# A Tale of Three Dust Populations: Variable $R_{\rm{V}}$ and Extreme
Polarization Along Sightlines Toward $\zeta$ Ophiuchi

Ashley N. Piccone  University of Wyoming
1000 E University Ave
Laramie, WY 82071  Henry A. Kobulnicky  University of Wyoming
1000 E University Ave
Laramie, WY 82071 Ashley Piccone<EMAIL_ADDRESS>
###### Abstract

Dust permeates the interstellar medium, reddening and polarizing background
starlight, but dust properties vary with local environment. In order to
characterize dust in a highly irradiated diffuse cloud, we measure the
reddening and optical polarization towards 27 stars surrounding the mid-
latitude $b$=$+$24° O9.2IV star $\zeta$ Ophiuchi, using new optical
spectroscopy and polarimetry. We incrementally deredden and depolarize with
distance, allowing us to distinguish dust components along these sightlines.
The data indicate three distinct dust populations: a foreground component
characteristic of average Milky Way dust ($R_{\rm{V}}$$\approx$3.1,
$d$$\lesssim$180 pc), a highly polarizing mid-distance component in the
vicinity of $\zeta$ Oph ($R_{\rm{V}}$$\approx$2.4, 200 pc$<$$d$$<$300 pc), and
a non-polarizing distant component ($R_{\rm{V}}$$\approx$3.6, 600
pc$<$$d$$<$2000 pc). Prominent 8 $\mu$m infrared striations spanning the field
of view likely have high Polycyclic Aromatic Hydrocarbon content and are
illuminated by $\zeta$ Oph. Foreground-subtracted polarizations roughly align
with these striations, which, we argue, lie immediately behind $\zeta$ Oph and
constitute the highly-polarizing mid-distance dust. This component polarizes
very efficiently ($P_{\rm{V}}$$>$9.1$E(B-V)$), implying a high degree of grain
alignment and suggesting that the bulk of the polarization occurs in a small
fraction of the volume. The large $R_{\rm{V}}$ in the distant component
reveals that dust above the Galactic Plane ($z$$>$250 pc) may contain a
greater fraction of large grains than the Milky Way average.

††facilities: WIRO, APO, ARC, Spitzer, IRSA††software: IRAF (Tody, 1986),
LACosmics (van Dokkum, 2001), PyHammer (Roulston et al., 2020), Rolling Hough
Transform (Clark et al., 2014)

##  1 Introduction

Dust is an integral component of the interstellar medium, infiltrating signals
from both Galactic and extragalactic objects. Interstellar dust extincts and
reddens background light, necessitating corrections in most astronomical
observations. Dust grains range in size depending on the environment and are
thought to follow a power law distribution as the result of formation and
destruction processes (Clayton et al., 2003). Precise corrections for dust
depend on understanding not only its spatial distribution but also the grain
size distribution and its extinction properties in all three dimensions. All-
sky infrared dust maps, like those from Schlegel et al. (1998) and Schlafly &
Finkbeiner (2011), provide a low resolution image of dust distribution in the
Milky Way. Schlafly et al. (2017) and Green et al. (2019) have revealed dust
populations as a function of Galactic position and distance. However, these
dust maps are not capable of revealing how grain properties vary as a function
of local environments nor have they completely constrained how those
properties may change above the Plane.

Dust is often characterized by its extinction in magnitudes at V band
($A_{\rm{V}}$) and ratio of interstellar extinction to reddening
($R_{\rm{V}}$). The two quantities are related by $A_{\rm{V}}$$=$
$R_{\rm{V}}$$E(B-V)$, where $E(B-V)$ is the color excess or reddening. The
average $R_{\rm{V}}$ in the Milky Way is $\approx$3.1 (Schultz & Wiemer,
1975). Larger $R_{\rm V}$ indicates an abundance of large dust grains, while a
smaller $R_{\rm V}$ indicates a shift toward smaller dust grains (Mathis &
Wallenhorst, 1981). The transition between dense and diffuse clouds at
$A_{\rm{V}}$$\approx$3.2 mag. corresponds to a transition in $R_{\rm{V}}$ as
well: dense clouds have large $R_{\rm{V}}$ (3.5–4.0), while diffuse clouds
have small or near-average $R_{\rm{V}}$ (Whittet et al., 2001). Large
$R_{\rm{V}}$ clouds show a reduction in the number of small dust grains,
possibly as a result of aggregation of small particles in dense environments
(Kim & Martin, 1996). In diffuse cloud environments, ultraviolet photons may
alter the grain size distribution in the opposite sense, leading to a small
$R_{\rm{V}}$ through the destruction and fragmentation of large grains
(Aannestad, 1995). Many studies using coarse maps of interstellar reddening
(for example, Green et al., 2019) to correct for dust assume
$R_{\rm{V}}$$\approx$3.1 and therefore do not account for dust properties that
may vary by sightline or even with distance along a single sightline.

While dust properties like $A_{\rm{V}}$ and $R_{\rm{V}}$ can be measured with
photometry and spectrophotometry, optical polarimetry of background stars
provides another tool to probe the size, orientation, and alignment of grains.
Hiltner (1949) and Hall (1949) first discovered that dust polarizes background
starlight, which is a consequence of non-spherical dust grains aligned
perpendicular to the interstellar magnetic field (Davis & Greenstein, 1951).
Radiative torques (RATs) have emerged as the dominant theory for grain
alignment. RAT theory suggests that helical dust grains are spun up by an
anisotropic radiation field so that their long axes are perpendicular to the
magnetic field (Lazarian & Hoang, 2007). A larger fraction of dust grains are
aligned and create a more polarized signal when the ambient radiation is along
magnetic field lines (Andersson et al., 2011). Grain alignment is therefore
likely enhanced near radiation sources having high specific intensity
(Andersson et al., 2015).

The mechanism of grain alignment depends on the size and composition of dust
grains and the radiative environment. By studying the dark star-forming cloud
$\rho$ Ophiuchi in far-infrared emission, Santos et al. (2019) discovered that
polarization fraction decreases with increasing column density (and hence,
extinction), possibly due to increased magnetic field disorder or a loss of
alignment efficiency deep within clouds. They proposed that warm dust grains
at the outskirts of clouds are aligned through RAT while inner cold grains are
shielded. While all grain alignment mechanisms fail at the center of dark
clouds, those with smaller extinctions are expected to show more efficient
alignment (Lazarian et al., 1997).

The high-space-velocity, hot, O9.2IV star $\zeta$ Ophiuchi makes an
interesting laboratory for examining extinction and polarization along
sightlines through a diffuse high-radiation environment. Because it is nearby,
at moderate Galactic latitude (b=$+$24°), and has a well-characterized
foreground (Serkowski et al., 1975; Tachihara et al., 2000; Liszt et al.,
2009; Choi et al., 2015; Siebenmorgen et al., 2020), the field of view around
the star allows for relatively unconfused measurements of dust properties with
distance. Hipparcos parallax measurements place $\zeta$ Oph at a distance of
112 pc (van Leeuwen, 2007), but more recent estimates from $Gaia$ suggest a
distance of 182${}^{+53}_{-34}$ pc (Bailer-Jones et al., 2018). Because
$\zeta$ Oph has an mG=2.46, it falls into a regime in which $Gaia$ distances
may have large systematic errors (Drimmel et al., 2019). However, Siebenmorgen
et al. (2020) used two other distance estimates, the Ca II distance scale and
the spectrophotometric distance, to calculate distances of 230${}^{+8}_{-12}$
pc. We will adopt a distance of 182${}^{+53}_{-34}$ pc for the remainder of
this work. Figure 2 illustrates the $\zeta$ Oph region and reveals the
prominent dust structures in infrared images from the Spitzer Space Telescope
(Spitzer). Red/green/blue represent 24/8/4.5 $\mu$m respectively. $\zeta$ Oph
is preceded by a high-surface-brightness bowshock nebula, first discovered by
Gull & Sofia (1979) in H$\alpha$ at a standoff distance of 299″ or 0.26 pc at
the adopted distance of 182 pc (Kobulnicky et al., 2019). The high proper
motion of $\zeta$ Oph is parallel to the symmetry axis of the bowshock nebula
and is shown by the magenta vector in Figure 2. Fainter infrared dust
structures also span the Spitzer image. These striations align approximately
perpendicular to the bowshock structure and parallel to the peculiar motion of
$\zeta$ Oph. The relationship between the fainter striations in Figure 2 and
the bowshock nebula is unclear. The striations are large and extend much
further than the bowshock itself and well beyond the pictured field of view.
These dust structures— the striations and the bowshock— are large in angular
size, making them both interesting and easily accessible for investigating
$A_{\rm{V}}$, $R_{\rm{V}}$, and polarization through this diffuse, high
radiation environment.

This work investigates the reddening and polarization along lines of sight in
the high-radiation, diffuse environment surrounding $\zeta$ Oph in order to
identify and characterize dust populations in that field as a function of
distance. Section 2 introduces new spectrophotometry from the Apache Point
Observatory, optical polarimetry from the Wyoming Infrared Observatory, and
data reduction. Section 3 presents the spectral types, reddening estimates,
and polarizations towards 27 background stars. Using available photometry in
conjunction with our observations, we identify three primary dust structures
located at various distances in the field of view. Section 4 explores the
three dust populations and their relationships to the projected magnetic field
and infrared striations. In Section 5, we summarize the conclusions from this
investigation.

