HAWC+ Far-Infrared Observations of the Magnetic Field Geometry in M51 and NGC 891
Terry Jay Jones, Jin-Ah Kim, C. Darren Dowell, Mark R. Morris, Jorge L. Pineda, Dominic J. Benford, Marc Berthoud, David T. Chuss, Daniel A. Dale, L. M. Fissel, Paul F. Goldsmith, Ryan T. Hamilton, Shaul Hanany, Doyal A. Harper, Thomas K. Henning, Alex Lazarian, Leslie W. Looney, Joseph M. Michail, Giles Novak, Fabio P. Santos, Kartik Sheth, Javad Siah, Gordon J. Stacey, Johannes Staguhn, Ian W. Stephens, Konstantinos Tassis, Christopher Q. Trinh, John E. Vaillancourt, Derek Ward-Thompson, Michael Werner, Edward J. Wollack, Ellen G. Zweibel
DDraft version August 19, 2020
Preprint typeset using L A TEX style emulateapj v. 01/23/15
HAWC+ FAR-INFRARED OBSERVATIONS OF THE MAGNETIC FIELD GEOMETRY IN M51 AND NGC 891.
Terry Jay Jones
Minnesota Institute for Astrophysics, University of Minnesota, Minneapolis, MN 55455, USA
Jin-Ah Kim
Minnesota Institute for Astrophysics, University of Minnesota, Minneapolis, MN 55455, USA
C. Darren Dowell
NASA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
Mark R. Morris
Department of Physics and Astronomy, University of California, Los Angeles, Box 951547, Los Angeles, CA 90095-1547 USA
Jorge L. Pineda
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
Dominic J. Benford
NASA Headquarters, 300 E Street SW, Washington DC 20546, USA
Marc Berthoud
Engineering + Technical Support Group, University of Chicago, Chicago, IL 60637, USA andCenter for Interdisciplinary Exploration and Research in Astrophysics (CIERA), and Department of Physics & Astronomy, a r X i v : . [ a s t r o - ph . GA ] A ug Jones et al.
Northwestern University, 2145 Sheridan Rd, Evanston, IL, 60208, USA
David T. Chuss
Department of Physics, Villanova University, 800 E. Lancaster Ave., Villanova, PA 19085, USA
Daniel A. Dale
Department of Physics & Astronomy, University of Wyoming, Laramie, WY, USA
L. M. Fissel
Department of Physics, Engineering Physics and Astronomy, Queenx92s University, 64 Bader Lane, Kingston, ON, Canada, K7L 3N6
Paul F. Goldsmith
NASA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
Ryan T. Hamilton
Lowell Observatory, 1400 W Mars Hill Rd, Flagstaff, AZ 86001, USA
Shaul Hanany
School of Physics and Astronomy, University of Minnesota / Twin Cities, Minneapolis, MN, 55455, USA
Doyal A. Harper
Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637, USA
Thomas K. Henning
Max Planck Institute for Astronomy, Koenigstuhl 17, D-69117 Heidelberg, Germany
Alex Lazarian
Department of Astronomy, University of Wisconsin, Madison, WI 53706, USA
Leslie W. Looney
Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, IL 61801, USA
Joseph M. Michail
Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), and Department of Physics & Astronomy,Northwestern University, 2145 Sheridan Rd, Evanston, IL, 60208, USADepartment of Astrophysics and Planetary Science, Villanova University, 800 E. Lancaster Ave., Villanova, PA 19085, USA andDepartment of Physics, Villanova University, 800 E. Lancaster Ave., Villanova, PA 19085, USA
Giles Novak
Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), and Department of Physics & Astronomy,Northwestern University, 2145 Sheridan Rd, Evanston, IL, 60208, USA
Fabio P. Santos
Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), and Department of Physics & Astronomy,Northwestern University, 2145 Sheridan Rd, Evanston, IL, 60208, USA and
51, NGC891 3
Max-Planck-Institute for Astronomy, K¨onigstuhl 17, 69117 Heidelberg, Germany
Kartik Sheth
NASA Headquarters, 300 E Street SW, DC 20546, USA
Javad Siah
Department of Physics, Villanova University, 800 E. Lancaster Ave., Villanova, PA 19085, USA
Gordon J. Stacey
Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
Johannes Staguhn
Dept. of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA andNASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Ian W. Stephens
Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA, USA
Konstantinos Tassis
Department of Physics and ITCP, University of Crete, GR-70013 Heraklion, Greece andInstitute of Astrophysics, Foundation for Research and Technology-Hellas, Vassilika Vouton, GR-70013 Heraklion, Greece
Christopher Q. Trinh
USRA/SOFIA, NASA Armstrong Flight Research Center, Building 703, Palmdale, CA 93550, USA
John E. Vaillancourt
Universities Space Research Association, NASA Ames Research Center, Moffett Field, CA 94035 andEnrico Fermi Institute, Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637, USA
Derek Ward-Thompson
Jeremiah Horrocks Institute, University of Central Lancashire, Preston PR1 2HE, United Kingdom
Michael Werner
NASA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
Edward J. Wollack
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Ellen G. Zweibel
Department of Astronomy, University of Wisconsin, Madison, WI 53706, USA ((HAWC+ Science Team))
Draft version August 19, 2020
ABSTRACTSOFIA HAWC+ polarimetry at 154 µ m is reported for the face-on galaxy M51 and the edge-ongalaxy NGC 891. For M51, the polarization vectors generally follow the spiral pattern defined bythe molecular gas distribution, the far-infrared (FIR) intensity contours, and other tracers of starformation. The fractional polarization is much lower in the FIR-bright central regions than in theouter regions, and we rule out loss of grain alignment and variations in magnetic field strength ascauses. When compared with existing synchrotron observations, which sample different regions withdifferent weighting, we find the net position angles are strongly correlated, the fractional polarizationsare moderately correlated, but the polarized intensities are uncorrelated. We argue that the lowfractional polarization in the central regions must be due to significant numbers of highly turbulentsegments across the beam and along lines of sight in the beam in the central 3 kpc of M51. For NGC891, the FIR polarization vectors within an intensity contour of 1500 MJy sr − are oriented very closeto the plane of the galaxy. The FIR polarimetry is probably sampling the magnetic field geometryin NGC 891 much deeper into the disk than is possible with NIR polarimetry and radio synchrotron Jones et al.measurements. In some locations in NGC 891 the FIR polarization is very low, suggesting we arepreferentially viewing the magnetic field mostly along the line of sight, down the length of embeddedspiral arms. There is tentative evidence for a vertical field in the polarized emission off the plane ofthe disk. Subject headings: galaxies: ISM, galaxies: magnetic fields, galaxies: spiral, galaxies: individual(M 51, NGC 891), polarization INTRODUCTION
A face-on and an edge-on galaxy each provides the ob-server with a unique advantage that enhances the studyof the properties of spiral galaxies in general. For a face-on galaxy, there is far less confusion caused by multiplesources along the line of sight, a minimum column den-sity of gas, dust and cosmic ray electrons, and a clearview of spiral structure. For an edge-on galaxy, the ver-tical structure of the disk is easily discernible, verticaloutflows and super-bubbles can be seen, and the fainter,more diffuse halo is now more accessible. M51 and NGC891 provide two well studied examples of nearly face-on(M51) and edge-on (NGC 891) galaxies. We are inter-ested in probing the magnetic field geometry in these twosystems to compare far-infrared (FIR) observations withoptical, near-infrared (NIR) and radio observations, andto search for clues to the mechanism(s) for generatingand sustaining magnetic fields in spiral galaxies.Over the past few decades, astronomers have detectedmagnetic fields in galaxies at many spatial scales. Thesestudies have been performed using optical, NIR, CO andradio observations (see Kronberg 1994; Zweibel & Heiles1997; Beck & Gaensler 2004; Beck 2015; Montgomery &Clemens 2014; Jones 2000; Li & Henning 2011, for ex-ample). In most nearly face-on spirals, synchrotron ob-servations reveal a spiral pattern to the magnetic field,even in the absence of a clear spiral pattern in the sur-face brightness (Fletcher 2010; Beck & Gaensler 2004). Ifmagnetic fields are strongly tied to the orbital motion ofthe gas and stars, differential rotation would quickly windthem up and produce very small pitch angles. The factthat this is clearly not the case is an argument in favorof a decoupling of the magnetic field geometry from thegas flow due to diffusion of the field (Beck & Wielebin-ski 2013), which is expected in highly conductive ISMenvironments (e.g. Lazarian et al. 2012).Radio observations measure the polarization of cen-timeter (cm) wave synchrotron radiation from relativis-tic electrons, which is sensitive to the cosmic ray electrondensity and magnetic field strength (Jones et al. 1974;Beck 2015). Li & Henning (2011) measured the mag-netic field geometry in several star forming regions inM33 by observing CO emission lines polarized due to theGoldreich-Kylafis effect (Goldreich & Kylafis 1981), al-though there is an inherent 90 ◦ ambiguity in the positionangle with this technique. Studies of interstellar polar-ization using the transmission of starlight at optical andNIR wavelengths can reveal the magnetic field geometryas a result of dichroic extinction by dust grains alignedwith