#  Associations Between Scattering Screens and Interstellar Medium Filaments

Ashley M. Stock David A. Dunlap Department of Astronomy & Astrophysics,
University of Toronto, 50 Saint George St., Toronto, ON M5S 3H4, Canada
Canadian Institute for Theoretical Astrophysics, University of Toronto, 60
Saint George Street, Toronto, ON M5S 3H8, Canada  Marten H. van Kerkwijk David
A. Dunlap Department of Astronomy & Astrophysics, University of Toronto, 50
Saint George St., Toronto, ON M5S 3H4, Canada

###### Abstract

Pulsar scintillation can be used to measure small scale structure in the
Galaxy, but little is known about the specific interstellar medium features
that cause scintillation. We searched for interstellar medium counterparts to
all scintillation screens for which absolute distances and scattering
orientations have been measured – a sample of 12 pulsars and 22 screens. For
one pulsar, PSR J0737-3039A, we re-analyze its scintillation screen and find
evidence for a highly anisotropic screen. Among the screens, we found that
eight are located inside of the Local Bubble, and a further six are less than
100 pc farther than its inner edge. Comparisons with tracers of ionized and
magnetized media did not find any new associations. Instead, for seven of the
pulsars analyzed, aligned H I filaments are seen for at least one of their
screens, for a total of 12 out of 22 screens. This result seems unlikely to be
due to chance: comparing with random trials, we estimate a likelihood of
finding 12 or more screens with aligned emission by chance of only 0.004%.
Estimating the significance of the amount of aligned emission (in standard
deviations over the mean), the probability of finding as much observed aligned
emission by chance is larger, at 1.7%, but still indicative of a real
correlation. Since H I filaments are preferentially associated with cold
neutral gas, and thus unlikely to cause scintillation, this may indicate both
the filaments and the screens are aligned preferentially by the same
mechanisms such as magnetic fields or shocks.

Interstellar scintillation (855) — Pulsars (1306) — Interstellar medium (847)

††software: Astropy (Astropy Collaboration et al., 2013; Price-Whelan et al.,
2018; Astropy Collaboration et al., 2022), MatPlotLib (Hunter, 2007), NumPy
(Harris et al., 2020), SciPy (Virtanen et al., 2020), pint (Luo et al., 2019,
2021), Rolling Hough Transform (Clark et al., 2014)

##  1 Introduction

The interstellar medium (ISM) contains a rich assortment of structures such as
clouds, filaments, shells, and bubbles. The structures’ size distribution in
the ISM has long been known to follow a power law, the “Big Power Law in the
Sky”. (e.g. Armstrong & Rickett, 1981; Armstrong et al., 1995; Chepurnov &
Lazarian, 2010). At large scales, from $10^{16}$ to $10^{18}{\rm\;m}$,
structures are observed directly, and the power law has been observed across
multiple phases of the ISM, with the emission of cold, neutral hydrogen (e.g.
Lazarian & Pogosyan, 2000) as well as warm, ionized hydrogen (e.g. Chepurnov &
Lazarian, 2010). Below $10^{14}{\rm\,m}$ the distributions are not observed
directly, but rather inferred from the scattering of compact radio sources,
such as pulsars and the cores of active galactic nuclei. From those indirect
measurements, the distribution has been suggested to extend all the way down
to $10^{6}{\rm\;m}$ (Armstrong & Rickett, 1981).

Compact radio sources are powerful probes of the ISM because they emit
spatially coherent light. As the light propagates through the inhomogeneous
ISM, it is scattered along many paths that interfere with each other, causing
the intensity and phase of the light to vary with frequency and time as the
source, observer, and scattering material move relative to each other. These
variations, collectively known as scintillation, thus encode information about
material along the line of sight to the source.

Scintillation is typically observed through the dynamic spectrum, which shows
mean intensity as a function of frequency and time. Bright regions, called
“scintles”, have typical frequency widths of several kHz to MHz and durations
on the order of minutes for pulsars and weeks for active galactic nuclei
(AGN), when observed at GHz frequencies. The characteristic widths are
quantified as the “decorrelation bandwidth” and “scintillation timescale”,
respectively (e.g., Cordes et al., 1985). Occasionally, “extreme scattering
events” are seen (e.g. Fiedler et al., 1987), large changes in intensity that
last much longer than the scintillation timescale and cover a much wider
frequency range than the decorrelation bandwidth (indeed, they often are
accompanied by changes in the scintillation timescale and decorrelation
bandwidth).

Although scintillation gives information about the electron density and size
distribution of the scattering medium, the nature of structures probed by
scintillation remains poorly understood. Scintillation must occur in partially
ionized gas, requiring electron densities likely higher than those in the
molecular (too cold) and hot ionized (too tenuous) phases of the ISM, i.e.,
most likely in the warm neutral or warm ionized phases.

Clear parabolic structures in “secondary spectra”, the power spectra of
dynamic spectra, and, more directly, interferometric observations suggest the
scattering is dominated by small numbers of localized, elongated structures
(e.g., Rickett et al., 2009; Brisken et al., 2010). These structures are
typically referred to as “screens”, which may take the form of sheets or
filaments. Sheet-like structures are particularly attractive, since if they
are aligned nearly parallel to the line of sight, they appear filamentary and
also solve the over-pressure problem, i.e. that the scintillation and extreme
scattering events require bending angles of order 10s of mas, which implies
column density gradients of order $1000{\rm\;cm^{-2}\,cm^{-1}}$, and thus, for
spherically symmetric structures, electron densities well higher than any
expected in the ISM. In contrast, for a sheet sufficiently aligned with to the
line of sight, typical ISM electron densities of $\sim\\!1{\rm\;cm^{-3}}$
would suffice to cause the same bending angles (Pen & Levin, 2014).

Under the assumption of thin, elongated screens, it is possible to model the
distances, orientations of elongation, and velocities of screens. These
properties can then be compared with properties of the ISM to potentially
establish connections. Surveys of ISM tracers lack the resolution needed to
observe directly structures on the scales that cause scintillation, but if the
scattering screen is part of a larger scale structure, associations might
still be found.

Early attempts to make associations used only sky positions and scattering
strengths of the screens. For instance, extreme scattering events of quasars
seem to be preferentially located near Galactic synchrotron filaments (loops)
and near the edges of shell-like H I structures within those filaments
(Fiedler et al., 1994). Scattering also appears enhanced for pulsars in the
direction of Galactic Loop I, possibly due to interaction between Loop I and
the Local Bubble (Bhat & Gupta, 2002).

Using both sky positions and velocities of screens, Walker et al. (2017) found
evidence that some screens were associated with hot stars. Specifically, they
found that two variable sources, PKS 1322$-$110 and J1819$+$3845, had sight
lines that passed within 2 pc of hot stars and for which the inferred
velocities of the screens matched those of the stars. Walker et al. (2017)
suggested that small, over-dense neutral clouds with tails ionized by hot
stars might be responsible for the scintillation.

For a few pulsars, more direct associations between screens and specific ISM
features have been made. The Crab pulsar, Vela pulsar, and PSR J0538$+$2817
are clearly scattered by their associated supernova remnants (Cordes et al.,
2004; Sushch et al., 2011; Yao et al., 2021). One of the scattering screens
towards PSR J1643$-$1224 is likely associated with an H II region, Sh 2$-$27
(Mall et al., 2022; Ding et al., 2023), while three of the scattering screens
of PSR B1133$+$16 (McKee et al., 2022) and one of the scattering screens of
B0656+14 (Yao et al., 2022) appear associated with the edge of the Local
Bubble.

A previously unexplored avenue for understanding the physical nature of
screens is their orientation. Measuring the orientation of screens generally
requires interferometric techniques (e.g. Brisken et al., 2010), or
observations over several months or years to fit for the annual and/or orbital
variation in scattering properties (e.g. Rickett et al., 2014; Reardon et al.,
2019; McKee et al., 2022). As a result, this has been done for very few
pulsars so far. Yet, this measurement is needed to constrain the inclination
of binary pulsars and could potentially be used to reduce errors in
measurements of parallax by correcting for the positional shifts induced by
the scattering.

In this paper, we use distances and orientations to investigate connections
between scintillation screens and structures in the ISM, by correlating screen
orientations with morphological features in tracers of different ISM
environments. In Section 2, we outline the screens and ISM tracers used for
comparison, and describe how we test for alignment. We discuss the screens for
each pulsar in detail in Section 3, and consider the results from all screens
in Section 4.

##  2 Data and Analysis

###  2.1 Scattering Screens

We collected information on scattering screens from the literature, limiting
ourselves to those with measurements of both distance and orientation of
anisotropy. For all sources, we verified carefully how orientation is defined,
and for PSR J0737$-$3039A we made new fits to existing scintillation
measurements (see Appendix for details). The results are summarized in Table
1. Further information can be found on-line in what we hope will become a live
database111https://github.com/scintillometry/screen-database, to which further
screen distances and orientations will be added, such as those expected from
the ongoing scintillation survey with with the Thousand Pulsar Array (Main et
al., 2023).

####  2.1.1 Screen Orientations

The screen orientations in Table 1 are given East of North, and are measured
along the long axis of the distribution of scattered images on the sky. This
filament orientation equals that inferred from direct imaging and tracing
annual arc curvature measurements; it corresponds to the direction of steepest
change in density and phase. The orientation is perpendicular to what is
inferred from scintillation timescales, which measure the direction associated
with the longest scintillation timescale and thus that of least change in
density and phase.

For an elongated set of scattering points, there is necessarily a
$180^{\circ}$ ambiguity in the orientation angle. We have chosen a convention
in which the angle is between 0 and $180^{\circ}$ so that the angle is towards
the Eastern side of the long axis of the scattering points, adjusting the sign
of the screen velocity appropriately if the original measurement from the
literature followed a different convention (i.e., we ensured the screen
velocity is positive if it has a positive component in right ascension).

####  2.1.2 Screen Kinematics

For most of the pulsars, information on the velocity of the screen is
available. We only use the component of the velocity parallel to the
structure’s scattering points (see Table 1), since for elongated distributions
of scattering points, there is little change in scintillation as one moves
perpendicular to them, and hence any velocity in that direction is highly
uncertain. Indeed, in some models for scintillation, such as those that
require highly aligned sheets (Pen & Levin, 2014), apparent variations
perpendicular to the long axis of the scattering points are almost certainly
due to different sheets at different distances.