##  2 Observations and Data Reduction

We selected stars in close angular proximity to $\zeta$ Oph that were
accessible to the observational limits of spectroscopy and polarimetry on a
2–4 m telescope. This resulted in twenty-seven target stars both directly
behind the bowshock nebula and in the surrounding field, with magnitudes
$m_{f}\leq 15.2$, where $m_{f}$ is the UCAC4 catalog optical photographic fit
model magnitude (Zacharias et al., 2013). Table 1 lists basic data for the 27
targets. Column 1 provides the target number that is referenced throughout
this paper. Column 2 lists the $Gaia$ identifier. Columns 3 and 4 provide the
right ascension and declination of the target, column 5 gives the UCAC4
optical magnitude, and column 6 gives the V-band magnitude from the AAVSO
Photometric All-Sky Survey (APASS; Henden et al., 2016). Where APASS data were
unavailable (targets #14, #15, and #17), we use Panoramic Survey Telescope and
Rapid Response System (Pan-STARRS; Chambers et al., 2019) photometry in g′ and
r′ and the transformations from Jester et al. (2005) for the V-band magnitude.
Column 7 gives the $Gaia$ distance from Bailer-Jones et al. (2018). Target
distances appear bi-modal (as seen in subsequent Figures 5 and 8) and fall
into two distinct groups: a “near group” (14 stars) with distances $\leq$600
pc and a “far group” (13 stars) with distances $\geq$1000 pc.

Table 1: Targets observed in the $\zeta$ Ophiuchi field. Target |  Gaia ID | R.A. | Dec. | mf | mV | d
---|---|---|---|---|---|---
|  | (°) | (°) | (mag.) | (mag.) | (pc)
$\zeta$ Oph | 4337352305315545088 | 249.2875 | -10.5669 | … | 2.56 | 182${}_{-34}^{+53}$
1 | 4338102545907455744 | 249.0266 | -10.5774 | 13.18 | 13.08 | 436.1${}_{-9.1}^{+7.9}$
2 | 4338102722003440000 | 249.0303 | -10.5656 | 13.01 | 13.21 | 2819${}_{-287}^{+358}$
3 | 4338103271759259392 | 249.0668 | -10.5238 | 14.55 | 14.51 | 3019${}_{-227}^{+265}$
4 | 4338102923864645120 | 249.1036 | -10.5442 | 11.84 | 11.90 | 224.0${}_{-2.0}^{+1.1}$
5 | 4338108288281067264 | 249.1334 | -10.4531 | 13.85 | 14.05 | 423.3${}_{-5.3}^{+4.7}$
6 | 4338103684076094464 | 249.1438 | -10.5379 | 13.33 | 13.38 | 252.2${}_{-2.2}^{+0.8}$
7 | 4338108460079758336 | 249.1620 | -10.4341 | 14.68 | 14.94 | 8434${}_{-1480}^{+2077}$
8 | 4338128972843559808 | 249.1805 | -10.4329 | 14.43 | 14.69 | 2420${}_{-170}^{+197}$
9 | 4338104199472164352 | 249.2086 | -10.5013 | 13.86 | 13.94 | 435.5${}_{-5.5}^{+4.6}$
10 | 4338103507980197248 | 249.2088 | -10.5421 | 12.74 | 13.13 | 1294${}_{-63}^{+68}$
11 | 4338104405630603904 | 249.2136 | -10.4704 | 14.61 | 14.97 | 278.3${}_{-2.5}^{+2.6}$
12 | 4338104405630602240 | 249.2170 | -10.4745 | 15.10 | 15.49 | 3247${}_{-375}^{+482}$
13 | 4338104126455487488 | 249.2367 | -10.4871 | 12.23 | 12.32 | 427.6${}_{-6.6}^{+6.4}$
14 | 4337353404830237056 | 249.2431 | -10.5256 | 14.67 | 14.72aaAPASS photometry was not available. Pan-STARRS photometry is used with transformations from Jester et al. (2005). | 489.2${}_{-7.1}^{+7.3}$
15 | 4337353370470494464 | 249.2637 | -10.5214 | 14.80 | 15.07aaAPASS photometry was not available. Pan-STARRS photometry is used with transformations from Jester et al. (2005). | 2500${}_{-190}^{+223}$
16 | 4337377181769178752 | 249.3271 | -10.4865 | 13.49 | 13.69 | 2350${}_{-125}^{+138}$
17 | 4337376700732832512 | 249.3277 | -10.5117 | 14.31 | 14.56aaAPASS photometry was not available. Pan-STARRS photometry is used with transformations from Jester et al. (2005). | 2537${}_{-190}^{+222}$
18 | 4337372543204454144 | 249.3699 | -10.5763 | 13.26 | 13.33 | 307.5${}_{-5.5}^{+4.5}$
19 | 4337376288415957120 | 249.3703 | -10.5152 | 14.91 | 15.21 | 4645${}_{-628}^{+842}$
20 | 4337376528934134144 | 249.3904 | -10.4833 | 14.79 | 14.90 | 2616${}_{-190}^{+222}$
21 | 4337376460214656896 | 249.3975 | -10.4786 | 14.50 | 14.75 | 2299${}_{-204}^{+246}$
22 | 4337372985583902848 | 249.4100 | -10.5507 | 15.17 | 15.44 | 4790${}_{-709}^{+975}$
23 | 4337347598034360704 | 249.4194 | -10.6498 | 13.39 | 13.51 | 552.4${}_{-6.4}^{+5.6}$
24 | 4337372852442084096 | 249.4617 | -10.5519 | 12.16 | 12.20 | 202.7${}_{-1.7}^{+1.3}$
25 | 4337359452144088448 | 249.4686 | -10.6339 | 13.39 | 13.42 | 490.4${}_{-5.4}^{+4.6}$
26 | 4337371787290173952 | 249.5049 | -10.5797 | 13.04 | 13.06 | 581.7${}_{-13.7}^{+13.3}$
27 | 4337375218965869568 | 249.5108 | -10.4688 | 12.90 | 12.95 | 526.5${}_{-10.5}^{+10.5}$

###  2.1 APO Spectrophotometry

We obtained spectra of the 27 targets using the Apache Point Observatory (APO)
Dual Imaging Spectrograph (DIS) on 2019 May 2 and 3 (21 targets) and 2021
March 30 (six targets). The two channels of the spectrograph covered 4000–5240
Å with a reciprocal dispersion of 0.62 Å pix-1 and 5720–6880 Å with a
reciprocal dispersion of 0.58 Å pix-1, both using a 1200 lines mm-1 grating.
Observations were taken with 1$\farcs$5–2″ slits oriented at the parallactic
angle. The seeing average was near 2″ over 1.3–1.7 airmasses. Exposure times
ranged from 300 s to 600 s with 1–2 exposures per star. The continuum SNR per
pixel ranged from 16–37 at 4500 Å and 40–71 at 6200 Å. The data were
wavelength calibrated using HeNeAr exposures every 1–2 hours. Observations of
spectrophotometric standard stars HZ 44, BD+33 2642, and BD+28 4211 from Oke
(1990) over airmasses 1.07–2.06 were used for flux calibration.

The spectra were processed in the standard manner with IRAF (Tody, 1986) tasks
to remove bias level using overscan regions on each exposure and correct for
pixel-to-pixel variations with continuum flat fields. We corrected for
atmospheric extinction over a range of airmasses with standard star data. The
extinction-corrected standard stars differ from the Oke (1990) spectra by no
more than 7% at extreme blue end and smaller percentages at the extreme red
end.

###  2.2 WIRO Polarimetry

Polarimetric observations of the 27 stars were made 2019 April 26–28, May 4,
and June 6 using the OptiPol optical polarimeter (Jones et al., 2008) at the
Cassegrain focus of the Wyoming Infrared Observatory (WIRO) 2.3 m telescope.
The instrument employs a Wollaston prism to image orthogonal polarizations
simultaneously onto a 10242 Apogee Alta F16M with Kodak KAF-16803 CCD array
with 9 $\mu$m pixels at a scale of 0$\farcs$12 pix-1 (when on-chip 4$\times$4
binning is used), yielding a 40″$\times$80″ field of view. A sequence of
exposures was obtained in the V-band filter for each target at four angular
positions (0°, 22.5°, 45°, and 67.5°) of a half-wave plate. Exposure times
ranged from 6–200 seconds, according to target brightness. Unpolarized
standards BD$+$33 2642, BD$+$28 4211 (Schmidt et al., 1992), and HD 154892
(Turnshek et al., 1990) were observed to determine the instrumental
polarization for each night.

The data from each position of the waveplate were processed in a standard
manner using IRAF (Tody, 1986) to remove contributions from dark current, bias
level, and pixel-to-pixel sensitivity variations. We used the LACosmics python
script (based on algorithms from and developed by van Dokkum, 2001) to clean
cosmic rays from the data. We used a custom python code to perform aperture
photometry on each image and compute the normalized q and u Stokes parameters
using the method from Tinbergen (2005).

Polarized standard stars HD 155197, HD 161056, and VI Cyg 12 (Schmidt et al.,
1992) were used to determine an instrumental position angle offset of 81.5∘
and verify the percent polarization. Average instrumental polarization was
small ($q$=-0.20, $u$=0.19). The instrumental polarization was subtracted in
the $q$–$u$ plane, and the calibrated Stokes parameters were calculated. Using
these quantities, the percent polarization ($P_{\rm{V}}^{\prime}$) and the
position angle East of North (P.A.) are given by the standard relations:
$P_{\rm{V}}^{\prime}$=$\sqrt{q^{2}+u^{2}}$ and
P.A.$=$$\frac{1}{2}\tan^{-1}\frac{u}{q}$. To correct the data for positive
bias, we used the relationship that $P_{\rm{V}}$=$\sqrt{P_{\rm{V}}^{\prime
2}-\sigma_{P}^{2}}$, where $\sigma_{P}$ is the polarization uncertainty
propagated from errors in $q$ and $u$ (Wardle & Kronberg, 1974).

Table 2 reports the polarimetric results. Column 1 lists the target number
corresponding to Table 1, columns 2 and 3 list the $q$ and $u$ values, column
4 lists the percent polarizations, $P_{\rm{V}}$, and 1$\sigma$ uncertainties,
and column 5 lists the position angles, P.A., and 1$\sigma$ uncertainties.

