arXiv:1806.06101v1 [astro-ph.GA] 15 Jun 2018 h aatcmdln pto above up complexes opt midplane dust High-resolution galactic filamentary the revealed have midplane. ex- images dust galactic cal extraplanar the probe However, outside to attempts isting midplane. many galactic been the have there at concentrated mostly are a oamgei ed(.. oeg 96 aain&Hoang & Lazarian 1996; perpendic Roberge direction (e.g., field a magnetic in a grains to dust lar are aspherical gains align of to dust axes tend aspherical processes long other which and in torque Radiative media aligned. a starli extinctio through of dichroic arises attenuation passes by selective wavelengths it the and optical is starlight extinction the of Draper Dichroic & in scattering Scarrott dust polarization 1990; from Clemens The & al. Montgomery et 1997; distribu Jones (Scarrott 2014). 1996; al. dust traced et Fendt galactic be 1996; large-scale to allow tions also spatial wavelengths the estimate dust. to extraplanar the galaxies of edge-on amount of and distribution maps models UV transfer the radiative (2014 developed for al. (2015) et Seon and Seon & ha- Shinn UV (2014) galaxies. and the highly-inclined Bregman of many & detection around 2012; Hodges-Kluck reported los Witt (2016) & al. (Seon et galactic 891 Hodges-Kluck 2014). the NGC al. above in et residing discovered Seon than reflectio dust first smaller (UV) extraplanar was ultraviolet is the plane The by stars to ap- illuminated due the dust. halo extraplanar should of nebula the height dust reflection of scale de- “diffuse” that extended the not The faint when was starlight a any, as studies. if pear these of in component, depth tectable dust optical the “diffuse” an fil- against relatively with The absorption clouds by “d dust 2004). preferentially implying traced thereby al. starlight, et are background Thompson al. et structures 2004; Alton 2000; amentary al. 1999, et Rossa 1997, Savage 2000; & (Howk galaxies ral ehooy ajo,313 Korea 34113, Daejeon, Technology, [email protected] ti elkonta aeil nlt-yesia galaxies spiral late-type in materials that known well is It rpittpstuigL using typeset Preprint oaiainmp ntevsbeadna-nrrd(NIR) near-infrared and visible the in maps Polarization D ATVERSION RAFT 2 1 srnm n pc cec ao,KraUiest fScie of University Korea Major, Science Space and Astronomy oe srnm n pc cec nttt,Deen 3405 Daejeon, Institute, Science Space and Astronomy Korea r bevdt cu vnotietegoerclyti du thin geometrically the outside even occur to observed are a on ob ossetwt ht(agn rm1 o4)ob 4%) to 1% from (ranging headings: that Subject with p consistent The v be model. to transfer by radiative found extinction the was in dichroic included the are and lane dust medium, that interstellar find also the We Way. dichr of Milky and the scattering in dust polarization both interstellar additio to in due model, polarizations transfer radiative include structu the in polarization layer extended dust thick vertically the reproduce to aitv rnfrmdl eedvlpdt nesadthe understand to developed were models transfer Radiative O A CTOBER T E OAIAINA RB FTIKDS IKI DEO GALAXIE EDGE-ON IN DISK DUST THICK OF PROBE A AS POLARIZATION tl mltajv 01/23/15 v. emulateapj style X 1. INTRODUCTION ,2018 8, aais S aais antcfils–plrzto ra – polarization – fields magnetic galaxies: – ISM galaxies: ut extinction dust, ∼ p nnab deo spi- edge-on nearby in kpc 2 & .Teeoe a Therefore, 1. PLCTO ONC891 NGC TO APPLICATION rf eso coe ,2018 8, October version Draft ,Korea; 5, K c and nce h as ght ense” WANG the u- n. i- Abstract n ) - - IL S otecmol-nw hnds ae.Temodels The layer. dust thin commonly-known the to n e efidi sesnilt nld geometrically a include to essential is it find we re, EON con,uiga loih iia ota ecie in described test that Benchmark (2017). to al. et int similar Peest scattering and (1996) algorithm dust up- al. et was by an Bianchi code effect 2001; using The polarization al. the et account, 2013). Gordon take al. et to 1996; detail ba- Steinacker dated al. 2011; The in et al. (Bianchi described et Baes observer. authors been the many have toward by algorithms image tech- Monte-Carlo “peeling-off” an sic a produce and in- to medium, that nique thin calculation scheme optically the models improve a in to ficiency code uses scattering” al. The and first et (Seon “forced photons cludes 2016). of MoCafe Draine scatterings & code Seon multiple 2015; transfer Seon three-dimensio radiative 2014; the Carlo using calculated Monte a particu- were dust-scattered in of starlight galaxies, models direct transfer edge-on radiative of 891, lanes NGC lar, dust the above served the explain to discussed also is patterns. 