( _ 2 - _ 1 ) = f_t , [ eq : qbar ] where @xmath9 is a two - dimensional unit vector for the effective velocity .
since @xmath10 is quadratic in image angles and @xmath11 is linear in image angles , @xmath10 will generally be quadratic in @xmath11 .
this is essential to explaining the parabolic curvature of the arcs .
if we make the reasonable assumption that the pulsar velocity is much greater than either the velocity of the earth or the screen , equations  ( [ eq : pbar])([eq : qbar ] ) can be simplified to p & = & f _ , [ eq : pnew ] + q & = & f_t , [ eq : qnew ] where @xmath12 , and we approximate @xmath13 by the measured proper motion speed , @xmath14 . a parabolic arc ( @xmath15 ) in the p - q plane then corresponds to a feature in the secondary spectrum of curvature f _ & = & ( ) f_t^2 .
[ eq : dyn - arc ] in this model , the curvature of the arcs is determined solely by the screen placement , the pulsar distance , and the pulsar proper motion .
thus , by measuring the curvature of the arcs in the secondary spectrum , we can determine a value for the screen placement that is consistent with the observations and assumed values of @xmath5 and @xmath16 , as in table  [ tab : screen ] .
gupta ( 1995 ) used diffractive bandwidth and timescale measurements to determine @xmath17 , the speed of the scintillation pattern past the observer ( cordes and rickett 1998 ) . assuming that the scattering is dominated by a thin screen
, one can determine the screen placement for which @xmath17 is consistent with @xmath16 .
this is determined from gupta s @xmath18 parameter by @xmath19 .
table  [ tab : screen ] shows that the values of @xmath20 agree well with those for @xmath21 , calculated with eq .
although the values of @xmath20 agree well with those for @xmath21 , the agreement may be only proportionate because there are significant uncertainties in both the distances and the iss parameters used by gupta ; also , scattering is likely to receive contributions from the distributed ism as well as from a screen . in particular , a recent study of b0919 + 06 ( chatterjee 2001 ) that compares scintillation velocity estimates , which are epoch dependent , and the parallax and proper motion determined from vlba observations , finds that a thin screen must be combined with a distributed medium such as that of the taylor & cordes ( 1993 ) model to bring agreement between the two velocity estimates . at some epochs
, the screen evidently causes multiple imaging of the pulsar .    from equation  ( 1 )
it can be seen that the vertical ( @xmath7 ) extent of arc features in the secondary spectrum is related to the angular extent of the scattering image along the effective velocity vector .
table  1 shows the typical angular extent of the filament , @xmath22 , and the corresponding linear size on the screen , @xmath23 , inferred from the value of @xmath7 for a generic model .
we analyze the distribution of power in the secondary spectrum with a sequence of vertical cuts , as in figure  [ fig : cuts ] .
the rapid decline of power above the arcs strongly limits the image geometries that are consistent with the data . in order to exclude power above the arc
, points must satisfy @xmath24 . referring to equations  ( [ eq : pbar])([eq : qbar ] ) ,
this constraint can be expressed as _ 2 ^ 2-_1 ^ 2 & & ( _ 2x-_1x)^2 , [ eq : inequality ] where the @xmath25  components are along the effective velocity vector .
a single extended image has many image pairs that violate this condition and , hence , will produce a large amount of power above the arcs , inconsistent with the behavior seen . hence , a multiple image geometry is required to produce the clearly delineated arcs we observe .
one configuration that satisfies eq .
9 , having no detectable power above the arcs , consists of a bright point - like image at the origin ( direct line of sight to the pulsar ) and a faint secondary image as a filled halo around it .
the interference between a point at the origin and any other image point can not produce power above the arcs because @xmath26 .
if the point - like image and halo have flux densities proportional to @xmath27 and @xmath28 , respectively , then the point - like source will produce a point - like feature at the origin of the secondary spectrum with power proportional to @xmath29 ( e.g.  cordes & wolszczan 1986 ) .
the inter - image interference between the point - source and the halo will produce power proportional to @xmath30 .
the self - interference between regions of the halo ( which _ will _ produce power above the arcs ) will be proportional to @xmath31 .
since this is smaller by another factor of @xmath32 from the inter - image term , then , for small @xmath32 , the only detectable power will be a point - source at the origin and power below the arcs .
although the point - source plus halo model is consistent with the observations , the scattering material in the screen would need to be inhomogeneous enough that the direct image of the pulsar would shine through , but rays slightly off - axis would be scattered . in essence , we would need to be seeing the pulsar through a break in the interstellar `` clouds '' , consistent with the time - variability of the arcs . on the other hand ,
there is strong evidence for scattering geometries based on filamentary structures @xcite .
however , the self - interference between filaments will lead to features which are inconsistent with our data .
any viable model based on filamentary features in the image plane must somehow hide these self - interference features as well as produce the observed parabolic arcs .
the formalism used here includes only geometric delays , whereas differential dispersive delays may be important in some cases .
the fact that the observed arcs conform to the geometric - only formalism implies that at least in some instances the dispersive effects are small .
we have examples of secondary spectra that show more complex behavior and will analyze them within the more general framework in a later paper .
an extended medium , as opposed to a single screen , also will be explored .
while there are many possibilities for source geometries , it is clear that a multicomponent scattered image is necessary . in future papers
, we will apply this method to better understand the structure of the ism on small spatial scales .
we thank t.  joseph  lazio for helpful discussions , the operators at arecibo for help with remote observations , and duncan lorimer for the development of an excellent remote observing interface .
we acknowledge support from the national science foundation : grant ast-9618408 to jmc and grant ast-9619493 to drs .
b0823 + 26 & 0.38 & 196 & 26 & 0.8 & 0.36 & 0.40 & 5.4 & 1.3 + b0834 + 06 & 0.72 & 174 & 31 & 0.6 & 0.33 & 0.36 & 4.0 & 1.9 + b0919 + 06 & 1.2 & 505 & 15 & 0.55 & 0.59 & 0.63 & 3.6 & 1.8 + b1133 + 16 & 0.27 & 475 & 11 & 1.15 & 0.49 & 0.46 & 5.4 & 0.7 +
we have made high - resolution , high - sensitivity dynamic spectra of a sample of strong pulsars at 430  mhz with the arecibo radiotelescope . for 4 pulsars we find faint but sharply delineated features in the secondary spectra . 
 these are examples of the previously observed `` crisscross '' or `` multiple drift slope '' phenomenon presumed to be due to multiple imaging of the pulsar by the interstellar medium . 
 the unprecedented resolution and dynamic range of our observations allow a deeper level of analysis . 
 distances to the dominant scattering screen along the line of sight are determined and are shown to agree well with those inferred from other scintillation phenomena . 
 multiple imaging of the pulsar by the ism is required . 
 a compact central image surrounded by a faint scattering halo , roughly circularly symmetric , is consistent with the data . 
 scattering from filaments may also be consistent . 
 the angular extent of the scattering material parallel to the direction of the pulsar velocity is @xmath0  mas , corresponding to a linear extent of @xmath1  au . 
 further observations of these features should allow better discrimination between models and an identification of the scattering structures .