A Scintillation Arc Survey of 22 Pulsars with Low to Moderate Dispersion Measures

Context: By providing information about the location of scattering material along the line of sight (LoS) to pulsars, scintillation arcs are a powerful tool for exploring the distribution of ionized material in the interstellar medium. Here, we present observations that probe the ionized ISM on scales of $\sim$~0.001 -- 30~au. Aims: We have surveyed pulsars for scintillation arcs in a relatively unbiased sample with DM<100 pc cm-3. We present multi-frequency observations of 22 low to moderate DM pulsars. Many of the 54 observations were also observed at another frequency within a few days. Methods: For all observations we present dynamic spectra, autocorrelation functions, and secondary spectra. We analyze these data products to obtain scintillation bandwidths, pulse broadening times, and arc curvatures. Results: We detect definite or probable scintillation arcs in 19 of the 22 pulsars and 34 of the 54 observations, showing that scintillation arcs are a prevalent phenomenon. The arcs are better defined in low DM pulsars. We show that well-defined arcs do not directly imply anisotropy of scattering. Only the presence of reverse arclets and a deep valley along the delay axis, which occurs in about 20\% of the pulsars in the sample, indicates substantial anisotropy of scattering. Conclusions: The survey demonstrates substantial patchiness of the ionized ISM on both au size scales transverse to the line of sight and on $\sim$~100~pc scales along it. We see little evidence for distributed scattering along most lines of sight in the survey.


INTRODUCTION
Nearly 55 years after their discovery (Hewish et al. 1968), radio pulsars continue to be versatile probes of fundamental physics, plasma processes under extreme conditions, and the distribution of ionized gas in the Galaxy. Since early pioneering studies (Scheuer 1968;Rickett 1969Rickett , 1970 , the unique wideband, pulsed character of the signal has been employed to explore the ionized component of gas along the LoS to these sources. With more than 3300 pulsars known , they probe a wide range of distances and astrophysical conditions along sight lines and undergird the effort to develop a detailed model of the ionized gas distribution in the Milky Way (Cordes & Lazio 2002;Yao et al. 2017).
Classical studies of radio wave scintillation toward pulsars (e.g. Cordes et al. 1985;Cordes 1986;Gupta et al. 1994;Löhmer et al. 2001;Bhat et al. 2004;Kuzmin & Losovsky 2007), provided a broad-brush view of the scattering along many lines of sight and the tools to interpret it. In the study of interstellar scintillation (ISS) there has been an emphasis on measuring the characteristic bandwidth ∆ν iss and timescale ∆t iss of the scintillation structure in twodimensional dynamic spectra (intensity as a function of radio frequency and time). This has yielded estimates of scattering angles toward pulsars, produced a better understanding of the distribution of scattering material along the LoS (Cordes & Rickett 1998), and also allowed the estimate of pulsar proper space velocities through the estimation of scintillation speeds (Cordes 1986;Gupta 1995).
However, the discovery that pulsar dynamic spectra often have an underlying low-level modulation manifested as highly-organized parabolic structures in the power spectrum of the dynamic spectrum (Stinebring et al. 2001) has provided a powerful new tool and uncovered several puzzles. The position of features in scintillation arcs can move on ∼week timescales or shorter Wang et al. 2018), whereas the qualitative appearance of arcs can change on several month timescales (Stinebring et al. 2001;Main et al. 2020;Reardon et al. 2020, amongst others).
Scintillation arcs arise when the following conditions are met (Walker et al. 2004;Cordes et al. 2006): a) scattering occurs in a relatively small fractional portion of the LoS (thin screen condition) 1 , b) the angular broadening function B(θ) has both a well-defined core and an outer halo; furthermore, the scintillation arc becomes narrower with a deeper valley, if the angular image on the sky is anisotropic and roughly aligned along the effective velocity vector.
Most previous observational scintillation arc studies (e.g., Hill et al. 2003;Wang et al. 2005;Hill et al. 2005;Rickett et al. 2011;Bhat et al. 2016;Safutdinov et al. 2017;Wang et al. 2018;Stinebring et al. 2019;Reardon et al. 2020;Yao et al. 2021;Rickett et al. 2021;McKee et al. 2022;Chen et al. 2022) have focused on a relatively small number of well-observed pulsars and have explored a range of diverse scintillation arc phenomena. No prior study has explored the prevalence of scintillation arcs toward a sample of pulsars with fairly uniformly applied selection criteria. Since scintillation arcs often indicate the presence of highly organized linear scattering features toward pulsars -and since the astrophysical origin of those features is not known -it is of particular interest to characterize the frequency of occurrence of the arcs.
In addition to the work mentioned above, there has been a substantial amount of precision scintillation arc workboth interferometric and single-dish -in the past 10 years or so. Much of this work was inspired by the remarkable interferometric study of PSR B0834+06 by Brisken et al. (2010), and work on interstellar holography (Walker & Stinebring 2005;Walker et al. 2008) laid important groundwork, too. Among other highlights in this scintillometry effort are several studies of binary pulsars (Rickett et al. 2014;Main et al. 2020;Mall et al. 2022), the detection of scattering from a supernova remnant around a pulsar (Yao et al. 2021), the location of multiple scattering screens toward nearby pulsars (Chen et al. 2022;McKee et al. 2022), and important new theoretical work (Simard et al. 2019a,b;Sprenger et al. 2021;Shi & Xu 2021;Baker et al. 2022).
Our approach in this paper is data-oriented with a minimum of model-fitting. After presenting necessary preliminaries, we start from a close inspection of features in the secondary spectra and proceed to more detailed analyses in the following sections. More specifically, in §2 we present the observations and our data processing methods. §3 focuses on secondary spectra production and the extraction of basic scintillation parameters from the data set. In §4, we closely inspect the secondary spectra from each of the 22 pulsars, highlighting salient arc features without much interpretation. We then group them into three sets based on the prominence of scintillation arcs. §5 develops an overall analysis of the observations and sets the results in a theoretical scattering context, with special attention to the DM and frequency dependence of arc parameters. We discuss the key results in §6 and summarize the paper in §7. All data used in this paper are being made available as described in §2.4. We have used the the ATNF Pulsar Catalogue (psrcat) database 2  extensively throughout this work.

OBSERVATIONS AND DATA PROCESSING
In this Scintillation Arc Survey (SAS) we studied scintillation arcs in 22 pulsars. The sources were chosen based on the following initial criteria: i) visible with either the Green Bank Telescope (GBT) or Arecibo, ii) dispersion measure DM < 50 pc cm −3 , and iii) 400 MHz flux density > 25 mJy. Later in the project we saw advantages to expanding DM coverage out to 100 pc cm −3 for at least several sources. We then included 6 pulsars visible from Arecibo in order to accomplish this. Because of Arecibo's sensitivity, we relaxed the flux density limit somewhat. See Table 1, which includes basic per-pulsar parameters such as source flux density, dispersion measure, transverse velocity, and previously measured scattering timescale.
In most cases we obtained multi-frequency dynamic spectra at two epochs separated by less than a week. However, the GBT 1400 MHz observations were made 14 years after those at the lower frequencies ( §2.1).
Three data sets are employed in this paper, two from the Green Bank Telescope and one from the Arecibo Observatory. They are described below. Observational details such as epoch of observation, center frequency, and bandwidth are given in Table 2.

GBT Observations
The observations in the first and largest portion of the dataset were made with the Robert C. Byrd Green Bank Telescope (GBT) between 2005 September 17 -24. For each of the 16 GBT sources a 60-min dynamic spectrum was obtained with a 10-s dump time of the Spectral Processor spectrometer. We used the Spectral Processor in a mode that produced N chans = 1024 across a bandwidth ranging from 5 MHz to 40 MHz in binary steps. The center frequencies of the two bands were 340 MHz and 825 MHz. Each front-end receiver was mounted at the prime focus, and only one front-end could be mounted at a time. Initial observations were made at 340 MHz for two days followed, five days later, by observations for two days with the 825 MHz receiver in place.   Another set of GBT observations, centered at 1400 MHz, was made during the period 2020 January -April. Dynamic spectra were obtained for 13 of the pulsars in the sample at this frequency, with the frequency range chosen to minimize the RFI based on diagnostic scans performed with the GBT. All observations used the VEGAS spectrometer with 8192 spectral channels across 100 MHz bandwidth, and spectra were written out every 10 s. These observations were made ≈ 15 yr later than for the low-frequency GBT data. Although the 1400 MHz data shed important light on the scintillation arc structure seen at lower frequencies, care is needed in comparing features at widely separated epochs.

Arecibo Observations
Observations were made with the William E. Gordon Arecibo Telescope between 2018 January 12 -15. Six pulsars were observed, three at the dual frequencies of 430 MHz and 1450 MHz. Successful observations of the other three were only possible at a single frequency, either 430 MHz or 1450 MHz. The Mock spectrometers were used for the observations, and bandwidths ranged between 2 MHz and 160 MHz, all with 4096 frequency channels and a 10 s interval between accumulated spectra.