respect to the magnetic field (e.g., Jones & Whit-tet 2015) where the asymmetric dust grains are proba-bly aligned by radiative alignment torques (Lazarian &Hoang 2007; Andersson et al. 2015). However, polarimet- Current address: Lincoln Laboratory, Massachusetts Institute ofTechnology, Lexington, Massachusetts 02421-6426 ric studies at these short wavelengths of diffuse sourcessuch as galaxies can be affected by contamination fromhighly polarized, scattered starlight. This light originateswith stars in the disk and the bulge, that subsequentlyscatters off dust grains in the interstellar medium (Joneset al. 2012). The optical polarimetry vector map of M51(Scarrott et al. 1987) was claimed to trace the interstel-lar polarization in extinction and does indeed follow thespiral pattern. As we will see later in the paper, it alsodemonstrates a remarkable degree of agreement with ourHAWC+ map of the magnetic field geometry. A morerecent upper-limit to the polarization measured at NIRwavelengths appeared to rule out dichroic extinction ofstarlight as the main polarization mechanism (Pavel &Clemens 2012). The scattering cross section of normalinterstellar dust declines much faster ( ∼ λ − between0.55 and 1 . µ m) than its absorption, which goes as ∼ λ − (Jones & Whittet 2015). It is therefore possi-ble that the optical polarization measured by Scarrott etal. (1987) is due to scattering, rather than extinction bydust grains aligned with the interstellar magnetic field,since polarimetric studies at these short wavelengths ofdiffuse sources such as galaxies can be affected by con-tamination from highly polarized scattered light (Wood& Jones 1997; Seon 2018). Nevertheless, the similaritywe will find between the optical data and FIR results isstriking, but if they are both indicating the same mag-netic field, then the non-detection in the NIR is a mys-tery. Note that we will find a similar dilemma in com-paring the optical and FIR polarimetry of NGC 891.Observing polarization at FIR wavelengths has someadvantages over, and is very complementary to, observa-tions at optical, NIR and radio cm wavelengths for thefollowing reasons. 1) The dust is being detected in po-larized thermal emission from elongated grains orientedby the local magnetic field (see the review by Jones &Whittet 2015), not extinction of a background source, asis the case at optical and NIR wavelengths. 2) Scatteringis not a contaminant since the wavelength is much largerthan the grains, and much higher column densities alongthe line of sight can be probed. 3) Faraday rotation,which is proportional to λ , must be removed from radiosynchrotron observations, and can vary across the beam,is insignificant for our FIR polarimetry (Kraus 1966).4) The inferred magnetic field geometry probed by FIRpolarimetry is weighted by dust column depth and dustgrain temperature, not cosmic ray density and magneticfield strength, as is the case for synchrotron emission.In this paper we report observations at 154 µ m of bothM51 and NGC 891 using HAWC+ on SOFIA (Harperet al. 2018) with a FWHM beam size of 560 and 550 pcrespectively. In all cases, we have rotated the FIR polar-ization vectors by 90 ◦ to indicate the implied magneticfield direction. This rotation is also made for synchrotronemission at radio wavelengths, but is not made for optical51, NGC891 5and NIR polarimetry where the polarization is caused byextinction (unless contaminated by scattering), not emis-sion, and directly delineates the magnetic field direction.The polarization position angles are not true vectors in-dicating a single direction, but the term ‘vector’ has sucha long historical use that we will use that term here todescribe the position angle and magnitude of a fractionalpolarization at a location on the sky. The polarizationis a true vector in a Q,U or Q/I,U/I diagram, but thistranslates to a 180 ◦ duplication on the sky. FAR-INFRARED POLARIMETRIC OBSERVATIONS
The 154 µ m HAWC+ observations presented in thispaper were acquired as part of SOFIA Guaranteed TimeObservation program 70 0609 and Director’s Discre-tionary Time program 76 0003. The HAWC+ imagingand polarimetry – resulting in maps of continuum StokesI, Q, U – used the standard Nod Match Chop (NMC) ob-serving mode, performed at 4 half-wave plate angles andsets of 4 dither positions. Multiple dither size scales wereused in order to even the coverage in the center of themaps.The M51 data were acquired during two flight series, onSOFIA flights 450, 452, and 454 in November 2017 andon flights 545 and 547 in February 2019. The chop throwfor the Nov. 2017 observations was 6.7 arcminutes at aposition angle of 105 degrees east of north. For the Feb.2019 observations, the chop throw was 7.5 arcminutesin the east-west direction. The total elapsed time forthe M51 observations was 4.6 hours. The observationswith telescope elevation > ◦ at the end of flight 547were discarded due to vignetting by the observatory door.Otherwise, conditions were nominal.The NGC 891 data were acquired on flight 450 andon flights 506 and 510 in September 2018. The chopthrow for all observations was 5.0 arcminutes at a posi-tion angle of 115 degrees east of north. The total elapsedtime for the NGC 891 observations was 3.2 hours. Fourdither positions with telescope tracking problems duringflight 450, which did not successfully run through thedata analysis pipeline, were discarded. Otherwise, ob-serving conditions were nominal. Data Reduction
All HAWC+ imaging and polarimetry were reducedwith HAWC+ data reduction pipeline 1.3.0beta3 (April2018). Following standard pipeline practice, we sub-tracted an instrumental polarization { q i , u i } , calibratedwith separate ‘skydip’ observations, having a medianvalue of (cid:112) q i + u i of 2.0% over the detector array. The fi-nal uncertainties were increased uniformly by ∼ − χ consistency check described by Santoset al. (2019). We applied map-based deglitching as de-scribed by Chuss et al. (2019). Due to smoothing with akernel approximately half the linear size of the beam, theangular resolution in the maps (based on Gaussian fits)is 14 (cid:48)(cid:48) FWHM at 154 µ m. Since both galaxies are wellout of the Galactic plane, reference beam contaminationis minimized.The flux densities in the maps were calibrated using ob-servations of Solar System objects, also in NMC mode.Due to the lack of a reliable, calibrated SOFIA facil-ity water vapor monitor at the time of the observations, the version 1.3.0 pipeline uses an estimate of far-IR at-mospheric absorption that is dependent on observatoryaltitude and telescope elevation, but is constant in time.For all observations, we used the default pipeline fluxcalibration factor, for which we estimate 20% absoluteuncertainty. For each galaxy, the maps from the twoflight series, analyzed separately, show flux calibrationconsistency to within 5% . For M51, we adjusted thecoordinates of the Feb. 2019 map (with a simple trans-lation in both axes) prior to coaddition with the Nov.2017 map. The relative alignment of the per-flight-seriesmaps for NGC 891 was within a fraction of a beam with-out adjustment.Alignment of the coordinate system for M51 suppliedby the pipeline was checked against VLA 3.6cm, 6.2cm,and 20.5cm (Fletcher et al. 2011), Spitzer 8 µ m(Smithet al. 2007), and Herschel 160 µ m maps (Pilbratt etal. 2010). We did this by matching 6 small, high sur-face brightness regions between our 154 µ m map andthe maps at the other wavelengths. We found that theHAWC+ map was consistently 4 ± (cid:48)(cid:48) south relative tothe comparison maps. For this reason, we have addedan offset of 4 (cid:48)(cid:48) N to our maps of M51. Since we are notmaking any comparisons of NGC 891 with high resolu-tion maps at other wavelengths, we made no adjustmentto the coordinate system for that galaxy.
Polarimetry Analysis
For both galaxies we computed the net polarizationin different synthetic aperture sizes, depending on thesignal-to-noise (S/N) in the data. The pixel size is 3 . (cid:48)(cid:48) ,or ∼ . (cid:48)(cid:48) ).We determined the effect of the Gaussian kernel on thecomputed errors by applying it to maps with randomnoise. As a result of this exercise, we increased the com-puted error by factors of 1.69 for the 2 × × × (cid:48)(cid:48) FHWM truncated at an 8 (cid:48)(cid:48) diameter and one having 7 . (cid:48)(cid:48) FHWM with truncation ata 15 . (cid:48)(cid:48) diameter. Jones et al.For this reason we have made extra cuts in Stokes I(total intensity) at a S/N of 50:1 for M51 and 30:1 forNGC 891, and increased the error for the largest syn-thetic aperture of 8 × intensities , and small spurious values will ad-versely influence the net polarization derived for regionsof low intensity, but not high intensity. For example, ata contour level of 100 MJy sr − between the arms, a 1MJy sr − value for Q that is due to a glitch, a bad pixel,or residual flux from image subtraction will produce a1% polarization that is not real. In the arm where theintensity is ∼
800 MJy sr − , this would contribute nomore than 0.12%. The final computed polarization wasthen corrected for polarization bias (Wardle & Kronberg1974; Sparks & Axon 1999) and cuts were made at afractional polarization for a final S/N of ≥ err map at σ > .