Table 2: Polarization data for the target stars in Table 1.

Target |  q (%) |  u (%) |  $P_{\rm{V}}$ (%) | P.A. (°) |  qf (%) |  uf (%) |  $P_{\rm{Vf}}$ (%) | P.A.f (°)
---|---|---|---|---|---|---|---|---
$\zeta$ Oph | $-0.45\pm 0.04$ | $-1.37\pm 0.04$ | $1.44\pm 0.04$ | $126.0\pm 0.8$ | … | … | … | …
1 | $-1.04\pm 0.28$ | $-0.36\pm 0.27$ | $1.06\pm 0.28$ | $99.5\pm 7.1$ | $-0.60\pm 0.28$ | $1.01\pm 0.27$ | $1.14\pm 0.27$ | $60.3\pm 6.8$
2 | $-1.26\pm 0.23$ | $-0.61\pm 0.25$ | $1.38\pm 0.23$ | $102.9\pm 5.0$ | $-0.82\pm 0.23$ | $0.76\pm 0.25$ | $1.09\pm 0.24$ | $68.5\pm 6.2$
3 | $-1.78\pm 0.21$ | $-1.00\pm 0.21$ | $2.03\pm 0.21$ | $104.7\pm 3.0$ | $-1.34\pm 0.21$ | $0.37\pm 0.21$ | $1.37\pm 0.21$ | $82.3\pm 4.3$
4 | $-0.60\pm 0.10$ | $-1.80\pm 0.10$ | $1.89\pm 0.10$ | $125.8\pm 1.5$ | $-0.15\pm 0.10$ | $-0.43\pm 0.10$ | $0.45\pm 0.10$ | $125.1\pm 6.3$
5 | $-1.41\pm 0.18$ | $-1.27\pm 0.18$ | $1.89\pm 0.18$ | $111.0\pm 2.7$ | $-0.96\pm 0.18$ | $0.10\pm 0.18$ | $0.95\pm 0.18$ | $87.0\pm 5.3$
6 | $-0.81\pm 0.42$ | $-1.82\pm 0.25$ | $1.97\pm 0.29$ | $123.0\pm 5.7$ | $-0.37\pm 0.42$ | $-0.45\pm 0.25$ | $0.48\pm 0.33$ | $115.5\pm 17.9$
7 | $-1.68\pm 0.25$ | $-0.97\pm 0.24$ | $1.92\pm 0.25$ | $105.0\pm 3.6$ | $-1.23\pm 0.25$ | $0.40\pm 0.24$ | $1.27\pm 0.25$ | $81.0\pm 5.3$
8 | $-1.38\pm 0.29$ | $-1.75\pm 0.28$ | $2.21\pm 0.28$ | $115.9\pm 3.7$ | $-0.93\pm 0.29$ | $-0.38\pm 0.28$ | $0.97\pm 0.29$ | $101.1\pm 8.0$
9 | $-1.54\pm 0.16$ | $-0.93\pm 0.16$ | $1.79\pm 0.16$ | $105.6\pm 2.6$ | $-1.10\pm 0.16$ | $0.44\pm 0.16$ | $1.17\pm 0.16$ | $79.1\pm 3.9$
10 | $-1.93\pm 0.23$ | $-1.08\pm 0.22$ | $2.20\pm 0.23$ | $104.6\pm 2.9$ | $-1.48\pm 0.23$ | $0.29\pm 0.22$ | $1.50\pm 0.23$ | $84.5\pm 4.2$
11 | $-2.07\pm 0.35$ | $-0.99\pm 0.35$ | $2.27\pm 0.35$ | $102.8\pm 4.4$ | $-1.62\pm 0.35$ | $0.38\pm 0.35$ | $1.63\pm 0.35$ | $83.4\pm 6.0$
12 | $-1.05\pm 0.25$ | $-1.89\pm 0.24$ | $2.15\pm 0.24$ | $120.5\pm 3.3$ | $-0.60\pm 0.25$ | $-0.52\pm 0.24$ | $0.76\pm 0.25$ | $110.3\pm 8.8$
13 | $-1.03\pm 0.07$ | $-0.85\pm 0.07$ | $1.33\pm 0.07$ | $109.8\pm 1.5$ | $-0.58\pm 0.07$ | $0.52\pm 0.07$ | $0.78\pm 0.07$ | $69.2\pm 2.6$
14 | $-2.13\pm 0.42$ | $-0.75\pm 0.42$ | $2.22\pm 0.42$ | $99.7\pm 5.3$ | $-1.68\pm 0.42$ | $0.62\pm 0.42$ | $1.75\pm 0.42$ | $79.9\pm 6.7$
15 | $-1.55\pm 0.29$ | $0.02\pm 0.31$ | $1.52\pm 0.29$ | $89.6\pm 5.7$ | $-1.10\pm 0.29$ | $1.39\pm 0.31$ | $1.75\pm 0.30$ | $64.2\pm 4.8$
16 | $-1.75\pm 0.25$ | $-0.89\pm 0.22$ | $1.95\pm 0.24$ | $103.5\pm 3.3$ | $-1.30\pm 0.25$ | $0.48\pm 0.22$ | $1.37\pm 0.25$ | $79.9\pm 4.6$
17 | $-1.68\pm 0.24$ | $-0.34\pm 0.23$ | $1.70\pm 0.24$ | $95.7\pm 3.9$ | $-1.23\pm 0.24$ | $1.03\pm 0.23$ | $1.59\pm 0.24$ | $70.1\pm 4.2$
18 | $-1.39\pm 0.39$ | $0.48\pm 0.39$ | $1.42\pm 0.39$ | $80.5\pm 7.6$ | $-0.94\pm 0.39$ | $1.85\pm 0.39$ | $2.04\pm 0.39$ | $58.5\pm 5.4$
19 | $-1.63\pm 0.40$ | $-0.72\pm 0.36$ | $1.74\pm 0.39$ | $101.9\pm 5.9$ | $-1.18\pm 0.40$ | $0.65\pm 0.36$ | $1.29\pm 0.39$ | $75.6\pm 7.8$
20 | $-1.20\pm 0.29$ | $-0.82\pm 0.28$ | $1.42\pm 0.29$ | $107.2\pm 5.6$ | $-0.75\pm 0.29$ | $0.55\pm 0.28$ | $0.89\pm 0.29$ | $72.0\pm 8.7$
21 | $-1.33\pm 0.30$ | $-0.23\pm 0.29$ | $1.32\pm 0.30$ | $94.9\pm 6.2$ | $-0.88\pm 0.30$ | $1.14\pm 0.29$ | $1.41\pm 0.29$ | $63.9\pm 5.9$
22 | $-2.04\pm 0.40$ | $0.66\pm 0.42$ | $2.11\pm 0.40$ | $81.0\pm 5.6$ | $-1.60\pm 0.40$ | $2.03\pm 0.42$ | $2.55\pm 0.41$ | $64.1\pm 4.5$
23 | $-1.22\pm 0.15$ | $-0.30\pm 0.15$ | $1.25\pm 0.15$ | $96.9\pm 3.4$ | $-0.77\pm 0.15$ | $1.07\pm 0.15$ | $1.31\pm 0.15$ | $63.0\pm 3.3$
24 | $-0.78\pm 0.07$ | $-0.75\pm 0.07$ | $1.08\pm 0.07$ | $111.9\pm 1.9$ | $-0.34\pm 0.07$ | $0.62\pm 0.07$ | $0.70\pm 0.07$ | $59.2\pm 2.9$
25 | $-0.58\pm 0.53$ | $-0.01\pm 0.46$ | $0.24\pm 0.53$ | $90.5\pm 22.7$ | $-0.13\pm 0.53$ | $1.36\pm 0.46$ | $1.29\pm 0.46$ | $47.8\pm 11.1$
26 | $-1.89\pm 0.23$ | $-0.15\pm 0.16$ | $1.88\pm 0.23$ | $92.3\pm 2.4$ | $-1.44\pm 0.23$ | $1.22\pm 0.16$ | $1.88\pm 0.20$ | $69.9\pm 2.9$
27 | $-1.45\pm 0.12$ | $-0.42\pm 0.12$ | $1.50\pm 0.12$ | $98.1\pm 2.3$ | $-1.00\pm 0.12$ | $0.95\pm 0.12$ | $1.38\pm 0.12$ | $68.3\pm 2.5$

footnotetext: f represents polarization values after subtracting $\zeta$ Oph
in the q–u plane.

Figure 2 shows the V-band polarization vectors overlaid on a 32′$\times$18′
version of the Spitzer field surrounding $\zeta$ Oph. The orientation of the
numbered white vectors demonstrates the polarization position angle for each
target in Table 1. The length of the vectors shows the percent polarization.
The legend illustrates 1% polarization at PA=0°. We also show the polarization
of $\zeta$ Oph at V band to be 1.44% at PA=126$\arcdeg$ (Serkowski et al.,
1975).

Figure 1: The $\zeta$ Oph field from Spitzer 24 $\mu$m, 8 $\mu$m, and 4.5
$\mu$m images. The bowshock nebula precedes the star and has a high surface
brightness. At a distance of 182 pc, the apex of the nebula is a projected
0.26 pc from $\zeta$ Oph. The magenta vector shows this distance and the
direction of the star’s motion. Fainter dust striations span the entire field
of view and are best traced in green (8 $\mu$m). White vectors show
$P_{\rm{V}}$ and P.A. relative to the $P_{\rm{V}}$=1% and P.A.=0° legend.
Numbers next to each vector provide the target identifier as in Table 1.

Figure 2: Foreground-subtracted polarization vectors, $P_{\rm{Vf}}$ and PAf,
overlaid on the same infrared images as in Figure 2. Blue dashed lines show
the orientation of the 8 $\mu$m dust striations above and below the bowshock
as traced by the Rolling Hough Transform from Clark et al. (2014), detailed in
Section 3.3.