Data Processing
Dynamic spectra were formed in the following fashion, similar to that done by Hill et al. (2003). Data were binned into a 3D cube: pulse phase, radio frequency, and sub-integration number (or time; 10-s per time slice). The cube was then collapsed along the pulse phase axis in order to locate the pulse. An ON pulse window was established by eye that contained more than 95% of the pulse energy. For these pulsars, the ON window was typically about 5-10% of the total pulse period. An OFF pulse region of the same size was then identified from the cumulative pulse profile.
The dynamic spectrum was formed from each sub-integration by calculating where ν is the radio frequency, < OFF(ν) > represents the average off-pulse spectrum (the bandpass), i indexes the sub-integrations, and the division by this denominator partially corrects for varying sensitivity across the band. When we substitute t for time (0 -60 m in 10-s increments) in place of sub-integration number and ν is also discrete, the dynamic spectrum will be denoted as S(t, ν) as displayed, for example, in the upper panels of Figure 1. Because of the location of the GBT in the National Radio Quiet Zone and the differential (ON -OFF) nature of the spectrum formation, radio frequency interference (RFI) was not a major problem in the analysis. Arecibo observations were more strongly affected by RFI, and the GBT/1400 MHz observations also had persistent RFI in several channels slightly below 1420 MHz.
Some pulsars have deep amplitude modulations due to broadband intrinsic pulsar variability p(t) such as nulling. Nulls appear as brief minima, which are often near zero amplitude. Across the spectrum these are detected at times offset by their relative dispersive delay (Rickett 1970). However, such offsets are smaller than our 10 sec time step for all the observed pulsars and so the nulls appear to be synchronous in the dynamic spectrum. For example, see B0525+21 and B1706-16 in figure sets 1.11 and 1.31-1. 33 We estimate the intrinsic modulation by averaging S(t, ν) over frequency at each 10s time step to obtain the pulsed time series p(t). As we describe below we subtract the estimated p(t) from S(t, ν) at each time step, in order to minimize its effect on the secondary spectrum.
The secondary spectrum (SS) is the primary data product of interest in the study, computed from the power spectrum of the dynamic spectrum (DS). Cordes et al. (2006) refer to this quantity as S 2 (f t , f ν ) = |S c (t, ν)| 2 , where the tilde denotes a Fourier transform, and the axes f t and f ν are conjugate to the t and ν axes, respectively. However, it has become more common in the literature to identify f t with differential Doppler frequency, f D , and the conjugate frequency axis, f ν , with differential Doppler delay, τ . We use that notation in what follows. An example of S 2 (f D , τ ) is shown in Figure 1 as well, where we follow the convention, standard in this field, of displaying S 2 using a logarithmic grayscale in order to encompass the large dynamic range often present in the data. Note that the color table for the display of S 2 depends sensitively on the upper and lower power limits displayed as defined in §3.
As noted above intrinsic pulsar variations p(t) modulate S(ν, t) synchronously across the entire bandwidth. Hence they contribute power to the SS along the f D axis S 2 (f D , τ = 0), which is set to zero by subtracting p(t) ). S 2 is computed via a finite discrete Fourier transform and there is a corresponding spectral response function in delay and Doppler, whose sidelobes can allow leakage of power from isolated peaks to spread through the SS. By subtracting the intrinsic p(t) from the DS we reduce the corresponding leakage to higher delays. We further reduce leakage of power from the peak near the origin of S 2 by applying a window function to the DS. We use a cosinesquared window to taper the outer 20% of the DS to zero in both time and frequency in order to reduce leakage due to broadband RFI and to residual effects of intrinsic pulse variation.

SECONDARY SPECTRUM -DATA PRESENTATION
We have assembled the 54 observations of the 22 pulsars as a figure set visible online. In each plot we show the dynamic spectra and associated secondary spectra together with two lower panels as described below. Of these, 13 pulsars were observed at three frequencies, 6 at two frequencies, and 3 were observed at one frequency only.
Examples of the display format are shown in Figure 1 as three plots for B0628-28 at frequencies 340, 825 and 1400 MHz. In each case the upper panel is the dynamic spectrum (DS) in standard gray-scale format with linear Upper panels are dynamic spectrum linearly scaled in units of the mean flux density; middle panels are secondary spectra S2 with decibel scaling. Lower left panels are auto-correlations of the dynamic spectra versus time lag (horizontal, minutes) and frequency lag (vertical, MHz). The lower right panels show curvature estimation by parabolic summation of S2 over a range in delay (defined by the blue and red rectangles in S2). The summation is plotted versus log of curvature η; all of the parabolas have apexes at the origin. As described in §5.3 the plain red and blue curves plot the direct linear summations for negative and positive fD, and the curves with x-marks are summations weighted by |fD|. The locations of the peaks in the weighted curves are flagged by vertical lines with a horizontal bar defining a width at 0.95 of the peak. Faint dotted red and blue parabolas are over-plotted on the SS at these estimated curvatures. The complete figure set (54 images) is available in the online journal.
scaling. The lower panel shows the secondary spectrum (SS) with decibel scaling chosen to emphasize the structure at low levels (ranging from white at the mean noise level S noise and saturating at black at a level 5dB below its global maximum). S noise is estimated from the mean of S 2 in a rectangular region away from areas of ISS, which is outlined in green. (Relative to the Nyquist limits τ N , f D,N in delay and Doppler, the noise region is 0.49τ N < τ < 0.95τ N and 0.44f D,N < f D < 0.93f D,N ) Also shown at the lower left of each plot is the auto-correlation function (ACF) of the DS versus offsets in time and frequency. Cuts along the axes are used to estimate the decorrelation times and bandwidths, as described in more detail in §5.1. The displayed range is set to be 5 times wider than the measured scales. Lower right panels in each plot, discussed in §5.3, show how we estimate the curvature of any parabolic arc structure present.

Overview
The 54 plots provide a visual description of the ISS. As has long been known, the scintillation appears as a random distribution of peaks in the DS, whose widths in frequency and time can be characterized from its ACF. Some such peaks (scintles) can appear tilted causing tilts in the ACFs. In traditional studies of ISS, the ACF widths are the main parameters extracted from an observation, and ISS was originally recognized by the narrowing in the ISS bandwidth for pulsars at increasing DM (Rickett 1970).
Scintillation arcs were discovered as systematic curved structures in S 2 (τ, f D ), often many decibels below the peak. The most common form of arc is a simple forward parabolic arc τ = η f 2 D , with its apex at or near the origin, as characterized by its curvature (η). In general we define arcs by secondary spectra that are peaked narrowly (or broadly) about such a parabola. Such arcs can exhibit a dip or valley along the delay axis near zero f D ; for example, see B0450-18 at 340 MHz (Figure 1.3).
Multiple forward arcs have been reported from some nearby pulsars: e.g. Putney and Stinebring, (2006  boundary which we call a bounding arc. The inner structure is more like a broad ridge than an arc. Note also that at 340 MHz the outer arc no longer acts as a sharp boundary. Similar differences between low and high frequencies are common throughout the survey data and are discussed further in §4. For B2310+42 we also show results at 1400 MHz, which we discuss in §4. A number of pulsars exhibit isolated peaks in their SS which may or may not lie near a forward parabolic arc. When such peaks follow a curved shape we refer to them as reverse arclets, which were discovered in pulsar B0834+06 (Hill et al. 2003). Reverse arclets have negative curvature and apexes that lie close to the underlying forward arc. Figure 1.3 shows similar reverse arclets for B0450-18, which we have analyzed in detail elsewhere (Rickett et al. 2021). Another example can be seen in Figure 1.5 for B0525+21. Reverse arclets can be understood as the interference of scattering from a discrete offset point with a central anisotropic scattered distribution (Walker et al. 2004;Cordes et al. 2006). Their apexes lie on the forward arc when the offset point lies along the axis of anisotropy. Their curvature equals the reverse of the forward arc when the scattering is localized in the same screen as the main forward arc. This situation can sometimes be recognized when a reverse arclet extends inwards as far as zero f D and passes through the origin. Arclets with forward curvature are rare. 3 Pulsar B1508+55 exhibits an unusual variation of flat arclets at 825 MHz and 1400 MHz (Figure 1.11). In another variation, Figure 1.2 for B0450+55 shows an isolated point in its SS, which is not extended in f D .
Another common feature is asymmetry in the intensity of S 2 versus differential Doppler f D , which appears as tilted scintles in the DS and a tilted ACF. 4 Asymmetry can also be seen between the height of the positive and negative peaks in the parabola summation curves. There may also be asymmetry in that the apex of an arc may be slightly offset to positive or negative f D , which can be due to refraction by a transverse gradient in the electron distribution somewhere along the LoS (Cordes et al. 2006).
Scintillation arc studies hold the promise of being able to locate scattering material along the LoS, at least in optimal cases. Dating back to the earliest days of ISS studies, the prevailing paradigm has been one of a pervasive turbulent medium punctuated by "clouds" of increased turbulence along the LoS. For example, see Cordes et al. (1991). Although there is no thorough analysis of how distributed scattering along the LoS will show up in the SS, several lines of argument indicate that it should produce a centrally concentrated (CC) region of power around the origin. An example of a SS that displays this distribution is shown in the left panel of Figure 3. The DS in this case consists of a large number of scintles with no evidence for fine structure within a scintle. Referring to the two higher frequency observations for this pulsar in the center and right panels, we see that the scintle structure broadens out with increased intra-scintle modulation in the DS and a corresponding tendency toward arc-like behavior in the SS. We will discuss this generic frequency development further in §5.5.

