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The Galactic Plane Infrared Polarization Survey (GPIPS): Data Release 4

The Galactic Plane Infrared Polarization Survey (GPIPS) seeks to characterize the magnetic field in the dusty Galactic disk using near-infrared stellar polarimetry. All GPIPS observations were completed using the 1.83 m Perkins telescope and Mimir instrument. GPIPS observations surveyed 76 sq-deg of the northern Galactic plane, from Galactic longitudes 18 to 56 deg and latitudes -1 to +1 deg, in the H-band (1.6 um). Surveyed stars span 7th to 16th mag, resulting in nearly 10 million stars with measured linear polarizations. Of these stars, ones with m_H<12.5 mag and polarization percentage uncertainties under 2% were judged to be high quality and number over one million. GPIPS data reveal plane-of-sky magnetic field orientations for numerous interstellar clouds for AV values to ~30 mag. The average sky separation of stars with m_H<12.5 mag is about 30arcsec, or about 60 per Planck polarization resolution element. Matching to Gaia DR2 showed the brightest GPIPS stars are red giants with distances in the 0.6-7.5 kpc range. Polarization orientations are mostly parallel to the Galactic disk, with some zones showing significant orientation departures. Changes in orientations are stronger as a function of Galactic longitude than of latitude. Considered at 10 arcmin angular scales, directions that show the greatest polarization fractions and narrowest polarization position angle distributions are confined to about ten large, coherent structures that are not correlated with star forming clouds. The GPIPS polarimetric and photometric data products (Data Release 4 catalogs and images) are publicly available for over 13million stars.


INTRODUCTION
The magnetic field in the cool, dusty, star-forming interstellar medium (ISM) of the Milky Way has not been well-described and the roles played by the magnetic field in cloud, clump/core, star, and planet formation and evolution are rather poorly understood. This is mostly due to a lack of high-quality, high-resolution data that can reveal the magnetic field in such settings and can be used to characterize the importance of the magnetic field. Yet knowledge of the field properties, especially strength and orientation, is vital to assessing the relative roles of gravity, turbulence, and magnetic fields in star formation (see review by Crutcher 2012).
Magnetic fields associated with the Milky Way were first revealed in the optical starlight linearpolarization studies of Hiltner (1949a,b) and Hall (1949), and the later surveys of Mathewson & Ford (1970) and Klare & Neckel (1977), who found strong associations of starlight polarization orientations with the Galactic plane orientation. Linear polarization of the light from background stars occurs because the intervening ISM contains spinning dust grains that are aligned with local magnetic field directions via the Radiative Aligned Torques (RATs) mechanism (Lazarian & Hoang 2007;Andersson et al. 2015). This results in anisotropic absorption (dichroism) of the isotropically emitted starlight.
Sky-projected magnetic field orientations are revealed as the linear polarization orientations of the electric field vector amplitudes of the stellar radiation. Published optical polarization studies were collected in the compendium of Heiles (2000) and studied by Fosalba et al. (2002). However, as shown by the latter, the stars in the Heiles (2000) collection predominantly had distances out to only ∼1 kpc and exhibited only up to a few magnitudes of visual extinction A V . Additionally, the average sky sampling of the stars measured for polarization was about one star per two square degrees, much too sparse to permit study of all but the closest, largest, and least-extincted molecular clouds.
Studies of radio synchrotron emission intensity and polarization have revealed much about the magnetic field in the hot, plasma phase of the Milky Way and in other galaxies (e.g., reviews by Beck et al. 1996;Noutsos 2012;Beck 2015;Haverkorn 2015;Han 2017;Akahori et al. 2018). Faraday rotation measurements of linear polarization from Galactic pulsars and distant AGN have been used to explore the symmetry of the Milky Way's halo magnetic field and to provide a glimpse of the nature of the disk magnetic field (e.g., Rand & Kulkarni 1989;Han et al. 1999Han et al. , 2006Brown et al. 2007;Van Eck et al. 2011;Han et al. 2018). However, cold molecular clouds contain little of the hot plasma traced by radio wavelength polarization Rotation Measures (RM), leaving the magnetic field in the star-forming ISM component inadequately explored.
Complex models of the Galactic magnetic field have been developed based on these radio continuum techniques (e.g., Ferrière & Schmitt 2000;Brown et al. 2007;Jaffe et al. 2010;Moss et al. 2010;Van Eck et al. 2011;Jansson & Farrar 2012;Han et al. 2018), with large numbers of model parameters used to characterize the halo and disk fields and including spiral arms. Yet agreement as to the number, pitch angles, and magnetic field directions along and between spiral arms has remained elusive for the Milky Way. This is partially due to our location within the Galactic disk and partially due to the lack of adequate magnetic field probes of the cool, star-forming molecular gas and dust that dominate the mass of the diffuse matter in the ISM.
This situation improved with the release of the Planck (Planck Collaboration Int. I 2011) polarization maps (Planck Collaboration Int. XIX 2015), which sampled the full sky at angular resolutions as fine as 5 arcmin for 353 GHz (850 µm) observations of the Galactic plane. Polarization at these wavelengths is due to modified thermal emission from anisotropic, spinning dust grains, which tend to align their long axes perpendicular to the local magnetic field orientation through the same RATs mechanism that produces optical and infrared starlight polarization. For emission polarimetry, the result is a linearly-polarized submm intensity whose maximum electric field amplitude orientation appears perpendicular to the sky-projected magnetic field orientation. These data still suffer from low angular resolution and line-of-sight confusion, however, as the optically thin submm wavelengths lead to the collection and averaging of signals from all emitting structures along the line-of-sight. This is especially problematic in the Galactic midplane, where the Planck lines of sight can extend to many tens of kpc, but the spiral arms and individual clouds whose magnetic properties are sought only span tiny fractions of these distances (Planck Collaboration Int. XXI 2015). Planck data have been particularly effective for the study of larger, relatively nearby clouds and filaments that are located away from the confusion presented by the Galactic plane (Soler et al. 2016;Planck Collaboration Int. XXXII 2016;Planck Collaboration Int. XXXV 2016). These studies find that the dust grain alignment, which is associated with magnetic field orientation, changes depending on the observed values of the gas and dust column densities, traced using the Histograms of Relative Orientation method (Soler et al. 2013;Planck Collaboration Int. XXXII 2016;Planck Collaboration Int. XXXV 2016) and other techniques (Planck Collaboration XII 2018).
On smaller angular scales, linearly-polarized thermal dust emission from the high column-density regions associated with massive star-forming cloud cores has been probed at mm, submm, and/or far-infrared (FIR) wavebands from the ground (Barvainis et al. 1988), from balloons (Cudlip et al. 1982;Hu et al. 2019), and from airborne platforms (KAO: Hildebrand et al. (1984); SOFIA: Chuss et al. (2018)). At these wavelengths, the magnetic field has been characterized over angular scales as fine as about ten arcsecs, but only for the small regions that are bright enough (many MJ sr −1 ) to permit polarization detection. Recently, the POL-2 instrument on JCMT has been used by the BISTRO team (see Ward-Thompson et al. 2017) to map and study thermal dust emission polarization across a number of star-forming cloud cores (e.g., Wang et al. 2019;Coudé et al. 2019) and to fainter surface brightness levels (Soam et al. 2018;Liu et al. 2019). Additionally, Zeeman Effect circular-polarization spectroscopy of cool molecular gas in dark clouds (Crutcher et al. 2009) and in masers associated with high-mass star formation regions (Fish et al. 2003) has revealed magnetic properties within some molecular cloud environments, but at low angular resolution and sensitivity for the former and only in the special locations and conditions associated with high-mass star formation for the latter.
Millimeter and submm interferometers have proven ideal for examining thermal dust emission polarimetry on the finest of size scales (e.g., Akeson & Carlstrom 1997;Rao et al. 1998;Girart et al. 2006;Hull et al. 2017), down to a few tens of AU, though scattering of submm emission by protoplanetary disks also yields strong polarization signals (Kataoka et al. 2015) and may greatly alter magnetic field interpretations. The physical extents of the regions studied are limited to less than a fraction of a parsec, typically, and so are inadequate to address the nature of magnetic fields affecting cloud and core/clump formation that takes place over larger size scales.
The Galactic Plane Infrared Polarization Survey (GPIPS: Clemens et al. 2012a, hereafter Paper I) was begun in 2006 to address the lack of data available for revealing magnetic field properties for the denser, star-forming material in the disk of the Milky Way. GPIPS was a ground-based survey covering 76 deg 2 of the northern Galactic plane, including the majority of the star-forming portion of the midplane, and matching the zone covered by the molecular gas probing 13 CO (J = 1 → 0) Galactic Ring Survey (GRS; Jackson et al. 2006). GPIPS observations were collected using the 1.83 m Perkins telescope located on Anderson Mesa outside Flagstaff, AZ which was operated by Lowell Observatory until 2019 June and Boston University thereafter. The Mimir near-infrared (NIR) imaging polarimeter and spectrometer (Clemens et al. 2007) was used to acquire the GPIPS data, which were reduced, calibrated, and analyzed using custom IDL-based software. The GPIPS project recently completed all observations and data processing, leading to this fourth data release (DR4 1 ).
The observations comprising GPIPS are summarized in Section 2. The characteristics of the data and released data products in DR4 are presented in Section 3 and in the Appendices. The Galactic latitude and longitude dependencies of polarization properties are explored in Section 4. Findings regarding the nature of the magnetic field in the Galactic disk are described in Section 5. Section 6 summarizes key GPIPS characteristics and the general findings. stellar photometry performed on each of the 16 HWP images for each field. The stellar brightness variations as a function of HWP angle (e.g., Figure 16 of Clemens et al. (2007)) were calibrated and analyzed to quantify the linear polarization attributes, which are listed in the polarization catalog (POLCAT: Paper III) data product. Photometric in-band calibration and astrometry were performed using the ∼200 2MASS (Skrutskie et al. 2006) stars detected in each Mimir FOV (Paper I).
Stellar photometry was obtained using a method based on point spread function (PSF) modeling and stellar neighbor removal followed by multi-aperture photometry, as described in Paper I. This method used stars in an image as the basis to create a detector-location dependent variable-PSF model for the image. The model was used to fit and subtract the brightness contributions from all stars within about 15 arcsec of each target star prior to the application of aperture photometry on the target star. This process was found to be necessary to achieve polarization SNR values similar to those expected from the photon noise of each target star (Paper I). The fitting and subtraction of nearest neighbors and subsequent aperture photometry of the target star was repeated for every PHOTCAT star appearing in each of the summed images.
Calibration of polarization efficiency, instrumental polarization contributions, and polarization position angle fiducials were based on observations of previously known polarized stars (Whittet et al. 1992) as well as (mostly unpolarized) globular cluster stars, particularly of globular clusters located far from the disk of the Milky Way. Both calibration procedures are described in the GPIPS calibration paper (Paper II). The stars in the globular cluster fields were used to map the instrumental polarization across the detector FOV of Mimir. This took the form of central (boresight) globular cluster placements as well as tens of placements of the globular clusters across the full Mimir FOV.
The resulting polarization percentage calibration uncertainty was at, or under, 0.10% (Paper II). Subsequent checks of Whittet et al. (1992) standards and monitoring of instrumental polarization for each observation indicated a lack of temporal evolution of calibration values.