003 Jy/pixel.This removed the outer regions of the images where therewas incomplete overlap in the dithered images. This finalcut made little difference in the M51 polarimetry resultswhere less than 10% of the image was removed. But,for NGC 891 about 20% of the image was removed andthe northern and southern extremes of the disk in NGC891 were excluded. Note that the edge-on disk in NGC891 is at least 10 (cid:48) long, and our HAWC+ image spansonly about 5 (cid:48) along the disk, centered on the nucleus.In an upcoming paper we will be working with existingand new HAWC+ data on M51 and will create smoothedimages starting with the raw data. M51
Introduction
M51 is not only a face-on spiral galaxy but also a two-arm, grand design spiral (e.g. Rand et al. 1992), at adistance of 8.5 Mpc (McQuinn et al. 2016). It is clearlyinteracting with M51b and tails and bridges in the outerregions of the two galaxies are shared, while in the innerregions of M51 the spiral structure appears to be unaf-fected by the companion. Our observations did not reachfar enough from the center of the galaxy to include M51b.Because of its low inclination, M51 shows well definedspiral arms and well separated arm and inter-arm re-gions. This makes M51 an excellent laboratory to studyhow the magnetic field geometry changes from arm tointer-arm regions due to the effect of spiral density wavesand turbulence. Star formation in M51 is located mostlyin the spiral arms and in the central region, but somegas and star formation are also detected in the inter-armregions (e.g., Koda et al. 2009). Molecular gas is stronglycorrelated with the optical and infrared spiral arms andshows evidence for spurs in the gas distribution (Schin-nerer et al. 2017). The magnetic field geometry M51 wasstudied at radio wavelengths by Fletcher et al. (2011),who find that the overall geometry revealed in the polar-ization vectors follows the spiral pattern, but there is de-polarization in their larger 15 (cid:48)(cid:48)
Fig. 1.—
Fractional polarization vector map of M51 at a wave-length of 154 µ m, with the vectors rotated 90 ◦ to represent theinferred magnetic field direction. Data points using a square6 . (cid:48)(cid:48) × . (cid:48)(cid:48) ‘half’ beam are plotted in black. Data points usinga 13 . (cid:48)(cid:48) × . (cid:48)(cid:48) ‘full’ beam are plotted in orange, and red vectorsare computed using a 27 . (cid:48)(cid:48) × . (cid:48)(cid:48) square beam. The red disk inthe lower left corner indicates the FWHM footprint of the HAWC+beam on the sky at 154 µ m. Colors in the underlying image definethe 154 µ m continuum intensity. Vectors with S/N ≥ affected by sub-beam scale anisotropies in the field ge-ometry. Our HAWC+ observations allow us to studythe magnetic field geometry as measured by dust emis-sion instead of cosmic ray electrons, and thereby samplethe line of sight differently, and also probe denser com-ponents of the ISM than is possible at optical and NIRwavelengths. Magnetic Field Geometry
The polarization vector map of M51 is shown in Figure1, where the polarization vectors have been rotated 90 ◦ to show the inferred magnetic field geometry. Fractionalpolarization values range from a high of 9% to a low of0.6%, about 3 σ above our estimated limiting fractionalpolarization of 0.2% (Jones et al. 2019). Clearly evidentin Figure 1 is a strong correlation between the positionangles of the FIR polarimetry and the underlying spiralarm pattern seen in the color map. This can be bettervisualized in Figure 2, where all the polarization vectorlengths have been set to unity, and only the positionangle (PA) is quantified.In spiral galaxies, the spiral pattern is often fitted witha logarithmic spiral (e.g. Seigar & James 1998; Davis etal. 2012; ? ) Shetty et al. (2007) found a pitch angle of21.1 ◦ for the bright CO emission in the spiral arms. Huet al. (2013) suggested 17.1 ◦ and 17.5 ◦ for each of thetwo arms using SDSS images, and Puerari et al. (2014)determined the pitch angle of 19 ◦ for the arms from 8 µ mimages. Also, several investigators find that the pitch an-gles are variable depending on the location (e.g., Howard51, NGC891 7 Fig. 2.—
Same as Figure 1, except all of the polarization vectorshave been set to the same length and color to better illustrate theirposition angles.
Fig. 3.—
Geometry used to de-project the polarization vec-tors so that their individual pitch angles can be calculated. Theinclination with respect to the plane of the sky is 20 ◦ and the ma-jor axis (labeled Y) of the ellipse (a circle in projection) is 170 ◦ east of north. We are assuming the magnetic field vectors in thedisk of M51 have no vertical component when computing the de-projection. The polarization vector is shown relative to a circle (inprojection), which has a pitch angle of zero. & Byrd 1990; Patrikeev et al. 2006; Puerari et al. 2014).M51 is not perfectly face-on, but rather is tilted to theline of sight. Shetty et al. (2007) used the values for theinclination of 20 ◦ and a position angle for the major axisof 170 ◦ from Tully (1974) in their analysis of the spiralarms seen in CO emission. This geometry is illustratedin Figure 3. Using these same parameters and assumingthe intrinsic magnetic field vector has no component per-pendicular to the disk, we can de-project our vectors andcompute their individual pitch angles using the geometryfrom Figure 3 (see Lopez-Rodriguez et al. 2019). Hav-ing de-projected our vectors, we can compare the pitchangles of our vectors with the pitch angle(s) of a modelspiral where we compute ∆ θ = PA FIR − PA spiral wherePA indicates pitch angle for the (de-projected) FIR po-larimetry vectors and the model spiral respectively.First, we assume a single pitch angle of 21.1 ◦ from the Fig. 4.—
Histogram distribution of ∆ θ between the pitch angleof our polarization vectors and a single pitch angle for the spiralarms of 21 . ◦ (Model 1). Radial distance is the fraction of thetotal number of measurements. The area in grey shows the actualdata and the solid lines show a simulation (see text) under theassumption that the pitch angles are intrinsically the same, andonly errors in the data contribute to the dispersion. CO observations for the model spiral arms, and compute∆ θ . We will call this Model 1. A normalized histogramof ∆ θ is shown in Figure 4. We simulated the expecteddistribution in ∆ θ under the assumption that the vec-tors and the spiral arm pitch angle were the same, andonly errors in the FIR polarization data were responsiblefor the dispersion in the angle difference. We generatedsimulated data assuming the errors in polarization posi-tion angle are Gaussian distributed for each vector andran a Monte Carlo routine that generated simulated dis-tributions, repeating 1000 times. Since the simulateddata are assumed to follow the arm exactly, the peakof the distribution function is set at ∆ θ = 0. When theobservational data and simulation are compared, the dis-tribution of observed ∆ θ is broader than the simulatedone with a standard deviation of σ = 23 ◦ compared to σ = 9 ◦ for the simulation. The observational data showsgreater departure from a single pitch angle than can beaccounted for by errors in the FIR polarimetry vectorposition angles alone.Next we modeled the spiral features with two pitchangles, with a change in pitch angle chosen to fit theFIR intensity data by eye. We will call this Model 2.The resulting model spiral arms are shown in Figure 5where the inner spiral arms at a radial distance of 137 (cid:48)(cid:48) from the center retain the 21.1 ◦ pitch angle based on theCO observations for part of the arms, and then a muchtighter pitch angle of 3.9 ◦ is used for the outer arms.Following the same procedure as before, we computedthe angle difference between the pitch angles of the po-larization vectors and the spiral arms and ran a simula-tion of these differences, assuming they are intrinsicallythe same, and only observational errors are responsiblefor the dispersion in the differences. For this two pitchangle case, the results are plotted in Figure 6. Evenwith the two pitch angle model, the dispersion in ∆ θ ismuch greater than can be accounted for by the observa-tional errors with nearly identical standard deviations toModel 1. To explore the spiral pattern in our polarimetryvectors in more detail, we separated the magnetic fieldvectors into arm, inter-arm, and center regions. Theseregions are classified according to the mask given in Fig-ure 1 of Pineda et al. (2018), where the center region isroughly the inner 3 kpc (in diameter). Note that we areinterpolating both models into the inter-arm region (seethe blue line in Figure 5). The distribution of ∆ θ for Jones et al. Fig. 5.—
Model 2 geometry using two spiral arm pitch angles(shown in grey) that we used to compute the distribution of ∆ θ for this case. The inner part has the pitch angle of 21 . ◦ , and theouter part a pitch angle of 3.9 ◦ . The green dashed and dottedlines are the inner resonance and the co-rotation radii respectively,described in Tully (1974). The angle φ is used to define a measureof distance along a spiral ‘feature’. That is, we assume the basictwo pitch angle model (shown in grey) extends between the arms(shown in blue). Fig. 6.—
Distribution of ∆ θ as in Figure 4, but using Model 2,which has two pitch angles. Grey and black represent the simu-lation and observations respectively. In the right hand figure, theobservation are subdivided into arm, inter-arm, and central regions(see text), which are indicated by blue, orange, and red color, re-spectively. The locations of the different regions are defined inPineda et al. (2018). Although very similar in appearance, the leftpanel is not identical to Figure 4 these separate regions is shown in the right hand panelof Figure 6. The vectors in the center group have a dis-tinct positive mean offset of 17 . ◦ , which means a moreopen spiral pattern compared to the model pitch angle.The inter-arm and arm groups have no clear offset fromzero, but the dispersion is still much larger than can beexplained by measurement errors alone.In Figure 5 we define φ , a measure of the angular dis-tance along a spiral feature, increasing from zero clock-wise around the galaxy (along the spiral features). Wedefine a spiral feature for each point in the map (seeFigure 5), and extrapolate back to the central region todetermine the angular distance φ . The pitch angle, av- Fig. 7.—