891 polarization the NGC observed of geometry in Large-scale field 891. magnetic NGC obse galaxy, pattern edge-on polarization an the in investigate to presented are UV the for responsible is which halo. reflection layer cau dust is extraplanar polarization the optical by interestin extended therefore, the is, It whether expected vestigate altitudes. not high a is at only extinction detected be dichroic If a polarization and/or plane, scattering 1996). galactic the from al. in et exists Fendt layer dust 1996; thin Draper & e Scarrott (Scarrott 1990; midplane galactic the in above found regions were bulge/halo features polarization optical extended 4565, conditio necessary wavelengths. a optical is the grains in source. dust polarization for of central presence the the around case, any pattern g polarization which t circular plane, scattering to a li the parallel scattered to the perpendicular polarization hand, polarized alon other net is the absorbed On a preferentially direction. yields field is magnetic This light that long direction. the so that along grains larger is of section axes cross extinction The 2007). i xicinwihi epnil o h observed the for responsible is which extinction oic eitddge fplrzto usd h utlane dust the outside polarization of degree redicted h oaiainlvli nacdi h clumpiness the if enhanced is level polarization the nodrt xli h xeddplrzto atr ob- pattern polarization extended the explain to order In calculations transfer radiative Carlo Monte paper, this In NGC and 891 NGC instance for galaxies, edge-on In ria antcfilsi h ue ein fthe of regions outer the in fields magnetic ertical tds,wt cl egtof height scale a with disk, st 1,2 pia oaiain neg-nglxe,which galaxies, edge-on in polarizations optical evdi G 891. NGC in served 2. AITV RNFRMODEL TRANSFER RADIATIVE itv rnfr–satrn – scattering – transfer diative ≈ 0 . p.I order In kpc. 2 S: oin- to g rising rved ives al. t sed ght the nal ef- nd he In to er o g n s 2 SEON were performed as described in Peest et al. (2017) and results For the stellar and dust distributions, three types of models similar to theirs were obtained. The code was also verified were investigated, as shown in Table 1. In the table, the optical using the polarization models given in Bianchi et al. (1996). depths of the dust disks are the central face-on optical depths The dust grains are assumed to be spherical and to have a of the exponential disks. Model A includes only a thin dust size distribution as given by the MRN model (Mathis et al. disk while Models B, C and D include an additional, geomet- 1977): n(a) ∝ a−3.5 (0.005µm < a < 0.25µm), where a is the rically thick dust disk. The model parameters for Model A are grain radius. The dielectric constants for the two dust compo- adopted from the best-fit values estimated for the V-band data sitions (astronomical silicates and graphites) are adopted from of NGC 891 in Xilouris et al. (1999). The parameters for the the ones givenby Draine & Lee (1984) and updated by Draine thick dust disk, used to represent the extraplanar dust in Mod- (2003). All the relevant properties (absorption and scattering els B, C and D, were adopted from the best-fit model for the cross sections, albedo, and Mueller matrix) were calculated Far-UV observation as given by Seon et al. (2014). Model B using the Mie scattering theory. We used the numerical phase is the same as Model A except that the bulge effective radius functions that were calculated with the Mie theory, instead and the bulge-to-total luminosity ratio are slightly reduced of using the approximate Henyey-Greenstein function. Poly- compared to those of Model A. The bulge light scattered by cyclic aromatic hydrocarbons are not included because they the extraplanar dust disk makes the bulge appear bigger than are not relevant for the present purpose. it really is. Therefore, the bulge parameters