Survey Quality Control
The GPIPS introduction paper (Paper I) listed three principal quality goals that the data needed to meet in order to be included in public data releases. The first was a seeing goal, which required the combined deep photometric image for an observed field to have 2 arcsec or smaller mean fullwidth-at-half-maximum (FWHM) stellar PSF profiles. In DR4, 99.4% of the FOVs meet this goal, with no FOV exhibiting a FWHM exceeding 2.25 arcsec. The second goal required the axis ratio of the PSF shape in the deep photometric image for each FOV to be smaller than 1.5, in order to prevent wind-driven telescope motion from corrupting PSF construction and photometry. All DR4 data products meet this goal. The final goal permitted rejection of no more than five images, of the 96 to 119 images comprising the observation of a single field, due to poorly formed PSF shapes or bad detector readouts. This goal was met by 99.5% of the final DR4 FOVs, with all FOVs having at least 89 good images that sampled all 16 HWP orientations. Note that some faint stars might not be detected in all 16 HWP images. The number of independent HWP image detections for each star is contained in the DR4 data products.
Additional data quality goals were found to be necessary and led to many of the GPIPS fields being re-observed. New goals included upper limits on the true pointing accuracy of each FOV relative to its target grid center direction, the amplitude of slow time-variations in sky transmission during the course of an observation, and the amplitude of fast time-variations in sky transmission (sky noise).
Goals also included an absence of zero-phase reset errors (Paper III) in the HWP rotation unit and a positive assessment of data quality with respect to the resulting polarization pattern as it appeared in each FOV. This latter set of tests were triggered by the discovery of artificial polarization patterns that appeared sometimes. The goal-identifying keywords and values for each FOV are listed in the Field Properties Summary Table in the DR4 distribution. These are described in Appendix A, with a shortened version of the Field Properties Summary Table presented as Table A1.
The overall high quality of the DR4 data, with respect to the many quality control checks and characterizations, was judged to have met the GPIPS project goals, leading to cessation of new observations on 27 June 2019.

GPIPS DR4 DATA PRODUCTS AND CHARACTERIZATIONS
The data processing steps involved in transforming the 96 to 119 raw instrument images that comprise an observation of a single FOV to the final photometry, polarimetry, and combined deep photometric image for that FOV are described in Paper I. No significant deviations from these steps occurred for DR4, with the exception of the inclusion of improved 2MASS and GLIMPSE (Benjamin et al. 2003) stellar matching, as noted in Appendix B.
The resulting data products released as DR4 take the form of a set of FOV-based products, a single data file containing unique star entries, supporting metadata files, and the Summary Table. Because of the overlapping FOV design of GPIPS, many stars appear in more than one FOV (Paper III). Duplicate stars were identified, their polarization properties averaged, and a single data file (Clemens et al. 2020) with unique star entries was developed from these self-matches and from the non-overlapping stars. Both forms of these data products, FOV-based and unique star based, are described below.

FOV-Based DR4 Data Products
The FOV-based data products follow the DR1 forms described in Paper III. They are, for each of the 3,237 FOVs, a file of stellar polarimetry (a POLCAT), a file of stellar photometry (a PHOTCAT), the deep photometric image (a FITS file), and printable image files (in PDF and Postscript) showing the deep image of the stars in a FOV overlaid with the UF1 (see Section 3.3 and Appendix C) high-reliability linear polarization orientation lines. The GPIPS stars were also matched to 2MASS stars and to GLIMPSE stars, as described in Paper III (but modified as described in Appendix B), and updated photometry from those data sets were included in the POLCAT and PHOTCAT files.
The characterizing properties of stars in each of the Gaia DR2 (Gaia Collaboration et al. 2016, 2MASS, GLIMPSE, and WISE (Wright et al. 2010) data sets that positionally matched to PHOTCAT and POLCAT stars, as described in Appendix B, are contained in additional DR4 files for each GPIPS FOV. In addition, copies of the hand-written observing logs for each night, the Field Properties Summary Table (shown in short form as Table A1), and a text file of explanatory Data Release Notes are included in DR4.
Information in the FOV-based PHOTCAT files include metadata related to the observations and data calibration as well as entries reporting the in-band photometric properties measured for each star. Similar information, augmented by the H-band polarization data for each star in the field, is contained in the POLCAT files. The set of data values for each star include an RA-ordered serial number, an equatorial coordinate based designation, the X (column) and Y (row) pixel locations where the star appears in the registered and combined deep photometric image, the mean X and Y pixel location of the star as it appears in detector coordinates (used for instrumental polarization correction), the J2000 R.A. and decl., the H-band magnitude (calibrated to the 2MASS H-band magnitudes for the stars in the FOV, but not corrected for color effects), internal and external uncertainties in the H-band magnitude, sky count level, debiased linear polarization percentage 3 P and its uncertainty σ P , the equatorial polarization position angle (EPA, or PA), the Galactic polarization position angle (GPA), the uncertainty in position angle (σ P A ), and the Stokes Q and U fractional values and uncertainties (as normalized by Stokes I).

Unique-Star DR4 Data Products
The FOV-based PHOTCATs were examined to find duplicate stars appearing in neighboring FOVs.
A master catalog of unique stars was constructed from the stars that had no duplicates plus the duplicate stars. For each set of duplicates, their polarization properties were averaged using inverse variance weighting of their Stokes U and Q values, followed by computation of the raw polarization percentage, its uncertainty, the debiased polarization percentage, the polarization position angle, and its uncertainty. The usage flag (UF) designation (see Section 3.3, below) was redetermined and could differ from the FOV-based designations due to lowered uncertainties in σ P .
The total number of PHOTCAT stars, after resolving duplicates, is nearly 14 million. The differences in the numbers of FOV-based star counts and unique star counts is 10.6% of the former. This indicates that the effective Mimir FOV size, accounting for dithering and field-to-field overlap, is about 9.5 × 9.5 arcmin 2 . Analysis performed using the unique star file will be more accurate in terms of accounting for the actual numbers of stars.
3 GPIPS debiased linear polarization percentages follow Paper I such that P = (P 2 RAW − σ 2 P ) 0.5 for the case where the measured P RAW is greater than its uncertainty σ P and zero otherwise. The unique star data file also contains photometric and parallax information based on crossmatching GPIPS to Gaia DR2, 2MASS, GLIMPSE, and WISE . The matching process and statistics of the match results are described in Appendix B, as are the contents and formats of the entries in the unique star data file (Clemens et al. 2020).