A majority of the stars in Figure 2 show similar position angles and
polarization percentages. The mean P.A. for the 27 targets is 103° with a
standard deviation of 11° and the mean $P_{\rm{V}}$ is 1.68% with a standard
deviation of 0.46%. The mean position angle of the polarization vectors is
smaller than that of $\zeta$ Oph, but the mean percent polarization is larger
than that of $\zeta$ Oph (Serkowski et al., 1975). Targets at similar
distances to $\zeta$ Oph, like #4 (224 pc) and #6 (252 pc), are in better
agreement with the position angle of $\zeta$ Oph than targets at larger
distances and have larger-than-average polarizations. Other stars at modest
distances (278–500 pc; #11, #13, #14) and beyond exhibit a rotation in
position angle relative to the nearest stars and have a notable uniformity in
$P_{\rm{V}}$ and P.A.

To examine the polarization beyond $\zeta$ Oph, we subtracted the polarization
of $\zeta$ Oph itself from each of our polarization measurements in the q–u
plane. For $\zeta$ Oph, q=$-$0.445 and u=$-$1.37 from Serkowski et al. (1975).
When added in quadrature, the errors from our measurements dominate over the
errors in the polarization of $\zeta$ Oph. Table 2 columns 6, 7, 8, and 9
provides the foreground-subtracted quantities, $q_{\rm f}$, $u_{\rm f}$,
$P_{\rm{Vf}}$, and P.A.f.111$q_{\rm f}$=$q$-(-0.445) and $u_{\rm
f}$=$u$-(-1.37). $P_{\rm{Vf}}$ and P.A.f are constructed in the usual manner
from these quantities.  Using the same notation as Figure 2, Figure 2 presents
the foreground-subtracted polarization vectors on the infrared Spitzer image.
This subtraction results in much smaller $P_{\rm{Vf}}$ for the three nearest
stars (targets #4, #6, and #24) and an abrupt change in P.A. for the rest of
the field. The foreground-subtracted mean values are $P_{\rm{Vf}}$=1.29% with
a dispersion of 0.47% and P.A.f=77.2° with a dispersion of 17.8°.

##  3 Analysis

###  3.1 Extinction Estimates

In order to investigate the interstellar extinction throughout the field of
view, we estimated $A_{\rm{V}}$ using four different methods. Three of these
methods, $A_{\rm{V}}$(spectra), $A_{\rm{V}}$(phot) and $A_{\rm{V}}$(RJCE),
assume $R_{\rm{V}}$=3.1 and are described in detail and compared below. The
fourth, complementary but separate method allows $R_{\rm{V}}$ to deviate from
the Milky Way average. The combination of these extinction estimates allows us
to examine the dust properties as a function of distance.

####  3.1.1 Determining Target Spectral Types

As a prerequisite to calculating extinction, we first determined the spectral
types of the target stars. We compared our continuum-normalized spectra to
continuum-normalized PHOENIX stellar models (Husser et al., 2013) to determine
approximate Teff by visual examination. As another check on the spectral
types, we used the spectral classification code PyHammer (Roulston et al.,
2020). Visual inspection agreed with the PyHammer results within about 300 K.

While our optical spectra provide an estimate of the effective temperature for
the target stars, their positions on the H-R diagram offer additional insight
regarding their evolutionary status (i.e. $\log$ $g$). Figure 3 plots the
absolute K magnitude (as computed from the distance modulus) versus Teff for
the near group (blue squares) and the far group (red squares).
Cyan/magenta/black tracks show 109.6/109/108 yr isochrones from Bressan et al.
(2012, PARSEC, version 1.2S, adopting solar metallicity)222As computed using
the web interface http://stev.oapd.inaf.it/cgi-bin/cmd on 2020 December 15..
The main sequence emanates from the lower right corner of the plot. The main-
sequence turnoffs are visible. The tracks change from points to encircled
points as the stars evolve into giants ($\log$ $g$ falls below 3). The near
group of stars at distances $d$$<$600 pc and $z$ heights $\lesssim$240 pc
above the Plane are consistent with near-main-sequence F–G V–IV stars (the
track of small cyan points), for which we may reasonably adopt $\log$ $g$=4.0
and metallicity [M/H]=0, appropriate for the Galactic disk population. The far
group of targets at distances $d$$>$1000 pc and $z$ heights $>$400 pc are
consistent with post-main-sequence giants with ages $<$1 Gyr (the track of
small magenta points as they transition into encircled points). At such young
ages, the far group cannot—despite their larger $z$ distances—be metal-poor
thick disk or halo stars. We adopt $\log$ $g$=3.0 and metallicity [M/H]=0 for
these objects. For the two most luminous objects, 2 and 7, which are also
among the most distant in our sample, we adopt $\log$ $g$=2.0. We created
similar plots with reduced-metallicity ($-$0.5 dex) isochrones for comparison
and found metallicity has negligible impact on the inferred ages and
gravities.

Figure 3: Absolute K magnitude versus effective temperature for the near group
of background stars (blue squares) and the far group (red squares). Colored
tracks show solar metallicity PARSEC (Bressan et al., 2012) isochrones at ages
of 109.6/109/108 yr, as labeled. Large symbols denote the approximate onset of
giants at $\log$g$<$3\. The near group is consistent with near-main-sequence
F–G stars while the far group consists of post-main-sequence giants.

Given these fundamental parameters ($T_{\rm eff}$, $\log$ $g$, [M/H]), we
assigned a PHOENIX model spectrum to represent the intrinsic spectral energy
distribution needed to characterize the interstellar extinction along each
sightline. Table 3 lists target number in column 1, adopted effective
temperature in column 2, adopted $\log$ $g$ in column 3, and corresponding
approximate spectral type in column 4. Our targets are F, G, and K stars that
correspond to PHOENIX model temperatures in the range 5000–6100 K, based on
the effective temperature versus spectral type sequence from Pecaut & Mamajek
(2013). By visual comparison of PHOENIX models to spectra, we estimate that
our classifications are accurate to $\pm$300 K, or approximately 3–4 subtypes.

####  3.1.2 Fitting for $A_{\rm{V}}$(spectra) with APO Spectra

As an initial extinction estimate, we calculated $A_{\rm{V}}$ using the APO
spectra. We smoothed the stellar model templates and the data to ten broad
wavelength intervals, as only the overall shape of the spectrum is needed to
fit for extinction. We normalized the stellar model from Table 3 and the flux-
calibrated spectra at the longest wavelength interval, but the derived
extinctions remain the same with any normalization. We then divided the
spectra by the corresponding PHOENIX model to obtain a curve that reflects the
wavelength-dependent interstellar extinction, $A_{\rm{\lambda}}$. The curve
was then fit using the Cardelli et al. (1989, equations 1, 2, and 3) optical
reddening parameterization with a fixed $R_{\rm{V}}$=3.1 to obtain
$A_{\rm{V}}$(spectra). The resulting range of $A_{\rm{V}}$(spectra) is
0.79–3.27 magnitudes, and values are tabulated in column 5 of Table 3.
Uncertainties on $A_{\rm{V}}$(spectra) (also shown in Table 3 column 5) are
dominated by uncertainty on the spectral type. We performed the same fitting
process using stellar models 300 K below and above the chosen model and used
the dispersion in the resultant values of $A_{\rm{V}}$(spectra) as the
1$\sigma$ uncertainties. The average uncertainty in $A_{\rm{V}}$(spectra) is
$\approx$0.3 mag.

####  3.1.3 Fitting for $A_{\rm{V}}$(phot) with Publicly Available Photometry

Because our spectra cover only the optical range of the spectrum, we also
estimated the extinction with photometry in the optical and IR. We performed
the same extinction calculation with APASS photometric data in B, V,
g′r′i′z′y′, Two Micron All Sky Survey (2MASS) JHK, and Spitzer 3.6 $\mu$m and
4.5 $\mu$m magnitudes as catalogued in the NASA/IPAC Infrared Science Archive
(IRSA) database. APASS data are available for 24 of the 27 target stars
(missing are #14, #15, and #17 on account of their proximity to $\zeta$ Oph).
For those targets, we used photometric data from Pan-STARRS.

We normalized the stellar model from Table 3 to the photometry at 4.5 $\mu$m,
then performed synthetic photometry on each model as described by Girardi et
al. (2002) using published filter transmission curves specific to each
bandpass. We divided the fluxes of the photometric measurements in each band
by the synthetic stellar model fluxes, then fitted for $A_{\rm{V}}$(phot)
using the same approach as above, including the Cardelli et al. (1989)
prescriptions for the optical and NIR. Column 6 of Table 3 lists
$A_{\rm{V}}$(phot) derived from the photometric data. The resulting range of
$A_{\rm{V}}$(phot) is 0.69–2.61 magnitudes. Uncertainties again are dominated
by uncertainties on the spectral type and are calculated in the same manner.
The average error in $A_{\rm{V}}$(phot) is $\approx$0.2 mag, somewhat smaller
than that of the spectra on account of the larger wavelength range used.

Figure 4 shows an example of the technique used to estimate interstellar
extinctions for target #1. The gray squares show the stellar model at each
bandpass (F9, 6000 K, $\log$ $g$=4.0) in AB magnitudes. The translucent blue
circles show the reddened APO spectrum smoothed to ten overall bins. Errors
represent the standard deviation in each bin. The translucent red stars show
the reddened photometry, which has errors directly from IRSA, APASS, and Pan-
STARRS that are often too small to be visible in the figure. The spectrum and
photometry differ slightly in AB mag prior to dereddening. This can be
explained with an arbitrary gray shift resulting from clouds affecting the
spectrophotometry during non-photometric conditions. However, the shape of
both the reddened spectra and photometry is always very similar, and that
shape determines the reddening and extinction. The bold blue circles show the
spectrum after dereddening by $A_{\rm{V}}$(spectra)$=$1.35${}^{+0.25}_{-0.26}$
and $R_{\rm{V}}$=3.1, and the bold red stars show the photometry after
dereddening by $A_{\rm{V}}$(phot)=$1.26^{+0.18}_{-0.20}$ and $R_{\rm{V}}$=3.1.
The two estimates agree within their uncertainties and provide a good match to
the model template.