Pitch angle of the FIR vectors (top), the deviation ofthese pitch angles from the spiral arms (middle), and the fractionalpolarization (bottom) depending on φ , an angular distance alongthe arm defined in 5, assuming Model 2 with the two pitch anglesfor the spiral arms. Vertical bars represent the standard deviationof the data within each bin, not an error in measurement. Red,blue, and orange represent the center, arm, and inter-arm group,respectively. eraged over intervals of φ = 40 ◦ , as a function of angulardistance along a spiral model line, is illustrated in Figure7. The top panel is the pitch angle of the FIR polariza-tion vectors. The middle panel plots ∆ θ , the differencebetween Model 2 and observed pitch angles. The lowerpanel shows the trend in fractional polarization with φ .We find no statistically significant difference in the trendsof fractional polarization with φ when comparing the armand interarm regions. The dispersion for ∆ θ in the inter-arm region is large, and departs from the trend seen inthe arm in the last data bin.Overall our FIR vectors follow the spiral arms in M51,but with fluctuations about the spiral arm direction thatare greater than can be explained by measurement er-rors alone. Stephens et al. (2011) found no correlationbetween the magnetic field geometry in dense molecularclouds in the Milky Way and Galactic coordinates, andthis may add a random component to the net positionangles we are measuring in our large 560 pc beam. How-ever, the relative contributions of emission from dense( n H >
100 cm − ) and more diffuse regions in M51 toour 154 µ m flux has not been modeled. The FIR vectorsin the central region indicate a more open spiral patternthan seen in the molecular gas (Shetty et al. 2007), op-posite to what one would expect if the magnetic fieldswere wound up with rotation. Although our data in theinter-arm region are relatively sparse, the fractional po-larization is statistically similar to the that in the arms,which are delineated by a higher FIR surface brightness.Houde et al. (2013) used the position angle structurefunction (Kobulnicky et al. 1994; Hildebrand et al. 2009;Houde et al. 2016) to characterize the magnetic tur-bulence in M51 using the radio polarization data from51, NGC891 9Fletcher et al. (2011). See section 3.4 for a comparisonwith the radio data. Analyzing the galaxy as a wholeand using a 2D Gaussian characterization of the randomcomponent to the magnetic field, they found the turbu-lent correlation scale length parallel to the mean fieldwas 98 ± ± r / B o = 1 . ± .
04, and this ratio is con-sistent with other work (e.g., Jones et al. 1992; Miville-Deschˆenes et al. 2008). Assuming the spiral pattern rep-resents the geometry of the ordered component, the ad-dition of a random component may explain our broaddistribution of position angles with respect to the spi-ral structure. Broadening of the distribution of ∆ θ by arandom component depends on the number of turbulentsegments in our beam. If we use the 100 pc turbulent cor-relation scale determined by Houde et al. (2013), thereare >
25 segments in our beam, which will largely ’aver-age out’ relative to the ordered component (see Figure 8in Jones et al. (1992)). A simple broadening of the dis-tribution due to this spatially small random componentwould not produce the number of position angles differ-ing by 60 − ◦ from the spiral pattern seen in Figure 6.However, all of the vectors that depart by more than 60 ◦ are in the inter-arm region and have S/N only between2.5:1 and 3:1. The distribution of ∆ θ for the arm region(only) is much more similar to the simulation, with amean value of only 5 ◦ . The dispersion, however, is stilla factor of 2 greater. Given the uncertainty in the con-tribution of a random component to the magnetic field,the FIR vectors in the arms (blue colored bars in Figure6) could be consistent with the spiral pattern we definedin Figure 5, but without a better determination of theturbulent component, we can not make a better deter-mination. Even with these uncertainties, there remainsa clear shift in the mean pitch angle for the center regionto a more open (greater pitch angle) pattern than seenin the CO and star formation tracers. More sensitiveobservations, in particular for the inter-arm region, willbe necessary to better define the correlation between theFIR vectors and the spiral pattern.Using broadband 20 cm observations with the VLA,Mao et al. (2015) studied the rotation measures in M51 indetail. They find that at 20 cm most of the observationsare consistent with an external uniform screen (halo) infront of the synchrotron emitting disk. The disk itselfproduces synchrotron emission that is partially depolar-ized on scales smaller than 560 pc (which is our beamsize), with most of the polarized flux originating in thetop layer of the disk, then passing through the halo. Thescale length for the rotation measure structure functionin the halo is 1 kpc, which is consistent with blowoutsand superbubbles from activity in the disk. Our FIR ob-servations are tied to the warm dust in the disk and are Fig. 8.—
The debiased polarized intensity plotted against theintensity at our wavelength of 154 µ m and derived hydrogen col-umn depth (see text). The vector data shown in Figure 1 wereused. The grey solid line is a linear fit to the data with a slopeof log I p154 µ m = 0 .
43 log I µ m ( α = − .
57) calculated by anorthogonal distance regression (ODR) weighted by the squares oferrors using scipy.odr module. Each dashed line of different colorrepresents the 2 . σ observation limit estimated from the errors inQ and U in each bin size. The grey dash-dotted line in the up-per left corner shows the maximum value of I p corresponding to amaximum fractional polarization of 9% (see text), and has a slopeof +1.0 ( α = 0). The horizontal dotted line corresponds to an em-pirical upper boundary seen in the data at I p = 25 MJy sr − andcorresponds to α = −
1. Finally, the line in the lower right handcorner shows the estimated ± .
2% limit in fractional polarizationprecision we can achieve with HAWC+ polarimetry (Jones et al.2019) in an ideal data set. largely insensitive to the magnetic field geometry in thehalo, but should be sensitive to the formation of super-bubbles which have their origin in the disk. We will beexploring the position angle pattern in more detail in alater paper.
Polarization – Intensity relation
In our previous FIR polarimetry of galaxies (Jones etal. 2019; Lopez-Rodriguez et al. 2019) we found that thefractional polarization declines with intensity and col-umn depth, and can often be characterized by a powerlaw dependency p ∝ I α . This trend is also common inthe Milky Way (e.g., Planck Collaboration et al. 2015),in particular in molecular clouds, and is commonly plot-ted as log(p) vs. log(I) (e.g., Fissel et al. 2016; Jones etal. 2015a; Galametz et al. 2018; Chuss et al. 2019). Inour previous papers we have used fractional polarizationp, but because of selection effects due to intensity cuts,the minimum measurable fractional polarization and aphysical maximum in the fractional polarization are dif-ficult to discern in that type of a plot. Instead, here weadopt plotting the polarized intensity I p as a function ofintensity or column depth. For comparison, a slope of α = − . . p ) vs. log(I). This caneasily be seen through the relation I p = pI.For M51, this comparison is shown in Figure 8. Thecolumn density was computed assuming a constant tem-perature for the dust, and is therefore a simple multi-plicative factor of the intensity. We used an emissivitymodified blackbody function assuming a temperature of25K (Benford & Staguhn 2008). The dispersion in de-0 Jones et al.rived temperature found using Herschel data was only ± . (cid:15) , which is proportional to ν β using a dust emis-sivity index, β , of 1.5 from Boselli et al. (2012). Wemade use of the relation of the hydrogen column den-sity, N(H + H ) = (cid:15)/ ( k µ m H ), with the dust mass ab-sorption coefficient, k , of 0 . g − at 250 µ m (Hilde-brand 1983), and the mean molecular weight per hydro-gen atom, µ of 2.8 (Sadavoy et al. 2013). The maximumexpected fractional polarization of 9% at ∼ µ m istaken from Hildebrand et al. (1995) and is within therange of dust models computed by Guillet et al. (2018)that were based on Planck observations. This upper limitnicely delineates the boundary seen in the maximum I p measured at low column depths in M51.Note that the lowest polarized intensities are associ-ated with the larger 27 . (cid:48)(cid:48) × . (cid:48)(cid:48) aperture (labeled two-beam), and averaging over this aperture could artificiallyreduce the computed polarization if there is significantvariation in position angle of the ordered component (notthe random component) to the field within the aperture.However, even a 45 ◦ variation in position angle for theordered component across the aperture would only re-duce the net polarization by 1 / √
2, yet the mean for thetwo-beam I p is at least a factor of 3 lower than for thehalf-beam data. Also, the large aperture results are con-centrated well away from the nucleus where the spatialvariation in position angle is less. The primary cause ofthe vertical separation between the different beam sizesin Figure 8 is S/N, rather than beam averaging. A simplelinear fit (in log space) to all of the data in Figure 8 has aslope less than +0 .