Stellar Usage Flag Designations
As described in Paper III and shown in Figure 16 there, a measure of reliability may be obtained from the values of polarization percentage uncertainty and H-band magnitude for each star. GPIPS stars that have m H < 12.5 mag and σ P < 2% were identified as being of high quality and were classified as UF1 (Usage Flag = 1) stars. Additionally, those UF1 stars with debiased polarization SNR (P SNR ≡ P /σ P ) exceeding three, corresponding to σ P A < 9.6 • , became the UF0 subset.
Outside of the values defining UF1, stars were classified as UF2 if they had 12.5 ≤ m H < 14 mag and 2 ≤ σ P < 10%. The remainder of the stars in the POLCATs were classified as UF3. The UF designation for each star is included in the FOV-based POLCAT files and in the unique star file. Note that the particular m H and σ P values that define the three UF types are tied to GPIPS observing details. Other data sets require different boundary values to invoke their UF classifications.
As explored in Paper III, the UF1 stars generally are of sufficient quality to yield polarization position angle uncertainties low enough for independent use to reveal magnetic field orientations.
The UF2 and UF3 stars are generally only useful for probing magnetic field properties when grouped and averaged by sky zone and/or magnitude. The SNR distributions of the stars, binned by UF value, are explored in more detail in Appendix C.    In Figure 1 The middle, C-panel of Figure 1 spans 2 • of Galactic longitude and presents each plotted GPIPS FOV as a single, gray-scale, rotated square with an inset red orientation line. The rotation of the field from the A-panel to the C-panel is due to the relative orientations of the equatorial orientation of Mimir and the Galactic plane. Each of the 41 FOVs shown in the C-panel is shaded to represent a single representative polarization percentage. These were computed as the medians of the UF1 star values for each FOV and are encoded as gray-scale values, where black represents the greatest polarization percentage. A single red orientation line is oriented in each FOV to display the similarly computed mean polarization position angle, in Galactic coordinates.
These representative values were obtained from the median values of polarization percentage and Galactic position angle (GPA) for the UF1 stars in each FOV, as described in Section 4. They represent a single, coarse characterization of the polarization properties for each FOV. Across the C-panel, the mean H-band polarization fraction is seen to vary from a low of 1% to a high of 3%, with the A-panel field exhibiting a value of 2.3%. The red lines show that the magnetic field being traced (at 10 arcmin resolution) is mostly parallel to the Galactic plane, but some FOVs also exhibit significant, coherent deviations of polarization position angle.
The bottom, D-panel of Figure 1 encompasses the entire GPIPS region with representations of polarization percentage and position angle that relate to those shown in the previous panels. The  as great as 2 mag were found in DR1. Such excesses implied that extinctions were being probed to about 30 mag of A V .
However, accurate distances to the GPIPS stars remained elusive until the release of Gaia DR2.
One important distance to establish is the minimum needed through the diffuse ISM to develop detectable NIR polarization signatures to GPIPS levels. This "near horizon" for GPIPS is likely beyond the extent of the Local Bubble (Lallement et al. 2003), but is it close enough to reveal magnetic fields for dark molecular clouds at 300-400 pc? The "far horizon" would be the distance limit beyond which GPIPS stars are too faint or too extincted to be detected. Both distances are needed to estimate the range of line-of-sight distances over which GPIPS data offer the most useful magnetic field information.
The matching of Gaia and GPIPS stars, described in Appendix B, led to the creation of FOV-based files of Gaia star information and their corresponding GPIPS star match identifiers. Examination of the characteristics of the stars with GPIPS-Gaia matches, and those without such matches, was performed to establish stellar characterizations and to reveal the GPIPS near-and far-horizons. (≡ π/σ π ) ≥ 0.5, and parallaxes π > −2 mas. These liberal limits were chosen to avoid introducing parallax bias (Luri et al. 2018;Bailer-Jones et al. 2018) to the sample population characteristics.
These criteria selected for just over 40% of all Gaia stars appearing in the GPIPS FOVs.
In Figure 2, contours shown in red represent the stellar count density of the selected Gaia stars in the mag-parallax plane that matched to POLCAT UF1 stars ("Gaia π + UF1" in the legend).
These matched stars account for only 3.4% of all Gaia stars but 46% of all POLCAT UF1 stars. The portion of the Figure exhibiting 50% of the peak density of counts of Gaia parallax stars ("Gaia π" hereafter) matched to UF1 stars (marked by the outermost solid red contour) spans g-band apparent magnitudes of about 14-18th and log parallaxes of −0.26 to −0.85, or distances of 1.8 to 7.1 kpc.
The blue contours in Figure 2 represent the density of counts of Gaia π stars matched to POLCAT UF2 stars, and the green contours represent the same for UF3 stars. They both span correspondingly fainter apparent magnitudes at somewhat closer distances than do the UF1 stars (red contours).
Ignoring extinction (but see the discussion regarding Figure 4 below), the g-band absolute magnitudes of the peaks of the UF1 (red), UF2 (blue), and UF3 (green) distributions, after correcting for the distance moduli implied in the parallaxes, are about 3.1, 5.0, and 6.7 mag at inferred mean distances of about 3.2, 2.3, and 2.0 kpc, respectively. (These, and other values are collected in Table 2) The brown contours in Figure 2 indicate the density of Gaia stars that meet the magnitude and parallax SNR selection criteria but for which no POLCAT star was matched. Again, ignoring extinction, the g-band absolute magnitude for the peak of this distribution is about 10.9 mag, at a distance of about 0.78 kpc. Hence, the Gaia π stars that match to POLCAT entries have brighter g-band apparent magnitudes and are at greater distances, and are thereby more luminous, than the Gaia π stars that do not match to POLCAT entries.
Establishing characteristic distances to the GPIPS stars (the near and far horizons) requires correcting the Gaia distances for the effects of dust extinction. This affects the optical, g-band magnitudes of Gaia more than it affects the NIR magnitudes of GPIPS. In Figure 3, contours of star counts in the (H − K) versus H-band color-magnitude plane have been colored-coded to identify nine selected subsets of stars. Stars in POLCATs that had Gaia π matches are represented by the red, blue, and green contour distributions, based on their UF1, UF2, or UF3 designations, as was done in Figure 2.
Stars in POLCATs with Gaia star matches that did not meet the parallax criteria ("Gaia no π"), are represented by the orange, purple, and cyan colored contour distributions, based on their UF1, 2, and 3 designations, respectively. GPIPS stars that did not match to any Gaia stars are shown by the yellow, magenta, and dark-green contours. All POLCAT NIR stellar magnitudes and colors included in the distributions were drawn from 2MASS (Skrutskie et al. 2006), subject to a (H − K) color uncertainty criterion of ≤ 0.5 mag. These 2MASS and Gaia selection criteria, taken together, tend to bias the distributions against faint and red stars. This is seen as the successively smaller fractions of the total POLCAT stars with increasing UF number in Table 2.
The groupings in Figure 3 reveal the expected magnitude boundaries separating UF1, 2, and 3 stars. These boundaries are seen as the node-like vertical contours near m H = 12.5 and 14 mag, which are manifestations of the imposed UF definitions. The right axis indicates approximate values of A V , from zero to 20 mag, using the NIR Color Excess method (NICE; Lada et al. 1994).  GPIPS stars with Gaia π matches tend to be less extincted than GPIPS stars of similar H-band brightnesses, but for which the Gaia matches yielded no parallaxes. The GPIPS stars not matching to Gaia stars are the most extincted of all, as already noted in the Figure 1.B discussion. For the POLCAT stars matched to Gaia π stars (the red, blue, and green contours), the UF1 distribution peak exhibits about 2 mag of A V greater than seen at the UF2 and UF3 peaks. The UF2+Gaia π distribution shows a bifurcation in A V , with components near 2 and 6 A V mag. The POLCAT stars matched to Gaia no π stars show distribution peaks offset from the Gaia π stars distribution peaks by 3.5, 5.5, and 4.0 A V mag for UF1, 2, and 3, respectively. The POLCAT stars not matched to Gaia stars show distribution peaks offset from the Gaia π stars distribution peaks by 10, 8.5, and 8.5 A V mag, respectively. The A V steps within each UF vertical group, of about 4 mag for Gaia π to Gaia no π and another 4 mag to the no-Gaia stars, show that Gaia selects the lowest extinctions while GPIPS without Gaia stars selects the most extincted stars. In Figure 4, extinctions and parallaxes for Gaia π stars matched to POLCAT entries are represented as the red-, blue-, and green-colored contours of stellar density for UF1-, UF2-, and UF3-matched stars, respectively, in the central, A-panel. The stars contributing to Figure 4 were required to have the same (H − K) color uncertainty ≤ 0.5 mag, parallax SNR ≥ 0.5, and parallax greater than −2 mas as for the previous Figure. POLCAT stars matched to Gaia π stars tend to have extinctions ranging from 0 to >6 mag of A V , and span distances of <0.5 to about 15 kpc. The distances corresponding to the locations of peaks in the contour distributions are similar to those described for Figure 2, for each of the three subsets of stars.
The lower, B-panel of Figure 4 shows the marginalization over NIR color as cumulative likelihoods (CL) of star count density with log parallax for each of the UF1, UF2, and UF3 samples that match to Gaia π stars and also satisfy the selection criteria applied to the 2MASS values. In the right, C-panel of Figure 4, the central panel distributions have been marginalized over parallax to create histograms of (H − K) colors of stars in the Gaia π, Gaia no π, and no-Gaia groups, shown as the blue, purple, and magenta curves, respectively. The histograms have been normalized by the sum of the stars contained in the 0.02 mag wide bins in both histograms. These histograms reveal similar extinction offsets between the ∼1.6 million Gaia π matched, the ∼1.1 million Gaia no π matched, and the 0.6 million Gaia -unmatched samples of about 4.5 mag of A V between each successive group, similar to what was seen in Figure 3.
The more distant UF1 stars with Gaia π matches were also found to be somewhat more extincted than the fainter UF2 and UF3 subsets, at least for the contours near the peak regions of the star count distributions. As shown in the C-panel of Figure 4, the stars without Gaia matches are even more extincted, on average, than the Gaia π-and Gaia no π-matched UF1 stars. Correcting for the extinctions corresponding to the peaks of the colored contour distributions in Figure 4.A. (see Table 2), the g-band apparent magnitudes found in Figure 2 become g-band absolute magnitudes M g of about −0.1, 3.4, and 4.5 mag, for the UF1, UF2, and UF3 samples, respectively.   In Table 2, the UF1+Gaia π matched stars span spectral types of G7-K2.5 in the giant luminosity class and A2-A7 in the dwarf class. However, the former is more likely to represent the stars in the  It is more difficult to assign distances and spectral types to POLCAT stars in the no-Gaia and Gaia no π subsamples. Figure 3 includes a reddening line that can aid in interpreting the nature of the stars in these subsamples. For example, the slope of the reddening line is such that the UF1+Gaia no π (orange contours) subset could be deextincted by about 4 A V mag to fall closely over the UF1+Gaia π (red) subset. If this is the case, then both subsets would have nearly identical spectral types and distances, with the Gaia no π subset merely suffering additional extinction, likely associated with denser molecular cloud directions. Interestingly, the UF1 no-Gaia (yellow contours) subset, if deextincted by 10 mag to the UF1+Gaia π value of about 4 A V mag would have brighter apparent magnitudes than the UF1+Gaia π subsample. This could be caused by the UF1 no-Gaia stars being closer or by having greater luminosities, perhaps caused by supergiants located at much greater distances. The very red (H − K) colors for the UF1, no Gaia stars, of 1.0 mag and beyond, cannot be due to nearby red dwarfs, however, as shown in the relative color-color diagram of Figure 19 in Paper III. Simulations of stellar types, distance, and extinctions with GPIPS and Gaia detection limits imposed as priors are beyond this present treatment. Yet, it does appear likely that all of the UF1 stars, across all Gaia -based subsets, are similar enough as to be recognized as red giants, many in the Red Clump, with various degrees of foreground reddening and extinction. The extinctions could be associated with individual dark clouds, with spiral arms that lie between 1 -7 kpc such as Sagattarius and Scutum, or even with the central Galactic Bar.
Figures 2, 3, and 4, taken together, provide the information necessary for identifying the near-and far-side GPIPS "horizons." As listed in Table 2, 99% of UF1 stars are located between distances of 0.35 and 11.9 kpc, with 90% between 0.63 and 7.5 kpc. Thus, there are sufficient UF1 and UF2 stars to conduct limited angular resolution polarization probes of molecular clouds as close as 350-400 pc as well as to characterize magnetic fields in spiral arms in the Galactic midplane.
Having established the bases and representative values for the GPIPS horizons, an exploration of the NIR GPIPS linear polarization properties for one FOV is described in the following.