ISS Decorrelation Widths
As is conventional procedure (e.g. Cordes et al. (1985); Gupta et al. (1994)), we estimated the frequency scale, ∆ν iss , and the time scale, ∆t iss , of the scintillation structure using the intensity autocorrelation function, R(ν, t), which we discuss in more detail in §5.1. These decorrelation scales are obtained, respectively, by determining where R(∆ν iss , 0) = 0.5 R(0, 0) and R(0, ∆t iss ) = 0.5 R(0, 0) and are presented in Table 3. (We note that this definition differs from the convention of Rickett (1970) and Cordes (1986), where the e −1 point is used in the autocorrelation time lag.) The fractional errors in them are estimated as the minimum of unity and N −1/2 iss , where N iss the number of independent ISS fluctuations over the observed bandwidth (B) and time span (T ). We define N iss ≈ ( B/2∆ν iss )( T /2∆t iss ), since ∆ν iss and ∆t iss are half-widths of the auto-correlations, and where = 0.2 accounts for the fact that the exponentially distributed intensity of the scintles leads to peaks in ISS that are sparsely distributed in time and frequency resulting in fewer independent ISS fluctuations (see equation (7) of Cordes (1986)). Although the value ( = 0.2) predicts conservatively large errors, we use it since it has been widely used in previous scintillation studies. It needs to be validated by complete statistical modeling of scintillation, which is beyond the scope of the paper.
It is also important to note that there are a few observations in which the scintillations have such a narrow frequency scale that they can be unresolved in the channel bandwidth of the spectrometer, We apply a simple quadrature correction for the resulting under-resolution in frequency. ∆ν corr = ∆ν 2 iss − δν 2 ), where δν is the channel bandwidth. A similar correction to the time scale ∆t iss is applied with the 10 s integration time for the spectrometer, in place of the channel bandwidth. There is one case in frequency and one case in time that this correction fails, giving an imaginary estimate; these cases are flagged in tabulating the results with an ellipsis indicating no valid data. There are a few other cases where the scintillations are so slow or so wide in frequency that a single scintle may cover the entire observing range, i.e. N iss 1, with correspondingly large errors.

Scintillation Arc Parameters
There is recognizable scintillation arc structure in more than half of the 54 secondary spectra plots. However, it is difficult to devise a simple yes/no criterion for the presence of parabolic arc structure. Consequently, we have analyzed each observation to estimate a number of specific measurable quantities. We elaborate on this further in § 5.3, but briefly describe the fundamental quantities here.
We quantify forward arcs in the secondary spectrum by estimating the curvature η of the underlying parabola τ = η f 2 D . We sum S 2 along parabolas that cover a range in curvature, and in many cases we find a clear maximum in the summation curve and assign a value η p to this dominant parabola (Table 3). As already noted, we occasionally also find a bounding arc outside this inner parabola; see §5.3 for details. We also include in the tabulated results a curvature credibility criterion, η cred , for each observation. It is a subjective evaluation of the reliability of the curvature estimate obtained by examining the parabola summation curve for each case: 2, 1 or 0. A compact maximum in the curve is rated 2; wide and double peaked curves are rated 1; cases where the peak is at the high or low limit in the search range or the secondary spectrum extends to the Nyquist delay are rated 0. In the latter situation, the DS may be unresolved in frequency, and only an upper limit can be estimated for the decorrelation bandwidth ∆ν iss . As detailed in §5.4, we define and tabulate a width measure ∆η to quantify how sharply S 2 is peaked about the forward parabolic arc.

COMMENTS ON INDIVIDUAL SOURCES
Using terminology and results from the previous sections, we qualitatively discuss results from the 22 pulsars below. We group them first by the prominence of the scintillation arc, followed by sorting them in RA. The three groupings used below have a connection with the η cred index. However, the discussion here is on a per-pulsar basis, and a number of pulsars have η cred = 2 or 1 at one frequency with a lower index at one or more observing frequencies. In some places, the signal to noise ratio (S/N) will be discussed qualitatively here. We treat it and parameters of the scintillation arcs quantitatively in §5.

Pulsars with a Definite Scintillation Arc
The 1400 MHz observation shows two fairly well-defined scintillation arcs. At 825 MHz, in data taken 14 years earlier, the scintillation arc structure is not well-defined, although there is a hint of an arc coincident with the dashed blue line in the 2nd quadrant of the SS. The CC of the 340 MHz data has a negative power asymmetry (i.e. quadrant 2 power is greater than quadrant 1), as does the CC at 825 MHz, observed 5 days later. Arc credibility indices η cred : 340 MHz, 825 MHz, 1400 MHz (0, 1, 1) We have reported on these observations in detail (Rickett et al. 2021). However, the 1400 MHz observation was not available at the time of that analysis. In that paper we found a 1D brightness distribution matched the data well, but the overall brightness function B(θ) was not consistent with simple Kolmogorov scattering in a thin screen. Instead, B(θ) scaled with frequency more slowly than Kolmogorov and various local peaks in B(θ) were trackable across narrow frequency intervals, but not between 340 MHz and 825 MHz. The 1400 MHz observation was made more than 14 years after the two at lower frequencies, so the LoS may be probing quite different ISM conditions. Two thin scintillation arcs are present. As discussed in §5.3.5, neither of these is consistent with the curvature of the heavily saturated scintillation arc visible at the two lower frequencies. Hence, this must be due to a different region of scattering along the LoS. Arc credibility indices η cred : 340 MHz, 825 MHz, 1400 MHz (2, 2, 2) The 3.7 s pulsar period and nulling causes modulation of the DS in time, particularly with our integration time of 10 s. But a criss-cross pattern is clear across the scintles, seen as reverse arclets in the SS. As commented on in §5.7, and widely in the scintillation arc literature since Walker et al. (2004), such reverse arclets are indicative of a nearly 1D brightness distribution. Our parabolic summing algorithm (lower right panel) reports a significantly wider arc on the RHS (positive Doppler) than on the LHS. This is due to the influence of power near the origin; an algorithm that intercepted the apexes of the inverted arclets would produce more nearly equal values of η for the two signs of Doppler frequency. Arc credibility index η The low frequency data show a CC core with a clear bounding parabola for power further from the core of the SS. The 825 MHz observation shows a compact CC core and two scintillation arcs or, alternatively, a boundary arc with an interior arc due to anisotropic scattering and a velocity vector with significant tilt to the major axis of the scattered image (Reardon et al. 2020). The 1400 MHz data are consistent with the trend, seen elsewhere in this survey and in previously published data, for scintillation arcs to become substantially sharper at higher frequency. Arc credibility indices η cred : 340 MHz, 825 MHz, 1400 MHz (1, 1, 1) 4.1.5. 1508+55 (Figure Set 1.11) This pulsar, relatively distant (2.10 kpc) for the survey, has the highest transverse velocity (963 km s −1 ) in the sample and one of the highest of the entire pulsar population 5 . The low frequency data show a clear CC core plus a very broad scintillation arc that also exhibits strong local maxima in the B(θ) distribution. This is even more pronounced at 825 MHz, where the highly unusual, flat-topped arclets are a prominent feature. All three frequencies show the presence of the same arc despite the fact that the pulsar has traveled approximately 2900 au transverse to the LoS during this time. Similar flat arclets were recorded by Marthi et al. (2021). Low curvature arclets could be due to localized scattering near the pulsar (i.e. small value of s) interfering with a core in brightness at small angles of deflection. The scattering geometry is complex for this pulsar, as documented by Bansal et al. (2020), who observed remarkable echoes of the pulse arriving 30 ms after the main pulse at 50 and 80 MHz that persisted over about 3 years. Also see Sprenger et al. (2022)  This is an excellent example of no scintillation arc at the lower frequency, but clear evidence for arcs at higher frequency. As discussed in §5.8, if we only had the 340 MHz observation we would classify this as a pulsar without a scintillation arc. Although the dynamic spectrum at 825 MHz shows about a dozen classical scintles, the secondary spectrum is remarkable in its sharpness and detail. The 1400 MHz observation, offset by 14 years, is fully consistent with the 825 MHz observation, showing a boundary arc with a filled interior that is similar to the signature expected for an anisotropic image with major axis not aligned with the effective velocity vector (Reardon et al. 2020). This pulsar, relatively distant (D = 2.39 kpc) for this survey, is fairly heavily scattered. It also has a large transverse velocity. It has been extensively studied for interesting propagation effects along the LoS. Michilli et al. (2018) observed pulse echoes delayed by about 10 ms near 150 MHz. They concluded that the echoes, which varied slowly over five years, were scattered by a dense plasma concentration of 100 cm −3 . Using LOFAR data, Donner et al. (2019) reported an episode of frequency dependent DM variation toward this pulsar. Similar to B2021+51 and B2045-16, but even more heavily scattered, the SS at 340 MHz is completely dominated by a CC. This is basically true at 825 MHz, too, although there is a hint of a scintillation arc developing. At 1400 MHz, even though the CC is still the dominant feature in the SS, the parabolic summing algorithm shows clear evidence for a broad symmetric scintillation arc. Yet another pulsar with a dominant CC at 340 MHz that displays a clear boundary arc at the two higher frequencies.
At 340 MHz, the DS has well-resolved scintles with high S/N. The SS shows broad power centered on the origin, with slight positive asymmetry to larger delay. There is a hint of a boundary arc but no valley. At 825 MHz, the DS has about a dozen well-resolved scintles, with no obvious modulation of them. However, the SS has a clear boundary arc with a shallow valley partly filled by SS power extending along the delay axis. The DS at 1400 MHz has three wide, moderately narrow scintles in it, with no obvious intra-scintle modulation. The resulting SS has an outer bounding arc with an inner arc, neither very distinct. The parabolic summing algorithm traces out the bounding arc on the LHS, but it appears to find a faint interior arc on the RHS. Taken together, these data illustrate the value of observing at multiple frequencies. They are consistent with strong plasma scattering with modest anisotropy (Cordes et al. 2006;Reardon et al. 2020). See §7 under B2217+47 on the effect of orientation of the anisotropy axis with the V eff vector. Arc credibility indices η cred : 340 MHz, 825 MHz, 1400 MHz (1, 1, 1) 4.1.11. B2327-20 ( Figure Set 1.22) This set of observations shows the value of scintillation data even when the S/N is not large. At 340 MHz, the DS has only moderate S/N with wide, tilted scintles crossed with finer modulation. There appears to be some broadband pulse modulation, perhaps nulling, which puts power onto the f D axis. The SS has a clear narrow arc, predominantly one-sided (negative asymmetry) with several loci of higher power along the arc. Although it is hard to tell from the low S/N observation at 825 MHz, the DS shows a loosely organized criss-cross pattern. The SS has a sharply defined arc with a deep valley and a slight negative power asymmetry. As can be seen in the quantitative results for η p in §5, the boundary arc detected at 1400 MHz, observed 14 years after the low frequency observations, is not consistent with the curvature of the λ 2 scaled values at lower frequencies. η p,1400 is approximately 7 times greater than η p,825 , when scaled by λ 2 . This places the scattering material as close as 40 pc from the Earth. Arc credibility indices η cred : 340 MHz, 825 MHz, 1400 MHz (2, 2, 0)