Figure 4: Reddening correction and extinction estimation for target #1. The
gray squares show the smoothed stellar model (6000 K, $\log$ $g$=4.0)
corresponding to the F9 spectral type. Blue circles show the reddened APO
spectrum (translucent) and APO spectrum after dereddening by
$A_{\rm{V}}$(spectra)$=$1.35${}^{+0.25}_{-0.26}$ and $R_{\rm{V}}$=3.1 (bold).
Red stars show the reddened photometry (translucent) and photometry after
dereddening by $A_{\rm{V}}$(phot)=$1.26^{+0.18}_{-0.20}$ and $R_{\rm{V}}$=3.1
(bold).

####  3.1.4 Calculating $A_{\rm{V}}$(RJCE) with the Rayleigh-Jeans Color
Excess Method

The Rayleigh-Jeans color excess (RJCE) method (Majewski et al., 2011) also
provides an estimation for $A_{\rm{V}}$ based on H band and 4.5 $\mu$m
photometry from 2MASS and Spitzer (Cutri et al., 2003; Fazio et al., 2004).
The H$-$4.5 $\mu$m color is a robust measure of extinction regardless of
temperature, metallicity, or surface gravity for the ubiquitous F–M stars that
populate most Galactic fields. Using the relationships
$A_{\rm{K}}$=0.918(H$-$[4.5$\mu$]$-$0.08) and $A_{\rm{V}}$=8.82$A_{\rm{K}}$
for $R_{\rm{V}}$=3.1, we determined $A_{\rm{V}}$(RJCE) and uncertainties, as
listed in column 7 of Table 3. $A_{\rm{V}}$(RJCE) ranges from 0.55–2.54 mag
with typical uncertainties $\approx$0.2 mag.

Table 3: Spectral types and extinction values for the target stars in Table 1. Target | Teff |  $\log$ $g$ | Sp. Type |  $A_{\rm{V}}$ (mag.) assuming $R_{\rm{V}}$ = 3.1 | $E(B-V)$
---|---|---|---|---|---
| (K) |  |  |  $A_{\rm{V}}$(spectra) |  $A_{\rm{V}}$(phot) |  $A_{\rm{V}}$(RJCE) | (mag.)
1 | 6000 | 4.00 | F9 | 1.35 ${}_{-0.26}^{+0.25}$ | 1.26 ${}_{-0.20}^{+0.18}$ | 1.43 $\pm$ 0.20 | 0.49 ${}_{-0.08}^{+0.08}$
2 | 5400 | 2.50 | G9 | 3.27 ${}_{-0.35}^{+0.33}$ | 2.61 ${}_{-0.25}^{+0.23}$ | 1.72 $\pm$ 0.20 | 1.07 ${}_{-0.11}^{+0.11}$
3 | 5600 | 3.00 | G6 | 2.33 ${}_{-0.31}^{+0.28}$ | 1.99 ${}_{-0.24}^{+0.21}$ | 1.52 $\pm$ 0.20 | 0.78 ${}_{-0.10}^{+0.09}$
4 | 5700 | 4.00 | G3 | 1.01 ${}_{-0.29}^{+0.26}$ | 0.81 ${}_{-0.23}^{+0.20}$ | 0.91 $\pm$ 0.20 | 0.35 ${}_{-0.09}^{+0.08}$
5 | 5800 | 4.00 | G2 | 1.70 ${}_{-0.28}^{+0.25}$ | 1.44 ${}_{-0.22}^{+0.19}$ | 1.28 $\pm$ 0.20 | 0.56 ${}_{-0.09}^{+0.08}$
6 | 5600 | 4.00 | G6 | 1.23 ${}_{-0.30}^{+0.26}$ | 0.99 ${}_{-0.24}^{+0.21}$ | 1.17 $\pm$ 0.20 | 0.48 ${}_{-0.10}^{+0.09}$
7 | 5500 | 2.50 | G8 | 2.72 ${}_{-0.36}^{+0.29}$ | 2.5 ${}_{-0.25}^{+0.22}$ | 2.23 $\pm$ 0.20 | 0.88 ${}_{-0.12}^{+0.09}$
8 | 5300 | 3.00 | K0 | 2.90 ${}_{-0.33}^{+0.32}$ | 2.28 ${}_{-0.27}^{+0.24}$ | 1.82 $\pm$ 0.20 | 0.90 ${}_{-0.10}^{+0.10}$
9 | 5700 | 4.00 | G3 | 1.29 ${}_{-0.29}^{+0.26}$ | 1.19 ${}_{-0.23}^{+0.20}$ | 1.20 $\pm$ 0.20 | 0.43 ${}_{-0.09}^{+0.08}$
10 | 5400 | 3.00 | G9 | 2.86 ${}_{-0.34}^{+0.29}$ | 2.36 ${}_{-0.26}^{+0.22}$ | 1.70 $\pm$ 0.20 | 0.87 ${}_{-0.11}^{+0.09}$
11 | 5300 | 4.00 | K0 | 2.40 ${}_{-0.32}^{+0.30}$ | 1.73 ${}_{-0.27}^{+0.24}$ | 1.83 $\pm$ 0.20 | 0.66 ${}_{-0.09}^{+0.10}$
12 | 5700 | 3.00 | G3 | 2.56 ${}_{-0.29}^{+0.29}$ | 2.24 ${}_{-0.22}^{+0.21}$ | 1.78 $\pm$ 0.20 | 0.77 ${}_{-0.09}^{+0.10}$
13 | 6100 | 4.00 | F9 | 1.30 ${}_{-0.25}^{+0.25}$ | 1.21 ${}_{-0.19}^{+0.18}$ | 1.66 $\pm$ 0.20 | 0.40 ${}_{-0.08}^{+0.08}$
14aaAPASS photometry was not available. Pan-STARRS photometry was used instead with transformations from Jester et al. (2005). | 5800 | 4.00 | G3 | 2.07 ${}_{-0.28}^{+0.25}$ | 1.54 ${}_{-0.22}^{+0.19}$ | 1.52 $\pm$ 0.20 | 0.63 ${}_{-0.09}^{+0.08}$
15aaAPASS photometry was not available. Pan-STARRS photometry was used instead with transformations from Jester et al. (2005). | 5300 | 3.00 | K0 | 2.30 ${}_{-0.33}^{+0.32}$ | 1.71 ${}_{-0.27}^{+0.24}$ | 1.85 $\pm$ 0.20 | 0.69 ${}_{-0.10}^{+0.10}$
16 | 5500 | 3.00 | G8 | 2.05 ${}_{-0.32}^{+0.29}$ | 1.83 ${}_{-0.24}^{+0.22}$ | 1.81 $\pm$ 0.20 | 0.52 ${}_{-0.10}^{+0.10}$
17aaAPASS photometry was not available. Pan-STARRS photometry was used instead with transformations from Jester et al. (2005). | 5500 | 3.00 | G8 | 2.31 ${}_{-0.32}^{+0.29}$ | 1.90 ${}_{-0.24}^{+0.22}$ | 1.09 $\pm$ 0.20 | 0.65 ${}_{-0.10}^{+0.10}$
18 | 5600 | 4.00 | G6 | 1.39 ${}_{-0.30}^{+0.27}$ | 1.09 ${}_{-0.24}^{+0.21}$ | 1.39 $\pm$ 0.20 | 0.39 ${}_{-0.10}^{+0.09}$
19 | 6100 | 3.00 | F9 | 2.70 ${}_{-0.27}^{+0.26}$ | 2.22 ${}_{-0.20}^{+0.18}$ | 1.12 $\pm$ 0.20 | 0.72 ${}_{-0.09}^{+0.08}$
20 | 5000 | 3.00 | K2 | 1.42 ${}_{-0.39}^{+0.33}$ | 1.41 ${}_{-0.32}^{+0.27}$ | 2.54 $\pm$ 0.20 | 0.39 ${}_{-0.12}^{+0.10}$
21 | 5400 | 3.00 | G9 | 2.38 ${}_{-0.34}^{+0.28}$ | 1.92 ${}_{-0.26}^{+0.22}$ | 1.38 $\pm$ 0.20 | 0.62 ${}_{-0.11}^{+0.09}$
22 | 5400 | 3.00 | G9 | 2.77 ${}_{-0.34}^{+0.29}$ | 1.95 ${}_{-0.26}^{+0.22}$ | 1.60 $\pm$ 0.20 | 0.59 ${}_{-0.11}^{+0.09}$
23 | 6100 | 4.00 | F9 | 1.64 ${}_{-0.25}^{+0.24}$ | 1.37 ${}_{-0.19}^{+0.18}$ | 1.26 $\pm$ 0.20 | 0.56 ${}_{-0.08}^{+0.08}$
24 | 5700 | 4.00 | G3 | 0.79 ${}_{-0.29}^{+0.26}$ | 0.69 ${}_{-0.23}^{+0.20}$ | 0.55 $\pm$ 0.20 | 0.30 ${}_{-0.09}^{+0.08}$
25 | 5800 | 4.00 | G3 | 1.14 ${}_{-0.28}^{+0.25}$ | 1.16 ${}_{-0.22}^{+0.19}$ | 1.15 $\pm$ 0.20 | 0.42 ${}_{-0.09}^{+0.08}$
26 | 6100 | 4.00 | F9 | 0.96 ${}_{-0.25}^{+0.25}$ | 1.04 ${}_{-0.19}^{+0.18}$ | 1.38 $\pm$ 0.20 | 0.35 ${}_{-0.08}^{+0.08}$
27 | 6100 | 4.00 | F9 | 0.84 ${}_{-0.25}^{+0.25}$ | 0.87 ${}_{-0.19}^{+0.18}$ | 0.99 $\pm$ 0.20 | 0.31 ${}_{-0.08}^{+0.08}$