Methods and Characterizations for One Field, GPIPS-1619
The data from the GPIPS-1619 field, shown in Figure 1.A, were used to explore methods of analyzing and characterizing the polarization properties of the stars for one FOV. This began with plots of basic data properties and proceeded to analyzes of distributions of those properties. The 197 UF1, 557 UF2, and 1172 UF3 stars in the POLCAT for GP1619 were trimmed to remove polarization upper limits (σ P ≥ P RAW ), as they contribute no meaningful GPA values. The remaining 179 UF1, 352 UF2, and 563 UF3 stars are plotted as the red, blue, and green symbols, respectively.
The 129 member subset of UF1 stars that exhibit P SNR (P /σ P ) ≥ 3 (equivalent to σ P A < 9.6 • ), and designated UF0, are plotted as filled light-brown squares, which appear within most of the red UF1 star location circles.
The UF1 (and UF0) stars, and many UF2 stars, exhibit GPA values in the 70 to 130 • range (Apanel) and P values in the 0.5 to 5% range (C-panel). The UF2 stars tend to exhibit higher P values than do the UF1 stars and this tendency is even stronger for the fainter, UF3 stars. Some of these higher polarization percentages could be real and could correlate with higher dust column densities and coherent magnetic field orientations, traceable through extinction. However, these fainter stars are more likely to exhibit higher P values due to noise bias and those values should be treated with caution (Paper III). Lower limits on P SNR alone are not sufficient to select high-confidence stellar polarizations, unless the limit values are quite high (e.g., greater than 3-5; Simmons & Stewart 1985).
In Figure  samples, respectively. The D-panel (center-bottom) shows the CL curves of P after being marginalized over GPA. However, the likelihood accumulation window was truncated at 10% of P , which affects the UF2 and UF3 CLs, as some of those stars have P values in excess of that limit. In that D-panel, the P medians of 2.4 and 2.7% for UF1 and UF0 are accurate, but the UF2 and UF3 medians of 4.4 and 6.5% represent only lower limits because of the truncation.
The GPA CLs, marginalized over P , but including the truncation at 10%, are shown in the E-panel    The GPA distributions of Figure 5 were used to compute a mean value of GPA and its standard deviation (∆ GP A ) for each UF subset of stars. These values were computed both in an unweighted fashion, without respect to individual GPA uncertainties, and using variance weighting by those uncertainties. (Note that Stokes U and Q averaging was not performed -the analyses used GPA values only.) The resulting values appear in Table 3. The first column in the Table indicates  Characterizing the properties of the Galactic disk magnetic field using GPIPS data products can proceed along many different paths, invoking a wide variety of data selection criteria. This could include, for example, utilizing all of the GPIPS stellar Stokes U and Q measurements, or alternatively, selecting only the data corresponding to high P SNR (e.g., ≥ 5). All choices of data selection schemes bring some type of bias, or focus, on a particular data range or ISM characteristic. High P SNR cutoffs select the highest quality polarization measurements, but reduce the number and spatial sampling that could reveal magnetic field properties with adequate confidence levels. Low P SNR cutoffs introduce excessive noise and false positives. In Appendix C, the UF1 stellar subset is shown to reveal similar properties to those found in the high P SNR UF0 subset. This reduces the need to restrict further analyses to the smaller UF0 subset, as the larger UF1 set is adequate for establishing overall magnetic field properties and correlations. The UF1 stars suffer less noise-biasing effects than fainter stars and so enable higher-significance differential comparisons of polarization properties between GPIPS FOVs than would be possible using UF2 and/or UF3 stars.  Across the full set of GPIPS FOVs, many of the resulting histogram probability functions were asymmetric and sometimes double-peaked. Hence, simple representative functions or fits, such as gaussians, cannot accurately characterize the actual distributions.
4 Angle-aliasing in the GPA histogram was reduced by accumulating the gaussian probability distributions across an angle range eleven times wider than the usual 0 to 180 • range, instead of truncating at the range boundaries, and then shifting and adding the probabilities outside the usual range into the bins within that range.
Accordingly, cumulative probability distributions were computed for the UF1 subset for each histogram and are overlaid as thin red lines in Figure 6. These were analyzed to find the quartile boundaries (Q1=25%, Q2=median, and Q3=75% cumulative probability). The resulting median P (hereafter P50) for this field is 2.32%, while the median GPA (hereafter GPA50) is 98.5 • . The combination of GPA50 in Figure 6.B being 98.5 • for UF1 stars while the weighted mean for the same stars in Table 3 is 102.9 • ± 0.3 • is evidence that the Figure 6.B UF1 distribution has some non-gaussian nature, despite it gaussian appearance. The values for the first and third UF1 quartile boundaries are 1.45 and 3.50% for P and 83.7 and 112.9 • for GPA, as indicated on Figure 6.
In order to obtain robust measures of the widths of the GPA distributions, the interquartile ranges, computed from the differences between the x-axis locations of the first and third quartiles (Q3 -Q1), were adopted. For the GPIPS-1619 GPA histogram, this width difference, designated WGPA, is 29.2 • for the UF1 stars. If the GPA distributions were perfectly gaussian, the gaussian width parameters would be 42.5% of the WGPA values, or about 12.4 • for the GPIPS-1619 FOV. This value is somewhat less than the standard deviations reported in Table 3

FOV-based GPIPS Characterization of Polarization and Magnetic Field Properties
In this Section, histograms of these four key characterizing quantities are presented, as are their distributions as functions of Galactic longitude and latitude, at the 10 arcmin angular resolution corresponding to the Mimir FOV size. This selection enables generation of high-significance values by quantifying the behavior of the properties of the many UF1 stars in each FOV, and doing so reveals both large-scale trends and moderate-scale departures from those trends. Detailed examination of properties on finer angular scales and across overlapping FOVs is needed, for example to establish the magnetic field properties associated with resolved molecular clouds (e.g., Marchwinski et al. 2012;Hoq et al. 2017), but is beyond the scope of this paper.
The large-scale, FOV-based characterizations begin with histogram analyses of the numbers of UF1 stars measured for polarization in each FOV, the median polarizations, the median Galactic position angles, and GPA widths, followed by representations of the sky distributions of these same quantities.  Table 4 lists the quartile boundaries for the distribution functions for each quantity.

Histograms of FOV-based Properties
The upper-left, A-panel in Figure 7 shows the distribution of numbers of UF1 stars in each FOV, binned by the base-10 logarithm of the number of star counts. The cumulative probability distribution is overplotted. As was done for the distributions in the GPIPS-1619 FOV, this cumulative distribution was analyzed to identify the distribution quartile boundaries. The median number of UF1 stars in a GPIPS FOVs is 252, while less than 25% of the FOVs have fewer than 188 stars and less than 25% have more than 378 stars.
The upper-right, B-panel of Figure 7 displays the histogram of the P50 (median debiased polarization percentage P ) for UF1 stars in each of the GPIPS FOVs. The median of this distribution is 1.53%, with quartile boundaries at 1.30 and 1.80%. This median is only 1.06 times greater than the value found in an analysis of the first 18% of the GPIPS FOVs (DR1-Paper III). These polarization percentages are smaller than optical wavelength values, which average closer to 5-7% in the interstellar medium (Hall 1949;Hiltner 1949a,b). This difference is expected due to the wavelength dependence of starlight polarization (Serkowski 1973;Serkowski et al. 1975;Wilking et al. 1980).
The lower-left, C-panel of Figure 7 displays the distribution of median Galactic polarization position angles (GPA50) for the UF1 stars in each GPIPS FOV. As found in Paper III, the distribution is centrally peaked, though offset by 13. • 3 from the expected, disk-parallel value of GPA = 90 • that characterizes most magnetic field models (e.g., Ferrière & Schmitt 2000). Over the region of the Galactic mid-plane surveyed by GPIPS in the first Galactic quadrant, the median magnetic field  orientation is not purely parallel to the Galactic disk. It also exhibits broad orientation deviation wings that extend to both Galactic pole directions.
The lower-right, D-panel of Figure 7 shows the distribution of interquartile ranges ( The offset of the median GPA from being purely disk-parallel and the wide range of position angles present in each GPIPS FOV indicate that magnetic field models dominated by strongly uniform, disk-parallel behavior may not be adequate to describe these characterizations. In order to ascertain how these key properties vary with location in the Galactic disk, their one-dimensional (1-D) and two-dimensional (2D) distributions were examined next.

Galactic Latitude and Longitude 1-D Behavior of FOV-based Properties
The same four, FOV-based quantities for each GPIPS FOV, derived from the UF1 stars, are plotted versus Galactic latitude in Figure 8 and versus Galactic longitude in Figure 9. In both Figures, stacked plots are shown that display log(N), P50, GPA50, and WGPA, respectively, from top to bottom. Black dots mark the values of each quantity measured for each of the GPIPS FOVs.
Galactic Latitude 1-D Behaviors -In Figure 8, in addition to showing the black points for the FOVbased values, a 10-point running average is shown as the blue curve, a linear fit with latitude is shown in red for three of the four quantities, and a gaussian fit with latitude is shown in red for the P50 plot.
The top, A-panel shows that log(N) displays a strong, high-angular frequency modulation (30 cycles over 2 • ) that is most easily seen in the blue running average curve. This modulation is likely due to the slight variation of FOV Galactic longitude with latitude, related to the equatorial grid used to conduct the GPIPS observations (e.g., Figures 12 to 15, below). The modulation suggests that the log(N) dependence on longitude will be more pronounced than it is on latitude. Ignoring this modulation, the overall log(N) dependence on latitude appears to show a slight depression in star counts from about B= −0.6 • to +0.1 • (depicted by the blue, running-average means falling below the red linear fit), coupled with a weak rise in counts for positive latitude values (or a decrease in star counts for negative latitude values). The mid-plane decrease in counts is likely due to extinction by distant dust cloud complexes in the disk, which are expected to have small angular scale heights. The decrease in counts for negative latitude may be caused by extinction from more nearby clouds with larger angular offsets. The red line shows the linear fit, namely: log 10 (N ) = (2.445 ± 0.004) + (0.041 ± 0.007) × GB, where GB represents Galactic latitude, in degrees.
The middle-top, B-panel of Figure 8 that presents P50 also exhibits some of the same effects of the longitude beating. In addition, it also shows a weak rise in value, by about 0.2-0.3%, centered near the mid-plane and falling toward the survey latitude limits. The data were fit with a gaussian, returning an amplitude of 1.760 ± 0.011%, a gaussian width of 1.53 ± 0.06 • , and center at GB=−0.160 ± 0.022 • .
This polarization rise near the Galactic equator may be due to polarization contributed by more distant dust cloud complexes or ones with higher dust column densities.
The fitted gaussian latitude width corresponds to a 3.6 • FWHM, which, if associated with the 2.6 kpc median distance inferred for the UF1 stellar count density in the Figure 4 Gaia -GPIPS comparisons described earlier, implies an NIR polarization Galactic disk thickness FWHM of 160 pc, only ∼30% thicker than the 120 pc FWHM for the CO-traced gas layer . A more realistic estimate might use half the distance to the UF1 star distribution as better representing the effective mean polarizing dust distance, resulting in an even thinner dust layer thickness, and one in agreement with the CO layer thickness. Both estimates are thinner than the 400 ± 30 pc exponential scale height found for the Galactic magnetic field model developed by Jansson & Farrar (2012) another indication that UF1 stars probe to distances well into the bulge along these longitudes, likely in the 5-7 kpc range. In Figure 9.A, there are also some significant decreases in UF1 star counts, especially near longitudes 24, 30, 35, 38, and 51 • and some apparent increases in star counts (e.g., near 21, 27, and 32 • ). The decreases span 0.5 to 2 • of longitude and may be due to large complexes of dust (and gas) foreground to the bulk of the background stars seen in the neighboring fields. They could also represent interarm regions with fewer stars between richer spiral arms. A more detailed comparison of GPIPS star counts to star counts for Gaia and GLIMPSE as well as to 2MASS (H-K) colors is described in Section 4.3.3 below.
The middle-bottom, C-panel in Figure 9 shows that GPA50 exhibits the most dramatic variations with longitude. Defining any low-order polynomial trend was difficult.  a few degrees of longitude, especially near longitudes 35, 40, and 52 • . In contrast to the generally uniform behavior of GPA50 with Galactic latitude (Figure 8), the GPA50 longitude behavior is strongly non-uniform. Quantitatively, the 10-point moving averages deviate by more than 30 • from disk-parallel orientations for over 30% of the longitude range surveyed (when averaged over latitude), compared to no such deviations for the latitude range survey (when averaged over all longitudes).
Magnetic field orientation deviations in the disk midplane zone are mostly dominated by longitude effects and are nearly unaffected by purely latitude effects.
The bottom, D-panel in Figure 9 shows that WGPA exhibits the same lack of overall change with longitude that it exhibited with latitude in Figure 8.  Figure 10 shows the Galactic longitude behavior of the base-ten logarithm of the star counts in the