5. This translates to a slope more neg-ative than α = − . ) ∼ . × cm − . Theslope then changes and becomes flat (I p = constant),and I p = 25 MJy sr − at greater column depth. Thisflat slope corresponds to a slope of α = −
1, as discussedabove. For M51, the change in slope for the upper limit inpolarized intensity occurs at approximately 1/3 the valueof N(H + H ) ∼ cm − found by Planck for polariza-tion in the Milky Way (see Figure 19 in Planck Collabora-tion et al. (2015)). As mentioned above, a strong declinein fractional polarization with column density was alsofound for FIR polarimetry of M82, NGC 253 (Jones etal. 2019) and NGC 1068 (Lopez-Rodriguez et al. 2019).Note that NGC 1068 has a powerful AGN which couldcreate a more complex magnetic field, but most of theFIR polarimetry samples only the much larger, surround-ing disk. Lopez-Rodriguez et al. (2019) suggested threepossible explanations for the decline in fractional polar-ization with column depth, assuming the emission is op-tically thin. Polarization may be reduced if there aresegments along the line of sight where 1) the grains arenot aligned with the magnetic field, 2) the polarization is canceled because of crossed or other variations of themagnetic field on large scales, or 3) there are sectionsalong the line of sight that contain turbulence on muchsmaller scale lengths than in lower column density linesof sight, contributing total intensity, but little polarizedintensity. Lopez-Rodriguez et al. (2019) considered thecontribution of regions that are sufficiently dense thattheir higher extinction may prevent the radiation neces-sary for grain alignment from penetrating. These regionsmake a very small a contribution to the FIR flux in theHAWC+ beam, simply because they are small in angularsize and very cold. Although these dense cores probablyexperience a loss of grain alignment, they cannot haveany effect on our observations of external galaxies. Anadditional explanation is the loss of the larger alignedgrains due to Radiative Torque Disruption (Hoang 2019)in very strong radiation fields, although any connectionof this process with higher column depth is not clear.The magnetic field in the ISM is often modeled using acombination of ordered and turbulent components (e.g.,Planck Collaboration et al. 2016; Miville-Deschˆenes et al.2008; Jones et al. 1992). The trend of fractional polariza-tion with column depth (Hildebrand et al. 2009; Houdeet al. 2016; Jones et al. 2015a; Fissel et al. 2016; PlanckCollaboration et al. 2016, 2018; Jones 2015b) providesan indirect measurement of the effect of the turbulentcomponent. For maximally aligned dust grains along aline of sight with a constant magnetic field direction, thefractional polarization in emission will be constant withoptical depth τ in the optically thin regime. This casewould correspond to a line in Figure 8 with a slope of+1.0 ( α = 0). If there is a region along the line of sightwith some level of variations in the magnetic field geom-etry, this will result in a reduced fractional polarization.Using a simple toy model, Jones (1989) and Jones et al.(1992) showed that if the magnetic field direction variescompletely randomly along the line of sight with a singlescale length in optical depth τ (not physical length), thenp ∝ τ − . (or, I p ∝ τ +0 . ). (See Planck Collaboration etal. (2016, 2018) for a very similar model). In real sources,more negative slopes of α = -1/2 to -1 are found in manyinstances ranging from cold cloud cores to larger molec-ular cloud structures to whole galaxies (e.g., Galametzet al. 2018; Fissel et al. 2016; Chuss et al. 2019; Lopez-Rodriguez et al. 2019). In more recent work employingMHD simulations, King et al. (2018) and Seifried et al.(2019) find that the ordered and random components aremore complicated than modeled by Jones et al. (1992).While Jones et al. (2015a) argued that a slope of α = − (cid:28)
560 pc) than other lower den-sity lines of sight. In this scenario, there are segmentsalong the line of sight that add total intensity, but addcorrespondingly very little polarized intensity due to tur-bulence in the field on scales significantly smaller thanour beam (see Figure 2 in Jones et al. (1992)).The model in Jones et al. (1992) assumes that the opti-cal depth scale at which magnetic field is entangled is thesame through the entire volume. This may not always betrue. First of all, the injection scale of the turbulence de-pends on the source of turbulent motions. The motionsarising from large scale driving forces, whether from su-pernovae or magnetorotational instabilities, may have acharacteristic scale comparable with the scale height ofthe galactic disk. The local injection of turbulence aris-ing from local instabilities or localized energy injectionsources, whatever they are, can have significantly smallerscales. These significantly smaller scales form the ran-dom component that would decrease the fractional po-larization compared to the simple model.We also point out another important effect that affectsthe polarization. Even if the turbulence injection scalestays the same, the scale at which the magnetic field ex-periences significant changes in geometry may vary dueto variations in the turbulence injection velocity. To un-derstand this, one should recall the properties of MHDturbulence (e.g., Beresnyak & Lazarian 2019). If theinjection velocity V L is larger than the Alfven velocity V A , the turbulence is superAlfvenic. Magnetic forces atthe injection scales are too weak to affect the motion ofat large scales and at such scales the turbulence followsthe usual Kolmogorov isotropic cascade with hydrody-namic motions freely moving and bending magnetic fieldsaround. However at the scale l A = LM − A , where L isthe turbulence injection scale and M A = V L /V A , the tur-bulence transfers to the MHD regime with the magneticfield becoming dynamically important (Lazarian 2006).The scale l A is the scale of the entanglement of magneticfield. This scale determines the random walk effects onthe polarization in the Jones et al. (1992) model. Evi-dently, l A varies with the media magnetization and theinjection velocity. These parameters change through thegalaxy and this can affect the observed fractional polar-ization at high column depths. To explore the nature In the presence of turbulent dynamo one might expect that I A eventually reaches L . However, the non-linear turbulent dynamo israther inefficient (Xu & Lazarian 2016) and therefore the temporalvariations in the energy injection and in Alfven speed are expectedto induce significant variations of l A . Fig. 9.—
The ratio of the total intensity at 154 µ m to thatat 20.5 cm. Color represents the ratio on a logarithmic scale,log(I µ m / I . ). The black contours indicate 100, 200, 300,400, 500, 1000, and 1500 MJy sr − at 154 µ m and the red contours0.3, 0.6, 0.9, 1.2, 1.5, 3.0, and 4.5 MJy sr − at 20.5 cm. of the turbulent component further, we next compare theradio synchrotron polarimetry with our FIR polarimetry. Radio Comparison
The magnetic field geometry of M51 seen in syn-chrotron polarimetry has been also been extensivelystudied (Beck et al. 1987; Fletcher et al. 2011). We cancompare the FIR emission with the synchrotron radiationat 20.5 cm and 6.2 cm using the data from Fletcher etal. (2011), which we obtained from ATLAS OF GALAX-IES at Max Planck Institute for Radio Astronomy . Werotated the 6.2 cm radio vector position angles by 90 ◦ to obtain the inferred magnetic field direction and madeno correction for Faraday rotation (Fletcher et al. (2011)found no statistically significant difference in fractionalpolarization between 3.6 cm and 6.2 cm wavelengths).The beam sizes at 20.5 cm and 6.2 cm are 15 (cid:48)(cid:48) and 8 (cid:48)(cid:48) (Fletcher et al. 2011), while our beam size at 154 µ m is14 (cid:48)(cid:48) . First, in Figure 9, we compare the total intensityat 154 µ m and at 20.5 cm, which has a similar beam sizeto that at 154 µ m. We have convolved the 154 µ m beamto the slightly larger beam at 20.5 cm assuming a Gaus-sian form for the beam shape. To be conservative in ourcomparison, we use only regions where all the pixels inthe 154 µm image have I / I err >
5. In Figure 9 we showthe color coded intensity ratio on a logarithmic scale,log(I µ m / I . ) along with the intensity contours at154 µ m and 20.5 cm.Overall, the synchrotron emission and the FIR emis-sion closely follow the grand design spiral pattern seen atother wavelengths. The arms are brighter than the inter-arm region at both wavelengths. However, the 154 µ m Fig. 10.—
Fractional polarization vector maps of M51 at a wave-length of 154 µ m (white) and 6.2 cm (black). The colors show theintensity at 6.2 cm convolved to our beam at 154 µ m. The scalebar for fractional polarization refers to the 6.2 cm data only. Thelengths of vectors at 154 µ m are the same as those in Fig. 1. Thethin white line roughly outlines the observed region at 154 µ m. emission shows greater contrast between the arm andinter-arm regions compared to the 20.5 cm emission, inmany locations by up to a factor of 3 greater contrast.This contrast ratio is highest in the arm to the southeastof the center, and in the arms near (but not directly at)the center of the galaxy. Basu et al. (2012) comparedSpitzer 70 µ m with 20 and 90 cm radio fluxes for fourgalaxies and found a greater FIR/radio flux ratio in thearms compared to the inter-arm region using 90 cm radiofluxes, but not for 20 cm fluxes. Based on our 154 µ mfluxes and the 20.5 cm data of M51, the FIR and radiomeasurements are not sampling volumes along the lineof sight in the same way.To first order, the dependence of synchrotron emis-sion on cosmic ray electron density and magnetic fieldstrength is I syn ∝ n ce B (e.g., Jones et al. 1974), whereI syn is the synchrotron intensity and n ce is the cosmicray electron density. Crutcher (2012) finds that the lineof sight component (only) of the magnetic field strength(typically 2 − µ G) in the diffuse ISM of the MilkyWay shows no clear trend with hydrogen density up to n H ∼
300 cm − , a density typical for photo dissociationregions and the outer edges of molecular clouds (Hollen-bach & Tielens 1999). At even higher densities the fieldstrength increases with density as B ∝ n kH with the ex-ponent k between 2/3 and 1/2 (e.g. Tritsis et al. 2015;Jiang et al. 2020), but these regions occupy a small frac-tion of the total volume of the ISM (Hollenbach & Tielens1999). We interpret our results as due to the synchrotronemission in M51 arising mostly in the more diffuse ISM,with denser regions contributing a smaller fraction. As-suming equipartition between the cosmic ray energy den- Fig. 11.—
Plot of the 154 µ m position angle against the 6.2cm position angle. 180 ◦ has been added to some position angles toaccount for the ambiguity at 0 ◦ and 180 ◦ . The Pearson correlationcoefficient for each region is higher than 0.75 and the p-values aresmaller than 10 − . The ODR best fit line weighted by the squaresof errors to all the data has a slope of 0.85 ± .