For comparison with the measured velocities, we calculate the expected
velocity for a structure following bulk Galactic rotation relative to the
Local Standard of Rest, listing in Table 1 both the component parallel to the
screen scattering points and the radial velocity – the latter for comparison
with frequency-resolved ISM tracers. We calculate the expected value for the
proper motion and kinematic Local Standard of Rest velocity for a screen as:

$\displaystyle v_{\ell}=$ $\displaystyle
d_{s}[B+A\cos(2\ell)-C\sin(2\ell)]\cos(b)$
$\displaystyle+U_{0}\sin(\ell)-V_{0}\cos(\ell),$ (1) $\displaystyle v_{b}=$
$\displaystyle-d_{s}[K+A\sin(2\ell)+C\cos(2\ell)]\sin(b)\cos(b)$
$\displaystyle+[U_{0}\cos(\ell)+V_{0}\sin(\ell)]\sin(b)-W_{0}\cos(b),$ (2)
$\displaystyle v_{\mathrm{LSRK}}=$ $\displaystyle
d_{s}[K+A\sin(2\ell)+C\cos(2\ell)]\cos(b),$ (3)

where $d_{s}$ is the distance to the screen from the Earth, and ($\ell,b$) are
its Galactic longitude and latitude. We used the Oort constants from Bovy
(2017),

$\left(\begin{matrix}A\\\ B\\\ C\\\
K\end{matrix}\right)=\left(\begin{matrix}15.3\pm 0.4\\\ -11.9\pm 0.4\\\
-3.2\pm 0.4\\\ -3.3\pm 0.6\end{matrix}\right){\rm km\,s^{-1}\,kpc^{-1}},$ (4)

and the velocity of the Sun relative to the Local Standard of Rest from
Schönrich et al. (2010),

$\left(\begin{matrix}U_{0}\\\ V_{0}\\\
W_{0}\end{matrix}\right)=\left(\begin{matrix}11.1^{+0.69}_{-0.75}\\\
12.24^{+0.47}_{-0.47}\\\ 7.25^{+0.37}_{-0.36}\end{matrix}\right){\rm
km\,s^{-1}}.$ (5)

Table 1:  Summary of associations between literature pulsar screens, Local
Bubble, and H I filaments

|  | Screen | Screen | Galactic | Screen | LB | Predicted H I |
---|---|---|---|---|---|---|---|---
Pulsar |  | Orientation | Velocity | Rotation | Distance | Distance | Radial Velocity |
Name | Screen | (∘) | (km/s) | (km/s) | (pc) | (pc) | (km/s) | Reference
J0337$+$1715 | a | $66.1_{-3.7}^{+3.7}$ | $4.25_{-0.42}^{+0.44}$ | $-10$ | $244_{-3.1}^{+5.1}$ | 139 | $-2.4$ | Gusinskaia et al. (in prep)
J0437$-$4715 | a | $134.6\pm 0.3$ | $-31.9\pm 0.3$ | $6.4$ | $89.8\pm 0.4$ | 287 | 0.5 | Reardon et al. (2020)
| b | $144\pm 6$ | $-50\pm 6$ | $-6.1$ | $124\pm 3$ |  | 0.7 |
J0613$-$0200 | 2014+ | $16\pm 2$ | $-1.2\pm 2.5$ | $-5.9$ | $300\pm 50$ | 251 | 2.5 | Main et al. (2020)
| 2013 | $144\pm 9$ | $-12.8\pm 2.8$ | $3.3$ | $330\pm 100$ |  | 2.3 |
J0636$+$5128 | a | 96.98${}^{+3.16}_{-3.63}$ | $-2.01^{+0.97}_{-1.15}$ | $-20.3$ | 262${}^{+98}_{-38}$ | 200 | $-3.5$ | Liu et al. (2023)
J0737$-$3039A | a | $88.6\pm 4.3$ | $-25.6\pm 1.5$ | 3.3 | $260\pm 51$ | 236 | 2.3 | This Work
B0834$+$06 | a | $155\pm 1$ | $-23\pm 1$ | $-12.9$ | $389\pm 5$ | 265 | 3.9 | Zhu et al. (2022)
| b | $136\pm 1$ | $-3.0\pm 3$ | $-12.1$ | $415\pm 11$ |  | 4.2 |
B1133$+$16 | b | 154${}^{+55}_{-37}$ | $101^{+98}_{-169}$ | 4.4 | $186^{+82}_{-87}$ | 243 | 0.7 | McKee et al. (2022)
| c | 120${}^{+24}_{-23}$ | $78^{+88}_{-47}$ | 0.1 | $134^{+27}_{-31}$ |  | 0.5 |
| d | 128${}^{+51}_{-39}$ | $-399^{+230}_{-135}$ | 8.4 | $197^{+67}_{-59}$ |  | 0.8 |
| e | 135${}^{+50}_{-38}$ | $-74^{+173}_{-142}$ | 5.5 | $186^{+69}_{-73}$ |  | 0.7 |
| f | 11.3${}^{+2.4}_{-2.3}$ | $-5.28^{+0.37}_{-0.42}$ | $-6.1$ | $5.47^{+0.54}_{-0.59}$ |  | 0.0 |
J1141$-$6545 | a | $28.0\pm 0.4$ |  $\cdots$ | 91.4 | $7200^{+300}_{-220}$ | 159 | $-96.1$ | Reardon et al. (2019)
B1508$+$55aaScreen a of this pulsar transitioned from weak to strong scattering which was modelled as a change in the screen orientation with other values fixed. Unlike other measurements, the screen velocity for screen a is given as the total magnitude of the screen transverse velocity rather than the projection of the velocity in the direction of the screen orientation. The direction of the screen velocity is $101\pm 17^{\circ}$ so the Galactic rotation is given as the projection along this direction. For full details see Sprenger et al. (2022). | a (weak) | $39.8\pm 2.0$ | $7.3\pm 1.4$ | 3.9 | $127.1\pm 1.5$ | 203 | $-0.1$ | Sprenger et al. (2022)
| a (strong) | $52.4\pm 0.4$ |  |  |  |  |  |
| b | $129.8\pm 2.0$ | $2\pm 55$ | 10.5 | $1940\pm 123$ |  | $-1.0$ |
J1603$-$7202 | a | $140\pm 13$ | $-5^{+15}_{-18}$ | $-54.3$ | $2500\pm 700$ | 189 | $-44.9$ | Walker et al. (2022)
J1643$-$1224 | a | $150\pm 4$ | $-10\pm 1$ | 9.1 |  $129\pm 15$ bbAssociated with H II region, Sh 2-27, which is embedded in the shell of the Local Bubble | 91 | $-0.4$ | Mall et al. (2022)
| b | $31\pm 9$ | $-6\pm 3$ | $-3.2$ | $340\pm 9$ |  | $-1.1$ |
J1909$-$3744 | a | $85\pm 6$ | $14\pm 10$ | 14.3 | $590\pm 50$ | 195 | $-3.7$ | Askew et al. (2023)

Note. — Screen Orientation gives the direction of the long axis of the
distribution of scattering images, which equals the direction of greatest
change in electron density of the scintillation screen (and thus perpendicular
to possible associated extended physical structures); Screen Velocity is
measured parallel to the direction of Screen Orientation unless otherwise
indicated and is relative to the Solar System barycentre; Galactic Rotation is
the expected transverse motion of gas relative to the Solar System barycentre
in the direction of the Screen Velocity; LB Distance is distance from Earth to
inner edge of Local Bubble wall from Pelgrims et al. (2020); Predicted H I
Radial Velocity is the expected radial Local Standard of Rest velocity from
Galactic rotation at the position of the screen. Screen distances are shown in
blue if the screen is within the inner edge of the Local Bubble and red if
outside of the inner edge of the Local Bubble by less than 100 pc.

###  2.2 ISM Tracers

Several ISM tracers were used to find structures with similar distance and/or
orientation as the scattering screen.

H$\alpha$ emission is a tracer of dense, warm ISM and H II regions, and might
be expected to be correlated with higher electron densities. We used the
composite all-sky map of Finkbeiner (2003) to identify structures. This map is
composed of images from the Wisconsin H$\alpha$ Mapper Sky Survey (WHAM-SS
Haffner et al., 2003), the Virginia Tech Spectral-Line Survey (VTSS, Dennison
et al., 1998), and the Southern H-alpha Sky Survey Atlas (SHASSA, Gaustad et
al., 2001). Since many of our sources are at high Galactic latitudes, however,
the H$\alpha$ emission was often low or the surveys were incomplete. We found
noticeable ISM structures only near PSR J0737$-$3039A and PSR J1643$-$1224.

Polarized emission can be used to trace ionized and magnetized ISM, which can
emit polarized light or depolarize background polarized sources. We used the
S-band Parkes All Sky Survey (S-PASS, Carretti et al., 2010) to search for ISM
structures, but found that the features that could be seen were too diffuse or
in regions of too low spatial resolution to provide meaningful comparisions
with the screen orientations.

The cold and warm neutral medium are traced by H I and dust. Electron
densities are (very) low, but correlation with scintillation screens might
still occur if there are changes in electron density at boundaries with
warmer, more highly ionized gas, or more generally if cold and warm gas are
co-aligned, e.g., due to a magnetic field. For investigating H I emission, we
used the Galactic All-Sky Survey (GASS, McClure-Griffiths et al., 2009;
Kalberla et al., 2010; Kalberla & Haud, 2015), Effelsberg-Bonn H I Survey
(EBHIS, Winkel et al., 2016), and Galactic Arecibo L-Band Feed Array H I
survey (GALFA-HI, Peek et al., 2011, 2018). In these surveys, sheet-like or
filamentary structures are commonly seen, and we can compare these with screen
orientations.

For dust emission, we used the 12, 25, and 60${\rm\,\mu m}$ IRIS all-sky maps
(Miville-Deschênes & Lagache, 2005). These maps showed similar morphology to
the H I emission but are not resolved by velocity, so filaments appear more
smoothed out. The similarity in morphology suggests that the filaments we
observe in H I represent real density structures, as demonstrated by Clark et
al. (2019), rather than features of the turbulent velocity field, as suggested
by, e.g., Lazarian & Yuen (2018).