of Model B were The dichroic extinction is calculated according to a pre- slightly reduced in order to produce a similar extent of the scription given by Wood (1997) and Wood & Jones (1997). model galaxy as that obtained in Model B, as will be shown Jones (1989a) found that the magnitude of dichroic polariza- later. tionat theK band(P ) is roughly proportionalto 2.23τ 3/4(%) We also calculated radiative transfer models (Models C and K K D) in a clumpy two-phase medium which consists of high- over a wide range of optical depths τK. Whittet et al. (2008) also found a similar relation between the polarization and density clumps and a low-density inter-clump medium. In −0.52 Models C and D, a “smooth” distribution of dust density hρi optical depth: PK/τK ≈ 5.08τV (%). Wood (1997) and Wood & Jones (1997) assumed that the proportionality rela- which is the same as that of Model B, was first produced. The probability of any cell being in a high-density state or a tion of Jones (1989a) holds over other wavelengths and ob- 3/4 low-density state is randomly determined, based on the fill- tained the polarization degree of PV =1.3τV (%) at the V ing factor of the clumps ( f = 0.2 and 0.15 for Models C band as a function of optical depth by combing the Serkowski and D, respectively). The high-density clumps are multi- law and the Milky Way interstellar extinction curve, as given plied by a factor of ρhigh/hρi = 4 (Model C) and 6 (Model in Jones (1989b). We also assume that the polarization rela- D), and the low-density medium by a factor of ρlow/hρi = tion measured at K holds at V, but adopted the relation found (1 − f ρhigh/hρi)/(1 − f )=0.25 (Model C) and 0.12 (Model by Whittet et al. (2008), and derived the polarization degree D). The resulting medium is statistically the same as that of 0.48 of PV =2.7τV (%) as a function of optical depth. At each Model B. The medium for Model D is clumpier than that for interaction point, the photon packet is polarized by an amount Model C. 2 of PV sin θ in a direction parallel to the local magnetic field. In general, edge-on galaxies show optical polarization Here, θ is the angle between the photon propagation direction within the dust lane with orientations parallel to the galactic and the magnetic field direction at the interaction location. plane (Scarrott et al. 1990; Scarrott 1996; Fendt et al. 1996; The photon packet is also polarized by an amount calculated Jones 1997; Montgomery & Clemens 2014). On the other through the Mueller matrix as it is scattered. The difference hand, polarization in the outer regions appears to be perpen- caused by the adopted dust models does not significantly alter dicular to the galactic plane. These observational results im- the present results and will be discussed later. ply that there is a large-scale toroidal magnetic field in the The galaxy model is composed of two stellar (disk + bulge) inner regions of galaxies and a vertical magnetic field in the and two dust (thin and thick disks) components. The stellar outer regions. We, therefore, considered three cases with re- and dust disks are described by “double-exponential” distri- spect to the magnetic field geometry for each model type in butions Table 1. In the first case, no dichroic effect was included, to disk disk − − ρ (r,z)= ρ0 exp r/R |z|/Z , (1) investigate the polarization effect due to pure scattering. In
the second case, the magnetic field geometry was assumed to where ρ is the star or dust density at the radial and vertical be toroidal, i.e., parallel to the galactic plane and perpendicu- coordinates r and z in the cylindrical coordinate system. ρ0 lar to the radial direction in the cylindrical coordinates. In the is the density at the galactic center. The radial scale length third case, the magnetic field was perpendicularto the galactic and vertical scale height are denoted by R and Z, respectively. plane, to mimic a poloidal magnetic field geometry. The two The luminosity density for the spheroidal bulge is given by the magnetic field geometries are rather simple, but appear to be de-projection function of a Sersic profile. The density profile good enough to demonstrate the dependence of polarization with a profile index n is given by pattern on the magnetic field geometry.