12 at the 1 − σ confidence interval. The contours show the probability density of0.3, 0.6, and 0.9 estimated by Gaussian kernel density estimation(KDE) using scipy.stats.gaussian kde module. KDE is a wayto estimate the probability density function by putting a kernel oneach data point, and we used Scott’s Rule to determine the widthof a Gaussian kernel. Fig. 12.—
Plot of the polarized intensity at 154 µ m against thepolarized intensity at 6.2 cm. The colors of dots indicate the differ-ent regions of arm (blue), inter-arm (orange), and center (red). Thesymbols and contours are the same as in Figure 11. The Pearsoncorrelation coefficients and p-values for the arm, inter-arm, andcenter are [0.014, 0.94], [0.1, 0.66], and [0.11, 0.56] respectively,indicating no correlation.
51, NGC891 13
Fig. 13.—
Plot of the normalized fractional polarization at154 µ m against the normalized fractional polarization at 6.2 cm.The normalization factor was 9% at 154 µ m and 70% at 6.2 cm(see text). The symbols and contours are the same as in Figure11. The Pearson correlation coefficients and p-values for the arm,inter-arm, and center are [0.38, 0.02], [-0.06, 0.82], and [0.68, 10 − ]respectively. The correlation coefficient for the entire data set is0.61 with a p value of 10 − . The slope of the best fit line to all thedata is 0 . ± . sity and the magnetic field energy density, Fletcher et al.(2011) find a moderately uniform magnetic field strengthof 20 − µ G in the arm and 15 − µ G in the inter-armregions of M51, suggesting the synchrotron emission ismore dependent on n ce than magnetic field strength inthose regions. In the denser star forming regions locatedin the spiral arms, the ratio of FIR to radio intensitymust be dominated by emission from warm dust in avolume that does not contribute as much proportionallyto the total synchrotron emission as it does to the FIRemission. Note that the very center of M51 has a syn-chrotron emission peak (Querejeta et al. 2016) due to aSeyfert 2 nucleus (Ho et al. 1997) emitting a relativelylow luminosity of L bol ∼ erg s − (Woo & Urry 2002),but the FIR emission peaks outside this region in the in-ner spiral arms (see Figure 5), and the AGN contributesvery little to the FIR flux.For comparison of the radio and FIR polarization, weused the observations at 6.2 cm instead of 20.5 cm be-cause depolarization in the beam by differential Faradayrotation is less (Fletcher et al. 2011). We first convolvedthe 6.2 cm I, Q and U maps to a 14 (cid:48)(cid:48) beam. We usedthe rms fluctuations in the convolved Q and U maps welloff the galaxy to estimate the error in Q and U. Assum-ing these errors, the fractional polarization could then becomputed and debiased in the same manner as our FIRpolarimetry (p debiased / p err > h m s +47 ◦ (cid:48) (cid:48)(cid:48) the 6.2 cm vectors angle away from the arm alongthe bridge of emission connecting to M51b, but the FIRvectors continue to follow the spiral pattern.The polarization position angles are compared quan-titatively in Figure 11, and show a strong overall corre-lation between the radio and FIR polarization vectors.Even though the emission mechanisms are completelydifferent, and the ISM in the respective beams is be-ing sampled differently, we find that the inferred mag-netic field geometry is essentially the same in a globalsense. In other words, the FIR polarization position an-gle weighted by dust emission (at varying temperatures)integrated along and across the line of sight is very simi-lar to the synchrotron position angle weighted by cosmicray density and field strength (squared), integrated alongthe same paths in most locations.Our goal in this section is to investigate whether thesynchrotron observations can shed light on the underly-ing cause of the strong decline in fractional polarizationwith intensity found at FIR wavelengths. For example,consider the hypothesis that there are segments acrossthe beam and along a line of sight associated with densegas and dust that have field geometries highly disorderedin our beam relative to the larger scale field, adding sig-nificant FIR total intensity but very little polarized in-tensity. In lower column depth lines of sight, these seg-ments (perhaps giant molecular clouds) may be absentor relatively rare, making proportionally less of a con-tribution to the total FIR intensity, and have less effecton the fractional polarization. Since the synchrotron po-larimetry is sampling the same line of sight differently,these segments may contribute differently to the polar-ized synchrotron emission.We compare the polarized intensity between the FIRand the radio in Figure 12 and the fractional polariza-tion in Figure 13. Although this may seem redundant,there are important differences between the polarized in-tensity and the fractional polarization. In the diffuseISM there is no clear dependence of dust grain align-ment on magnetic field strength (Planck Collaborationet al. 2015; Jones 1989, 2015b). Thus, in the FIR neitherpolarized intensity nor fractional polarization are depen-dent on magnetic field strength, but they are stronglydependent on the magnetic field geometry (Planck Col-laboration et al. 2018, 2016; Jones et al. 1992). For syn-chrotron emission, the polarized intensity is dependenton magnetic field strength and the magnetic field geom-etry, but the fractional polarization is dependent only onthe field geometry, as is the case in the FIR. Thus, weshould expect no correlation between polarized intensityat the two wavelengths, but there should be a correlationbetween their fractional polarization if they are indeedsampling the same net magnetic field geometry.In Figure 12, there is no correlation seen between thepolarized intensity at FIR and 6.2 cm wavelengths for thehigher surface brightness central region (red contours),the arm region (blue contours), or the inter-arm region(orange contours). For fractional polarization (Figure13), we have normalized both the FIR and 6.2 cm polar-ization with respect to their maximum expected values.We used p max = 70% at 6.2 cm based on computationalresults in Jones & Odell (1977). There is a modest cor-4 Jones et al.relation for the entire data set, with the greatest cor-relation in the center region. Note again that the cen-tral region has very weak fractional polarization at bothwavelengths.For the arms (see Figure 7), we do not see a significantdifference in fractional polarization for our FIR observa-tions when compared to the inter-arm region. At radiowavelengths, Fletcher et al. (2011) found that the inter-arm region has a greater fractional polarization than thearms (see their Table 2), which they attribute to a moreordered field in the inter-arm region. This difference be-tween FIR and radio observations suggests variations inthe magnetic field geometry are similar between the armand inter-arm regions as sampled by FIR polarimetry,but that the greater column depth in the arms may havecaused enough Faraday depolarization across the beamto further reduce the fractional polarization at 6.2 cm.Finally, the high surface brightness central region showsvery weak fractional polarization at both wavelengths.Here the radio and FIR beams must sample a more com-plex magnetic field geometry with highly turbulent seg-ments across the beam and along individual lines of sightwithin the beam. This more complex magnetic field ge-ometry reduces the net fractional polarization at bothFIR and radio wavelengths with, perhaps, added Fara-day depolarization in the beam at 6.2 cm. Polarizedemission in this region is sampled differently at the twowavelength regimes, hence producing uncorrelated po-larized intensities. Yet the net position angles stronglyagree, the fractional polarizations are moderately corre-lated, and both techniques yield the same net magneticfield geometry in the beam. We will explore this inter-pretation more carefully in a later paper. NGC 891
Introduction
At a distance of 8.4 Mpc (Tonry et al. 2001), NGC 891presents an interesting case for an edge-on galaxy thatis a late type spiral with similar mass and size comparedto the Milky Way (Karachentsev et al. 2004). Like theMilky Way, NIR polarimetry of NGC 891 reveals a gen-eral pattern of a magnetic field lying mostly in the plane(Jones 1997; Montgomery & Clemens 2014). Radio syn-chrotron observations are also consistent with this gen-eral field geometry, but extend well out of the disk intothe halo (Krause 2009; Sukumar & Allen 1991). Accord-ing to models by Wood & Jones (1997), highly polarizedscattered light may be a contaminant affecting the opti-cal and NIR polarization in edge-on systems producingpolarization null points at locations along the disk, wellaway from the nucleus. Montgomery & Clemens (2014)do not find evidence for the predicted null points alongthe disk, but do find null points at other locations thatthey associate with an embedded spiral arm along theline of sight. Optical polarimetry (Scarrott & Draper1996) revealed (unexpected) polarization mostly verti-cal to the plane, with only a few locations in the NEshowing polarization parallel to the disk. The opticalpolarimetry was attributed to vertical magnetic fields,but Montgomery & Clemens (2014) argued that the op-tical polarimetry was contaminated by scattered light.Scattering in the halo of light from stars in the disk andthe bulge, as modeled by Wood & Jones (1997) and Seon (2018), may be a more likely explanation for the opticalpolarization. Note that the NIR and FIR polarimetrypenetrate much deeper into the disk than is possible atoptical wavelengths.