Dust emission maps also include polarized intensity information, which
correlates with the orientation of the Galactic magnetic field integrated
along the line of sight. We explored this a little, but did not find any
correlation. Similarly, we considered the Gaia-2MASS 3D dust maps (Lallement
et al., 2019) as a way to compare with distances of screens, but our results
were inconclusive. For completeness, we note that we also looked at CO maps
(Dame et al., 2001), but found that those had too low a spatial resolution to
identify filaments, and also covered only the Galactic plane and thus are
available for only a few of our pulsars.

###  2.3 Filament Analysis

In our initial visual inspection, we noticed filamentary structure in H I that
appeared aligned with the expected direction of lowest density gradient (i.e.,
perpendicular to the scattering point orientation) for PSR J0737$-$3039A, and
hence our analysis focuses on H I filaments. However, we also looked for
H$\alpha$ filamentary structure for the two sources for which significant
emission was seen, PSR J0737$-$3039A and PSR J1643$-$1224.

To identify filamentary structures and measure their orientation, we use the
Rolling Hough Transform (RHT), developed by Clark et al. (2014). For each
pixel in an image, the RHT counts the number of pixels within a window with
diameter $D_{w}$ that are correlated with each other along given orientations.
The “RHT Spectrum” at that pixel position is then the fraction of correlated
pixels along an orientation in the window, with only those over a threshold
$Z$ recorded. The threshold and window size, combined with the pixel scale
$\Delta x$ of a given survey, set a minimum filament size that can be
identified, $ZD_{w}\Delta x$; we list relevant numbers for the different
surveys in Table 2. For each of our pulsars, we look for filaments in the RHT
spectrum at the sky position of the pulsar, and for the direction
perpendicular to that of the scattering points.

Figure 1:  H I filaments near PSR J0737$-$3039A. The velocity channels around
$14{\rm\;km/s}$ show a filament well aligned with the orientation of the
pulsar’s scattering screen. Left column, top: H I brightness temperature
integrated over velocites between $-11.5$ and $14.8{\rm\;km/s}$ relative to
the kinematic local standard of rest. The location of the pulsar is marked
with a red dot, and the window for the Rolling Hough Transform analysis with a
red open circle. Left column, middle: Rolling Hough Transform spectra at the
position of the pulsar for a range of velocity channels, using colours from
the panel below. The orientation of the pulsar’s scattering screen is marked
with a grey shaded region. Left column, bottom: H I line profile towards the
pulsar, with a colour bar overlaid to show the velocity channels used above.
Middle column: H I brightness temperature for different velocity channels (as
labelled). The region covered is indicated by the inset box in the top left
panel. Right column: Corresponding Rolling Hough Transform backprojections.
The complete figure set (10 images) is available in the online journal. Table
2:  Rolling Hough Transform Parameters and Survey Resolutions

| GASS | EBHIS | GALFA-HI
---|---|---|---
$\theta_{\mathrm{FWHM}}$ (arcmin) | 16 | 10 | 4
$\Delta v_{\mathrm{LSRK}}$ (km/s) | 0.824 | 1.288 | 0.184aaFor the Rolling Hough Transform analysis, the data were rebinned to 1.288 km/s.
$\Delta x$ (arcmin/pix) | 5 | 3.26 | 1
RHT window $D_{w}$ (pix) | 45 | 45 | 60
Minimum filament size (deg) | 1.87 | 1.22 | 0.54

Note. — $\theta_{\mathrm{FWHM}}$ is the angular and $\Delta v_{\mathrm{LSRK}}$
the spectral resolution of the survey. A Rolling Hough Transform threshold
$Z=0.5$ was used to calculate the minimum filament size.

In Figure 1, we show the H I emission data and associated RHT spectra for each
pulsar. For each of the sources, we used the highest resolution H I survey
available. For three sources (PSR J0337+1715, PSR B0834+06, and PSR B1133+16),
data from both the GALFA-HI survey and EBHIS surveys were available. We found
that the two surveys agreed on alignments for these, although the higher
resolution made the GALFA-HI data superior, with more filaments identified and
narrower ranges of orientation angle.

The H I data is resolved into velocity channels that give some information
about the distance to the structures. The conversion between velocity and
distance is complicated by the complex velocity structure of the gas, but
still allows us to separate very distant emission from the mostly nearby
structures that we are interested in. Hence, we include a velocity constraint
in our requirements for alignment.

Note that because Galactic rotation does not change quickly with distance,
each H I velocity channel includes information from several hundreds of
parsecs of gas, potentially with overlapping filaments of differing
orientations. In contrast, scintillation screens occur at specific locations
along the line of sight, so these are unlikely to correlate well with averaged
values of alignment (and indeed, we did not find evidence of correlation with
orientation from dust polarization). This complicates the definition of
alignment, especially for lines of sight with multiple screens.

###  2.4 Tests for Alignment

To determine where a screen is aligned with a filament, we need to define what
constitutes being aligned, as well as to estimate how likely it is that the
alignment is due to chance. We tried two methods, one where we set somewhat
ad-hoc specific requirements, and another where we attempt to turn these
constraints into a numerical score. For each method, we quantify the
statistical significance by simulating 2,000 random screens for each real
screen, with random orientation and positions randomly chosen in
$5^{\circ}\times 5^{\circ}$ squares of the sky centred on the corresponding
pulsar. A trial consists of one realization of a random screen for each real
screen.

Note that the two methods effectively test different questions, viz., whether
an aligned filament is present, or whether the amount of aligned emission is
significant. As we will see below, both methods suggest that the screens are
likely associated with filaments, but the estimated probabilities of it being
due by chance are quite different.

####  2.4.1 Method 1: Specific Requirements for Alignment

For our first method, we consider a filament aligned with a screen if:

  1. 1.

Its velocity is within $\sim\\!13{\rm\,km/s}$ of that expected from Galactic
rotation (19 velocity channels for EBHIS and GALFA-HI data, 33 velocity
channels for GASS data), i.e., offset by no more than roughly the speed of
sound (for all pulsars with multiple screens, this selects essentially the
same velocity range for all screens);

  2. 2.

The screen orientation is within $15^{\circ}$ and the error in the screen
orientation added in quadrature of a peak in the RHT spectrum (where
$15^{\circ}$ is a guess at the systematic uncertainties involved in estimating
the filament orientation);

  3. 3.

At least 70% of the pixels are aligned in one velocity channel; and

  4. 4.

At least 60% of pixels are aligned in each of four contiguous channels.

Note that the last two conditions are similar to setting thresholds on the
RHT, so this method is independent of choice of $Z$ as long as $Z\leq 0.6$.
The likelihood of a screen classification as aligned arising by chance was
then determined from the fraction of random screens in a similar region of the
sky that were classified as aligned. Similarly, the total likelihood of
finding by chance as many screens aligned as observed, was determined from the
number of trials where the number of aligned random screens were equal to or
greater than the number of aligned real screens.

While this method is fairly straightforward, it is somewhat ad-hoc and sets
hard cut-offs. Furthermore, it is biased towards finding alignment by
comparison with only the closest peak in the RHT spectrum (though this should
not affect probabilities, as the trials share this bias).

####  2.4.2 Method 2: Using an Alignment Score

To create a quantitative score for whether a screen is aligned, we use a
procedure inspired by the above method: we convolve the RHT spectrum with a
filter in both orientation and velocity, and look for peaks at the screen
orientation angle. In orientation angle, to account for both the screen
orientation measurement uncertainty $\delta\theta$ and our assumed systematic
uncertainty of $15^{\circ}$ in the orientation of the filament relative to
that of a screen, we filter using a Gaussian with a width
$\sigma=\sqrt{(15^{\circ})^{2}+(\delta\theta)^{2}}$. For the velocity
direction, to prioritize true filaments that extend over multiple velocity
channels, we filter using a top hat with a width of four channels for the
EBHIS and GALFA-HI data and six channels for the GASS data. For each real and
random screen, we then find the maximum value of the filtered RHT spectrum at
the observed screen orientation and calculate a score $X$ of how many standard
deviations above the mean of the filtered RHT spectrum the maximum is.

For each real screen, we estimate the probability $p_{\mathrm{scr,}i}$ of its
score arising by chance from the fraction of the random samples that has a
higher value of $X$ than the real screen. For all screens, we can then
calculate a combined probability
$p_{\mathrm{tot}}=\prod_{i}p_{\mathrm{scr,}i}$ (i.e., the joint probability),
and use fraction of the trials with higher $p_{\rm tot}$ as an estimate of the
likelihood that screens and filaments seem aligned by chance.

To get a sense of the uncertainties in our estimates, we repeat the above
procedure for two values of the threshold: our main choice, $Z=0.6$, which
aims to correspond to the threshold of method 1, and an extreme choice for
comparison, $Z=0$, i.e., simply counting the number of aligned pixels with
positive flux.

##  3 Results for Individual Pulsars

###  3.1 PSR J0737-3039A

This project began by investigating possible associations of structures in the
interstellar medium with the scattering screen towards PSR J0737$-$3039A, a
$23{\rm\;ms}$ pulsar in a binary with another, regular, $2.8{\rm\;s}$ pulsar,
PSR J0737$-$3039B (Lyne et al., 2004). The ability to time both pulsars (until
Pulsar B precessed out of sight in 2008), short orbital period of
$2.4{\rm\;hr}$, and eccentric orbit makes this system ideal for tests of
general relativity. Accordingly, this system has been studied very well (e.g.,
Lyne et al., 2004; Kramer et al., 2006, 2021a, 2021b).

Several studies have also used the scintillation of PSR J0737$-$3039A to
determine system and screen properties (Ransom et al., 2004; Stinebring et
al., 2005; Rickett et al., 2014). An interesting surprise was that the
secondary spectra of this pulsar seem to show only one arc, indicating a
single dominant screen (Stinebring et al., 2005), even though the system is
very close to the Galactic plane ($\ell=245^{\circ},b=-4.5^{\circ}$), and the
line of sight thus traverses gas with relatively large column densities and
more complicated kinematics.