Pulsars with a Probable Scintillation Arc
This is one of the most heavily scattered pulsars in the SAS. With 4096 frequency channels across only 2 MHz of bandwidth, the frequency resolution is barely adequate to resolve the scintles, and even Arecibo's sensitivity is not quite adequate to display a clear secondary spectrum. However, with a careful choice of the color table, spanning only 10 dB in power, we are able to see a tilted bar of power (negative asymmetry) extending out to more than 200 µs. At 1450 MHz, the tilted SS shows a wide faint arc (negative asymmetry) with shallow valley. It appears that the CC merges into a broad scintillation arc as opposed to being a simple tilted concentration with quasi-elliptical contours. This pulsar has very similar scintillation characteristics to B0523+11. They both show narrow scintles at the lower frequency, consistent with strong scattering through the same region of plasma. At the higher frequency a similar asymmetrical CC emerges with arclike properties at higher delay. Since a plasma wedge is one mechanism for an asymmetrical power distribution in arcs, the same sense of asymmetry is, perhaps, a linkage in the source of dominant scattering for these two pulsars. We note that they are relatively close on the sky (12.7 • ) and that B0523+21 and B0540+23 have DMs of 79.4 and 77.7 pc cm −3 , respectively. At a screen location of s = 0.5, the angular separation would require a transverse screen extent of approximately 190 pc, however. Despite these similarities, the curvature of their scintillation arcs are significantly different, with the value for B0523+11 placing the scattering material about 600 pc from Earth and about twice that value for B0540+23 (see details in §5 and Table 3 There appears to be a bounding arc in the SS of the 340 MHz observations. Observations at the two higher frequencies were too low in S/N and contaminated with RFI in order to show anything clearly in the respective SS. The observations at both 340 MHz and 825 MHz are high S/N, but have inadequate frequency resolution. At 1400 MHz, the frequency and time resolution are adequate, and there is some hint of unorganized wispiness around the CC core. Close inspection of the 825 MHz SS shows a slight bifurcation of the power distribution (along the f D = 0 axis) near the Nyquist frequency in delay. Observations of higher frequency resolution and longer time duration would be needed to explore further the possibility of a scintillation arc in this pulsar. Arc credibility indices η cred : 340 MHz, 825 MHz, 1400 MHz (0, 0, 1) 4.2.6. B1706-16 (Figure Set 1.13) This is a nulling pulsar, which causes extra power along the f D axis. This is also a low-velocity pulsar, which causes problems because ∆t iss is long relative to a typical observation length, particularly at the two higher frequencies. The 825 MHz SS suggests a bounding arc with a slight negative power asymmetry. As was the case with B2310+42, the η p value on the left looks more reliable than that on the right because of the more prominent boundary arc on the left. Although only 700 pc away, the LoS to this pulsar (l = 10.3 • , b = −13.5 • ) is heavily scattered. The extremely narrow and brief scintles at 340 MHz make this DS and SS unusable. At 825 MHz, the scintles are easily visible in the the relatively high S/N DS. (There is a defect in the spectrum near 818 MHz that has only been partially corrected in cleaning the data.) The parabola traced out on the SS, determined by the parabolic summing algorithm, is unlikely to be reliable except as a rough guide for the curvature of a scintillation arc that would need to be explored at higher frequency. Arc credibility indices η cred : 340 MHz, 825 MHz (0, 0)

ANALYSIS OF THE SECONDARY SPECTRA
We report on detailed analysis of the data in this section. The first two subsections present results of a more classical scintillation analysis, focused on the DS. The remainder of the subsections concentrate on detailed analyses of the SS. Throughout §5 we refer to parameters extracted from the data set in a uniform manner and presented in Table 3 for all 54 observations.

Scintillation Parameter Estimation
The scintillation decorrelation time ∆t iss and bandwidth ∆ν iss were already defined in §3.2, as the half-widths in time and frequency of the autocorrelation function (ACF) R(ν, t) of the DS. Here we provide additional information about the way we construct R(ν, t). For many pulsar observations in the SAS the contribution of noise to the ACF is unimportant. However, noise is significant in some of our data and needs to be corrected. In order to correct the ACF for system noise we started from S 2 and estimated the mean noise level in the SS from a rectangular region outlined in green in the SS figures away from the ISS. (See §5.3 for how we identify a rectangle in delay-Doppler (DD), where the ISS signal is evident, which we refer to as the DD box.) The inverse Fourier transform of S 2 , after subtracting the mean noise level from every pixel, yields the autocorrelation function of the ISS, R(ν, t), versus lags in frequency and time. The result, as plotted in the lower left subpanels of Figure 1, is free from a spike at zero lag due to additive white noise, which would be present when the autocorrelation is computed directly from the dynamic spectrum. Hence we use the value R(0, 0) to estimate the scintillation variance, corrected for noise, in defining the decorrelation widths. Its square root gives the rms needed for estimating modulation index.
It also allows us to define a signal-to-noise ratio as the ratio of the scintillation variance to the noise variance, found by summing the noise level S noise over delay and Doppler. We include this ratio of signal variance to noise variance in Table 3. Note that the signal-to-noise ratio for S 2 itself is typically higher, since the ISS only spans part of the observed domain, while the noise is uniform out to the Nyquist point in delay and Doppler. Consequently we also tabulate a signal-to-noise for the ISS, defined as the ratio of the variance in ISS summed over the DD box, divided by the variance of the noise, summed over the same DD box, which approximates a matched filter for the ISS. We tested the S/N estimation process against simulated data with known signal-to-noise ratio and found it reported accurate values within the statistical uncertainties.   Table 3 continued on next page  . smax is the estimate of primary screen location (maximum distance from the pulsar; see Equation (11)). The Arc Power Asymmetry is κ ≡ (R -L)/(R + L), where R is the peak parabolic summation on the RHS (f D > 0) and L is the corresponding peak power on the LHS of the parabola. Columns (6) and (8) are finite scintle estimates of the uncertainty in ∆νissand ∆tiss, respectively. See text for details.

Pulse Broadening Time
The pulse broadening time τ scatt is a useful measure of scattering along a LoS and an important parameter to know when planning a timing or scintillation observation. Although many of the parameters in the ATNF psrcat database  are extremely well-determined, others such as τ scatt,1GHz , the pulse broadening time scaled to 1 GHz, are drawn from a wide range of disparate observational programs conducted over the last 50 years. The heterogeneous nature of psrcat τ scatt data is increased because values are typically determined by frequency domain techniques for relatively lightly scattered pulsars and time domain techniques for moderate to heavily scattered pulsars. In this section we report 22 newly determined values of τ scatt,1GHz and compare them with currently tabulated psrcat values.  is available online with a similar plot for each of the pulsars. The black points are estimates and 1-σ uncertainties of τ iss at each of the available frequencies. The red line represents the weighted linear least squares fit through these points. We report a value, marked by a filled blue circle, where that line crosses 1 GHz, and we assign an uncertainty to it from the least squares fit. The psrcat value is marked with a circled green A. The dashed black line has a logarithmic slope of −4. (b) The τ iss,1GHz values from the SAS are plotted against the DM values. The red line is a weighted least squares fit. It has a logarithmic slope of 2.08, which is close to the τ ∝ DM 2 behavior expected for scattering in a uniformly turbulent medium. However, it is clear that the line is a very poor fit to the data if the individual errors are to be believed, and they are well-determined at the high DM part of the plot. See the text for further comments.
Figure 4(a) shows τ scatt values calculated from the observed ∆ν iss values using τ scatt = (2π ∆ν iss ) −1 . The error bars on the individual points are calculated from the formula for the number of independent scintles used by Cordes (1986). Since most of the uncertainties are not too large we use the approximation of a symmetric uncertainty in the log of the displayed value. The best-fit line represents the weighted (w i = 1/σ 2 i ) least squares fit through these points in a log-log representation. The interpolated or, in the case of some pulsars with only two observed frequencies, extrapolated values at 1 GHz are noted with a blue filled circle and a 1-σ uncertainty from the linear least-squares fitting process. This is the value and uncertainty reported in Table 4. In the case of a single-frequency observation, τ iss was determined from the single ∆ν iss value assuming τ iss ∝ ν −4 . Figure 4(b) plots our determinations of τ scatt,1GHz versus DM . Although the best-fit line has a logarithmic slope close to the value of 2.0 expected for uniformly distributed scattering, we believe that this is coincidental as indicated by the poor match to points with small error bars for data with log 10 DM 1.6. See further comments below.
Plots such as this comprised the first observational evidence that showed how the strength of ISS increases with the interstellar column depth of electrons (Rickett, 1969). Many studies have shown that τ scatt typically increases more steeply than ∝ DM 2 (Sutton 1971;Bhat et al. 2004), expected for uniformly distributed scattering, particularly for longer lines of sight through the Galaxy. Since pulsars are concentrated in the Galactic plane and toward the Galactic

Note-Column
(2) is the number of frequencies available to estimate τscatt. Columns (3) and (4) give the value and uncertainty of τscattthat we determine, referenced to ν = 1 GHz using an assumed τscatt ∝ ν −4 relations. See text for details. Columns (5) and (6) give information about the slope of the best fit line in the equivalent of Figure 4(a) for each pulsar. Column (7) gives the psrcat value of τscatt, also referenced to 1 GHz. Column (8) gives the ratio between the SAS value and the psrcat value.
Center, the steeper DM dependence is interpreted as increasing concentrations of turbulent plasma toward the inner Galaxy. The survey observations extend only to about 3 kpc and so do not add new distance dependence. Table 4 shows substantial discrepancies between τ scatt,1GHz from psrcat and those from the SAS. The ratio of the two (column 8) is evenly split between ratio > 1 and ratio < 1 (10 instances of each; two comparisons missing). To quantify the severity of the discrepancy, we took all the ratios less than 1 and found their reciprocals. Combining these with the ratios greater than 1, we found the median of the list to be 3.3, giving some indication of the difficulty of measuring this parameter. It is well known (e.g. Gupta et al. 1994;Ramachandran et al. 2006) that τ scatt is time variable, sometimes by at least a factor of 3 in both directions, which no doubt accounts for some of the discrepancies in values, both between the SAS values and the psrcat values and probably within our own survey.