bulge bulge − 1/n −(2n−1)/2n 3. RESULTS ρ (r,z)= ρ0 exp bnB B , (2) Figure 1 shows the simulated polarization maps at V for where Model A, in which only a thin dust disk is included in the r2 + z2/q2 radiative transfer calculation. In the top panel, no dichroic B = p . (3) R extinction is included in the calculation. The polarization is e found to be mostly vertical to the galactic plane (centrosym- ′′ Here, q is the minor to major axis ratio and Re the effective metric around the bulge) and restricted within about ±20 radius. In this study, a de Vaucouleurs’ profile corresponding (±1.0 kpc at the distance of NGC 891, 9.5 Mpc) from the to a Sersic profile with n =4(bn =7.67) was used. plane. Degree of polarization is less than ∼ 1%. The highest Polarization in NGC 891 3 polarizations of ∼ 1% occur within the dust lane (|Y| . 5′′ or clumpy model (Model C) under the same magnetic field struc- 0.25 kpc) from the plane. We also note that the polarization ture. The degree of polarization appears to be equal to or is weaker in the bulge region than in the outer regions. These greater than 4% only when both the dichroic extinction and are consistent with the previous results obtained for edge-on clumpiness are taken into account. We also note that the over- galaxy models in Bianchi et al. (1996) and Peest et al. (2017). all extent of the galaxy map is larger than those in Figures 1 If the magnetic field is parallel to the galactic plane (mid- and 2. This is because the clumpier medium results in less ef- dle panel), the polarization in the inner regions is very small ficient absorption and more extended scattering features com- and parallel to the galactic plane. This is attributed to dichroic pared to the smoother medium. We obtained similar polariza- extinction by dust grains aligned by toroidal magnetic fields. tion patterns even when the model parameters were adjusted On the other hand, vertical polarizations are shown in the to make the resulting surface brightness map resemble that outer regions in which scattering is dominant. There are po- shown in Figures 1 and 2. larization null points near a radius of 100′′ in the dust lane. In the null points, the vertical polarization due to scatter- 4. DISCUSSION ing is cancelled out by the parallel polarization due to the In this study, we developed radiative transfer models which dichroic extinction along the toroidal magnetic field. The reproduce the overall structure of the optical polarization null points are indeed found in optical polarization maps maps observed in NGC 891. We found that the extended opti- of edge-on galaxies (Scarrott et al. 1990; Draper et al. 1995; cal polarization provides strong evidence for the existence of Montgomery & Clemens 2014). the extraplanar dust which has been inferred from the obser- If the magnetic field is vertical to the plane (bottom panel), vations of ultraviolet reflection halos. the dichroic polarization enhances the polarization degree due There is further evidence suggesting the existence of a to scattering. However, in all three cases in Figure 1, the po- thick dust disk. Hodges-Kluck& Bregman (2014) exam- larization is very small or negligible outside the dust lane. ined the possibility that the UV halos in highly-inclined This is because the stellar scale height is much larger than the galaxies originate from stars in the halos. However, they dust scale height. At high galactic altitudes, stars are viewed found that the dust scattering nebula model is most consis- through a very small amount of dust and hence the polariza- tent with the UV observations. Observations in the mid-IR tion arising from scattering or dichroic extinction is very low. and far-IR (FIR) wavelengths also provide evidence of the The above models are, however, in contrast to the NIR and extraplanar dust (Alton et al. 2000; Irwin & Madden 2006; visible polarization maps, which show significant polariza- Burgdorf et al. 2007; Verstappen et al. 2013; Bocchio et al. tion structures outside the dust lane (Scarrott & Draper 1996; 2016). In particular, Bocchio et al. (2016) found that the FIR Scarrott 1996; Fendt et al. 1996; Jones 1997). In particular,a emission in NGC 891 is best fit with the sum of a thin and a degree of polarizationof up to 4% was foundin the bulge/halo thick dust component, and the scale height of the thick dust regions of NGC 891 by Fendt et al. (1996). The polarization component was consistent with the result given by Seon et al. patterns observed in the bulge/halo regions suggest the exis- (2014). tence of a large scale dust layer above the midplane. Seonet al. (2014) found that the UV halos in NGC 891 Figure 2 shows the results for the case in which an addi- were well reproduced by a radiative transfer model with two tional, thick dust disk with a scale height of 1.6 kpc and a exponential dust disks, one with a scale height of ≈ 0.2–0.25 central face-on optical depth of 0.3 at V is also included. It kpc and the other with a scale height of ≈ 1.2–2.0 kpc. The can be immediately recognized that the polarization signature central face-on optical depth of the geometrically thick disk is now visible even at the bulge and high altitudes in all three was found to be ≈ 0.3–0.5 at the B band (≈ 0.23–0.38 at V). cases. In the middle panel, the null polarization points occur In this study, we demonstrated that the extended polarization at about 100′′ in the dust lane, as in the middle panel of Fig- structures can be well reproduced by thick dust disk with a ure 1. The degree of polarizationis about 1.2–1.5times higher scale height of 1.6 kpc and a central face-on optical depth of than the case in which no thick dust disk is included. In the 1.3 at V. We also varied the scale height and optical depth case of vertical magnetic field (bottom panel), up to ∼ 3% po- of the thick dust disk within the ranges found in Seon et al. larization degree is found, which is close to the maximum po- (2014). The degree of polarization was slightly lowered as larization of ∼ 4% measured in NGC 891 (Fendt et al. 1996). the optical depth or the scale height was altered. However, no The polarization vectors within ∼ 50′′ from the galactic center significant difference was found. are mainly perpendicular to the plane. It is also clear that the The observed polarization vectors, especially at V-band, bottom panel with the vertical magnetic field shows higher are in general parallel to the galactic plane in the central degree of polarizations compared to the two other cases, in part, but perpendicular to the galactic plane in the outer re- which the magnetic field is absent or parallel to the galactic gions. Therefore, we may conclude that the magnetic fields plane. We also note that the degree of polarization in gen- are in general vertical (or poloidal) except the central part, eral rises with distance from the midplane, as observed in the where the magnetic fields are mainly toroidal. This is con- optical polarization maps. sistent with the result obtained from polarized radio emission The galaxy models in Figures 1 and 2 consist of smooth (Sukumar & Allen 1991; Dumke et al. 1995; Krause 2009). It dust and stellar components. For better models, we need to is clear that the vertical polarizations in the outer regions can consider the clumpiness of the interstellar medium (ISM). The mostly be attributed to scattered starlight. However, without polarization map for Model C, in which the ISM is clumpy, the effect of dichroic extinction and/or clumpiness, the pre- is shown in Figure 3. A polarization degree of up to ∼ 4% dicted degree of polarization is slightly lower than the ob- is found, which is consistent with the observational result of served values (middle panel of Figure 2). In our models, Fendt et al. (1996). Figure 4 shows the polarization map for both the dichroic polarization and the clumpiness are also re- Model D. The resulting degree of polarization in both mod- quired to reproduce the observed polarization of up to 4% els is higher than in Figure 2. It is also found that a clumpier (Fendt et al. 1996). model (Model D) always yields higher polarization than a less However, it is noteworthy that Montgomery & Clemens 4 SEON