####  3.1.5 Comparisons Between Extinction Estimates with $R_{\rm{V}}$=3.1

To examine the validity of each $A_{\rm{V}}$ estimate, we compared the three
values for each target in Figure 5. The left panel plots $A_{\rm{V}}$(phot)
versus $A_{\rm{V}}$(spectra) in black circles and $A_{\rm{V}}$(phot) versus
$A_{\rm{V}}$(RJCE) in blue squares. The line shows the 1:1 correspondence
between the estimates. The black points show that $A_{\rm{V}}$(spectra) and
$A_{\rm{V}}$(phot) are tightly correlated with a slope slightly less than
unity. The strong correlation, with a Pearson correlation coefficient of 0.97,
between $A_{\rm{V}}$(spectra) and $A_{\rm{V}}$(phot) affirms the consistency
of these independent optically-based measurements. The blue points show that
$A_{\rm{V}}$(phot) and $A_{\rm{V}}$(RJCE) are correlated at small extinctions
but then diverge, falling consistently above the 1:1 relation at higher
extinctions. $A_{\rm{V}}$(phot) and $A_{\rm{V}}$(RJCE) are not well-
correlated, with a Pearson correlation coefficient of 0.57 for all target
stars.

Figure 5: (left) $A_{\rm{V}}$(phot) versus $A_{\rm{V}}$(spectra) in black
circles and $A_{\rm{V}}$(phot) versus $A_{\rm{V}}$(RJCE) in blue squares. The
solid line shows what would be a 1:1 correspondence between estimates. (right)
$A_{\rm{V}}$(phot) in black and $A_{\rm{V}}$(RJCE) in blue versus distance and
distance above the Galactic Plane. Some target numbers are shown for clarity.
The green point marks $\zeta$ Oph, and the near and far groups are labeled.
$A_{\rm{V}}$(RJCE) is consistently smaller than $A_{\rm{V}}$(phot) at large
extinctions and distances.

The right panel of Figure 5 shows $A_{\rm{V}}$(phot) and $A_{\rm{V}}$(RJCE)
versus distance (lower x-axis) and distance above the plane (upper x-axis).
Black points show $A_{\rm{V}}$(phot) and blue points show $A_{\rm{V}}$(RJCE).
The green point designates $\zeta$ Oph ($A_{\rm{V}}$=1.02 mag, $d$=182 pc),
with its extinction arising within multiple foreground cloud complexes and an
H II region (Wood et al., 2005; Choi et al., 2015). The dashed vertical line
marks the scale height of dust in the Galactic Plane, $z=125^{+7}_{-7}$ pc
(Marshall et al., 2006). In the near group of targets, $A_{\rm{V}}$(RJCE) is
similar to $A_{\rm{V}}$(phot), with means of 1.27$\pm 0.09$ mag and 1.17$\pm
0.08$ mag, respectively (uncertainties represent the error of the mean). In
the far group, $A_{\rm{V}}$(RJCE) consistently falls below $A_{\rm{V}}$(phot)
with means of 1.70$\pm 0.11$ mag and 2.05$\pm 0.09$ mag, respectively. Figure
5 indicates that $A_{\rm{V}}$(RJCE) is systematically less than
$A_{\rm{V}}$(phot) in the far group.

Regardless of measure used, it is clear that the extinction increases with
distance. The far group has an average $A_{\rm{V}}$(phot) 0.88 mag larger than
the near group and an average $A_{\rm{V}}$(RJCE) 0.43 mag larger than the near
group. The Pearson correlation coefficient between distance and
$A_{\rm{V}}$(phot) for all targets is 0.73, implying positive linear
correlation. The correlation between distance and $A_{\rm{V}}$(RJCE) is
smaller: 0.5 for all targets. By examining the near and far group separately,
we find that correlation in the far group is lower than in the near group for
both $A_{\rm{V}}$(phot) and $A_{\rm{V}}$(RJCE). The difference between
$A_{\rm{V}}$(phot) and $A_{\rm{V}}$(RJCE) in the far group suggests that the
extinction depends on the wavelength range used for its calculation (visible
vs. IR photometry), which indicates a departure from the average reddening
curve in the Milky Way.

####  3.1.6 Determining $E(B-V)$ and Incrementally Dereddening Along the Line
of Sight

The discrepancy between extinction estimates (primarily in the far group)
motivates a technique to explore the properties of the different dust
populations with distance. We therefore developed a tool to perform
Incremental DeReddening Along the Line of Sight (IDEALS), allowing us to
investigate both $A_{\rm{V}}$ and $R_{\rm{V}}$ as a function of distance.

Following Fitzpatrick et al. (2019), we constructed the extinction curve for
the targets over optical and infrared wavelengths. Using the B, V, and
g′r′i′z′y′ magnitudes from the APASS database (or Pan-STARRS when required)
and the 2MASS JHK and Spitzer 3.6 $\mu$m and 4.5 $\mu$m magnitudes, we
normalized the stellar model from Table 3 and photometry at V band and
performed synthetic photometry on each model as described for
$A_{\rm{V}}$(phot). For comparison to the previous estimates, we assumed the
Fitzpatrick et al. (2019) empirical extinction curves and fit for the best
$A_{\rm{V}}$; however, we also allowed $R_{\rm{V}}$ to vary. We directly
calculated the color excess, $E(\lambda-V)$, at each bandpass relative to V
band in order to encompass both $A_{\rm{V}}$ and $R_{\rm{V}}$ into one
measure. Table 3 column 7 lists $E(B-V)$ for each target. We then expressed
the reddening relative to V band in the standard nomenclature from Johnson
(1965),

$k(\lambda-V)~{}=\frac{E(\lambda-V)}{E(B-V)}.$ (1)

Figure 6 plots $k(\lambda-V)$, the extinction curve, versus inverse
wavelength. Black lines show the extinction curves from Fitzpatrick et al.
(2019)333These closely match the Cardelli et al. (1989) analytic extinction
curves.. Line styles denote different $R_{\rm{V}}$, with larger $R_{\rm{V}}$
creating a steeper slope in $k(\lambda-V)$. Labels along the bottom mark
standard bandpasses at their corresponding inverse wavelength. Blue and red
points denote average values of $k(\lambda-V)$ for the near and far groups,
respectively. Error bars represent the error of the mean within each band. Any
systematic errors on our adopted stellar $T_{\rm eff}$ would merely shift the
points up or down together relative to the reddening curves. While they are
similar in the optical, the near group of targets (blue) follows a smaller
$R_{\rm{V}}$ trend than the far group (red) in the infrared. However, both
groups are close to the Milky Way average of $R_{\rm{V}}$=3.1, shown by the
solid black line.

Figure 6: Extinction curves represented by the reddening relative to V-band,
i.e., E($\lambda$-V) per $E(B-V)$ versus inverse wavelength in microns. Blue
points mark the mean and error of the mean for the near group of 14 stars, red
points mark the mean of the far group of 13 stars, cyan stars are the mean of
the near group with the reddening of $\zeta$ Oph subtracted, and magenta stars
are the mean of the far group with the reddening of the near group subtracted.
Green circles represent $\zeta$ Oph. Tracks denote the canonical Milky Way
reddening curves from Fitzpatrick et al. (2019) for a range of $R_{\rm
V}$=2.0/2.5/3.1/4.1, according to the legend.

The green circles in Figure 6 show the extinction curve of $\zeta$ Oph. Owing
to its brightness, there are no measurements of $\zeta$ Oph on a modern
photometric system. Accordingly, we adopted optical BVRI magnitudes from
Johnson (1965) and used the equations of Jester et al. (2005) and Fernie
(1983) to transform these into g′r′i′z′ magnitudes. In the infrared we used
the 2MASS JHK and Spitzer 3.6 and 4.5 $\mu$m fluxes from IRSA and employed the
corresponding zero points to obtain magnitudes. At 3.6 and 4.5 $\mu$m the
Spitzer fluxes are $\sim$30% smaller than the ground-based measurements of
Gehrz et al. (1974), so we adopted the average of the two fluxes. For the
intrinsic spectral energy distribution we selected the $T_{\rm eff}$ = 31,000
K, $\log$ $g$ = 4.5 “BT-settl” model atmosphere of Allard et al. (2011) which
yields very similar results to the older Castelli & Kurucz (2003) models.
Despite larger uncertainties resulting from the photometric transformations,
the reddening curve for $\zeta$ Oph is consistent with mean interstellar
$R_{\rm V}$=3.1 dust, indicating that the dust in the $d$$<$182 pc foreground
is “average”..

To examine $R_{\rm{V}}$ with distance, we constructed reddening curves for the
near and far groups with their average foreground reddening removed. This is
the crux of the IDEALS technique: it can explore dust properties at different
distances along a line of sight by incrementally removing a well-determined
foreground. Cyan stars in Figure 6 show the near group with the reddening of
$\zeta$ Oph subtracted. With the foreground ($\zeta$ Oph) removed, the near
group follows a smaller mean $R_{\rm{V}}$$\approx$2.4. Magenta stars show the
far group with the average reddening of the near group subtracted. After
subtracting the average of the near group, the far group has a noticeably
greater mean $R_{\rm{V}}$$\approx$3.6.