Rickett et al. (2014, R14 hereafter) used orbital and annual variations in the
scintillation timescale to determine the screen distance and orientation, but
found two different solutions, one more and one less asisotropic. To elucidate
which one was better, we re-fit the scintillation timescales, choosing fit
parameters somewhat better suited for constraining screen properties and using
the updated pulsar timing ephemeris from Kramer et al. (2021b). Details of our
fits are given in the Appendix, but here we simply note that the results are
largely consistent with those of R14, with the biggest difference being the
adopted pulsar distance ($d_{p}$): R14 used $d_{p}=1.5{\rm\;kpc}$, based on
the parallax measurement of Deller et al. (2009), while we use
$d_{p}=0.735{\rm\;kpc}$, the weighted average of parallax and timing
parallaxes given by Kramer et al. (2021b). Since we find the same fractional
distance, $s=1-d_{s}/d_{p}=0.7$ (with $d_{s}$ the distance of the screen), our
fit places the screen closer, at $d_{s}=260\pm 50{\rm\;pc}$ compared to the
$450{\rm\;pc}$ inferred by R14.

We also found clearer evidence that the scattering screen is highly
anisotropic, with its line of images nearly aligned with right ascension, at
$\sim\\!88\fdg 6$ East of North. We made fits for several possible values of
the inclination but found that these had very little effect on the screen
properties; in Table 1, we list the result for what formally is our best fit,
with an inclination of $i=89\fdg 35$.

Comparing the screen orientation with H I surveys, we find possible alignment
with an H I filament that spans velocities in the range of 14 to
$27{\rm\;km/s}$; see Figure 1. The radial velocities of the possibly aligned
filament somewhat exceed the expected radial velocity from Galactic rotation
($2.28{\rm\;km/s}$). We note, however, that the tangential velocity of the
scattering screen is also in excess of what is expected from Galactic rotation
by a similar amount, $14{\rm\;km/s}$. Despite the rather complex web of
filaments in this section of the sky, the range of orientations identified
with RHT is quite small. Applying the RHT to the H$\alpha$ data did not
identify filaments in front of PSR J0737$-$3039A.

For this particular pulsar, the evidence for the presence of an aligned H I
filament is suggestive but in itself inconclusive: Method 1 finds similarly
aligned filaments for 31.8% of the random trials, while Method 2 shows that
for only 1.2% of the trials there is aligned emission equally or more
significant than that for the pulsar for a threshold of 0.6 or a more similar
44.3% for a threshold of 0.0. The large discrepancy is likely due to this
pulsar being close to the Galactic plane: while the line of sight to PSR
J0737-3039A has only two clear filaments, many of the randomly chosen nearby
lines of sight have multiple filament orientations. Hence, they relatively
easily fulfill the requirements for Method 1, which just looks for an aligned
structure, while for Method 2, which also looks at the strength of of the
aligned filament relative to others, those multi-filament trials are less
likely to give a significant signal (at least if a cut-off is imposed). As
will become clear for the other pulsars, this large a discrepancy between the
two methods is not common, but it nevertheless shows how strongly the
significance of a result can depend on the choice of detection criteria.
Overall, we find the association suggestive.

One of the most prominent ISM structures along the line of sight to PSR
J0737$-$3039A is the Gum Nebula. The Gum Nebula is a large, irregular shell
with a radius of $22.7\fdg\pm 0\fdg 1$ centred at a distance of about 450 pc
(Purcell et al., 2015). It likely is an H II region with the shell resulting
from the winds of hot stars in its interior (Purcell et al., 2015). The nebula
and shell would have large density variations and thus likely favorable
conditions for forming structures that could cause scintillation.

The distance to the Gum Nebula is inconsistent with the screen distance
assuming roughly spherical geometry, although the irregular shape of the
nebula could mean that it extends closer. Indeed, Kramer et al. (2021b) argue
that PSR J0737$-$3039A is likely behind the Gum nebula, and suggest an
extension of it, seen in emission near the pulsar’s position, could be the
source of the scintillation screen. This might be the case if this extension
is substantially closer to us than the rest of the nebula, or if the distance
to the pulsar’s screen is larger, as would be the case if the pulsar were at a
distance more like that inferred from the VLBI parallax and thus further away
than indicated by timing.

The Gum Nebula’s shell’s expansion has been found to be slow and non-uniform,
but the back face is expanding at $8.5{\rm\;km/s}$ while the front face is
expanding at $14{\rm\;km/s}$ (Woermann et al., 2001). This expansion would
suggest a filamentary structure on the front face of the nebula would have a
radial velocity of about $-11{\;\rm km/s}$ (after accounting for the motion of
the centre of the nebula relative to Galactic rotation of 3.6 km/s used in
Woermann et al. (2001)), which is inconsistent with the 14 to $27{\rm\;km/s}$
radial velocity of the potentially aligned filament.

While an association with the Gum Nebula may be possible, the screen distance
is perhaps more suggestive of an association with the Local Bubble wall.
Radial velocities of stars near the surface of the Local Bubble are around 5
to 9 km/s in excess of the Local Standard of Rest, and idealized modelling of
the expansion of the Local Bubble gives a current expansion rate of
$6.7^{+0.5}_{-0.4}$ km/s (Zucker et al., 2022). This is somewhat smaller than
the velocity of the filament but in the same direction.

In summary, we find a neutral hydrogen filament that is aligned with the
screen. There might be an association of the screen with either the Local
Bubble or the Gum Nebula. Both also have significant H I components, with the
Local Bubble wall defined by an increase in neutral gas and dust, and the Gum
Nebula being surrounded by an H I shell. The distance to the scintillation
screen and the velocity of the potentially aligned H I filament favour the
Local Bubble wall.

###  3.2 PSR J0337+1715

PSR J0337$+$1715 is a millisecond pulsar in a hierarchical triple system. The
pulsar is in a 1.6 day orbit with a white dwarf within a 327 day orbit of
another white dwarf. The orbital parameters of this system are well known from
pulsar timing and the effects of three-body interactions (Voisin et al.,
2020). The screen parameters for this system were fit from nine years of
scintillation measurements by Gusinskaia et al. (in prep).

There is substantial H I emission along the line of sight, but the orientation
of the screen is not consistent with any identified H I filament. Indeed,
while an aligned filament was found only for 5.3% of our trials for nearby
lines of sight, the maximum observed amount of aligned emission is less than
the mean, and higher maxima are found for 96.9% of the trials in method 2
(with $Z=0.6$).

###  3.3 PSR J0437-4715

PSR J0437$-$4715 is a millisecond pulsar in a 5.76-day binary with a white
dwarf. It has a precisely measured distance that places it very near to us, at
$156.79\pm 0.25$ pc (Reardon et al., 2016). Using 16 years of archival data,
Reardon et al. (2020) was able to make precise measurements of two screens
from arc curvature variations, with a primary screen at $89.8\pm 0.4$ pc and a
fainter, secondary screen at $124\pm 3$ pc. Two other arcs were identified in
the data, implying this pulsar has at least four screens, but there was
insufficient signal to measure the properties of these additional screens
(Reardon et al., 2020).

Some filamentary structure is identified in front of this pulsar that appears
to be aligned with both screens. H I emission in the direction of this pulsar
is very weak (peaking at $\sim 1{\rm\;K}$ in 1.288 km/s channels), which could
influence the reliability of identifying filaments. However, the H I
morphology does not appear to be dominated by noise.

From our trials, the probability of finding a chance association for a single
screen was quite large, at 37.3%. The likelihood that both screens would be
aligned by chance was found to be 4.9%, which looks more significant, but
depends in part on the two observed screens having very similar orientation,
while in the trials the orientations are randomized. For the trials, we found
that 7.6% had stronger aligned emission than the nearer, primary screen, and
11.0% of trials showed stronger aligned filaments than the farther, secondary
screen.

###  3.4 PSR J0613-0200

PSR J0613$-$0200 is a millisecond pulsar in a relativistic binary with a white
dwarf companion in the Galactic plane (Lorimer et al., 1995). From a seven
year dataset, Main et al. (2020) fit for the orientation and distance to its
screen using scintillation arcs, ignoring the contribution of orbital motion
to the velocity of the system. Increased scattering was observed in 2013 that
could indicate a different screen. The arc measurements in 2013 were not fit
well either by a model that assumed a single screen for the full seven year
dataset nor when fitted separately, resulting in the large error in the
distance to this screen. The best fits for both screens are shown in Table 1.

For both screens, we find possible aligned H I filaments. In this region of
sky the likelihood to find at least one screen aligned by chance is 23.9% and
the likelihood of two screens being aligned by chance is 1.7%. The latter may
exaggerate the case for aligned filaments, however, given that filaments are
identified in front of this pulsar over a wide range of angles. Indeed, we
found that 50.7% of trials showed more significant aligned flux than the 2013
screen and 22.5% of trials showed more alignment flux than the 2014 and
onwards screen. Hence, the association, like for most screens taken on their
own, is rather tentative.

###  3.5 PSR J0636+5128

PSR J0636$+$5128 is a millisecond pulsar in a binary with a period of 1.6
hours (Alam et al., 2021). The properties of the screen were determined by Liu
et al. (2022, 2023) using the scintillation timescale and decorrelation
bandwidth from 2.5 years of data and ignoring the effect of the orbital motion
(which is small for this system, so did not significantly decrease the quality
of the fit).

There is substantial H I emission along the line of sight, with a clear
filament identified between 2 and $10{\rm\;km/s}$ (exceeding the predicted
radial velocity from Galactic rotation by 5 to $13{\rm\;km/s}$). This
filament, however, is not aligned with the screen but instead nearly
perpendicular. The likelihood of finding a chance alignment along this line of
sight is 20.9%, and 65.3% of trials showed more aligned emission than this
screen.

###  3.6 PSR B0834+06

Using very long baseline interferometry (VLBI), Brisken et al. (2010) mapped
the positions of images on the sky for the screens of PSR B0834$+$06\. They
identified a roughly 40 mas line of images corresponding to the main arc of
the secondary spectra, as well as cluster of images offset by about 10 mas
from the pulsar position. The cluster of images was suggested to be due to
multiple scatterings of the light by the two screens (Liu et al., 2016), with
the second screen terminating so that the pulsar was not seen through it. This
model, which was confirmed in detail by the phase retrieval analysis done by
Zhu et al. (2022), gives very accurate orientations.

There is a clear filament centred around 100∘ that is inconsistent with either
screen. In this region of the sky the likelihood of finding at least one
aligned screen by chance is 11.0%. Despite the lack of a specific aligned
filament, only in 9.8% of the trials there was more aligned emission than what
is seen for the main screen, i.e., the fainter filament visible in the RHT at
the corresponding position angle is not entirely insignificant. In contrast,
36.6% of the trials had more aligned emission than was observed for the second
screen.