Correlated Behaviors of FOV-based Properties
To explore the nature of possible correlations among the four key characterizing quantities, a cornerplot representation was developed, using the median-value characterizations for each of the GPIPS FOVs, and is shown in Figure 11. For each of the six panels in the Figure,  The upper-left, A-panel in Figure 11 shows how P50 and the log of the number of UF1 stars in each field are related. There is a peak likelihood at about 1.5% for P50 and 240 stars per field (log(N)∼2.37) with gaussian-like decays away from the peak. There is a weaker, secondary peak at 1.5% in P50 and log(N)∼2.7, which comes from the longitude range less than 34 • , as it is only in that range that such high UF1 star counts are seen in Figure 9. This local increase could be due to distant bulge stars. There is also a minor tertiary peak at 1.25% for P50 and 2.8 for log(N), which corresponds to the L=27 • count increase and polarization dip seen in Figure 9.
The middle-left, B-panel in Figure 11 compares GPA50 with log(N), revealing the likelihood peak at 75 • of GPA50 and 210 stars per field. The secondary and tertiary peaks noted appear to blend into one, weaker peak near GPA50 = 90 • and log(N) = 2.7.
The middle-right, C-panel in Figure 11 compares GPA50 with P50, showing a likelihood peak at about 1.7% and 77 • , respectively. Near 1.4% of P50, the GPA50 values extend from zero to 180 • , suggesting that angle aliasing may be present. As the P50 values increase beyond 1.5%, the GPA50 range decreases and GPA50 values appear to move closer to a disk-parallel (GPA=90 • ) orientation.
There are few fields with P50 values below 1%, as was already shown in Figure 7.B., and this could be a consequence of the UF1 selection criteria.
The lower-left, D-panel in Figure  The lower-center, E-panel in Figure 11 shows a strong anti-correlation of WGPA and P50, which was suggested in the discussion of the previous section. While there does appear to be a likelihood peak near 1.7% and 35 • , the overall curved shape of the contours indicate some degree of correlation.  stars on average (log(N) = 1.9). The most populous FOVs, shown in red colors, contain 1,000 or more UF1 stars. The general rise in number of UF1 stars for GL < 34 • is likely due to the contribution of bulge red giant stars in addition to the disk stars sampled at all longitudes, as noted earlier.
In Figure 12, three extended zones of enhanced numbers of UF1 stars in the FOVs are apparent.
These span Galactic longitude 18-21.5 • for positive latitudes down to midplane ones, longitudes 24-29 • for mostly negative latitudes (though with a small secondary peak to positive latitudes at longitude 27.5 • ), and from longitudes 31.9-33.2 • for only negative latitudes. These three zones appear to account for the three peaks in the run of log(N) versus longitude in the lowest panel of Figure 9 and in the photometric panels (A, B, C) of Figure 10. P50 versus Galactic longitude and latitude -The Galactic longitude and latitude distribution of UF1 median percentage polarization P50 is shown for the GPIPS FOVs in Figure 13. The false-color mapping scheme spans from about 0.8 to 3.0%, though the maximum value across the map is closer to 5% and the average is about 1.5% (Figure 7.B). Regions of polarization percentage greater than that average (light blue to green colors) tend to be found closer to the mid-plane. Comparing Figure 13 to Figure 12, the zones of higher star counts in Figure 12 are seen in Figure 13 to exhibit lower median polarization percentages (e.g., longitudes 32 − 33 • , latitudes ≤ 0 • ). The reverse is also true-lower star count regions tend to exhibit higher polarization percentages (e.g., longitude 30.6 • , latitude −0.4 • ), likely the signature of dust along those latter sight lines both extincting and polarizing the background starlight. This trend is more pronounced in Figure 13 than in Figure 11.A, so seeing the trend in Figure 13 helps reveal the weak anti-correlation of log(N) with P50 that is present in Figure 11.A.
The roughly 25-30 regions showing the greatest polarization percentages (red colors) in Figure 13 have small angular extents. They also tend to be surrounded by regions of higher than average polarization (green colors), which are themselves more extended. The natures of these high-P50 regions are explored further in Section 5.2.  for estimating magnetic field strengths from linear polarization data has an inverse dependence on polarization position angle dispersion, a direct linear dependence on gas velocity dispersion, and a square root dependence on gas density. Assuming the latter two quantities exhibit roughly constant mean values across all FOVs (a weak, but useful first step), the red highlighted zones in Figure 15 could represent regions of locally stronger magnetic field strength. In Figure 15, the overall impression is one of a relatively uniform background of WGPA values near 31 • (green colors; ∆ GP A ∼ 13 • ), with many small regions and 9-10 larger regions of low-WGPA values, seen as red-colored zones. High-WGPA values are present in many small zones and a few larger zones, but in fewer numbers of regions, both small and large, than for the low-WGPA zones. Low-WGPA FOVs correlate with high-P50 FOVs, as already noted in the discussion related to Figure 11.E and as examined in Section 5.2

DISCUSSION AND APPLICATIONS
The types of studies made possible by GPIPS data will be different in nature and scope than those performed using other existing magnetic field probes. The data contained in GPIPS DR4 include more than 1 million measured stellar polarizations of high quality that have the potential for being used individually (UF1 type; Paper III). The UF2 and UF3 stars account for another nearly 9 million stars, but need careful distance selection and averaging to return magnetic field information. Planck polarization at 353 GHz, with its 5 arcmin resolution, yields about 6 million independent samples across the entire sky, but only 11 thousand across the GPIPS zone. The pulsar and extra-galactic The science applications of the GPIPS data will likely be many, and are well beyond the scope of this introductory presentation. GPIPS data from earlier data releases have been used to create the first resolved map of the plane-of-sky magnetic field strength for a molecular cloud (Marchwinski et al. 2012) and used with deeper K-band (2.2 µm) Mimir polarimetry to map the magnetic field strength across an Infrared Dark Cloud (Hoq et al. 2017).
In the following, example studies based on comparisons of GPIPS to Planck yielded some new findings and insights. The first comparison involved the plane-of-sky polarization position angle orientation distributions of Planck and GPIPS. The second was a deeper look at the anti-correlation of WGPA and P50.

Plane-of-Sky Polarization Orientation Distributions Comparison
The histograms of Galactic polarization position angle using GPIPS NIR background starlight polarimetry were shown in Figure  The exact reason for the difference in GPA distributions between GPIPS and Planck remains unknown. It could arise from differences in the effects of angular resolution and/or the line-of-sight distances probed. The GPIPS angular sampling is orders of magnitude finer than Planck achieves, so GPIPS could be resolving structures that are too small to be resolved by Planck . Yet many of the features found here in the GPIPS 2-D (e.g., Figure 14) and 1-D (e.g., Figure 9) plots span angular sizes that are much larger than the Planck polarization resolution. Line-of-sight effects could be causing Planck beams to integrate dust emission over much longer distances than are probed using GPIPS, again leading to smoothing of GPIPS-resolved changes by the Planck observations and analyses. GPIPS findings, derived from polarizations of background stars, will necessarily be limited in the line-of-sight distances that can be probed, as stellar faintness and extinction both contribute to detection limitations (Paper I, and Section 4.1, above). However, the presence of the Galactic bulge in the GPIPS stellar distributions (Figure 9 and Figure 12) shows that the GPIPS far horizon must extend to at least 5-7 kpc from the sun.
The question of exactly why GPIPS and Planck differ in their inferred GPA distributions remains unanswered and may have to wait until robust models of the Galactic magnetic field, at spatial and angular resolutions finer than currently exist, become available for testing.
5 Planck Collaboration Int. XIX (2015) reported position angles ψ for the peak of the electric field vector, which is perpendicular to the magnetic field orientation for thermal dust emission. Those angles are rotated by 90 • here to become GPA values.

The Anti-Correlation of WGPA and P50
The anti-correlation of WGPA and P50 seen in Figure 11.E has been seen previously in Planck polarization data (e.g., Figure 23 of Planck Collaboration Int. XIX 2015) and perhaps in SCUBA submm polarization data even earlier (Poidevin et al. 2010). More recent Planck analysis (Planck Collaboration XII 2018) used a larger region of the sky over which to find a width-polarization relation they argued was of the form S × P = constant, where S is a measure of polarization position angle dispersion and P is the fractional polarization measured at 353 GHz.
In Planck Collaboration XII (2018), an analytic model was constructed using gaussian fluctuations containing combinations of uniform and random (turbulent) magnetic fields for multiple zones along the line of sight to test the observed S × P relation, and a strong anti-correlation was found between S and P . They argue that this anti-correlation is a direct result of magnetic field topology and should be a general property of the Galactic magnetic field.
To examine whether GPIPS was also returning similar results, the plot of WGPA versus P50, which should be closely equivalent to the S versus P plots in the Planck papers, was recast in the log-log form used in the Planck papers and is presented as the A-panel of Figure 16. There, each black dot is plotted at the log-based location corresponding to the median UF1 polarization (P50) and the interquartile range (WGPA) for one GPIPS FOV. The red line represents the best fit robust linear regression, resulting in a slope of −1.266 ± 0.014. This power law index is similar to the −1 value dictated by the S ×P relation. But, the measured index misses negative unity by almost twenty times its uncertainty. While the GPIPS data appear to be generally consistent with the Planck findings, there are key differences.