Scintillation Arc Curvature
The most fundamental parameter of a scintillation arc is its curvature, η. In this section we explore many aspects, both theoretical and observational, of arc curvature as it occurs in the survey.

Fundamental Relations
Under the simple hypothesis of partial or fully 1-D scattering caused in a single screen located at some distance, the predicted curvature depends on the distances and angles involved as follows (Cordes et al. 2006): where where the distance of the observer from the pulsar is D psr and from the screen is (1 − s)D psr ; ψ is the angle between the effective velocity V eff and the long axis of the scattering. The velocities of the observer V obs , the screen V scr and the pulsar V psr are summed as vectors. However, in what follows we assume that V eff is dominated by the motion of the pulsar. If the scattering is isotropic the same relations are obtained with cos ψ = 1. V eff depends on the transverse velocity of the pulsar V psr and also that of the observer and the screen, both of which we assume to be negligible relative to that of the pulsar (see Cordes et al. 2006 for the full expressions).

Methodology for Estimating Arc Curvature
As can be seen in the examples in Figures 1-3, S 2 typically peaks sharply near the origin, and arcs are only recognized at many decibels below the peak. Hence we focus on rectangles in Delay-Doppler space away from the origin, selected visually where S 2 is significantly above the noise floor. The rectangles are defined by f DA > |f D | > f DB , τ A > τ > τ B , which we refer to as the DD box. The curvature is estimated in separate DD boxes for positive and negative f D , with box coordinates listed in the online version of Table 3.
Elaborating on the discussion in §3.2.2, we use two methods to estimate η. In the first, we examine cross-cuts through S 2 over a range of fixed delays. We tabulate the location in f D of the maximum in each cross-cut separately for both positive and negative f D . We then fit a parabola to the resulting set of peak locations in (f D , τ ). The fitted curvature is the estimate η c .
In the second method we sum S 2 along each parabola from a search range in η p . Examples of the search, as parabolasummation versus curvature η p are plotted in the lower right hand sub-panels of Figures 1-3. For each η p we compute the sum of S 2 (f D , τ ) − S noise at each delay, interpolated in f D on each parabola. The search range in η p is centered on the value η A = τ A /f 2 DA defined by the parabola that passes through the outer corner of the DD box, with 50 equal steps in log(η) between 0.1η A and 10η A . S 2 is summed in linear power over all delays between τ B and τ A and covers f D out to the Nyquist frequency, but excluding f D = 0. Separate summations over positive and negative f D are plotted in red and blue, respectively. This method is similar to a Hough transform (Bhat et al. 2016).
The solid lines in Figures 1-3 plot the direct summations, while the lines with "x" markers are summations of S 2 weighted by |f D |. Such a weighting is motivated by the theoretical relationship between S 2 and a one-dimensional model for scattered brightness. In this model (e.g. Stinebring, Rickett, & Ocker 2019), the S 2 contribution from interference between each pair of brightness components is divided by |f D |, which is thus compensated by the weighting. Note that our weighting is the same as the Jacobian of the transformation to "normalized Doppler profiles" as used in curvature estimation by Reardon et al. (2020), which does not assume one dimensional scattering. It differs from the theta-theta mapping method of Baker et al. (2022), which is based on one-dimensional scattering.
As a consequence of the weighting, however, an obvious broad peak in the weighted parabola summation, such as in B77+47 at 340 MHz (Figure 3), does not necessarily correspond to visible parabolic arc structure in S 2 . For the same pulsar at 825 MHz, the summation curve only reaches its peak at the maximum curvature searched, and so only a lower limit on η is given. However, the curve does exhibit a sharp rise beyond which it flattens somewhat. This behavior is characteristic of a parabolic boundary in S 2 outside of which S 2 drops off sharply. In the survey there are several examples of this behavior, which is expected in the presence of a core of lightly scattered waves that interferes with a broadened distribution.
We now compare the two methods of estimating curvature. The estimates of curvature from positive and negative Doppler are averaged for each method giving an overall η c and η p for each observation. These are included in Table 3 and compared in the left panel of Figure 5. There is a satisfactory agreement between the two methods. However, since the cross-cut method relies on finding the single highest peak at each delay, it can have quite large errors, and in what follows we focus on η p as our curvature estimator. Note that the weighted η p can give an apparently reliable Figure 5. Curvature. Left: Comparison of the two methods (maxima in cross cuts and parabolic summation) for estimating curvature described in the text, averaged from positive and negative Doppler frequencies. As discussed in §3.2.2 we have created a subjective credibility index (0,1,2) for the ηp estimate and plot green error bars to indicate low credibility index. Right: The pseudo-curvature ηiss, which is defined below in equation 7, plotted versus the observed ηp for data with credibility index greater than zero and valid results for the corrected ∆νiss and ∆tiss. measure of curvature, even in the absence of a visible parabolic arc in S 2 . As an example, the secondary spectrum in the left panel of Figure 3 exhibits no arc-like features, but there is a broad peak in the weighted parabola summation defining a specific curvature that is not seen in the unweighted summation.
We include an estimate of the error in curvature, calculated from the upper η p,u and lower η p,l range for which the parabola summation is above 95% of its peak. This is illustrated in the lower right panels of Figure 3. Note however, that it is not a formal error estimate as we do not have a statistical model for the systematic variations in S 2 . We arbitrarily choose 95% reduction since the arcs represent only a small fraction of the total power in S 2 (equal to the variance in the DS), and so also only a small fraction of the parabolic sum. Another estimate could be made at say 50%, which would include a much wider range especially with double peaks and curves that saturate at the search limit. The limits are included with each estimated η p in Table 3. These limits are also useful in characterizing the width of the arc as elaborated on in §5.4.

How Curvature Is Related to the Basic ISS Parameters
Under the same single screen anisotropic scattering assumptions made in §5.3.1, we examine the relationship to be expected between the curvature and the basic ISS parameters. The characteristic time and frequency scales are related to the characteristic angular width on the long axis of the scattered brightness at the observer (θ d ) as follows: We eliminate the dependence on θ d in the following combination and obtain a quantity proportional to the curvature in equation 2. η iss = 2π∆t 2 iss /∆ν iss = cD eff /(2ν 2 V 2 eff ) = η In the right panel of Figure 5 we plot η iss as defined in equation 7, against the curvature estimated from the parabola summation η p . The points follow this relation and so confirm our basic assumptions. 6 Note that this result was already implied in the analysis of arcs by Cordes et al. 2006. They introduced scaled variables p and q as: which are related by the basic arc equation p = q 2 . In § 5.7 we explore what additional insights are obtained from presenting SS in normalized (pq) coordinates.
In the next section we examine how to use the curvature η p or η iss to estimate screen distance. However, we note that they both suffer from the same problem: the screen location s and the angle ψ, which appear in D eff and V eff , are not separable in a single observation. While there are cases where the orbital motion of the Earth or of a pulsar in a binary system can be used to break this degeneracy (e.g. Stinebring et al. 2005;Reardon et al. 2020;McKee et al. 2022) we do not have a sequence of observations necessary to pursue this further.

Single Screen Model -Estimating Screen Distance
How consistent is the assumption of a single screen (or, more generally, a single "dominant" screen) with the results of the survey? We start from the definition of the theoretical curvature for a mid-placed screen: where the pulsar velocity and distance and the observing frequency are expressed in convenient units (V psr,100 = V psr /10 5 m s −1 ). We can then write equation 2 as The theoretical quantity η 0.5 can be evaluated for each observation, using the published values for the pulsar distance and velocity, obtained from psrcat and listed in Table 1, for 20 of the 22 pulsars. The left panel of Figure 6 shows the measured curvature (average of η p from positive and negative f D ) plotted against η 0.5 . In the plot a solid blue line joins observations of the same pulsar at 2 or 3 frequencies.
If the values were consistent with each other the line should have unit slope (parallel to the red line), corresponding to λ 2 scaling for η. While many show reasonable agreement there are several discrepancies. There are two pulsars in particular that stand out, B0450-18 and B2310+42, which are highlighted. They are notable because η is larger at 1400 than at 825 MHz, and so we examine them in detail in §5.3.5.
As can be seen in the figure and from equation 10, the actual value of η can be above or below η 0.5 , depending on the values for s and ψ. However, since cos 2 ψ ≤ 1 we can constrain s ≤ s max = η/(η + η 0.5 ).
(11) (This is the same estimate for s used in Putney & Stinebring 2006.) For isotropic scattering in a single thin screen, the equality can yield a direct estimate of screen distance D scr = D psr (1 − s max ). In the right panel of Figure 6 we plot such estimates against the distance to each pulsar. Assuming an isotropic single screen scattering model, the 1-3 frequencies observed would yield the same D scr ; in many cases the points, joined by a vertical line, do form a cluster. We might expect that low DM pulsars can be better modeled by discrete screens causing single or multiple well-defined arcs. Hence we flag the narrow arcs by a red cross, but they show only a weak preponderance for small D psr . Another consideration here is the range in observing dates and the substantial proper motion of the pulsars. In particular, the Green Bank observations at 1400 MHz were 14 years later than the observations at lower frequencies, and are flagged separately.