3/4 (2014) found a different V- and H-band orientation pattern was PV =2.2τV (%) if the polarization relation at K obtained in the outer disk of NGC 891. They argue that polarization in Jones (1989a) and the MRN dust model are combined in verctors are unreliable tracers of the magnetic field. The op- deriving the relation. The differences are mainly caused by tical polarization vector orientation on the northeast side of uncertainties in the polarization relation and the dust extinc- the galaxy appears to differ between Scarrott & Draper (1996) tion cross section. The overall polarization level was slightly and Fendt et al. (1996). Therefore, a definite conclusion on 3/4 reduced when the relation PV =1.3τV (%) was adopted, but the magnetic field orientation cannot be drawn from the V- no substantial difference was found. band data alone. We also note that the polarization vector Note that we assumed spherical dust grains when calculat- within the dust lane will be very low or erratic if a large-scale ing the Mueller matrix and adopted an empirical approach to magnetic field is absent or the magnetic fields are more or take into account the dichroic polarization effect. A more de- less random in the central region. This would be the case of tailed treatment of the dichroic polarization can be found in NGC 891, in which no clear pattern of polarization vectors are Reissl et al. (2014) and Reissl et al. (2016). In their approach, found in the dust lane (Scarrott & Draper 1996; Fendt et al. the scattering phase function depends not only on the incident 1996). photon direction but also on the alignment of dust grains. We The maximum degree of polarization for a single scattering also note that the clumpy models (Models C and D) were de- in our dust model is only marginally lower than that calcu- vised to demonstrate that the clumpiness is also an important lated in White (1979), but significantly greater than the model factor in studying polarizations. Spiral partterns were not in- of Weingartner & Draine (2001). For instance, the maximum cluded in the present radiative transfer models. It may be nec- polarization degree at the V band is 36% in our dust model, essary to use more realistic density models. However, more while 38% and 24% were found in the models of White detailed models are beyond the scope of the present work. (1979) and Weingartner & Draine (2001), respectively. The dust model of White (1979) used the same MRN’s size dis- tribution of dust grains, but adopted different dielectric con- This work was supported by the National Research Founda- stants than ours. The polarization degree due to dichroic ex- tion of Korea (NRF) grant funded by the Korea government 3/4 (MSIP) (No. 2017R1A2B4008291). Numerical simulations tinction assumed in Wood & Jones (1997) is PV =1.3τV (%), 0.48 were partially performed by using a high performance com- which is lower than the relation (PV =2.7τV ) used in this puting cluster at the Korea Astronomy and Space Science In- study. It was found that the degree of dichroic polarization stitute.