Locating Strong and Weak Magnetic Field Regions
In Planck Collaboration Int. XIX (2015), the highest PA-dispersed regions were argued to form boundaries between isolated segments characterized by high-P values and low-PA dispersions (their . Data points are colored red, blue, green, black, and gray to indicate the data subsample to which they were assigned -red for the S1 highest-P50/lowest-WGPA FOVs subset through the other colors to gray for S5, representing the lowest-P50/highest-WGPA FOVs subset. (Right-lower, C-panel): Histogram of the numbers of GPIPS FOVs falling into 41 bins along the X P W axis.
Histogram colors are the same as for the data points in the B-panel.
to be a few degrees. Since GPIPS data exhibit a similar anti-correlation of S and P , the question of whether similar isolated segments of low PA-dispersion are surrounded by high PA-dispersion regions in GPIPS was examined to try to learn about these potentially magnetic-dominated zones.
The Figure  Multi-Dimensional Analysis of Coherent High-P/Low-WGPA Structures - Figure 17 offers a two-fold comparison of the relative locations of the S1, S2, and S3 high-P50/low-WGPA selected FOVs (red, green, and blue points, respectively) and the S5 low-P50/high-WGPA selected FOVs (gray points).
The top, A-panel of Figure 17 presents the Galactic longitude and latitude distribution of those FOVs.
There appear to be many distinct clumps of multiple GPIPS FOVs exhibiting high-P50/low-WGPA values. The largest of these clumps show central cores comprised of S1 (red) points surrounded, or bordered, by S2 (blue) and S3 (green) FOV points. Under the assumption of rough uniformity of gas velocity dispersion and density over FOV sizes, these could signify zones of high magnetic field strength being embedded in somewhat weaker field regions. Alternatively, they could signify zones where the magnetic field is purely in the plane of the sky, and so maximizes P50 values and minimizes WGPA ones, while being surrounded by regions of more mixed, less uniform, magnetic field inclination angles.
The S5 (gray) FOV points also show multiple resolved regions, but these tend to be located mostly at the Galactic latitude limits of the survey region. As these zones contain somewhat fewer UF1 stars and lower P50 values, the S5 regions could represent either lower extinction zones, weaker magnetic field zones, or zones with more random magnetic field orientations and/or inclinations.
There does appear to be a rough anti-correlation of S5 fields with the S1, S2, and S3 fields in longitude and latitude space, but concluding that the high-WGPA S5 fields are defining boundaries around, or between, low-WGPA S1, S2, and S3 fields seems unsupported in these GPIPS data.
Instead, the high-P zones appear to be surrounded by more average (e.g., S4 -not shown in these plots for clarity) magnetic field strength (or orientation coherence) regions.
The bottom, Figure 17 B-panel shows GPA values versus Galactic longitude locations of the FOVs.
Many of the same groupings of colors remain coherently located in this plot. Thus these regions of higher-P50/lower-WGPA appear to be associated with resolved, coherent magnetic fields, at least locally, that have nearly constant plane of sky orientations (GPAs).
Resolved Strong Field Regions -In order to obtain some quantitative evaluation of this clustering behavior, and to locate these potentially strong magnetic field regions, coherent groupings of points The spatial coherence seen for the S1, S2, and S3 FOVs in the top panel is also present as coherent GPA values for each distinct structure in the lower panel. This is not the case for the S5 (gray) FOVs, which show much less GPA clustering. Light brown rectangles indicate the extents of the ten groups described in the text and listed in Table 5.
were identified visually in Figure 17. Groups needed to exhibit agreement in subsample designation (S-number or plotted color), Galactic longitude and latitude, and GPA so as to remain identifiable as distinct clumps. Subjectively, there appear to be about ten such large groups, each of which has multiple high-P50/low-WGPA (strong B-field) S1 (red) FOVs, many S2 (blue) FOVs, and many S3 (green) FOVs. There are also some lesser groups that have one or no S1 FOVs. The longitude and latitude center locations as well as angular and GPA spans for the ten major groups are summarized in Table 5 and are shown as light brown rectangles in Figure 17.
In Table 5, the first column is a group sequence number, ordered by increasing Galactic longitude.
The second column offers designations, based on the mean Galactic longitude of the group. The next column lists the longitude range spanned by each group, followed by the latitude range spanned. The fifth column lists the GPA range spanned. The sixth column lists the total number of the highest-P S1 (red) and S2 (blue) GPIPS FOVs contained within each group. These two extreme FOV type appear to be more clustered in the Figure 17 A-and B-panels than do the S3 (green) FOVs and so were chosen to define the group extents and contents.
The total number of S1 and S2 GPIPS FOVs contained within the ten groups is 132. This is about 68% of the total number of S1+S2 FOVs. That is, the highest-P50/lowest-WGPA FOVs appear to be the most clustered class of FOVs. This would seem to argue that resolved regions with strong magnetic fields are not uniformly distributed but instead are localized to perhaps 10-12 major structures. The average S1+S2 FOV count per group is about 13. For circular groups, this is equivalent to a diameter projection spanning about 0.4 • , or 18 pc for an average assumed distance of 2.6 kpc (see Section 4.1). While it is possible that these groups represent just the highest-P50 centers of larger coherent structures, it is difficult to imagine that the groups found here also happen to be located within structures having sizes of several degrees, as the Planck analyses (Planck Collaboration Int. XIX 2015) would suggest.
The remaining 2,334 S4 GPIPS FOVs (72%), colored black in the right panel of Figure 16, were also plotted in the same form as for the high and low P50 fields shown in Figure 17. Those S4 fields, exhibiting more typical values of P50 and WGPA, were found to be mostly uniformly distributed in  Galactic longitude and latitude, absent the regions already selected by the high and low P50 fields.
The average fields were also distributed somewhat uniformly along the GPA plot, though following the trends seen in Figure 9.C, with no groupings as obvious as those listed in Table 5.
Thus, the S5 (gray; low P50) fields seem to mostly occupy the survey latitude boundaries, the S1, S2, and S3 high-P50 fields (red, blue, green) are mostly found in about ten resolved groupings, and the more moderate P50/WGPA FOVs are fairly uniformly distributed.
The positions and extents of the ten high-P50 groups listed in Table 5 Table 5 was weak-4 of 11 for the WMAP regions and only 2 of 15 for the RMS objects. Some of these massive star forming regions are also likely at distances too great for GPIPS to have been able to probe. The generally poor matching of high-P/low-WGPA regions with zones of massive star formation may indicate that strong and/or uniform magnetic field conditions are not prevalent in such settings.
Are these high-P50/low-WGPA groups physical objects with strong magnetic field strengths, or are they regions where the magnetic field just happens to be well-aligned and mostly in the plane of the sky? Establishing magnetic field strengths for the regions rests on application of the DCF method, and thereby requires high-quality information for gas velocity dispersions and gas volume densities across the regions, or Zeeman Effect high-resolution and high-sensitivity molecular line spectroscopy.
These are beyond the scope of this paper, but should be pursued. color-coded into the same S1, S2, and S3 high-P50 (red, blue, green), S4 average-P50 (black), and S5 low-P50 (gray) GPIPS FOV classifications, as per the previous discussion. The overall impression is that the S1, S2, and S3 FOVs occupy lesser values of WGPA compared to the S4 and S5 points, but this merely reflects the way the FOVs were chosen for type/color classification. There is a clear asymmetry of FOVs with GPA50, with all subsets of FOVs showing distribution centers less than GPA50 = 90 • . The S5 low-P50 (gray) points seem to exhibit a GPA50 spread with the least central concentration-that is, they have the most uniform distribution of GPA50 values.

GPA Distributions Comparison
To examine how the various subsamples of FOVs are distributed in GPA50, scaled histograms were formed and are shown as the upper-right, B-panel in Figure 18. The points in the upper-left, A-panel were binned by GPA50 separately for each of the subsamples. The resulting histograms were scaled to the same integrated number of FOV counts as in the (typical) S4 sample (black histogram; 2,334 FOVs) and successively offset by 300 counts. All five histograms show mostly similar behavior: a broad peak near GPA50 = 75 • , with a slow decay to lesser GPA50 values and a faster decay to greater GPA50 values. Hence, all GPIPS FOVs appear to be drawn from nearly the same parent GPA50 distribution. However, subtle differences can be seen, especially when comparing the high-P50 S1 (red) and low-P50 S5 (gray) histograms. The high-P50 S1 histogram appears to have a more concentrated peak region and no counts beyond GPA50 = 120 • . The low-P50 S5 histogram has a broader peak region and a broader distributed region, with significant FOV counts beyond GPA50 = 120 • .
These small differences were enhanced by forming differences of the high-P50 and low-P50 histograms against the average-P50 histogram. The S1 (red), S2 (blue), and S3 (green) histograms were added and scaled to the total FOV counts in the S4 (black) histogram, and these two resulting histograms were differenced to create the purple histogram in the lower-left, C-panel of Figure 18.
Similarly, the S5 low-P50 histogram (gray) was scaled to the S4 (black) histogram and differenced, to survives to become the S5-S4 (gray) histogram in the D-panel is essentially just the negative of the S4 (black) histogram in the B-panel.
In summary, the strong (or uniform) magnetic field candidate zones, traced by the high-P50/low-WGPA GPIPS FOVs, appear to have a slight preference for exhibiting GPA50 values consistent with magnetic fields that are disk-parallel, while the low-P50/high-WGPA GPIPS FOVs appear to have mostly random magnetic field orientations. These properties are somewhat in agreement with the findings reported for Planck polarization data in Planck Collaboration Int. XIX (2015), though no strong evidence is found here for the high-WGPA (weak field) FOVs to be located surrounding the low-WGPA (strong field) FOVs, and the size scales of the high-P50 groups are much smaller than for the Planck -identified regions.