Apparently Discrepant Frequency-Scaling of the Curvature
As noted above B0450-18 and B2310+42 both show discrepant frequency scaling in the estimated curvature η p . Figure 2 displayed the observations for B2310+42 at three frequencies. In each case the curvature estimation comes from the lower right panel. The major discrepancy is that η p is a factor 2.5 higher at 1400 MHz than at 825 MHz, but it should be a factor 0.35 smaller. While the observing dates at 340 and 825 MHz differ by only 5 days, the 1400 MHz observations were 14.3 years later. Similarly for B0450-18 the 1400 MHz observation were 14.4 years later than those at the lower frequencies. Pulsar B0450-18 moved a transverse distance of 79 AU and B2310+42 moved 376 AU in the Figure 6. Left: Curvature ηp versus single screen theory η0.5; points without error bars represent estimates with zero credibility index. Points connected by a blue line are from the same pulsar at 2 or 3 frequencies. Two pulsars with discrepant frequency scaling between 1400 and 825 MHz are highlighted. Right: Single screen hypothesis: Distance to the screen (Dpsr(1 − smax)) versus distance to each pulsar, assuming isotropic scattering. If the scattering were anisotropic this becomes a minimum screen distance. Observations of the same pulsar are joined by a blue line, and marked by a black circle for 1400 MHz observations in 2020. The small symbols mark curvature estimates classified as low credibility. Narrow arcs are defined by ∆ log η < 0.2 as estimated from the parabola summation plots. 14 years. Many previous arc observations have shown evidence for significant structure in the interstellar plasma on AU scales, implying that interstellar scattering is due to a very patchy distribution of plasma. Thus we interpret the discrepancies in the frequency scaling as due to changes in the plasma columns over the 14 years.
These changes in η p imply localized plasma concentrations at differing distances (unless the scattering were highly anisotropic with a change in orientation to the pulsar velocity), which is also illustrated by the widely differing values of s max in the right hand panel. For B2310+42 the 825 MHz result shows a well defined boundary arc whose curvature is 0.2 sec 3 ; scaling this to 1400 MHz predicts 0.07 sec 3 . However, the value estimated is about 0.3 sec 3 , but with substantial differences between positive and negative f D . The SS at 1400 MHz has a poorly defined boundary arc at positive f D . In a close inspection of the parabolic summation curve one can see this as a sharp rise in the summation at log 10 η p ∼ −1.1 (η p ∼ 0.08 sec 3 ), and so might be due to scattering at the same distance as the boundary arc at 825 MHz seen 14 years earlier.
Now consider the results for B0450-18 shown in Figure 1.3 (and already published by Rickett et al., 2021). At 825 MHz the strong forward arc has η p ∼ 0.7 ± 0.3 sec 3 and is modulated by prominent reverse arclets. However, at 1400 MHz there is a narrow forward arc with curvature η p ∼ 1.8 sec 3 , in stark disagreement with the expected scaling from 825 MHz η p = 0.24 sec 3 . Note that in the right panel s max ∼ 0.05 estimated from the earlier observations of the pulsar at 340 and 825 MHz implies a screen near the pulsar. Even though our earlier analysis found anisotropic scattering, a low value of s still holds since cos 2 ψ ≤ 1. Thus the later value of s max ∼ 0.2 must be due to a new scattering screen substantially farther from the pulsar.

Arc Width
We now characterize the relative prominence of arcs in the secondary spectrum. In particular, we attempt to parameterize sharpness of an arc by its width and the depth of the valley along the delay axis. Using the analysis from §5.3.2, we define a relative width of the arc: ∆η = log 10 [η p,u /η p,l ].
(12) The left panel of Figure 7 plots ∆η against DM and shows that arcs at low DM are typically narrow, and at larger DM the arcs usually widen, and ∆η covers a wide range. We also use the parabola summation curves in an attempt to quantify the relative depth of any valley in SS near the delay axis. We divide the peak in the summation curve by the summation of SS parallel to the delay axis (at f D = 1 resolution increment in f D ) over the same range in delay as used in the parabola summation; the result is a ratio R v between typical SS amplitude along an arc and its value near the delay axis. We avoid f D = 0 which is influenced by the bandpass normalization.
In the right panel of Figure 7 we investigate how R v is related to the arc width ∆η, defined by equation 12. In the plot we flag the points by their credibility index. It illustrates how the narrow arcs with deep valleys are often classified as η cred = 2. Note that in some cases R v < 1, which signifies a ridge along the delay axis rather than a valley, disrupting the curvature estimation. The right panel of Figure 7 shows that narrower arcs are associated with deeper valleys; thus the general increase in ∆η with DM corresponds to a decrease in valley depth R v with DM . Figure 7 provides observational evidence that narrow arcs with deeper valleys are mostly seen at low dispersion measure. Such a trend is expected since narrow arcs imply localized scattering from a thin region, and at larger distances (or DMs) it becomes more likely that the pulsar signal is scattered in multiple regions making arcs broader and less distinct.

Theoretical Conditions for Arcs
In section 5.3.1 we gave the theoretical relations for the curvature of parabolic arcs due to a single localized scattering screen. Here we describe the form of the secondary spectrum for scattering by random irregularities in electron density, under some specific statistical assumptions, concerning their underlying spatial spectrum and their distribution along each LoS. Consider, first, a thin region modeled as a phase-changing screen (phase screen) at a particular distance along the path from a pulsar. Further, assume transverse variations in phase that follow the Kolmogorov spatial spectrum.
The ISS observed in pulsars has narrow bandwidth, characterized by δν iss which is typically much less than the central frequency in the observations. Thus the scintillations are strong in the sense that the rms variation of flux density is comparable to the mean flux density (see, e.g. Rickett 1990). Under strong scintillations there is negligible flux density from un-scattered waves. However, the refractive index in the plasma varies as frequency −2 , and at frequencies above about 10 GHz, typically the ISS becomes weak (rms less than mean) and δν iss increases becoming comparable to the central frequency. Such conditions give rise to a narrow forward arc in the SS caused by the interference of the unscattered wave with an angular spectrum of scattered waves. This forward parabola acts as an outer boundary, below which the SS is zero and above which S 2 is related by a simple expression to the angular spectrum in brightness.
At the other extreme, asymptotically strong scattering is due to the mutual interference between all possible pairs of scattered waves, as in the double integral equation (8) of Cordes et al. (2006).
In Figure 8 we show the SS predicted in asymptotic strong scattering for a screen with a Kolmogorov phase spectrum. The scattering is isotropic in the left panel; it is slightly anisotropic in the center and right panels, with axial ratio AR = 1.5 and orientation angles ψ = 0, 90 deg, respectively. The SS is calculated numerically by Fourier transforming the expressions for the frequency-time correlation function given by Lambert and Rickett, (1999). (Note that the low level ripples in the SS near the delay axis are due to insufficient dynamic range in the computation.) See Figures 9  and 10 in Reardon et al. (2020) for similar computations, which also exhibit boundary arcs in the secondary spectra. Figure 8. Theoretical secondary spectra for strong scattering in a screen with a Kolmogorov phase spectrum. Format as for the observations. Left: Isotropic (axial ratio = 1). Center: Anisotropy axial ratio=1.5, velocity along major spatial axis (ψ = 0) Right: axial ratio=1.5 velocity perpendicular to major spatial axis (ψ = 90) . The lower left panel is the autocorrelation function R(ν, t) versus normalized frequency lag (vertical) and normalized spatial lag (horizontal); the lower right panel is an estimation of parabolic curvature from the secondary spectrum.
In all three panels of Figure 8 the parabola summation curves show significant peaks and yield estimates for both the curvature and the arc width parameter ∆η. All three SS plots also exhibit a boundary arc, and demonstrate that boundary arcs do not require anisotropic scattering. They can be seen even with modest anisotropy (axial ratio AR = 1.5) and when the orientation angle ψ = 90 • . The boundary arc is caused by the interference of slightly scattered waves at very small angles with waves scattered at relatively large angles, similar to weak scintillation. It is a property of the isotropic Kolmogorov spectrum that there is a bright compact core in the angular spectrum and also a tail of brightness at larger angles falling as angle −11/3 . The power law nature of this tail causes S 2 to decay slowly with delay, making the arc visible out to delays that are many times larger than the characteristic scatter-broadening time.
The center panel (ψ = 0, AR = 1.5) has the lowest interior SS levels (deepest valley) and the right hand panel (ψ = 90, AR = 1.5) has the highest interior SS levels. These differences can also seen from the parabola summation curves where the peak summation is greater than the summation at the maximum η, where the parabola lies close to the delay axis.
We do not have a full theory for the form of the SS when the scattering is distributed all along the path from the pulsar. Under such conditions the tight quadratic connection between delay and Doppler frequency breaks down, which will certainly broaden any arcs and broaden any sharp boundary. As a first approximation the SS can be considered as the superposition of the SS from multiple discrete screens, ignoring the effect of second (or higher) order scattering. This approximation superimposes parabolic arcs of differing curvatures arising at differing distances and of differing velocities, and any anisotropy would likely be randomized in angle. Thus the overall SS would exhibit few distinct parabolic arcs, but more likely become quite fuzzy and broadened curves of parabola summation with increased ∆η. Note, however, Simard et al. (2019a) describe a precise theory for SS scattered by two discrete screens.