###  3.7 PSR B1133+16

PSR B1133$+$16 is relatively nearby, at $372\pm 2$ pc (Deller et al., 2019)
and has displayed up to six different scintillation arcs (McKee et al., 2022).
By tracing how those arcs changed with time over a 30 year baseline, McKee et
al. (2022) found screen parameters for five screens. There are large error
bars in the fitted values as often not all arcs can be seen and it is
difficult to identify which arc corresponds to which screen. Although the
relative brightness of the arcs vary with time, the scattering regions remains
statistically similar over 30 years, placing a lower limit on the transverse
width of the scattering region of $\sim\\!4\arcsec$, corresponding to a size
of $\sim 0.0035\,$pc at a distance of 186 pc.

For the purpose of our statistical analysis, we consider screens c, d, and e
as one screen, since their orientations and expected radial velocities
overlap. These screens all show probable alignment with hydrogen filaments. A
filament is also found within the uncertainties of the orientation of screen
f. The weak H I emission along this line of sight means that velocity channels
with velocities above 5 km/s are dominated by noise and give unreliable but
low percent orientations, below the 60% threshold used to determine alignment.
The likelihood of chance alignment of at least one of three screens in this
region of the sky is 10.2%, and 0.12% for at least two screens. We found that
77.3% of trials had stronger aligned emission than screen b (which was not
considered aligned), 66.6% had more than screen c/d/e, and 56.8% had more than
screen f. Given the large error bars on the orientations of the screens, it is
unsurprising that their alignment is not very significant.

###  3.8 PSR J1141-6545

PSR J1141$-$6545 is a millisecond pulsar in a relativistic binary with a white
dwarf companion. Most of the orbital parameters of this pulsar are measured to
high precision from pulsar timing. The distance to the pulsar, however, is
less well constrained, but Reardon et al. (2019) fit the distance to the
pulsar as well as screen properties from the scintillation timescale. Their
best fit for the distance to the pulsar was $10^{+4}_{-3}\,$kpc with a screen
at 7.20${}^{0.30}_{-0.22}\,$kpc. The fitting did not assume a one-dimensional
screen, instead the screen was fit as an ellipse (using a method similar to
that of Rickett et al. 2014). The axial ratio of the ellipse was found to be
$2.14\pm 0.11$, so the screen may not be very filamentary or may need to be
described by more than one linear screen.

No filaments were identified in front of this pulsar in the velocity range
searched. This is not surprising since the filaments at this distance are
likely to be unresolved and hence the H I emission is low. Consequently, we do
not include this pulsar in our statistical analyses.

###  3.9 PSR B1508+55

The secondary spectra of PSR B1508$+$55 usually display a single arc with flat
arclets, which was explained as a result of two-screen scattering by Sprenger
et al. (2022). The screen creating the main arc is nearby, at a distance of
$127.1\pm 1.5$ pc and the second screen is located close to the pulsar, at a
distance of $1940\pm 123$ pc (Sprenger et al., 2022). The morphology of the
secondary spectra of this pulsar also appears to change, from a fuzzy arc to a
thin arc with clear inverted arclets. This change in morphology is modelled as
being caused by a change from strong to weak scattering of the closer screen,
accompanied by a change in orientation from $142.4\pm 0.4^{\circ}$ to
$129.8\pm 2.0^{\circ}$ (Sprenger et al., 2022). Sprenger et al. (2022) noted
that the closer screen is 1.37 pc from the line of sight of an A2 star at a
distance of $120\pm 8$ pc, but found no candidate associations for the further
screen.

A screen with orientation $142.4\pm 0.4^{\circ}$ is consistent with being
aligned with an H I filament. However, this filament’s orientation of
approximately $144^{\circ}$ is less consistent with the orientation of
$121\fdg 8\pm 2\fdg 0$ of the weak-scattering screen. The probability of
finding at least one screen is aligned by chance in this region of the sky is
27.5%. Both screens showed much stronger aligned emission than random trials,
with only 9.9% of trials having stronger aligned emission than the weak-
scattering screen and 1.5% of trials have more than the strong-scattering
screen.

We do not find an alignment H I filament for the distant screen, but this may
be expected: it may be too far away to be resolved and thus too faint. We thus
exclude the distant screen from our statistical analysis.

PSR B1508$+$55 is quite distant ($2.10^{+0.13}_{-0.14}\,$kpc) but has a very
large proper motion (implying a velocity of $936^{+61}_{-64}$ km/s, Chatterjee
et al. 2009). Given that the scintillation properties of PSR B1508$+$55 have
changed as it crosses different ISM environments (Sprenger et al., 2022), one
might worry about a mismatch in time. The EBHIS data was collected between
2010 and 2011, and Sprenger et al. (2022) used data from 2020 to 2022. Between
2011 and 2021 the pulsar would have moved $-0.74\arcsec$ in RA and
$-0.62\arcsec$ in declination, i.e., much less than the pixel size of the
EBHIS data. We therefore do not expect to see changes in the H I emission
structure that would explain the changes in scintillation properties.

###  3.10 PSR J1603$-$7202

Walker et al. (2022) fit scintillation arc measurements for PSR J1603$-$7202\.
During the 12 years covered, PSR J1603$-$7202 displayed a significant increase
in dispersion measure accompanied by decreases in scintillation timescale and
decorrelation bandwidth, which Walker et al. characterize as an extreme
scattering event. The dispersion measure then plateaued before decreasing to
pre-event levels. Motivated by these changes in the line of sight ISM
environment during their data set, Walker et al. (2022) allow for fits to
different screens in different epochs. If only one screen is considered, their
best fit orientation is $140\pm 13^{\circ}$ from Galactic North, at a distance
of 2.47 kpc. For three screens, all had orientations consistent with
$120^{\circ}$, but with distances between 2.52 kpc and 3.33 kpc.

In Table 1, we include only the single screen model. Filaments identified with
RHT are not consistent with orientations of either $140^{\circ}$ or
$120^{\circ}$. However, given the large distances to the screen(s) it is not
obvious that filaments would be resolved, and hence we exclude this pulsar
from our statistical analyses.

###  3.11 PSR J1643$-$1224

PSR J1643$-$1224 is a millisecond pulsar in a 147 day orbit with a white dwarf
companion, at a distance of $760\pm 16\,$pc (Desvignes et al., 2016). Using
five years of scintillation arc measurements, Mall et al. (2022) modelled the
scintillation screen(s) of PSR J1643$-$1224\. The secondary spectra for this
pulsar displayed a single arc that appears to alternate between a thin arc,
indicative of anisotropic screen, and a more diffuse arc that could in
principle be indicative of either an isotropic screen or of multiple
anisotropic screens. But scatter broadening of the pulsar image favours the
solution with two anisotropic screens (Ding et al., 2023).

For comparison with H I filaments, we use the fit for two anisotropic screens.
The distances of the two screens were $129\pm 15$ and $340\pm 9{\rm\,pc}$. The
distance to the closer screen is consistent with that of the H II region, Sh
2-27, centred at $112\pm 3\,$pc (Ocker et al., 2020) with a diameter of 34 pc
(Harvey-Smith et al., 2011).

Both screens have probable alignment with an H I filament. We also compared
the orientation of screens with H$\alpha$ filaments and, although filamentary
structure was identified in front of this pulsar, the filaments were not
aligned with the screens. The alignment with H I and not H$\alpha$ could
suggest that the changes in electron density responsible for the nearer screen
do not arise in the H II region itself, but rather at, e.g., the interface
with neutral hydrogen surrounding it. The likelihood that at least one of the
screens is aligned by chance is 72.8%, and that of both being aligned is
23.9%. We found that 15.0% of trials had stronger aligned emission than the
closer screen, while 85.1% of trials had stronger aligned emission than the
farther screen.

###  3.12 PSR J1909$-$3744

PSR J1909$-$3744 is a very precisely timed millisecond pulsar due to its
narrow pulse width, which has enabled a precise distance measurement, of
$1.152\pm 0.003{\rm\,kpc}$ (Reardon et al., 2021). The pulsar is in a binary
with white dwarf companion. The scintillation screen of PSR J1909$-$3744 was
modelled using 13 years of scintillation arc measurements by Askew et al.
(2023). They searched for nearby H$\alpha$ sources and hot stars but found no
associations.

We identify prominent filaments in front of the pulsar with orientations
around $150^{\circ}$, inconsistent with the orientation inferred for the
scintillation screen. The likelihood of chance alignment for this line of
sight is 28.2% and 24.8% of trials showed stronger aligned emission than this
screen.

##  4 Aggregate Results

###  4.1 Filament Alignment

We found that for six of the eleven pulsars analyzed there were possibly
aligned H I filaments for at least one of their screens, for a total of 12 of
22 screens with possible alignments (see the summary in Table 3). All of the
possible aligned screens were within 600 pc from Earth, and all but one within
340 pc. There is an observational bias towards measuring the scintillation of
less scattered, brighter pulsars which are typically nearby and therefore have
nearby screens. The H I filament analysis is also biased towards nearby
filaments since, for a given physical size, nearby filaments have larger
angular size and are thus more easily identified.

We evaluated the significance of the probable alignment of the full sample of
pulsars using the methods outlined in Section 2.4. We ignored screens that are
greater than $1{\rm\;kpc}$ away and counted screens c, d, and e of PSR
B1133+16 as one screen since they share the same orientation within their
errors. With these adjustments, we are left with 17 screens, for 10 of which
we found an aligned filament. Comparing this with our random trials, we found
that only in 0.004% of those 10 or more screens were classified as having
aligned filaments; for the trials, the expected number of aligned screens was
3.02. For the second method, which is based on the significance of the aligned
flux, the evidence is less strong, but still highly suggestive: only 1.70% of
the random trials showed more significant aligned flux than the real data
using a threshold $Z=0.6$ for the RHT. If the threshold is ignored, and the
full RHT spectrum with a threshold of $Z=0$ is used, then only 0.90% of our
trials had more aligned flux than the real data. We thus conclude that the
alignment of scintillation screens with H I filaments seen for our sample is
unlikely to be due entirely to chance.