The Planar Field Geometry
Our 154 µ m polarimetry of NGC 891 is shown in Fig-ure 14 where the colors and symbols are the same asdescribed for M51. To show the magnetic field geom-etry more clearly, we set the fractional polarization toa constant value in Figure 15. Along the center of theedge-on disk, the vectors align very close to the plane ofthe disk everywhere except in the extreme NE. There,a few vectors are perpendicular to the disk, suggestinga vertical magnetic field, which will be discussed below.Clearly evident in both the NIR polarimetry (Jones 1997;Montgomery & Clemens 2014) and the radio synchrotronpolarimetry (Krause 2009; Sukumar & Allen 1991) is an ∼ ◦ tilt for many of the polarization vectors relativeto the galactic plane to the NE of the nucleus. Figure8 in Montgomery & Clemens (2014) best illustrates thisoffset, and it is not seen in the FIR vectors.The distribution of ∆ θ between the position angle ofour rotated polarization vectors and the major axis isshown in Figure 16. We used 21 ◦ as the position anglefor the major axis of the galaxy (Sofue et al. 1987). Inan identical manner to M51, we simulated the expecteddistribution under the assumption that the polarizationvectors intrinsically follow the major-axis of the galaxyand only observation error causes any deviation. In Fig-ure 16 the grey solid line shows the distribution for allthe data whereas the solid, light grey bars show the dis-tribution only for regions with intensity higher than 1500MJy sr − , which isolates the bright dust lane (see Fig-ure 14). When constrained to the bright dust lane, thesimulated distribution and the observed distribution arevery similar, with a formal p-value for this comparison is0.97.Although more penetrating than optical polarimetry,NIR polarimetry at 1 . µ m still experiences significantinterstellar extinction in dusty, edge-on systems (e.g.,Clemens et al. 2012; Jones 1989). In a beam contain-ing numerous individual stars mixed in with dust, theNIR fractional polarization in extinction will saturateat A V ∼
13, or A H ∼ .
5, (Fig. 4, Jones 1997). At154 µ m, the disk is essentially optically thin ( τ ∼ .
05 forA V = 100, Jones et al. (2015a)), thus the FIR polarime-try penetrates through the entire edge-on disk. One in-terpretation of our FIR polarimetry is that the NIR issampling the magnetic field geometry on the near sideof the disk, where the net field geometry shows a tilt inmany locations, perhaps due to a warp in the disk (Oost-erloo et al. 2007). The FIR polarimetry is sampling themagnetic field geometry much deeper into the disk, wherethe net field geometry is very close to the plane. Theradio synchrotron polarimetry at 3.6 cm from Krause(2009) used a much larger beam of 84 (cid:48)(cid:48) , and could beinfluenced by strong Faraday depolarization in the smallportion of their beam that contains the disk, which hasa much greater column depth than is the case for theface-on M51. Their net position angles may be sensitiveonly to the field geometry in the rest of the beam, alsopossibly influenced by the warp. Whatever the explana-tion, the FIR polarimetry along the disk within 2 (cid:48) of the51, NGC891 15nucleus clearly indicates that the magnetic field directiondeep inside NGC 891 lies very close to the galactic plane.There are two regions of enhanced intensity in the diskabout 1 (cid:48) on either side of the nucleus, designated by col-ored outlines in Figure 14. These locations also corre-spond to intensity enhancements seen in a radio map ofthe galaxy made by combining LOFAR and VLA ob-servations (Mulcahy et al. 2018), and in PACS 70 µ mobservations as well (Bocchio et al. 2016). Those stud-ies attribute such enhancements to the presence of spiralarms and the enhanced star formation associated withthem, but do not present a model of the emission fromthe disk. These features are 3 − along (parallelto) the line of sight, which results in much lower polariza-tion (e.g., Jones & Whittet 2015). This could be the ex-planation for the very low polarization in our two brightspots, and could also explain the origin of the enhance-ment in intensity, since a line of sight down a spiral armwill pass through more star forming regions. However,the regions of low polarization seen at NIR wavelengthsand FIR wavelengths are not coincident, rather the NIRnull points are located further out from the center ofthe galaxy. Given the greater penetrating power of FIRobservations, it is possible we are viewing more deeplyembedded spiral features than is accessible by NIR po-larimetry, which is more sensitive to the front side of thedisk. Vertical Fields
Dust in emission is detected above and below the diskof NGC 891. At FIR wavelengths, Bocchio et al. (2016)find a thick disk component to the dust emission witha scale height of ∼ . (cid:48)(cid:48) ). At NIR wavelengths,Aoki et al. (1991) measure a scale height of 350pc (8 . (cid:48)(cid:48) )for the stellar component, significantly smaller than thedust scale height. There are a handful of vectors in Fig-ure 14 that lie off the bright disk in the halo of NGC891. Five of these vectors are consistent with a verticalmagnetic field geometry, in strong contrast to the disk.At optical wavelengths, Howk & Savage (1997) imagedvertical fingers of dust that stretch up to 1.5 kpc off theplane, also suggestive of a vertical field extending intothe halo. Optical polarimetry of the NE portion of thedisk (Scarrott & Draper 1996) has a few vectors parallelto the plane, but the majority are perpendicular to theplane. Although the optical polarimetry was interpretedas evidence for vertical magnetic fields by Scarrott &Draper (1996), the NIR polarimetry from Montgomery &Clemens (2014) and modeling by Wood & Jones (1997)and Seon (2018) indicate that scattering of light orig- inating from the central region can be a major effect.Without significant dust to shine through (causing inter-stellar extinction), it is difficult to produce measurableinterstellar polarization in extinction (Jones & Whittet2015).The optical polarization vectors in Scarrott & Draper(1996) are typically 1–2 % in magnitude ∼ (cid:48)(cid:48) off theplane using a 12 (cid:48)(cid:48) beam. Based on our 154 µ m contours,this corresponds to about 400 MJy sr − , or A V ∼ . V (Serkowskiet al. 1975), but recent work shows this can be as highas p(%) = 5A V for low density lines of sight out of theGalactic Plane (Panopoulou et al. 2019). For an opti-mum geometry of a screen of dust with a uniform mag-netic field geometry entirely in front of the stars in thehalo, a maximum fractional polarization of ∼
2% wouldbe expected. For a mix of dust and stars along the lineof sight and turbulence in the magnetic field, the ex-pected fractional polarization would be even less. Al-though Howk & Savage (1997) estimated A V ∼ − (cid:48)(cid:48) wide,considerable unpolarized starlight emerging between thefilaments would be contributing as well. At optical wave-lengths it is not clear there is enough extraplanar dust toshine through to cause significant polarization in extinc-tion ∼ (cid:48)(cid:48) off the disk, but plenty of dust to scatter light(a mean τ sc ∼ . emission from warm dust, and generally the fractionalpolarization is observed to be highest at low FIR opticaldepths (Chuss et al. 2019; Planck Collaboration et al.2015; Fissel et al. 2016), but there must be enough warmdust in the beam to produce a measurable signal. Forour observations of NGC 891, a vertical scale height of1.5 kpc corresponds to 36 (cid:48)(cid:48) , or 2.7 beamwidths for our154 µ m observations. The surface brightness at this ver-tical distance for most of the disk is ∼
100 MJy sr − (A V ∼ . (cid:48)(cid:48) ) off the plane, the surface brightness rangesfrom 300 MJy sr − to 500 MJy sr − , a range in which5% polarization is easily detectable. Note, if NGC 891were face-on, this halo dust emission would contributevery little to the total flux in our beam compared to thedisk.We draw the tentative conclusion that the several154 µ m vectors in the halo that are perpendicular tothe disk are indicative of a vertical magnetic field ge-ometry in the halo of NGC 891. No evidence for ver-tical fields was found in radio observations by Krause(2009), but they had a very large 84 (cid:48)(cid:48) beam. Using a 20 (cid:48)(cid:48) beam, Sukumar & Allen (1991) find hints of a verticalfield on the eastern side of the southwest extension of thedisk, just east of the region outlined in green in Figure14, where we suggest we are looking down a spiral arm.Mora-Partiarroyo et al. (2019) made radio observationsof NGC 4631, an edge-on galaxy with an even more ex-tended halo than NGC 891, using a 7 (cid:48)(cid:48) beam. They find6 Jones et al. Fig. 14.—