Arc Width Versus Frequency
As discussed throughout §4, a striking aspect of the observed SS is the systematic broadening of the arcs at the lower frequencies as in Figures 1 and 2, for example. We interpret this as the widening of the scattered brightness distribution as the scintillations become stronger. Here we discuss how the width of the arcs changes for plasma scattering in a single screen with a Kolmogorov spectrum, for which we have a complete theory.
As noted above, a boundary arc is caused by the interference of a bright core of slightly scattered waves with those scattered at relatively large angles, which fall off in brightness as an inverse power law in the Kolmogorov spectrum. The power law is important in that the steeper decrease of a Gaussian spectrum suppresses the amplitude of the arc (see figures 5 and 7 of Cordes et al., 2006).
Consider now the scaling versus frequency of the SS for an isotropic Kolmogorov spectrum displayed in the left panel of Figure 8. The key idea is that the angular width of the core in scattered brightness increases steeply with wavelength and so the boundary arc also widens with wavelength.
As noted in §5.3.3, the SS from a thin plasma screen can be expressed as a function of normalized delay p and normalized Doppler q. Hence, we can use p, q variables to describe how arcs depend on the observing frequency. Let the delay and Doppler at wavelength λ 1 be τ 1 and f D1 . Using p, q from equation 8 we can scale them to the delay and Doppler at wavelength λ 2 as follows: θ o,1 is the characteristic width of the scattered brightness function at wavelength λ 1 , similarly for wavelength λ 2 . For scattering in a plasma θ o ∝ λ 2 Consequently in scaling the calculated SS from a frequency ν 1 to a lower frequency ν 2 , the delay axis is stretched by a factor (ν 1 /ν 2 ) 4 and the Doppler axis is stretched by the lesser factor (ν 1 /ν 2 ). In and 2.9, in delay and Doppler, respectively). In practical observations the spectrometer channel width at 340 MHz is much finer than at 825, displaying the SS out to much greater delays, which is chosen here to be 4 times greater.

Analysis of SS Using Normalized (pq) Coordinates
The strong correlation between η iss and η p , described in § 5.3.3, suggests that we explore the SS in terms of normalized (pq) coordinates, in which a scintillation arc has the simple form p = q 2 . For convenience, we will call such parabolas pq arcs. In Figure 10 we plot three examples of SS overlaid in pq coordinates, since there is good agreement between η p and η iss .
In panel a we have a case of strong inverted arclets and a deep valley along the τ axis, conditions indicative of a nearly 1D scattering profile made up of discrete local brightness peaks (Rickett et al. 2021). It is simple in this case to fit the η p parabola since it should coincide with the apexes of the inverted parabolas. However, it is remarkable that the η iss parabola has nearly the same curvature since it is determined solely by the widths of the DS ACF -which are (inversely) related to the widths near the origin of the SS -where there is little diffuse power.
Considering Figure 10(b), the power distribution is much more diffuse. Again, the η p parabola is determined by the outlying features of the SS, although the precision of its curvature will be hampered by the blurriness of these features. However, the η iss parabola, which is just determined by the central region of the DS ACF, matches the η p curvature well. Note the wide valley near the τ axis, indicative of anisotropic scattering in a thin screen. This high-velocity pulsar exhibits several intriguing scintillation phenomena that are under current investigation. 7 Finally, in Figure 10(c) (see also Figure 2) we have almost the opposite situation as in panel (a): it is clear how the DS ACF will yield a good measurement of η iss since there is power centered on the origin in the SS, but it is surprising that a (weighted by |f D |) parabolic summing of power along the SS plane results in such close agreement with the ACF-determined η iss value.

Scintillation Arcs Tend to Disappear at Low Frequency: Is This a Problem?
The multi-frequency aspect of this survey is a key asset, particularly when observations were made within a few days of each other as were the Green Bank 340 MHz and 825 MHz observations and observations of the three Arecibo pulsars with multi-frequency data. Consider a direct comparison of the SS for pulsar B2021+51 at 340 MHz and 825 MHz as shown in the left two panels of Figure 11. The pq arc does not coincide with the boundary arc. However, this could simply be due to a mis-estimation of the ∆ν iss and ∆t iss parameters, a more exaggerated form of the case shown in Figure 10(a). The more important difference between panels (a) and (b) is the absence of a boundary arc at the lower frequency. Is this surprising? Displaying the SS using normalized coordinates should remove the issues with scaling of axes that were discussed in §5.6. If the underlying assumptions hold, the low frequency SS should appear similar to that of the high frequency one in this normalized display.
The main additional assumptions are (reordered to match the list order): an inhomogeneity spectrum in the screen that supports fluctuations at a small enough spatial scale to provide the high angle scattering needed to produce the arc; thin screen scattering with a screen that does not truncate the beam at lower frequency (Cordes & Lazio 2001;Geyer et al. 2017); and adequate S/N ratio to detect a scintillation arc.
Here we explore these possibilities: 1. truncated screen: that the scattered beam has become so large that it extends beyond the physical extent of the scattering material 2. inner scale: that there are no plasma fluctuations present at the small physical size needed to produce the halo power 3. S/N inadequate: that the observation at 340 MHz has insufficient sensitivity to reveal the low level scintillation arcs at high delay Considering the first possibility, we use the information in Tables 1 and 3 to find that the screen must deflect a maximal ray at 340 MHz by about 2 mas. The coherence scale s 0 in the screen necessary to do so can be found from s 0 = λ/(2πθ scatt ) (e.g. Equation 2.4 in Rickett 1990) and is s 0 ≈ 1.5 × 10 4 km. This is substantially larger than values of the inner scale of turbulence, which are in the range ∼ 200 − 2000 km (Spangler & Gwinn 1990;Molnar et al. 1995;Bhat et al. 2004;Rickett et al. 2009). Hence, it is unlikely that the absence of a scintillation arc at 340 MHz is caused by a deficit of irregularities at the coherence scale.
Possibility 2 proceeds similarly. The width of the 340 MHz beam as it passes through the screen is ≈ 2 au, a typical value for pulsars in this survey. In order for this to explain the absence of a scintillation arc at 340 MHz there would need to be a gap of this size in the medium producing the scattering. The material that produces the scintillation arc observed five days later at 825 MHz would need to comprise a small areal fraction of the ∼ 35 times larger low-frequency beam and hence be diluted in its ability to produce a scintillation arc. While not impossible, this seems unlikely.
Finally, we consider the option that the S/N of the 340 MHz observation is insufficient to allow detection of a scintillation arc. As is evident from inspection of the figures and Table 3, the S/N at 340 MHz is substantially lower than for the 825 MHz observation. When we approximately match the S/N of the two observations by adding white Gaussian noise to the 825 MHz data, we obtain the result in Figure 11(c). Although there is a hint of a scintillation arc visible, slightly more additive noise would suppress the arc at 825 MHz entirely. Hence, we consider this to be the most likely explanation: the observation was simply not sensitive enough to detect the presence of the arc visible in the 825 MHz data.

DISCUSSION
We draw a number of conclusions from the qualitative and quantitative analysis of the survey data in the preceding sections. We discuss those conclusions below.

Scintillation Arcs Are Prevalent
Satisfactory S/N was obtained in 54 observations of 22 pulsars (at 1-3 frequencies) whose DMs range from 5.7 to 84 pc cm −3 . Estimates of characteristic widths in frequency ∆ν iss and time ∆t iss were obtained from the ACFs of DS. In all cases a curvature estimate was made by summing SS along forward parabolas, weighting ∝ |f D |. In more than half the observations the summation exhibits a credible peak from which a curvature η p was estimated and a relative width parameter ∆η is defined. These estimates are classified by a subjective credibility index (η cred : 0, 1, 2: a compact maximum in the curve is rated 2; wide and double peaked curves are rated 1; cases where the peak is at the high or low limit in the search range or the secondary spectrum extends to the Nyquist delay are rated 0). Of the 54 observations, 13 ranked as 2, 21 ranked as 1, and 20 ranked as 0. Thus we have evidence for forward arcs in 34 of 54 observations. In observing 22 pulsars, 19 exhibited an arc ranked η cred ≥ 1 at one frequency or more.

Scintillation Arcs Are More Prominent at Higher Radio Frequencies
As discussed in §5.6, the much stronger scaling of the SS delay axis with frequency compared to the scaling of the Doppler axis results in the suppression of scintillation arcs at a radio frequency that depends upon the degree of scattering along the LoS.

Scintillation Arcs Are Narrower in Low DM Pulsars
Figure 7 demonstrates that narrow well-defined arcs are common at low DM, but become rare at higher DM. It is well-established that a sharp scintillation arc can only be produced if the dominant scattering occurs in a relatively small fraction of the LoS, what is commonly referred to as a thin screen, although the transverse extent of the scattering region and its physical characteristics are left unspecified, e.g. Walker et al. (2004); Cordes et al. (2006). Many of the narrower arcs at low DM are consistent with scattering from a localized plasma screen whose distance from the pulsar is no more than s max D psr .
The trend toward narrow arcs at low DM follows naturally from a model for the ISM in which a pervasive but relatively low-scattering plasma is combined with isolated regions or clouds of enhanced electron density n e , enhanced electron density variance n 2 e , or both. Such a trend is to be expected if the scattering is distributed along the LoS from each pulsar. This decrease in arc definition with path length could be due to either multiple thin regions along the path or to a more general extended distribution in the scattering plasma.