Table 3:  Summary of statistics |  |  |  | Method 2
---|---|---|---|---
|  | Method 1 | ($Z=0.6$) | ($Z=0.0$)
Pulsar | Screen | Aligned? | (%) | X | (%) | X | (%)
J0337$+$1715 | a | N | 5.3 | $-0.4$ | 96.9 | $-0.2$ | 99.9
J0437$-$4715 | a | Y | 20.8 | 4.8 | 7.6 | 2.5 | 5.9
| b | Y | 21.4 | 4.7 | 11.0 | 2.5 | 5.6
J0613$-$0200 | 2014+ | Y | 12.8 | 2.7 | 22.5 | 2.0 | 15.8
| 2013 | Y | 12.8 | 1.4 | 50.7 | 1.4 | 56.6
J0636$+$5128 | a | N | 20.9 | $-0.3$ | 65.3 | 0.7 | 53.6
J0737$-$3039A | a | Y | 31.8 | 5.5 | 1.2 | 1.6 | 44.3
B0834$+$06 | a | N | 5.4 | 4.0 | 9.8 | 3.2 | 0.6
| b | N | 5.9 | 1.9 | 36.6 | 1.8 | 21.4
B1133$+$16 | b | N | 3.4 | 1.2 | 77.3 | 0.9 | 66.7
| c/d/e | Y | 3.8 | 1.5 | 66.6 | 0.8 | 78.2
| f | Y | 3.5 | 0.9 | 56.8 | 1.0 | 58.1
B1508$+$55 | a (weak) | N | 14.6 | 3.6 | 9.9 | 2.2 | 6.4
| a (strong) | Y | 15.0 | 4.8 | 1.5 | 2.6 | 1.1
J1643$-$1224 | a | Y | 48.3 | 3.5 | 15.0 | 2.2 | 14.6
| b | N | 48.4 | 0.6 | 85.1 | 0.6 | 93.7
J1909$-$3744 | a | Y | 28.2 | 2.9 | 24.8 | 1.9 | 30.6
Combined probability | 0.004 | 1.70 | 0.90

###  4.2 Screen Velocities

We compared the measured screen velocities with the expected velocity from
Galactic rotation at the position of the screen (both values are listed in
Table 1). The majority of screens (14 of 22) have velocities within 20 km/s of
the Galactic rotation. Since the sound speed of the ISM is roughly 10 km/s
(Goldreich & Sridhar, 1995), the differences are not inconsistent with what is
expected from random motion and/or slowly expanding or contracting
interstellar medium, especially taking into account that most of the sample of
screens are at high Galactic latitudes ($>20^{\circ}$ out of the plane), where
motions are less well explained with Galactic rotation models.

Some exceptions to the screen velocities being comparable to the Galactic
rotation velocities are the screens of PSR J0437$-$4715 and PSR B1133$+$16\.
For PSR J0437$-$4715, both screens are approximately 40 km/s in excess of the
Galactic rotation. Since both are located inside the Local Bubble, this may
simply reflect that this is a hot bubble blown by multiple supernova remnants
(see below), in which higher velocities are perhaps expected. For B1133+16,
some of the best-fit screen velocities are even larger, at more than $70$
km/s, but they also have large error bars, of more than 50%. Indeed, while
four of the five screens have best-fit screen velocities more than $20$ km/s
in excess of Galactic rotation, only two (screens c and d) have velocities
inconsistent with Galactic rotation within the 1$\sigma$ uncertainties. Hence,
while this hints at more rapidly moving ISM, the large uncertainties hinder
any strong conclusions. It would seem worth measuring those velocities more
accurately, e.g., using a dedicated VLBI campaign rather than relying on
annual variations in arc curvature.

###  4.3 Local Bubble

We examine connections between the distances to the scintillation screens and
the Local Bubble. The Local Bubble is a low density, irregularly shaped cavity
with radius of $\sim 100-300$ pc filled with hot ($\sim 10^{6}$ K), mostly
ionized gas surrounded by a thick wall ($\sim 100$ pc) of dense, neutral gas.
The Local Bubble is thought to have formed from a series of supernova shocks
10 to 15 million years ago, with surviving stars now located in the Sco-Cen
association (Maíz-Apellániz, 2001). Observations of nearby ($\lesssim 200$ pc)
molecular clouds indicate they all lie at the surface of the Local Bubble with
filamentary or sheet-like structure elongated along the surface of the bubble
(Zucker et al., 2022). The density contrast and sheet-like structures,
combined with Earth’s location within the cavity, would seem to make the
surface of the Local Bubble a highly favourable environment for scintillation.

To estimate distances to the inner edge of the Local Bubble, we use the model
of Pelgrims et al. (2020) with 10 harmonic modes. The resulting distances
along the line-of-sight for each of our pulsars are listed in Table 1. Along
some lines of sight, particularly at higher Galactic latitudes, this model may
overestimate the distance to the wall due to the resolution of dust map used
in modelling. It also does not account for regions where the Local Bubble does
not have a wall, sometimes referred to as a Local Chimney (e.g. Welsh &
Lallement, 2012).

Taking the distances at face value, we find that 11 of the 22 screens are
within 100 pc of the Local Bubble wall, with five beyond and six in front of
the nominal distance. However, three of the latter are located well within the
cavity of the Local Bubble, more than 100 pc from its inner edge.

A particularly interesting case is PSR J0437$-$4715 which, at a distance of
$156.79{\rm\,pc}$, is itself located inside the cavity of the Local Bubble
(the inner edge is at $\sim\\!240{\rm\,pc}$). It is perhaps surprising that
many of the screens are located within the low density Cavity, but
measurements of stellar absorption indicate several discrete clouds, even
within 15 pc of Earth, that can cause scintillation of AGNs (Redfield &
Linsky, 2008; Linsky et al., 2008).

The H II region thought to cause the scintillation of the main screen of PSR
J1643$-$1224, Sh 2-27, is located just outside of the Local Bubble, within the
Ophiucus star formation region, where star formation is thought to have been
triggered by the collision of the expanding Local Bubble with the surrounding
ISM (Zucker et al., 2022).

##  5 Conclusion

Our results showed correlations between the orientations of scintillation
screens and hydrogen filaments that are unlikely to be due entirely to chance.
Our estimates of the likelihood of alignment vary between different methods
(0.004% and 1.7%), but are both suggestive of a real association. If the
correlation in alignment between scintillation screens and hydrogen filaments
is physical, it implies there is correlation between alignment of ISM
structures across many orders of magnitude of spatial scale – from the milli-
arcsecond scales of scintillation to the degree scales of H I emission. Where
there were overlapping H I surveys of different scales, it appeared that
filaments were aligned in both the lower and higher resolution maps. However,
higher resolution maps gave narrower orientations and more filaments. Even at
the smallest resolution of 4 arcmin, the filaments did not appear to be
resolved. This could impact the conclusions of alignment if substructure
within filaments is not aligned with larger scale structure.

Scintillation requires fairly large gradients, $\gtrsim\\!10{\rm\,cm^{-2}/cm}$
(Pen & Levin, 2014), in the column density of electrons, but this may not
translate to large volumetric electron density variations. Electron density
gradients could be expected on the surfaces of cold neutral filamentary
structures if they are embedded in warmer ISM, such that there is a transition
from cold neutral to warm ionized phases creating a partially ionized skin on
the filament. We did not see a correlation with H$\alpha$ emission that would
trace the warm ionized medium but this is, at least partially, due to
insufficient spectral and angular resolution of the H$\alpha$ maps.

The correlations in orientation of scintillation screens and H I filaments do
not necessarily indicate a physical connection; instead, H I filaments could
be tracers of the conditions that create scintillation screens. For instance,
H I filaments appear to trace large-scale magnetic field orientation (Clark et
al., 2014), and it seems plausible that the same magnetic field has ionized
media aligned with it that may cause the scintillation (see for example Gwinn,
2019), or that the scintillation occurs in magnetic reconnection sheets (Pen &
Levin, 2014).

Independently, our results suggests it is worthwhile to try to measure more
screen orientations, and in particular try to improve the precision, e.g.,
using VLBI (as so far done only for PSR B0834+06 by Brisken et al. 2010).
Furthermore, higher-resolution H I studies would show more clearly whether
filaments are truly associated with the scintillation regions, or simply trace
similarly oriented structures.

Deeper understanding of the ISM environments for scintillation will require
connections with multiple ISM tracers, ideally with true distances. While
distances to ISM structures are generally not known, 3D ISM tomography is
rapidly advancing, particularly in dust, allowing for detailed distance
measurements of, e.g., the Local Bubble, as well as of more isolated H I
filaments using the correlations between dust and H I. Similarly, our
understanding of the 3-dimensional structure of the Galactic magnetic field is
rapidly improving, which may provide another indication of what causes the
scintillating structures.

## Acknowledgments

We thank Barney Rickett for sharing the data on the double pulsar system, and
for clarifications on his results; Antoine Marchal, Bryan Gaensler, and Peter
Martin for helpful discussions about the interstellar medium; Susan Clark for
discussions about the Rolling Hough Transform; Jing Luo for assistance in the
usage of pint; and Vincent Pelgrims for help in the usage and understanding of
his Local Bubble model. We also thank the University of Toronto and broader
scintillometry community for insights and support. MHvK is supported by the
Natural Sciences and Engineering Research Council of Canada (NSERC) via
discovery and accelerator grants.

The Wisconsin H$\alpha$ Mapper and its H$\alpha$ Sky Survey have been funded
primarily by the National Science Foundation. The facility was designed and
built with the help of the University of Wisconsin Graduate School, Physical
Sciences Lab, and Space Astronomy Lab. NOAO staff at Kitt Peak and Cerro
Tololo provided on-site support for its remote operation. The Virginia Tech
Spectral-Line Survey (VTSS) is supported by the National Science Foundation.
The Southern H-Alpha Sky Survey Atlas (SHASSA) is supported by the National
Science Foundation. This work has made use of S-band Polarisation All Sky
Survey (S-PASS) data. This research has made use of NASA’s Astrophysics Data
System Bibliographic Services.

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##  Appendix A Properties of the Scintillation Screen of PSR J0737$-$3039A

We make a new fit for the scintillation screen properties of PSR J0737$-$3039A
based on the scintillation timescale data and analysis of Rickett et al.
(2014), hereafter referred to as R14. This new fit was motivated by two
factors: (1) the original work found a rather large scintillation screen
velocity, especially for the most anisotropic case ($>100$ km/s); and (2) the
pulsar timing measurements of this pulsar were recently updated by Kramer et
al. (2021b), including a significantly different distance to the pulsar.
Below, we outline the details of the model we use, following the description
and nomenclature of R14, and present the results of the fits.