Remaining Questions
The How well do magnetic fields follow spiral arms? If material (stars, gas, and dust) flows into and through the arms, how does that affect the spiral magnetic field? Do cool gas and dust clouds acquire magnetic fields in spiral arms or do they retain magnetic fields established at formation?
Magnetic fields in the Milky Way and external galaxies may be apportioned into large-scale (uniform), medium-scale (anisotropic random), and small-scale (random, tangled, or turbulent) aspects (see reviews by Beck 2015;Haverkorn 2015). What can the wealth of cold-ISM-probing GPIPS data reveal about the natures of the magnetic field on these different size scales in comparison to the corresponding hot-ISM values? What are the mean sizes of magnetically-coherent zones or cells (e.g., Jones et al. 1992)? What is the GPIPS-measured ratio of uniform-to-random magnetic field strength and how does it change with location? The remaining almost 9 million will be most useful when considered together in Bayesian or other analysis methods in conjunction with archival photometric, parallax, and spectroscopic data.
Here, the high-quality GPIPS data for each of the 3,237 observed 10 × 10 arcmin fields-of-view Checks and evaluations of data obtained for GPIPS were performed as the data were collected, reduced, and analyzed to develop provisional data products. Observations judged to have not met the quality standards described below were rejected and the FOV(s) were re-observed as needed to obtain the high quality data required for inclusion in the final GPIPS DR4 data products. Table A1 presents a shortened, representative portion of the Field Properties Summary Table, which is contained in the full DR4 file set. The FOV rows selected for presentation in Table A1 highlight FOVs that passed all of the quality controls and a couple of FOVs that did not fully meet one quality test. In the Table,  Paper I. Sky Noise levels above 1.2% were judged excessive and those FOVs were re-observed. Of the 3,237 FOVs, only one FOV exceeded this criterion and was retained (its Sky Noise value was 1.3%).
The number of images rejected from each observation set for poor PSF shapes is listed in column ten. At least 89 acceptable images per FOV were required for an observation to be included, and the number of accepted images is listed in column eleven. This criterion ensured that multiple images would sample all 16 HWP orientation angles.
Column twelve lists a Pattern Score for each FOV. These were formed by combining seven different quantitative evaluations of the polarization percentage and orientation patterns for each FOV. They were used to assess whether the resulting polarization patterns resembled parallel orientation directions or orientation directions that aligned tangentially (i.e., swirls), if the polarization percentage increased with offset from the image center, and other negative characteristics. These evaluations uncovered several observing or data reduction failures, including cases of frozen HWP rotation, bad flat-field images, and other issues. A custom software tool, coded in IDL, was created to view the polarization pattern for each FOV observing set and to apply the seven evaluations. These component scores were combined to be the Pattern Score, scaled to range from −9 to +9.
Strongly negative Pattern Scores correlated with non-physical, swirl-like orientation patterns that also had polarization percentages rising with radial offset from image centers, neither of which should occur. Strongly positive Pattern Scores showed highly-parallel polarization orientations and an absence of data problems. Score values less than zero indicated possible problems, and those FOVs were re-observed. Some FOVs exhibited complex polarization orientation patterns resulting in mid-range, but mostly positive, Pattern Scores. Re-observation of many of these FOVs recovered the same complex polarization patterns, reinforcing their veracity. First re-observations of negative-scoring FOVs generally did not yield polarization patterns consistent with the initial observations, so these FOVs were re-observed until the patterns became stable in subsequent observations, which resulted in their Pattern Scores becoming positive.   To this, an additional 1.5 arcsec wide outer zone was added to extend the field sizes to provide some margin for individual star matching, as described below. The resulting search field sizes averaged about 9.9 × 9.9 arcmin, somewhat smaller than the Mimir instrument FOV. The effective field size for the archival catalog searches is about 1% larger than the effective DR4 FOV size (see Section 3.2), which should bias the matching statistics only slightly.
Archival stars were matched to GPIPS stars in each FOV for each of the four catalogs using cone searches with maximum relative projected radial offsets of 1.25 arcsec between GPIPS stars and archival catalog stars. This value was selected based on using matches of test FOVs employing a set of trial cone angle values. Star matching was performed starting from the brightest to the faintest GPIPS stars in each FOV, and similarly brightest to faintest archival catalog stars, to minimize false matches that might have resulted from the large numbers of faint stars. A few GPIPS stars were found to have potential matches to multiple archival catalog stars within the radial offset limit. For these cases, color values were computed for each star (e.g., Gaia g-band minus Mimir H-band) and were combined with the radial offset values using gaussian probability functions to select the single most likely stellar match. Stars, once matched, were removed from the remaining GPIPS and archival catalog potential matching pools.
B.1. Match Rates Table B2 provides summaries of the numbers and rates of stellar matches of archival catalogs to GPIPS. Additionally, for the POLCAT stars, the matching numbers and fractions for each of the UF1 (and its UF0 subset, listed in italics), UF2, and UF3 star subsets are indicated. Using Table B2, reverse match rates, for example the fraction of Gaia stars that have GPIPS POLCAT UF1 matches, may be computed from the match numbers divided by the total entries for each of the four archival catalogs across the GPIPS FOVs. These totals are listed in the final row of Table B2.
The greatest match rates of GPIPS to archival catalogs occurs for GLIMPSE. The lowest GLIMPSE match rate is 70.6% for PHOTCATs and the highest is 99.4% for the UF0 subset of UF1 GPIPS stars.
For every UF stellar category, the rate of matching to GLIMPSE stars is higher than it is to any of the other three archival catalogs. This is a distinct improvement compared to the GPIPS DR1 matching approach and offers the opportunity to use H-band from GPIPS and M -band equivalent (4.5 µm) from GLIMPSE to quantify line-of-sight extinction using the (H-M) colors with the Rayleigh-Jeans Color Excess method (RJCE; Majewski et al. 2011).
In Table B2, the Gaia DR2 columns report the matching stellar numbers and rates for GPIPS stars for the case of no application of the parallax evaluation (the "All" column) and for matching to stars with the potentially useful parallax criteria (the "Parallax" column).
Overall, GPIPS POLCAT match rates with the archival catalogs are somewhat greater than PHOT-CAT ones, as the latter contains more faint stars than the former. The overall GPIPS POLCAT match rates are about 58% for Gaia (40% for Gaia stars with parallaxes), 74% for 2MASS, 86% for GLIMPSE, and 17% for WISE . WISE is generally more sensitive than the Spitzer Infrared Array  13,879,724 7,750,932 9,198,385 18,331,898 2,109,578 Camera (IRAC) (Fazio et al. 2004), used to conduct the GLIMPSE observations, for directions away from the Galactic plane. But, WISE has coarser angular resolution than IRAC, resulting in a brighter confusion limit in the Galactic plane and fewer sources per GPIPS FOV than for GLIMPSE in the same wavebands.
In Table B2, there is a trend of increasing GPIPS match rates as UF number decreases, corresponding to increasing apparent brightness. The one interesting exception is the POLCAT UF0 subset matching to Gaia , which shows somewhat lower rates than the larger UF1 sample which contains UF0. This could be caused by the greater P values in UF0 arising because of their greater dust column densities and thereby greater A V values. This in turn would affect Gaia matches through the optical g-band brightness limit, as these shorter wavelengths would suffer the greatest extinctions.
The archival catalog matching information was integrated into GPIPS in two ways, one related to the FOV-based data products and one related to the unique star data file.

B.2. FOV-Based Archival Catalog Stellar Match Data Files
For the FOV-based products, the 2MASS and GLIMPSE matching stellar information was directly integrated into the PHOTCAT and POLCAT files for each of the 3,237 GPIPS FOVs. These 2MASS and GLIMPSE values supersede the values listed in the GPIPS DR1 through DR3 listings, as follows.
Prior to DR4, only the highest-quality 2MASS data were included in GPIPS files by requiring an "A" photometry quality rating for each of the J-, H-, and K-band 2MASS magnitudes (Skrutskie et al. 2006 were directly matched to GPIPS stars and were included in GPIPS files. This approach greatly increased the fraction of GPIPS entries with GLIMPSE matches, especially those for which 2MASS matches were lacking due to faintness. The Gaia DR2 stellar data were further examined to determine the quality of the parallax information provided in DR2. Stars with possibly useful parallax values for GPIPS applications by potential users were judged to be those for which the parallax SNR (π/σ π ) was greater than 0.5 and the parallax value was greater than −2 mas. As noted earlier in the text, these liberal limits will mainly remove non-detection upper limits and spurious values while avoiding potential population biases (Luri et al. 2018;Bailer-Jones et al. 2018). These do not include the additional criteria on g-band mag, H-band mag, or (H − K) color uncertainties that were applied to create Figures 2, 3, and 4 and the associated summaries presented in Table 2.
For each of Gaia DR2, 2MASS, GLIMPSE, and WISE , the FOV-based approach generated one data file per FOV for each of these four archival catalogs. In each file, every archival star contained within the FOV search area for that catalog is listed, along with PHOTCAT and POLCAT star identifiers for each matching GPIPS star. This approach provides bidirectional matching information and enables characterizing match success rates. Note that these match rates are somewhat optimistic, in the sense that not every match of an archival star to a GPIPS star will necessarily provide uniformly high quality stellar information. Users are strongly encouraged to evaluate the uncertainties listed for each reported value for matches between GPIPS and the archival entries.
Each Gaia , 2MASS, GLIMPSE, and WISE match file has metadata for the GPIPS FOV number, search center sky direction in R.A. and decl., and field search size in the R.A. and decl. directions.
Each match file has one row for each archival star found in the search field. for WISE ), followed by the star designation unique to that catalog.
Gaia DR2 match files contain similar metadata, star numbers, GPIPS star numbers, and R.A. and decl. values as reported in Gaia DR2. Next, each row lists the Gaia g-band magnitude, g-band mag.
uncertainty, parallax, parallax uncertainty, proper motions and their uncertainties in the R.A. and decl. directions, and the Gaia star designation label.