Narrow Arcs Do Not Imply Anisotropy
Narrow arcs do not, by themselves, imply an anisotropic plasma, but they are consistent with a power-law spatial spectrum. The rich detail revealed in the reverse arclets reported for B0834+06 implies highly anisotropic plasma structures in the local ISM Brisken et al. 2010). The main forward arc with a deep valley along the delay axis in B1133+16 is also evidence for highly anisotropic local scattering (Stinebring et al. 2019). However a result of our analysis is the recognition that boundary arcs do not necessarily imply anisotropic scattering (see also Reardon et al. 2020). Under the conditions of strong scintillation that apply to our observations, relatively narrow Negative (neg) asymmetry means stronger power for positive delay on the negative side of the fD axis; conversely for positive (pos) asymmetry. b Approximate physical size (au) on the screen with these assumptions: s = 0.5, fD= 10 mHz, ν0 = 1 GHz, velocity dominated by the pulsar. Scalings: l10mHz ∝ sfD/(V ν) boundary arcs can be caused by isotropic scattering when the underlying plasma density fluctuations follow some types of power law versus wavenumber. While we have shown examples from screens that follow the Kolmogorov turbulence spectrum, other power law spectra can also cause forward arcs. As analyzed earlier by Cordes et al. (2006), forward arcs can be expected from spectra with a range of power law exponents; the simplest way to characterize them is via the structure function for phase perturbations that they impose on a propagating radio wave. Cordes et al. (2006) show examples with phase structure functions that follow a power law versus spatial lag having exponents α ≤ 2, where the corresponding exponent in a 3-dimensional wavenumber spectrum is α + 2. The key point is that no extended arcs are seen unless α < 2. Media consisting of Gaussian-profiled density concentrations causing interstellar lenses are likely modeled by α = 2, and so probably do not manifest parabolic arcs. Thus the defining property of the plasma density structures that cause arcs is the form of their high wavenumber spectrum rather than any anisotropy. Kolmogorov turbulence provides one possible physical origin for such fine scales in the plasma.

Reverse Arclets and Power Asymmetries Indicate a Patchy Scattering Medium
Reverse arclets are seen in the SAS in the following pulsars (see §4 for more details): B0450-18, B0525+21, B1540-06 and B2327-20, whose distances range from 0.4 to 1.2 kpc. In addition, B1508+55 (D = 2.10 kpc) shows discrete arclets, which appear to be flat (i.e. low curvature). Overall the presence of arclets, and the relative frequency independence of their inferred angular locations , implies highly localized centers of scattering (or refraction) across the transverse dimension and an anisotropic image on the sky (Walker et al. 2004;Cordes et al. 2006;Pen & Levin 2014;Reardon et al. 2020).
Power asymmetries in the SS along the scintillation arc and, in particular, between negative and positive f D values, have been noted since early in the study of the phenomenon (Cordes et al. 2006). In addition, discrete patches of power can be present, generally associated with reverse arclets. In a few cases it has been possible to track their motion from negative to positive f D values along the arc Wang et al. 2018). We see evidence of both phenomena in the survey data. The occurrence of power asymmetry and discrete structure in scintillation arcs for the 22 pulsars in the survey is summarized in Table 5.
Two explanations have been advanced for power asymmetry along the arc: 1) the presence of a refractive gradient across the image (Cordes et al. 2006;Coles et al. 2010;Reardon et al. 2020) and 2) spatial variation of the properties of the scattering screen transverse to the LoS (e.g. Hill et al. 2005). These mechanisms are not mutually exclusive since a patchy medium, by which we mean variations in the scattering strength transverse to the LoS, will necessarily have substantial n e gradients.
In Table 3 the asymmetry index κ quantifies the power along the LHS (negative f D ; κ < 0) of the arc compared to along the RHS. In Figure 12 we note a slight tendency toward more instances of negative κ values (33 vs. 21 positive), and the four largest values of |κ| are all negative. However, the sample is small, and this is likely a statistical fluctuation. (The f D < 0 side of the SS is the material that is out in front of the projected path of the pulsar across the sky ).) Figure 12. Histogram of arc power asymmetry index defined as κ ≡ (R -L)/(R + L), where R is the arc power for f D > 0 and L is the arc power for f D < 0. Negative values of κ represent scattering material out in front of the projected path of the pulsar across the sky.
Kolmogorov density variations do not, in general, lead to substantial refractive shifts of the image. In particular, it is rare to find refractive shifts as large as the width of the scattering disk size. There is no way to adjust this fact for a Kolmogorov medium because it arises from the relative shallowness of the inhomogeneity power law. During the 1980's this was a subject of substantial theoretical attention with a leading idea being inhomogeneity power laws with an index β > 4, where this index in the inhomogeneity power law has a value of β = 3.67 for a Kolmogorov medium (Blandford & Narayan 1985;Goodman & Narayan 1985;Romani et al. 1986;Goodman et al. 1987). As an alternative to explanations associated with power law density variations, the idea of discrete lenses was introduced (Clegg et al. 1998). More recently, highly inclined corrugated sheets viewed at nearly grazing incidence (Pen & King 2012;Pen & Levin 2014) and noodle-like models (Gwinn 2019; Gwinn & Sosenko 2019) have been proposed.
As can be seen in Table 5, just under half of the pulsars in the survey show evidence for power asymmetry or discrete structures in the SS or both. The last column in this table presents an approximate size scale, l 10mHz , probed by the scintillation arc observations. Note that in the SS it is the separation of features in two coordinates, Doppler and delay, that allows discrete patches of power to be identified. On the other hand, the occurrence of tilted scintles in the DS was noticed soon after the development of systematic scintillation observations (Hewish 1980 and references therein).
The evidence for thin screen regions of scattering implies localization along the LoS direction. Together with the power asymmetries and reverse arclet structure in the SAS, these paint a picture of a very patchy distribution in the plasma responsible for the ISS within the ∼ 3 kpc region sampled.

The Galactic Distribution of Plasma Scattering
The study by Alves et al. (2020) revealed a coherent sheet-like structure that they refer to as the Radcliffe Wave, a 2.7-kpc-long filament of gas corresponding to the densest part of the Local Arm of the Milky Way. In addition, the understanding of the Local Bubble has improved markedly with the recent publication by Zucker et al. (2022). There, using new spatial and dynamical constraints including recent Gaia data and carefully curated velocity information, they produce a three-dimensional map of dense gas and young stars within 200 pc of the Sun. They find evidence for stars preferentially concentrated near the edge of the Bubble at about 100 pc from the Sun. The boundaries are seen to be star-forming regions and are partially ionized by UV radiation from nearby stars. The structure and distribution of truly local interstellar clouds is also relevant. Linsky et al. (2019) and Linsky & Redfield (2021) find partially ionized clouds on the scale of parsecs.
Our survey for scintillation arcs provides evidence for occasional localized plasma concentrations within about 1 kpc (sec 6.1 & 6.3). The observations are consistent with the earlier more detailed observations of multiple discrete arcs in some nearby pulsars (e.g. Putney & Stinebring 2006; see also Reardon et al. 2020). The reverse arclet phenomenon gives further evidence for discrete plasma concentrations down to au scales. However, the physical origin of the clumps remains a mystery.
The evidence for the isolated concentrations of scattering plasma has to be reconciled with the strong evidence that the interstellar scatter broadening time for pulsars increases steeply with DM , and so with pulsar distance. There is an absence of narrow arcs from pulsars beyond a few kpc in our survey, which is consistent with cumulative scattering along the LoS from many such concentrations at a wide range of distances (and so with differing arc curvature). At present we lack a proper theory for the SS that would be observed through multiple plasma screens. While the SS from nearby pulsars can be understood by the superposition of arcs singly scattered by each screen, the SS due to successive scattering by multiple plasma screens have not been studied beyond the two screen analysis of Simard et al. (2019a).
Pulsar dispersion and scattering studies over more than 40 years have resulted in a fairly consistent picture of the ionized gas within ∼ 5 kpc of the Sun (Taylor & Cordes 1993, Cordes & Lazio 2002, Yao et al. 2017). Overall, the geometry consists of relatively sparse regions of enhanced plasma scattering on scales smaller than 1 kpc that are increasingly concentrated toward the Galactic plane and toward the center of the Galaxy. The models typically assume that the plasma density is "turbulent," following a power-law spectrum versus wavenumber over the micro-scales responsible for the ISS, but the strength of the turbulence varies widely over the much larger Galactic scales. Thus the turbulence level varies on scales ranging from parsecs to au and indeed down to the diffractive scale at 10 6 − 10 8 m. In NE2001 some such concentrations are identified as known HII regions, but other clumps of denser scattering are added to model specific pulsars that exhibit extra scatter broadening. (See Mall et al. 2022 for an in-depth study of one such region associated with the pulsar J1643-1224 seen behind the HII region  In order to model the arclet phenomenon and the multiple forward arcs in pulsar B1133+16 (see McKee et al. 2022 andPutney &, for example), many more clumps are implied. A smaller scale is needed such that the mean free path for a pulsar sightline to intersect a clump is on the order of 100-500 pc. Ocker et al. (2021) have proposed turbulence at stellar bow-shocks as the possible location of enhanced scattering. Scattering could even be caused in the plasma-spheres that surround hot stars, while Walker et al. (2017) proposed elongated plasma structures drawn out in the stellar winds from hot stars. Motivated by evidence of extreme 1D scattering images for some pulsars, Pen & Levin (2014) proposed weak waves propagating along magnetic domain boundary current sheets as the origin of scintillation arcs.
The foregoing discussion suggests the big-picture hypothesis that the arc-causing clumps are so widely distributed that they are the building blocks for all of interstellar scattering. We suggest that the ISM contains multiple bubbles creating a foam-like structure with compressed regions of gas (neutral and plasma) at their interfaces, some of which cause observable arcs. The 50 -100 pc distance is comparable to the distance between the arc-causing clumps in the LoS to B1133+16 for which McKee et al. (2022) identified six discrete arc-causing screens along the 360 pc LoS. If this path is typical of much longer paths through the Galaxy, it would explain the rarity of narrow arcs at higher DM , since it would be unlikely that a single arc would dominate the SS for pulsars beyond a kiloparsec or so. Thus it