###  3.2 A Highly Polarizing Dust Component

Observations of 180 sightlines from Serkowski et al. (1975) indicate that
while polarization and color excess are not correlated, there is a maximum
amount of polarization per unit reddening of $P_{\rm{V}}$=9.1$E(B-V)$. In
their sample, only rarely do stars fall above this limit. More recent
measurements (for example, Andersson et al., 2015) continue to support this
observational upper limit. Figure 7 plots $P_{\rm{Vf}}$ versus
$E(B-V)_{\rm{f}}$ (the foreground-subtracted color excess, adopting
$E(B-V)$=0.33 mag. for $\zeta$ Oph) for the near group to examine the
polarization efficiency of dust between $\zeta$ Oph and the stars in the
immediate background. The dashed line shows the observational limit proposed
by Serkowski et al. (1975), and the shaded region denotes the “permitted”
region below this limit. The foreground-subtracted polarizations (labeled by
target number) in the near group are high, often above the limit. This
suggests that the near group of stars lies behind or is embedded within a
population of dust grains more efficiently polarizing than the typical ISM.

Figure 7: Percent polarization versus color excess with the foreground of
$\zeta$ Oph removed from each. The dashed line shows the observed maximum
polarization per unit reddening of dust, $P_{\rm{V}}$=9.1$E(B-V)$ (Serkowski
et al., 1975). Many targets in the nearby group fall above the line and are
therefore highly polarized for the amount of reddening.

The negative color excess of target #24, along with its close distance
($d=203$ pc), may indicate that it lies in the foreground of $\zeta$ Oph,
which is entirely possible when taking into account the uncertainties in the
$Gaia$ distance of $\zeta$ Oph. To analyze this possibility, we replicated
Figure 7 with the color excess and polarization of target #24 as the values
for foreground subtraction. Target #24 has an $E(B-V)$=$0.30^{+0.08}_{-0.09}$
and a raw polarization of $P_{\rm{V}}$=1.09$\pm$0.07% at 111.9$\pm$1.82°.
Although the group of targets in Figure 7 shifts slightly to the right, the
figure and foreground-subtracted polarizations and color excesses remain
essentially the same despite the choice of foreground reference star.

###  3.3 The Bowshock and Striation Dust Structures

While the bowshock is certainly in close proximity to and associated with
$\zeta$ Oph, the location and properties of the infrared striations present in
Figures 2 and 2 are less clear. Both the bowshock and striations appear in all
three wavelengths of the Spitzer images, but most strongly at 8 $\mu$m, a
wavelength dominated by Polycyclic Aromatic Hydrocarbons (PAHs) that are
excited by the UV radiation from hot stars. The clear signature of PAH
emission from the striations demands illumination by UV photons,
circumstantially placing them in close proximity to $\zeta$ Oph. As an O9.2IV
star ($T_{\rm eff}$=31,000 K, $R_{\star}$=7.2 $R_{\odot}$), $\zeta$ Oph
dominates the radiant energy in its vicinity. From the catalog of Galactic OB
stars (Reed, 2003), we find no other O or early B stars within 50 pc of
$\zeta$ Oph. At a distance of $z$$\sim 74$ pc above the Plane, $\zeta$ Oph is
the leading candidate for the source of far-UV photons exciting the PAH
molecules (Tielens, 2008) in the striations. The ratio of specific intensities
at 8 and 24 $\mu$m, $I_{\rm 8}$/$I_{\rm 24}$, is $\approx$0.14 for the
bowshock (redder in Figure 2) and $\approx$0.20 for the striations (greener in
Figure 2), suggesting a larger PAH contribution in the latter. Likewise, the 8
$\mu$m to 4.5 $\mu$m (a band free of PAH contributions) ratio increases from
$\approx$8.5 in the bowshock to $\approx$20 in the striations. This is similar
to the value observed in established high-PAH photon-dominated regions
(Churchwell et al., 2006; Deharveng et al., 2009). The disparate colors
between the bowshock and striations indicate two distinct dust structures
having a different set of physical conditions and possibly different grain
properties.

To quantify the orientation of the dust striations and compare them to the
polarization position angles in this field, we employed the Rolling Hough
Transform from Clark et al. (2014). Their code reads images and calculates
$R(\theta,x,y)$, a function that encodes intensity as a function of angle,
$\theta$, for components in the image at locations $x$ and $y$. We performed
this process using regions of the 8 $\mu$m Spitzer image lying directly above
and below the prominent bowshock structure, excluding the bowshock because of
its high intensity and dominance over the diffuse striations. By integrating
$R(\theta,x,y)$ for each $x$ and $y$ with Equations 7 and 8 from Clark et al.
(2014), we obtained the overall orientation angles for the striated regions
directly above and below the bowshock. In Figure 2, the blue dashed lines show
the average orientation of the striations above and below the bowshock, 51.6°
and 57.2°, respectively.

##  4 Discussion

The extinction and polarization data provide a clear picture of the dust along
these lines of sight. While the foreground dust masks most of the variation in
the form of the extinction curve, removal of that component reveals the
interesting structures beyond.

###  4.1 Dust Populations Along the Line of Sight

The correlation between $A_{\rm{V}}$(RJCE) and $A_{\rm{V}}$(phot) decreases at
greater extinctions and distances. This is clearly demonstrated in Figure 5
and in the correlation coefficients calculated in Section 3.1.5. This
indicates—most dramatically at larger extinctions— a departure of the
reddening curve from the Milky Way average, the shape of which is assumed in
the three methods used in Figure 5. We conclude from Figure 5 that the
reddening curve for the high-extinction, far group differs from that of the
low-extinction near group.

The $k(\lambda-V)$ trends in Figure 6 suggest that the near group of stars is
reddened by a population of dust with $R_{\rm{V}}$$\approx$2.4, while the far
group is reddened by a population of dust with $R_{\rm{V}}$$\approx$3.6. The
small $R_{\rm{V}}$ in the near group indicates an excess of small grains (as
discussed in Section 1) just behind $\zeta$ Oph in a “mid-distance cloud”. An
excess of large grains (or deficit of small grains) above the Galactic Plane,
located in a “distant cloud”, could plausibly explain the high $R_{\rm{V}}$ in
the far group. On its own, the far group shows minimal correlation between
extinction and distance (Pearson correlation coefficient of 0.47 for
$A_{\rm{V}}$(phot) and 0.21 for $A_{\rm{V}}$(RJCE)) in Figure 5. This
indicates that the additional extinction affecting the far group lies in the
600–2000 pc gap separating the two groups, thereby extincting the far group
somewhat uniformly, although the dispersion of extinctions suggests some
patchiness in dust coverage. Of course, both of these dust components
idealized as discrete slabs may actually consist of smaller constituent
clouds.

Figure 8 illustrates the preferred configuration of dust along the line of
sight. The top panel shows $P_{\rm{Vf}}$ versus distance. The second panel
shows $E(B-V)_{\rm{f}}$, the foreground-subtracted color excess. The two
bottom panels show $A_{\rm{Vf}}$ and $R_{\rm{Vf}}$, which were obtained by
dereddening using the foreground parameters of $\zeta$ Oph444$E(B-V)$=0.33
from Ducati (2002); Pecaut & Mamajek (2013) and refitting the Fitzpatrick et
al. (2019) extinction curve. Shaded gray regions represent the proposed two
discrete dust populations that lie in the background of $\zeta$ Oph: a highly
polarizing mid-distance 200–300 pc component and a non-polarizing 600–2000 pc
distant component.

In the top panel, $P_{\rm{Vf}}$ increases sharply just beyond targets #4, #6,
#24 (203–252 pc) from 0.5% to as high as 2%. The substantial increase in
polarization occurs in the same dust that creates only a small increase in
color excess ($\Delta$E(B-V)$\approx$0.08, visible in the second panel). This
suggests a mid-distance dust component with high grain alignment efficiency
somewhere in the vicinity of 200–300 pc. These sightlines raise the
interesting possibility that the bulk of interstellar polarization may take
place within a very small volume fraction of the ISM if such highly polarizing
dust structures are common. The polarization then levels off below 2% at large
distances. Although there is some dispersion in the far group, the
polarization is consistently between 1–2%.

Figure 8: $P_{\rm{Vf}}$, $E(B-V)_{\rm{f}}$, $A_{\rm{Vf}}$, and $R_{\rm{Vf}}$
with distance. Gray regions represent likely locations of dust along the line
of sight, the highly polarizing mid-distance dust and the non-polarizing dust
at a greater distance. Only some target numbers are shown for clarity.

As distance increases, $E(B-V)_{\rm{f}}$ also increases for the first few
targets, then flattens for the remainder of the near group. The dispersion in
$E(B-V)_{\rm{f}}$ becomes greater at larger distances, and the mean
$E(B-V)_{\rm{f}}$ is larger than in the near group. $A_{\rm{Vf}}$ reflects the
same trends as $E(B-V)_{\rm{f}}$, increasing consistently with distance.
Because $E(B-V)_{\rm{f}}$ and $A_{\rm{Vf}}$ increase with distance, but
$P_{\rm{Vf}}$ does not, we conclude that the distant dust population (located
between 600-2000 pc) extincts background light but does not create a
noticeable polarization signature. This lack of polarization signature at
large distances may stem from a tangled magnetic field, a weak or absent
magnetic field, or a magnetic field oriented along the line of sight. We are
not able to distinguish which of these scenarios is at work, so we simply
refer to this dust component as non-polarizing.

The bottom panel shows $R_{\rm{Vf}}$, the best fit for $R_{\rm{V}}$ after
dereddening by the foreground of $\zeta$ Oph. For the targets with the lowest
$A_{\rm{Vf}}$ and nearest distances (#4 and #6), fits of $R_{\rm{Vf}}$ are
unreliable because there is very little reddening to fit, so $R_{\rm{Vf}}$ is
set arbitrarily to zero. The $R_{\rm{Vf}}$ of the near group is low
(1.8$\pm$0.7), matching the $R_{\rm{V}}$$\approx$2.4 obtained for the
foreground-subtracted near group in Figure 6. $R_{\rm{Vf}}$ increases with
distance towards the far group to 2.6$\pm$0.4. After further dereddening by
the average extinction of the near group, the far group shifts towards a
larger $R_{\rm{V}}$$=$3.1$\pm$1.0 (matching the $R_{\rm{V}}$$\approx$3.6
obtained in Figure 6).