###  A.1 Scintillation Model

The scintillation timescale, $T_{\rm{ISS}}$, is the time it takes for the
auto-correlation function of the source brightness to fall by a factor $e$.
Hence, the scintillation timescale depends on the spatial scale of phase
changes on the screen, known as the mean diffractive scale ($s_{0}$), as well
as the relative velocities of the source, observer, and screen.

The velocity of the line of sight can be decomposed into the barycentric
velocity of the pulsar binary, $\mathbf{V}_{\mathrm{C}}$ and the orbital
velocity of the pulsar. The barycentric velocity is given by,

$\mathbf{V}_{\mathrm{C}}=\mathbf{V}_{\mathrm{P}}+\mathbf{V}_{\mathrm{E}}s/(1-s)-\mathbf{V}_{\mathrm{IS}}/(1-s),$
(A1)

where $\mathbf{V}_{\mathrm{P}}$ is the proper motion of the pulsar center of
mass, $\mathbf{V}_{\mathrm{E}}$ is the velocity of Earth,
$\mathbf{V}_{\mathrm{IS}}$ is the velocity of the screen and
$s=1-(d_{\mathrm{screen}}/d_{\mathrm{psr}})$ is the fractional distance from
the pulsar to the screen. This velocity is related to the commonly used
“effective velocity” as
$\mathbf{V}_{\mathrm{C}}+\mathbf{V}_{\mathrm{P,orbital}}=\mathbf{V}_{\mathrm{eff}}/(1-s)$.

The orbital motion is most easily calculated in the reference frame of the
pulsar orbit, defined such that $\hat{z}$ points from the Sun to the
barycentre of the orbit, $\hat{x}$ is aligned with the line of nodes of the
pulsar orbit, and $\hat{y}=\hat{z}\times\hat{x}$. The transformation from
equatorial coordinates to the pulsar orbital frame is done by rotating the
velocities by the longitude of ascending node, $\Omega$, which is a free
parameter. The geometry of the model is shown in Figure 2. In x-y coordinates,
the average orbital velocity is given as
($V_{\mathrm{o}}e\>{\sin}\>\omega,V_{\mathrm{o}}e\>{\cos}\>\omega\>{\cos}\>i)$,
where $\omega$ is the argument of periastron. $V_{o}$ is the average orbital
speed, given as $V_{o}=2\pi a/(P_{\mathrm{b}}\sqrt{1-e^{2}})$ where $a$ is the
semimajor axis of the orbit, $P_{b}$ is the orbital period, and $e$ is the
eccentricity of the orbit.

To determine screen parameters from the orbital harmonic coefficients, a
single, potentially anisotropic scattering screen is assumed. The anisotropy
of the screen is described by its axial ratio, $A_{\mathrm{R}}$, and the
orientation of its major axis, $\psi_{\mathrm{AR}}$. Since $A_{\mathrm{R}}$ is
unbounded, R14 define a variable
$R=(A^{2}_{\mathrm{R}}-1)/(A^{2}_{\mathrm{R}}+1)$ which ranges from 0
(isotropic) to 1 (linear). These parameters are contained within the following
variables:

$\displaystyle a$
$\displaystyle=\left[1-R\>{\cos}(2\psi_{\mathrm{AR}})\right]/\sqrt{1-R^{2}},$
$\displaystyle b$
$\displaystyle=\left[1+R\>{\cos}(2\psi_{\mathrm{AR}})\right]/\sqrt{1-R^{2}},$
$\displaystyle c$
$\displaystyle=-2R\>{\sin}(2\psi_{\mathrm{AR}})/\sqrt{1-R^{2}}.$ (A2)

The scintillation timescale will depend on the orbital angle $\phi$ (which,
like R14, we define relative to the line of nodes, as $\phi=\theta+\omega$,
with $\theta$ the true anomaly). This dependence can be fitted by five orbital
harmonic coefficients ($K_{0},K_{S},K_{C},K_{S2},K_{C2}$) as

$T_{\rm{ISS}}(\phi)=K_{0}+K_{S}\sin(\phi)+K_{C}\cos(\phi)+K_{S2}\sin(2\phi)+K_{C2}\cos(2\phi).$
(A3)

The orbital harmonic coefficients are defined in terms of the physical
parameters as,

$\begin{split}K_{0}=&[0.5\>V_{\mathrm{o}}^{2}(a+b\>{\cos}^{2}\>i)+a(V_{\mathrm{C}_{x}}-V_{\mathrm{o}}e\>{\sin}\>\omega)^{2}+b(V_{\mathrm{C}_{y}}+V_{\mathrm{o}}e\>{\cos}\>\omega\>{\cos}\>i)^{2}\\\
&+c(V_{\mathrm{C}_{x}}-V_{\mathrm{o}}e\>{\sin}\>\omega)(V_{\mathrm{C}_{y}}+V_{\mathrm{o}}e\>{\cos}\>\omega\>{\cos}\>i)]/s_{\mathrm{p}}^{2}\\\
K_{\mathrm{S}}=&-V_{\mathrm{o}}[2a(V_{\mathrm{C}_{x}}-V_{\mathrm{o}}e\>{\sin}\>\omega)+c(V_{\mathrm{C}_{y}}+V_{\mathrm{o}}e\>{\cos}\>\omega\>{\cos}\>i)]/s_{\mathrm{p}}^{2}\\\
K_{\mathrm{C}}=&V_{\mathrm{o}}\>{\cos}\>i[c(V_{\mathrm{C}_{x}}-V_{\mathrm{o}}e\>{\sin}\>\omega)+2b(V_{\mathrm{C}_{y}}+V_{\mathrm{o}}e\>{\cos}\>\omega\>{\cos}\>i)]/s_{\mathrm{p}}^{2}\\\
K_{\mathrm{S2}}=&-0.5cV_{\mathrm{o}}^{2}\>{\cos}\>i/s_{p}^{2}\\\
K_{\mathrm{C2}}=&\;0.5V_{\mathrm{o}}^{2}(-a+b\>{\cos}^{2}i)/s_{\mathrm{p}}^{2}.\\\
\end{split}$ (A4)

Here, the size of the resolution element of the screen, $s_{\mathrm{p}}$, is
related to the mean diffractive scale, $s_{0}$ by
$s_{\mathrm{p}}=s_{0}/(1-s)$.

Since the mean diffractive scale is frequency dependent, scintillation
timescales of data from observations in different frequency bands cannot be
directly compared. In order to combine data, R14 used normalized orbital
harmonic coefficients ($k_{0}=K_{0}/K_{\mathrm{C2}}$,
$k_{\mathrm{s}}=K_{\mathrm{S}}/K_{\mathrm{C2}}$, etc.), which are independent
of the mean diffractive scale.

Figure 2: Schematic showing the coordinate systems used. The $x-y$ plane is
oriented with $x$ along the line of nodes of the orbit. It has its origin at
the equatorial coordinates $\alpha$, $\delta$ of the pulsar, but is rotated
East of North (around equatorial coordinates ) by the longitude of ascending
node, $\Omega$. The direction parallel to the semi-major axis of the screen
resolution is rotated counterclockwise from the $x$ axis by the angle,
$\psi_{\mathrm{AR}}$. The orientation of the screen as seen from Earth, $\xi$,
is measured East of North, again defined as that of the long, “parallel” axis.
The screen resolution element is shown in purple for an axial ratio of 2.06,
corresponding to an anisotropy parameter of $R=0.62$. It is to scale for an
observation at $820{\rm\;MHz}$ and a distance of $262{\rm\;pc}$ (using the
fractional distance to the screen of $s=0.643$ and a pulsar distance of
$735{\rm\;pc}$). For comparison, the projected path of the pulsar over eight
orbits is shown for $i=89\fdg 35$, using grey dots, each separated by ten
seconds. Note that it is the parallel direction along which to expect any
filamentary structure, but it is the perpendicular direction along which the
scintillation timescale changes fastest, and for which the screen velocity can
be best constrained.

In our fits, we depart from the fitting method used in R14 in two ways, to
minimize the effect of covariances on the properties of the screen. First, we
fit directly for the angle $\xi$ of the scintillation screen on the sky
(measured East from North, and constrained to fall in the range 0 to
$180^{\circ}$), making the orientation $\Omega=\xi+\psi_{\rm AR}$ of the
pulsar orbit a derived parameter (rather than vice versa). This is because
orbital motion directly constrains relative orientations between the screen
and the orbits: $\psi_{\rm AR}$ for the pulsar, and $\xi$ for the Earth.
Indeed, in the fits from R14, one sees that $\Omega$ and $\psi_{\rm AR}$ are
strongly correlated, while their difference $\Omega-\psi_{\rm{AR}}=\xi$ is
well constrained.

Second, we represent the velocity of the screen in directions parallel and
perpendicular to the screen’s semi-major axis rather than along the orbital
$x$ and $y$ coordinates as done in R14. This is because in the limit that
$R\rightarrow 1$ (i.e. a one-dimensional screen) the scintillation timescale
is completely independent of motion parallel to the screen orientation, and
hence the velocity along this direction becomes indeterminate. By using
velocity components in the screen coordinates, this uncertainty is directly
captured by the fits, while in any other coordinate system, the velocities and
uncertainties in both directions would be affected by it.

###  A.2 Data and Fitting

We fit for physical parameters of the pulsar and scattering screen using the
normalized orbital harmonic coefficients presented in R14. These coefficients
were measured from 17 observations taken between December 2003 and July 2005,
using the 100 m Robert C. Byrd Green Bank Telescope at either 1850 MHz with a
bandwidth of 800 MHz or 820 MHz with a bandwidth of 50 MHz. For details about
the observations and data reduction, see R14.

For the velocity of the Earth, $\mathbf{V}_{\mathrm{E}}$, we used the JPL
DE401 ephemeris (Park et al., 2021). The Earth velocity was calculated only
for the beginning of the observation since the change in Earth velocity during
an observation is very small. The interstellar plasma velocity,
$\mathbf{V}_{\mathrm{IS}}$, and the fractional distance to the screen, $s$,
were assumed to be constant between all epochs. Orbital phases and scales for
pulsar A were inferred using pint (Luo et al., 2019, 2021), using the
parameter file from Kramer et al. (2006) for comparison with R14, and that
from Kramer et al. (2021b) for the results presented here. Measurements of
Shapiro delay constrain the value of $\sin i$ but are degenerate with the sign
of $\cos i$. Like R14, we fit the scintillation timescales with the
inclination fixed for both signs of $\cos i$ as well as fitting $i$ as a free
parameter. The inclinations used were $i=88.7^{\circ}$ or $91.3^{\circ}$ from
Kramer et al. (2006), and $i=89.35^{\circ}$ or $90.65^{\circ}$ from Kramer et
al. (2021b).