Polarization vector map of NGC891 at a wavelengthof 154 µ m, in which the E vectors are rotated 90 ◦ to representthe inferred magnetic field direction. Data points using a square6 . (cid:48)(cid:48) × . (cid:48)(cid:48) ‘half’ beam are plotted in black. Data points using a13 . (cid:48)(cid:48) × . (cid:48)(cid:48) ‘full’ beam are plotted in orange, and red vectors arecomputed using a 27 . (cid:48)(cid:48) × . (cid:48)(cid:48) square beam. The red disk in thelower left corner indicates the FWHM footprint of the HAWC+beam on the sky at 154 µ m. Vectors with S/N ≥ µ m continuum intensity andgrey contours show 1000, 1500, 2000, 2500 MJy sr − . Two regionsdiscussed in the text are outlined by blue and green boxes. the magnetic field in the halo is characterized by strongvertical components. Examination of the Faraday depthpattern in the halo of NGC 4631 indicated large-scalefield reversals in part of the halo, suggesting giant mag-netic ropes, oriented perpendicular to the disk, but withalternating field directions. Our FIR polarimetry, whichis not affected by Faraday rotation, cannot distinguishfield reversals (since the grain alignment is the same),and would reveal only the coherent, vertical geometry,such as we see in our observations in the halo of NGC891. Brandenburg & Furuya (2020) present numerical re-sults of mean-field dynamo model calculations for NGC891 as a representative case for edge-on disk systems,but our observations do not have enough vectors for adetailed comparison. Polarization – Intensity Relation
Figure 17 plots the polarized intensity against the in-tensity and column depth for NGC 891. Other than usinga temperature of 24 K for the dust (Hughes et al. 2014),the procedure for calculating the column depth from thesurface brightness at 154 µ m is the same as for M51.NGC 891 shows a clear trend in I p vs. I, with a simi-lar slope to that found for M51, and shows evidence fora horizontal upper limit as well. However, unlike M51,the decrease in polarization in the bulge is not quite asstrong, and more of the very low fractional polarizationvalues are located in the disk away from the nucleus.Also unlike M51, the data at lower column depth in ei- Fig. 15.—
Same as Figure 14, except all the polarization vectorshave been set to the same length to better illustrate the positionangles.
Fig. 16.—
Distribution of ∆ θ between the position angle of ourpolarization vectors and the major-axis the galaxy. A positive valuemeans counter-clockwise rotation from the major-axis. The Greysolid line shows the distribution of all data and the grey shadedregion that of the data only in the region with intensity higherthan 1500 MJy sr − . The black solid line indicates a simulationmade under the assumption that the polarization vectors followthe major-axis of the galaxy and only errors in the data contributeto the dispersion. ther the disk or the halo generally lie well below the up-per limit of p = 9% in Figure 17, although this may bepartially due to smaller number of vectors compared toM51. Presumably, the more complex line-of-sight mag-netic field geometry through an edge-on galaxy reducesthe net polarization compared to the face-on geometryfor M51. Spiral structure seen edge-on can present arange of projected magnetic field directions along a lineof sight, crossing nearly perpendicular to some arms, butmore down along other arms in our beam.The two regions with low polarization delineated inFigure 14 by green and blue outlines are shown in Figure17 using the same colors. These are the two regions wespeculated were lines of sight down a spiral arm, reducingthe fractional polarization. There is only one detectionin these regions and all the rest of the data points are3 σ upper limits, indicating a low fractional polarizationcompared to the general trend. Until a model of the spi-51, NGC891 17 Fig. 17.—
Plot of the polarized intensity against the intensity at154 µ m. The vectors shown in Figure 14 were used. A grey solidline is a fit to the data, where log I p154 µ m = 0 .
42 log I µ m. Allother lines are the same as in Figure 8. The green and blue upperlimits and boxed blue points are described in Section 4.4 of thetext. ral structure in NGC 891 is developed, we can only iden-tify these two locations as potential indicators of spiralfeatures. CONCLUSIONS
In this work we report 154 µ m polarimetry of the face-on galaxy M51 and the edge-on galaxy NGC 891 usingHAWC+ on SOFIA with projected beam sizes of 560and 550 pc respectively. We have drawn the followingconclusions:1. For M51, the FIR polarization vectors (rotated 90 ◦ to infer the magnetic field direction) generally follow thespiral pattern seen in other tracers. The dispersion in po-sition angle with respect to the spiral features is greaterthan can be explained by observational errors alone. Forthe arm region, the position angles may be consistentwith the spiral pattern, but uncertainties in the contri-bution of a random component to the magnetic field pre-vents us from making a more definitive statement. Thecentral region, however, clearly shows a more open spiralpattern than seen in the CO and dust emission.2. Even though the FIR (warm dust) and 6.2 cm (syn-chrotron) emission mechanisms involve completely differ-ent physics and sample the line-of-sight differently, theirpolarization position angles are well correlated. The or-dered field in M51 must connect regions dominating thesynchrotron polarization and the FIR polarization in asimple way.3. Both the 6.2 cm synchrotron and FIR emissionshow very low fractional polarization in the high sur-face brightness central region in M51. There is a moder-ate correlation in fractional polarization between the twowavelengths, yet the polarized intensity shows no corre-lation anywhere in the galaxy. The low polarization islikely caused by an increase in the complexity of the mag-netic field and a greater contribution from more turbu-lent segments in the beam and down lines of sight withinthe beam. The lack of correlation between polarized in-tensity at both wavelengths indicates that the magneticfield strength, which influences the polarized intensity at6.2 cm, but not in the FIR, is not the cause of the low fractional polarization at FIR wavelengths. Lack of grainalignment can also be ruled out. We conclude that alongindividual lines of sight, different segments must be con-tributing to the total and polarized intensity in differentproportions at the two wavelengths.4. Within the arms themselves, we find a similar frac-tional polarization to the inter-arm region in dust emis-sion, unlike the synchrotron emission, which has a lowerfractional polarization in the arms relative to the inter-arm region. This suggests the turbulent component tothe magnetic field (as sampled by FIR emission) is similarto that in the inter-arm region, but that the synchrotronemission may be additionally influenced by some Faradaydepolarization in the arms.5. For NGC 891, the FIR vectors within the high sur-face brightness contours of the edge-on disk are tightlyconstrained to the plane of the disk. Dispersion in po-sition angle about the plane can be explained by errorsin the measurements alone. This result is in contrast toradio and NIR polarimetry which show a clear depar-ture from planar at many locations along the disk. Weare probably probing deeper into the disk of NGC 891than is possible with NIR and synchrotron polarimetry,revealing a very planar magnetic field geometry in theinterior of the galaxy.6. There are two locations along the disk of NGC 891that show very low polarization and may be locationswhere the line of sight is along a major spiral arm, re-sulting in lower fractional polarization. These two lo-cations line up with FIR intensity contours, but do notcorrespond to nulls in the NIR polarimetry, thought tobe due to the same cause. Likely, the NIR is sensitive tospiral features that are closer to the front side of the diskdue to extinction obscuring such features deeper into thedisk.7. There is tentative evidence for the presence of verti-cal fields in the FIR polarimetry of NGC 891 in the halothat is not present at NIR wavelengths and is only hintedat in radio observations. At FIR wavelengths there isdust above and below the disk in emission, but this dustmay not be enough to produce polarization in extinctionat optical or NIR wavelengths.These data are the first HAWC+ observations of M51and NGC 891 in polarimetry mode. The brighter regionswithin the spiral arms of M51 and the disk of NGC891are well measured. However, the inter-arm regions inM51 and the halo of NGC 891 are less well measured,and these two regions will require deeper observations tobetter quantify the arm– inter-arm comparison in M51and the presence of vertical fields in NGC 891. ACKNOWLEDGEMENTS
We thank Larry Rudnick for many useful discussionson radio polarimetry.Portions of this work were carried out at the JetPropulsion Laboratory, operated by the California In-stitute of Technology under a contract with NASA.The authors wish to thank Northwestern’s Center forInterdisciplinary Exploration and Research in Astro-physics (CIERA) for providing technical support duringthe development and usage of the HAWC+ data analysispipeline.A.L. acknowledges support from National ScienceFoundation grant AST 1715754.8 Jones et al.
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51, NGC891 1951, NGC891 19