While an average $R_{\rm{V}}$ for the Milky Way is established, it is based on
O-, B-, and A-type stars near the mid-Plane and does not account for possible
variations throughout the Galaxy (Schultz & Wiemer, 1975; Sneden et al.,
1978). $R_{\rm{V}}$ is known to vary between values near two (Larson et al.,
2000) to more than six (Johnson, 1965). Whittet (1977) discovered variations
with Galactic longitude that suggest changes in the size distribution of dust
grains in the local spiral arm. Dust at high Galactic latitudes is known to be
inconsistent with standard reddening laws, and no single $R_{\rm{V}}$ can
explain observations of both the optical and ultraviolet extinctions toward
extragalactic sources (Peek & Schiminovich, 2013). It is fair to assume that
dust properties vary throughout the Milky Way, possibly changing significantly
along sightlines outside of the Galactic Plane like $\zeta$ Oph ($b$=24°). HD
210121 (B7II) lies below the Galactic Plane and is also obscured by a diffuse
cloud. The sightline towards that star has a low $R_{\rm{V}}$$\approx$2.1
(Larson et al., 2000), demonstrating that the smaller-than-average
$R_{\rm{V}}$ in the near group may be a more global trend for diffuse clouds
like those towards $\zeta$ Oph. In fact, many high latitude clouds have
enhanced abundances of relatively small dust grains (Larson & Whittet, 2005).

###  4.2 Magnetic Field Characteristics and Relation to Dust Structures

Figure 7 indicates that the mid-distance dust directly behind $\zeta$ Oph is
highly polarizing. It is likely that the high polarization per reddening
arises from dust behind $\zeta$ Oph, as that star itself falls far below the
Serkowski limit, with $E(B-V)$=0.33 and $P_{\rm{V}}$=1.44% (Serkowski et al.,
1975). This highly polarizing component is not entirely novel, as Gontcharov &
Mosenkov (2019) found sources in an all-sky polarization survey with
$P_{\rm{V}}>$9.1$E(B-V)$. They explain that this may be the result of an
underestimate in $E(B-V)$, a non-standard reddening law, or simply a violation
of the observational upper limit. In our case, the nearby group of stars has
an $E(B-V)_{\rm f}$ that is well-constrained. The high $P_{\rm{V}}/E(B-V)$
ratio, which is substantially in excess of the limit from Serkowski et al.
(1975), may then be the result of the non-standard reddening law seen in the
near group or dust that is more efficiently polarized than typical ISM
material.

The polarization vectors in Figure 2 show the direction of the projected
magnetic field with an average P.A.=77° and a dispersion of 18°. The Rolling
Hough Transform provides an average direction for the striations below and
above the bowshock (blue dashed lines in Figure 2) of 57.2° and 51.6°,
respectively. This indicates that the polarization vectors are aligned with
the infrared dust striations in the field of view. Taken together, the
infrared images, polarization data, and striation orientation reveal a
striated (P.A.$\approx$55°) PAH-emitting cloud spanning the field of view in
close proximity to $\zeta$ Oph that hosts the aligned grains that polarize
background starlight at a similar position angle.

The main arc of the bowshock is approximately perpendicular to the projected
magnetic field, while the proper motion of $\zeta$ Oph is parallel. The
magnetic field does not appear to follow the filaments in the bowshock, nor is
there any apparent deviation in P.A. even near the highest surface brightness
portions of the nebula. The location and morphology of the bowshock are likely
a result of the motion of $\zeta$ Oph and do not depend on the magnetic field
orientation. Evidently, the bowshock contributes negligibly to the
polarization, while the background striated medium is the strongly polarizing
agent.

###  4.3 An Optically Thin Bowshock Nebula

A brief examination of specific targets shows that there are small-scale
angular variations across the field of view, as well as variations along
adjacent lines of sight. For example, Target #22 has a significantly larger
$P_{\rm{Vf}}$ than target #19 (2.56% versus 1.25%), despite the smaller
$E(B-V)_{\rm{f}}$ (0.27 versus 0.40), similar location (within $\approx$2′),
similar P.A.f (64° versus 76°), and almost identical distance (4790 pc versus
4645 pc). Targets #11 and #12 lie within 30″ of each other, but at very
different distances (278 pc and 3246 pc, respectively). Target #12 is
understandably more reddened at a large distance, but has a smaller
$P_{\rm{Vf}}$ (0.45% versus 1.60% for #11) and very different PAf (110° versus
83° for #11) than surrounding targets. The areal density of background sources
is not sufficient to probe small-scale dust variations in a rigorous manner,
but the variations on small angular scales and with distance are clear.

We have not sampled enough targets to determine if the bowshock nebula affects
extinction. We find no clear difference in extinction between targets located
directly behind (on) the bowshock versus off the bowshock. It is likely that
distance is the primary parameter driving extinction, as seen in Figure 8.
However, given that the optical depth of the bowshock at optical and UV
wavelengths is expected to be small, it is not surprising that the prominent
infrared nebulae does not produce an obvious signature of increased
extinction. The median ratio of nebular far-infrared luminosity to stellar
luminosity is $L_{\rm IR}$/L${}_{*}\approx$0.003 in bowshock nebulae ($<$0.001
in the case of $\zeta$ Oph), indicating that only a small fraction of the
stellar energy is intercepted and re-radiated by the dust in the nebula
(Kobulnicky et al., 2017). The vast majority of infrared bowshock nebulae are
optically thin, at least globally, a conclusion echoed by Henney & Arthur
(2019). This does not rule out the possible existence of optically thick
clumps on small scales, but it does constrain them to have a small covering
factor. The probability that one of the observed sightlines toward background
stars would intercept such a clump is small, so the lack of an unambiguous
signature in the extinction or polarization of background targets is
unsurprising.

##  5 Summary

Using optical polarimetry and spectrophotometry, we have examined the
polarization and reddening along the lines of sight to the 27 background stars
surrounding the O9.2IV star $\zeta$ Oph. We have developed a technique to
incrementally subtract foreground reddening and polarization. This has allowed
us to characterize the dust along the line of sight to the target stars,
probing differences that would otherwise be masked by a sightline average.

  1. 1.

The dust characteristics along the sightlines surrounding $\zeta$ Oph vary
with distance and can be represented as three distinct populations: the
foreground dust ($R_{\rm{V}}$$\approx$3.1), the highly polarizing mid-distance
dust ($R_{\rm{V}}$$<$3.1), and the non-polarizing distant dust
($R_{\rm{V}}$$>$3.1). The superposition of different dust populations along
the line of sight leads to a sightline-averaged $R_{\rm{V}}$ that is close to
typical for the ISM, masking pronounced variations in the reddening curve with
distance.

  2. 2.

After subtracting the foreground characterized by the polarization of $\zeta$
Oph, the position angles become approximately parallel to the PAH-emitting
infrared striations. The polarization most likely arises from the mid-distance
dust responsible for those striations. We conclude that the dust is located
behind—but in close proximity—to $\zeta$ Oph and is illuminated by the star’s
UV irradiation. With the foreground $R_{\rm{V}}$=3.1 dust removed, the mid-
distance dust has an $R_{\rm{V}}$$\approx$2.4, suggesting an overabundance of
small dust grains.

This mid-distance dust (200–300 pc) is highly polarizing. It has a
polarization efficiency larger than the limit observed by Serkowski et al.
(1975, $P_{\rm{V}}$/$E(B-V)$$>$9.1). The high $P_{\rm{Vf}}$/$E(B-V)_{\rm{f}}$
toward a number of stars over a limited path length ($\approx$200 pc)
indicates that large changes in polarization can occur over small increments
in dust column density. This suggests that a very small fractional ISM volume
containing populations of unusually small, highly aligned grains may dominate
the interstellar polarization signature.

  3. 3.

The distant dust (600–2000 pc) does not create a distinct polarization
signature and has $R_{\rm{V}}$$\approx$3.6. The lack of polarization may stem
from many factors, like a non-existent or tangled magnetic field or a magnetic
field oriented along the line of sight. The larger-than-average $R_{\rm{V}}$
implies an excess of large dust grains at large distances above the Galactic
Plane ($z$$>$250 pc). In the simplest case, this may hold true for the entire
Milky Way above the Plane.

A complete understanding of variations in dust properties is essential in
correcting for extinction and motivates further investigation into
$R_{\rm{V}}$ above the Plane to obtain a clear picture of dust properties
throughout the Galaxy. The reddening map from Green et al. (2019) is dependent
on $R_{\rm{V}}$, and they emphasize that extinction maps derived from their
reddenings without knowledge of the spatial dependence of $R_{\rm{V}}$ will
introduce large-scale, spatially dependent systematic errors. Precision
supernova surveys (Betoule et al., 2014; Scolnic et al., 2018) and follow-up
of optical transients from neutron star and black hole mergers (Abbott, 2017;
Anand et al., 2021) are just two examples of programs that require accurate
corrections for extinction. The onslaught of accurate distances from $Gaia$
and publicly available spectral and photometric data make future studies of
the extra-planar extinction curve practical, while these applications make it
pressing.

We thank Matt Povich and Dan Clemens for helpful exchanges that contributed to
this manuscript. This research has made use of the NASA/IPAC Infrared Science
Archive, which is funded by the National Aeronautics and Space Administration
and operated by the California Institute of Technology. Ashley N. Piccone
acknowledges support from NASA through grant 80NSSC21K1847.

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