###  A.3 Results

Table 4: Fitted Parameter, with 1$\sigma$ credible intervals | $\cos i>0$ | $\cos i<0$ |  $i$ free
---|---|---|---
Parameter |  $V_{\rm{IS},\parallel}$ free | $V_{\rm{IS},\parallel}=0$ |  $V_{\rm{IS},\parallel}$ free | $V_{\rm{IS},\parallel}=0$ |  $V_{\rm{IS},\parallel}$ free | $V_{\rm{IS},\parallel}=0$
i (deg) | 89.35 | 89.35 | 90.65 | 90.65 | 87.8 $\pm$ 1.2 | 88.85 $\pm$ 0.54
s | 0.646 $\pm$ 0.040 | 0.665 $\pm$ 0.031 | 0.614 $\pm$ 0.047 | 0.613 $\pm$ 0.045 | 0.708 $\pm$ 0.013 | 0.695 $\pm$ 0.023
$\xi$ (deg) aaScreen orientation measured east from declination axis | 178.6 $\pm$ 4.3 | 11.9 $\pm$ 4.7 | 174.2 $\pm$ 3.0 | 167.6 $\pm$ 3.9 | 176.3 $\pm$ 3.7 | 15.8 $\pm$ 5.0
R | 0.87 $\pm$ 0.11 | 0.63 $\pm$ 0.14 | 0.969 $\pm$ 0.057 | 0.840 $\pm$ 0.083 | 0.76 $\pm$ 0.17 | 0.44 $\pm$ 0.19
$\psi_{\rm{AR}}$ (deg) | 43 $\pm$ 10 | 34.9 $\pm$ 7.0 | 141.5 $\pm$ 8.9 | 148.7 $\pm$ 7.0 | 73 $\pm$ 13 | 43.6 $\pm$ 9.2
$V_{\rm{IS},\perp}$ (km/s) | -25.6 $\pm$ 1.5 | 23.7 $\pm$ 1.3 | -23.6 $\pm$ 1.9 | -21.9 $\pm$ 1.3 | -25.3 $\pm$ 1.7 | 25.3 $\pm$ 1.4
$V_{\rm{IS},\parallel}$ (km/s) | -46 $\pm$ 36 | 0 | 100 $\pm$ 120 | 0 | -47 $\pm$ 28 | 0
$N_{\rm{dof}}$ | 58 | 59 | 58 | 59 | 57 | 58
$\chi_{\nu}^{2}$ | 1.88 | 1.85 | 2.15 | 2.30 | 1.81 | 1.95
$d_{s}$ (pc) bbScreen distance uses pulsar distance $d_{p}=735\pm 60$ pc | 260 $\pm$ 51 | 246 $\pm$ 23 | 284 $\pm$ 55 | 284 $\pm$ 33 | 215 $\pm$ 18 | 224 $\pm$ 17
$\Omega$ (deg) | 42 $\pm$ 11 | 47 $\pm$ 12 | 136 $\pm$ 12 | 136 $\pm$ 11 | 69 $\pm$ 10 | 59 $\pm$ 14

To test our fitting routine, we first used parameters like in R14. We found
consistent results, except that our calculated reduced chi-squared values
($\chi_{\nu}^{2}$) differed somewhat, for reasons we do not quite understand
but possibly simply related to having somewhat different codes and
ephemerides. For all further fits, we used the updated pulsar timing values
from Kramer et al. (2021b). These give very similar results, which is not
unexpected, since for our purposes, all parameter changes except for the
distance are relatively small.

One of the biggest changes in the new timing parameters for PSR J0737$-$3039A
is the distance to the pulsar. In our fit setup, the only effect of changing
the pulsar distance is that it changes the systemic velocity of the pulsar
binary, $\mathbf{V}_{\mathrm{P}}$. R14 used
$V_{\rm{P}\alpha}=-17.8{\rm\;km/s}$ and $V_{\rm{P}\delta}=11.6{\rm\;km/s}$
based on the distance of $1.15^{+0.22}_{-0.16}{\rm\;kpc}$ determined by Deller
et al. (2009). More recent astrometry yields a distance of $770\pm
70{\rm\;pc}$, while the parallax inferred from timing implies
$465^{+134}_{-85}{\rm\;pc}$ (Kramer et al., 2021b). As in Kramer et al.
(2021b), we adopted a weighted mean of those distances, of $735\pm
60{\rm\;pc}$, and combine that with the the proper motion of
$(-2.567,2.082){\rm\;mas/yr}$ to calculate the velocities.

To see whether we could constrain the distance through scintillation, we tried
separate fits with each of these three distances. We found that we could not;
all that changes is the fitted screen velocity (proportionally to distance).
This is not surprising, since constraining the distance requires constraining
the pulsar angular orbital velocity, but for a nearly edge-on orbit and a
nearly one-dimensional screen, this is highly degenerate with the angle
$\psi_{\rm AR}$ between the screen and the orbit222For an overview, see
https://screens.readthedocs.io/en/latest/#modelling-scintillation-velocities.,
which we cannot constrain well at all.

Apart from the distance, the fits yield consistent results for all other
properties of the screen: a fractional distance from the pulsar $s\simeq 0.7$,
a high anistropy of $R\simeq 0.9$, a roughly N-S orientation, and a
perpendicular velocity of $v_{\perp}\simeq-25{\rm\;km/s}$. These values
consistent with those of R14.

In all cases, the nominal parallel screen velocity is rather large but also is
much more uncertain than the perpendicular velocity, as expected for
anisotropic screens. To test whether a large parallel screen velocity is
required to obtain a good fit, we set $V_{\rm{IS},\parallel}=0$ km/s and
repeat the analysis. Using the Akaike Information Criterion (AIC), we find
that large velocities are not required: fits with $V_{\rm{IS},\parallel}=0$
km/s are indeed worse but not by much, with the AIC increased from 121 to only
125 in the $i=89.35^{\circ}$ case (and from 137 to 146 for $i=90.65^{\circ}$,
and from 117 to 125 with $i$ left free). The fit also gives somewhat different
axial ratios (systematically lower, between 0.44 and 0.84) and screen
orientations (between 167.6∘ and 195.8∘), but only very slight changes in the
perpendicular velocity (between 21.9 km/s and 25.3 km/s) and fractional screen
distance (between 0.613 and 0.695). The fact that there is some sensitivity to
the parallel velocity suggests the screen is not fully linear (or that there
is a contribution from a second linear screen).

We conclude that the dominant screen is anisotropic, and that our parameters
of interest, the screen distance, orientation, and perpendicular velocity, are
well constrained.

Figure 3: H I filaments near PSR J0337+1715. H I brightness temperature
integrated over velocities of $-16.5$ to $11.5{\rm\;km/s}$ relative to the
kinematic local standard of rest. The identified H I filaments are not aligned
with the screen. Layout as in other figures.  Figure 4: H I filaments near PSR
J0437-4715. H I brightness temperature integrated over velocities of $-13.2$
to $13.2{\rm\;km/s}$ relative to the kinematic local standard of rest. There
is probable alignment of H I filaments with both screens. Layout as in other
figures.  Figure 5: H I filaments near PSR J0613-0200. H I brightness
temperature integrated over velocities of $-11.5$ to $11.7{\rm\;km/s}$
relative to the kinematic local standard of rest. There is probable alignment
of H I filaments with both screens. Note there is a cutoff in the H I
brightness temperature map due to the declination cutoff of -5∘ for the EBHIS
survey and a similar cutoff in the Rolling Hough Transform backprojections
corresponding to one Rolling Hough Transform window from the edge of the H I
data. This did not affect the filament measurements at the position of the
pulsar. Layout as in other figures.  Figure 6: H I filaments near PSR
J0636+5128. H I brightness temperature integrated over velocities of $-15.4$
to $7.8{\rm\;km/s}$ relative to the kinematic local standard of rest. The
identified H I filaments are not aligned with the screen. Layout as in other
figures.  Figure 7: H I filaments near PSR B0834+06. H I brightness
temperature integrated over velocities of $-9.3$ to $17.2{\rm\;km/s}$ relative
to the kinematic local standard of rest. The identified H I filaments are not
aligned with either screen. Note there is a cutoff in the H I brightness
temperature map due to the declination cutoff of $-1.17^{\circ}$. This did not
affect the filament measurements at the position of the pulsar. Layout as in
other figures.  Figure 8: H I filaments near PSR B1133+16. H I brightness
temperature integrated over velocities of $-12.8$ to $15.2{\rm\;km/s}$
relative to the kinematic local standard of rest. At velocities above
$7.8{\rm\;km/s}$ the emission is dominated by noise. The errors in the
orientations of screens c, d, e, and f are shown as $10^{\circ}$ which is an
underestimate of the measurement uncertainties but allows for them to be more
easily distinguished from each other. Screens c, d, and e have probable
alignment with H I filaments. Layout as in other figures.  Figure 9: H I
filaments near PSR B1508+55. H I brightness temperature integrated over
velocities of $-14.1$ to $9.1{\rm\;km/s}$ relative to the kinematic local
standard of rest. The error in the orientation of the strong scattering screen
a is shown as $10^{\circ}$ which is an underestimate of the measurement
uncertainty but allows for it to be more easily distinguished from weak
scattering screen a. There is probable alignment of an H I filament with
strong scattering screen a, but not with the other screens. Layout as in other
figures.  Figure 10: H I filaments near PSR J1643-1224. H I brightness
temperature integrated over velocities of $-10.7$ to $15.7{\rm\;km/s}$
relative to the kinematic local standard of rest. Both screens have probable
alignment with an H I filament. Layout as in other figures.  Figure 11: H I
filaments near PSR J1909-3744. H I brightness temperature integrated over
velocities of $-15.7$ to $10.7{\rm\;km/s}$ relative to the kinematic local
standard of rest. The identified H I filaments are not aligned with the
screen. Layout as in other figures.

  *[ISM]: interstellar medium
  *[VLBI]: very long baseline interferometry