REFERENCES Alton, P. B., Xilouris, E. M., Bianchi, S., Davies, J., & Kylafis, N. 2000, Roberge, W. G. 1996, in Polarimetry of the interstellar medium. A&A, 356, 795 Astronomical Society of the Pacific Conference Series; Vol. 97; Baes, M., Verstappen, J., De Looze, I., et al. 2011, ApJS, 196, 22 Proceedings of a conference held at Rensselaer Polytechnic Institute; Bianchi, S., Ferrara, A., & Giovanardi, C. 1996, ApJ, 465, 127 Troy; New York; 4-7 June 1995; San Francisco: Astronomical Society of Bocchio, M., Bianchi, S., Hunt, L. K., & Schneider, R. 2016, A&A, 586, A8 the Pacific (ASP); |c1996; edited by Wayne G. Roberge and Doug C. B. Burgdorf, M., Ashby, M. L. N., & Williams, R. 2007, ApJ, 668, 918 Whittet, 401 Draine, B. T. 2003, ApJ, 598, 1026 Rossa, J., Dettmar, R.-J., Walterbos, R. A. M., & Norman, C. A. 2004, AJ, Draine, B. T., & Lee, H. M. 1984, ApJ, 285, 89 128, 674 Draper, P. W., Done, C., Scarrott, S. M., & Stockdale, D. P. 1995, MNRAS, Scarrott, S. M. 1996, QJRAS, 37, 297 277, 1430 Scarrott, S. M., & Draper, P. W. 1996, MNRAS, 278, 519 Dumke, M., Krause, M., Wielebinski, R., & Klein, U. 1995, A&A, 302, 691 Scarrott, S. M., Rolph, C. D., & Semple, D. P. 1990, in IN: Galactic and Fendt, C., Beck, R., Lesch, H., & Neininger, N. 1996, A&A, 308, 713 intergalactic magnetic fields; Proceedings of the 140th Symposium of Gordon, K. D., Misselt, K. A., Witt, A. N., & Clayton, G. C. 2001, ApJ, 551, IAU, Durham, University, England, 245–251 269 Seon, K.-I. 2015, JKAS, 48, 57 Hodges-Kluck, E., & Bregman, J. N. 2014, ApJ, 789, 131 Seon, K.-I., & Draine, B. T. 2016, ApJ, 833, 201 Hodges-Kluck, E., Cafmeyer, J., & Bregman, J. N. 2016, ApJ, 833, 58 Seon, K.-I., & Witt, A. N. 2012, The Spectral Energy Distribution of Howk, J. C., & Savage, B. D. 1997, AJ, 114, 2463 Galaxies, 284, 135 —. 1999, AJ, 117, 2077 Seon, K.-I., Witt, A. N., Shinn, J.-H., & Kim, I.-J. 2014, ApJ, 785, L18 —. 2000, AJ, 119, 644 Shinn, J.-H., & Seon, K.-I. 2015, ApJ, 815, 133 Irwin, J. A., & Madden, S. C. 2006, A&A, 445, 123 Steinacker, J., Baes, M., & Gordon, K. D. 2013, ARA&A, 51, 63 Jones, T. J. 1989a, ApJ, 346, 728 Sukumar, S., & Allen, R. J. 1991, ApJ, 382, 100 —. 1989b, AJ, 98, 2062 Thompson, T. W. J., Howk, J. C., & Savage, B. D. 2004, AJ, 128, 662 —. 1997, AJ, 114, 1393 Verstappen, J., Fritz, J., Baes, M., et al. 2013, A&A, 556, 54 Krause, M. 2009, RMxAC, 36, 25 Weingartner, J. C., & Draine, B. T. 2001, ApJ, 548, 296 Lazarian, A., & Hoang, T. 2007, MNRAS, 378, 910 White, R. L. 1979, ApJ, 229, 954 Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425 Whittet, D. C. B., Hough, J. H., Lazarian, A., & Hoang, T. 2008, ApJ, 674, Montgomery, J. D., & Clemens, D. P. 2014, ApJ, 786, 41 304 Peest, C., Camps, P., Stalevski, M., Baes, M., & Siebenmorgen, R. 2017, Wood, K. 1997, ApJL, 477, L25 A&A, 601, A92 Wood, K., & Jones, T. J. 1997, AJ, 114, 1405 Reissl, S., Wolf, S., & Brauer, R. 2016, A&A, 593, A87 Xilouris, E. M., Byun, Y. I., Kylafis, N. D., Paleologou, E. V.,& Reissl, S., Wolf, S., & Seifried, D. 2014, A&A, 566, A65 Papamastorakis, J. 1999, A&A, 344, 868 Polarization in NGC 891 5