B.3. Unique Star Data File Contents and Archival Match Information
As an alternative to the FOV-based data files, the unique star data file (Clemens et al. 2020) collects all GPIPS photometry and polarimetry and all matching stellar data appropriate to each GPIPS star, with data fields for each star as listed in the example entry shown as Table B3. The unique star file contains entries for 13,861,329 GPIPS stars found in the 3,237 PHOTCAT files.     Most of the data fields in the unique star file are conventional and are based on existing GPIPS (Paper III), 2MASS, GLIMPSE, Gaia DR2, and WISE catalogs and can be interpreted using Table B3 and  In Table B3, the NHWP field most often lists the number of distinct HWP images (up to 16) in which a non-overlapping star was detected. Faint stars might fail to be detected in all 16 HWP images for a FOV, so this field can be useful for culling faint polarization candidates. For overlapping FOVs, NHWP carries the sum of all constituent HWP detection counts, resulting in a maximum value for this field of 64, as is the case for the example star properties listed in Table B3. For stars with PHOTCAT magnitudes but no PHOTCAT matches, the NHWP fields were set to 99. Combining the GPSTAR and NHWP field information will provide adequate insight into whether a multiply observed star was detected in sufficient HWP images to be useful.
Finally, the UF field carries the 1, 2, and 3 values associated with the UF1, UF2, and UF3 classifications described in the text. Note that for multiply observed stars, this classification was reassessed after the stellar polarization data were merged from the multiple observation values. This could result in a lower UF value than appear in the FOV-based single observations of the star. Also, for stars in the PHOTCAT-based unique star file that do not have GPIPS polarization data (e.g., no POLCAT star matches), the UF field was set to −99.
Two potentially useful classes of data are absent in this combined data file. The first is the detailed photometric and polarimetric information obtained for the duplicate stars that appear in more than one GPIPS FOV because of the overlapping nature of the survey. The polarization information for these stars is merged, as described below, in the unique star file, though FOV-identifying information for each merged star is in the GPSTAR array. The second class of missing data are the FOVbased files of archival data, especially of the archival stars in those files that are not matched to GPIPS stars. These unmatched stars are fully absent in the unique star file and are only listed in the FOV-based files. A less vital third class of missing information involves some of the ancillary polarization information, such as where each star appears on the Mimir detector FOV, which is used for instrumental polarization correction. Any later recalibration of the GPIPS polarization, resulting from updated instrumental polarization corrections, will need to utilize the FOV-based POLCATs and/or to rebuild the unique star file. The fourth, minor, missing element is the metadata for each GPIPS FOV, normally included in the PHOTCATs and POLCATs and supported by the electronic copies of the hand-written observing logs. The GPSTAR array entries provide information about the original FOVs and star numbers in the constituent observations so that these data may be referenced in the FOV-based data products if needed.
Despite these absences, the DR4 unique star data product is potentially the most useful for accessing GPIPS, as it contains virtually all relevant photometric, polarimetric, and parallax data for conducting a wide variety of studies with the least data accessing software overhead.

C. POLARIZATION SIGNAL TO NOISE CHOICES AND EFFECTS
In Figures 1 through 5 in the text, the Usage Flag (UF) designations introduced in Paper III are seen to reveal important aspects about the nature of these designated stars and the ISM they probe.
One aspect of a uniform survey, such as GPIPS, being applied to a wide range of stellar brightnesses is that there is a nearly continuous and wide range of resulting linear polarization signal-to-noise ratios present in the sample of stars. Which ratio values to include and which to reject for a particular scientific study depends on the goals and questions posed. For the purposes of this paper, and its primarily FOV-based median polarization (and magnetic field) characterizations, what is the best balance between the number of stars selected for analysis and the signal-to-noise criterion applied to select them that will also accurately reveal the properties of the magnetic field being surveyed?
The UF2 and UF3 classified stars were previously (Paper III) shown to be generally unsuitable as individual probes of plane-of-sky magnetic field properties, though they could serve such purposes with suitable sample-or area-averaging. Addressed here is the question of whether the UF1 stars are suitable or whether additional, more stringent, signal-to-noise criteria must be applied in order to extract meaningful magnetic field properties from the GPIPS data.
In the following subsections, the UF1 and UF0 polarization properties for the GPIPS-1619 field are compared, the polarization signal-to-noise distributions for all GPIPS stars are considered, and differences between UF1 and UF0 WGPA (see Section 4.2.2) properties are examined for all GPIPS Figure C1. Histograms of debiased polarization percentage P (Left, A-panel) and Galactic position angle GPA (Right, B-panel) for UF1 stars (red lines) and UF0 stars (those with P SNR ≥ 3; yellow lines) in GPIPS-1619 (previously shown as Figure 6 for the UF1 stars only). These histograms were constructed using accumulated gaussian distribution representations for the properties of each star. Cumulative probability distributions for the UF1 stars are shown as the smooth red curves that connect points centered in each bin and are referenced to the right axis labels. Vertical red dashed lines and labels identify the locations of the three quartile boundaries of the cumulative distributions for the UF1 stars. The similar quartile boundaries for the UF0 stars are shown as the vertical dashed yellow lines.
FOVs as functions of the numbers of stars in each FOV as well as the P50 and WGPA values in each field. The conclusion from this examination is that the UF1 stars, those with m H < 12.5 mag and σ P < 2%, are shown to reveal magnetic field properties in the GPIPS-1619 field nearly as well as their UF0 subset. Also, consideration of the full set of GPIPS FOVs does not change this conclusion.
C.1. GPIPS-1619 Comparisons Figure C1 presents the same histograms of P and GPA for the UF1 stars found in the GPIPS-1619 FOV as was previously displayed as Figure 6, but here adds histograms in yellow for the UF0 stars that additionally meet a P SNR ≥ 3 criterion. Analysis of the UF0 histograms yields P quartile boundaries of 1.76, 2.57, and 3.73% and GPA quartile boundaries of 86.5, 99.2, and 111.6 • , which are indicated as vertical, dashed, yellow lines at the quartile locations. These UF0 star polarization properties do not differ greatly from those derived from the larger UF1 set, though the UF0 P values are biased to greater values through rejection of lesser polarization percentages.
C.2. Polarization Signal-to-Noise Distribution Properties Figure C2.A (top panel), shows histograms of all POLCAT stars as a function of raw (not debiased) polarization signal-to-noise (PSNR ≡ P RAW /σ P ) for the UF1, UF2, UF3 subsets and for all GPIPS stars, as red, blue, green, and black curves, respectively. Figure C2.B (lower panel) shows their cumulative distributions. Vertical dashed gray lines indicate where P RAW /σ P is unity. When their raw polarization values are debiased to become P , all stars to the left of the unity lines would become polarization upper limits. Hence, the P RAW /σ P distributions capture better the full range of GPIPS data quality than would the debiased (P SNR) distributions.
In Figure C2.A, the UF2, UF3, and combined ("All") GPIPS distributions exhibit peaks that are located somewhat to the right of the PSNR unity line. Their cumulative distributions (B-panel) show that their median values are also close to unity P RAW /σ P . That the combined GPIPS distribution follows closely the UF2 and UF3 distributions is because those subsamples dominate in numbers of stars over the UF1 sample (90% vs 10%). The UF1 histogram, however, is shifted to higher PSNR values. Its cumulative distribution (B-panel) shows that 20% of UF1 stars have P RAW /σ P of unity or less and 80% of the UF1 stars show P RAW /σ P in excess of unity.

C.3. Effects of Different P SNR Selections
Next, a sweep of P SNR criterion choices was performed for the GPIPS-1619 FOV stellar data, followed by a limited comparison of results for two P SNR criterion choices for the full set of GPIPS FOVs. The evaluating quantity was the interquartile range WGPA, selected as likely the most sensitive to changes in the nature of the polarization properties of the different stellar subsamples.
For the GPIPS-1619 examination, subsets were drawn from the UF1 stars, applying additional P SNR criteria that stepped from zero through the UF0 value of three and on to five. The resulting  run of WGPA versus P SNR for the GP1619 FOV is presented in Figure C3. In the Figure, the blue diamonds and blue connecting lines show the decrease in WGPA values as P SNR is increased. The red triangles and connecting lines show the numbers of stars meeting the P SNR criteria. Both curves fall with increasing P SNR, as fewer stars in the GPIPS-1619 FOV meet the selection criterion. The overall decrease in WGPA, with P SNR ranging from zero to five, is about 32% for this FOV while the number of stars decreases by 70%. The lower WGPA values might signal greater coherence of the magnetic field in the plane of the sky, but the associated lower star numbers could also be suggesting the introduction of a bias due to, for example, the selected stars only sampling higher extinction lines of sight. Such lines of sight could be limited to only a small, dusty region within the FOV and not representative of the magnetic field properties across the full FOV.
To uncover the nature of possible biases introduced by the addition of a P SNR criterion to the UF1 selection criteria, a representative ratio R was developed. It was computed from the ratio of the WGPA value found when selecting a stellar subsample of UF1 stars using the UF0 criterion (P SNR ≥ 3) to the WGPA value for the UF1 stars alone (e.g., R ≡ WGPA UF0 /WGPA UF1 ). There is a well-defined peak, near the median, with a mean of 0.66 and standard deviation of 0.12. Where R has the greatest spread include low-P50 and high-WGPA FOVs. In those FOVs, R values can be as small as 0.2, likely because the UF0 GPA histogram has collapsed due to having too few constituent stars per FOV. Some R values for low-P50 and high-WGPA FOVs exceed unity, again likely signifying too few UF0 stars are present with which to form meaningful GPA histograms. While UF0 stars, and UF1 stars, are both fine for sampling FOVs where P50 is high and WGPA is low, UF1 stars appear to be better for sampling the low-P50 and/or high-WGPA FOVs. Figure C4. Behaviors of the ratio R (WGPA for UF0 stars divided by WGPA for UF1 stars) for each FOV. The greatest confidence polarization properties will be obtained by selecting the greatest P SNR values, such as those of the P SNR ≥ 3 UF0 subset. However, even across the 76 deg 2 of the inner Galactic plane surveyed by GPIPS, such stars are relatively rare. The UF0 stars account for only 2.8% of the stars measured for polarization and sample the survey area at 70 arcsec mean separation.
Relaxing the P SNR criterion admits some low confidence polarization values, but does not appear to introduce strong log(N), P50, GPA, or WGPA biases relative to the UF0 subset and may avoid possible problems associated with the UF0 stars in the low-P50 FOVs. The UF1 WGPA values are greater than the UF0 ones, but by a mostly predictable ratio. Also, electing to characterize the Galactic disk magnetic field properties via the UF1 subsample increases the stellar probe numbers by more than a factor of four, leading to halving of the mean angular sampling separation. For the purposes of the FOV-based median comparisons of polarization (magnetic field orientation) properties offered in the text, the UF1 choice seems appropriate. User-based studies must carefully assess their own selection criteria against their specific science goals.
The overall conclusion is that the UF1 selection criteria result in FOV-based samples of stars with measured polarization properties that are able to probe and characterize magnetic field orientations adequately and without the possible biases (especially against low-P50/high-WGPA FOVs) introduced when adding additional P SNR cutoffs. CLUT was judged to do better at retaining discrimination of displayed value to color than was done