TABLE 1 MODEL PARAMETERS

Parameter Model A Model B, C, D

Scale height of stellar disk Zs 0.4 0.4 Scale length of stellar disk Rs 5.4 5.4 Bulge to total luminosity ratio B/T 0.3 0.2 Bulge effective radius Re 1.5 1.0 Bulge axial ratio q 0.5 0.5 τ thin Optical depth of thin dust disk V 0.8 0.8 thin Scale height of thin dust disk Zd 0.25 0.25 thin Scale length of thin dust disk Rd 7.7 7.7 τ thick Optical depth of thick dust disk V 0.3 thick Scale height of thick dust disk Zd 1.6 thick Scale length of thick dust disk Rd 7.7 Inclination angle θinc 89.8 89.8

− − − − −

− − − − −

− − − − −

FIG. 1.— V-band polarization maps for Model A in which only a thin dust disk is considered. (top) No dichroic extinction is included. (middle) Mag- netic field is assumed to be toroidal (parallel to the galactic plane). (bottom) Magnetic field is assumed to be vertical (perpendicular to the plane). The intervals between contours are in units of half-magnitude. 6 SEON

− − − − − -0.5

(mag) Intensity − − − −

− − − − −

FIG. 2.— V-band polarization maps for Model B in which both thin and thick dust disks are considered. (top) No dichroic extinction is included. (middle) Magnetic field is assumed to be toroidal (parallel to the galactic plane). (bottom) Magnetic field is assumed to be vertical (perpendicular to the plane). Polarization in NGC 891 7

− − − − −

− − − − −

− − − − −

FIG. 3.— V-band polarization maps for Model C in which the medium is assumed to be clumpy. Magnetic field is assumed to be vertical. (top) No dichroic extinction is included. (middle) Magnetic field is assumed to be toroidal (parallel to the galactic plane). (bottom) Magnetic field is assumed to be vertical (perpendicular to the plane). 8 SEON

− − − − −

− − − − −

− − − − −

FIG. 4.— V-band polarization maps for Model D in which the medium is assumed to be clumpy. Magnetic field is assumed to be vertical. The medium for Model D is clumpier than that for Model C. (top) No dichroic extinction is included. (middle) Magnetic field is assumed to be toroidal (parallel to the galactic plane). (bottom) Magnetic field is assumed to be vertical (perpendic- ular to the plane).