The strength and structure of the magnetic field in the galactic outflow of M82
Enrique Lopez-Rodriguez, Jordan Guerra, Mahboubeh Asgari-Targhi, Joan T. Schmelz
DD RAFT VERSION F EBRUARY
9, 2021Typeset using L A TEX twocolumn style in AASTeX62
The strength and structure of the magnetic field in the galactic outflow of M82 E NRIQUE L OPEZ -R ODRIGUEZ , J ORDAN
A. G
UERRA , M AHBOUBEH A SGARI -T ARGHI , AND J OAN
T. S
CHMELZ
1, 41
SOFIA Science Center, NASA Ames Research Center, Moffett Field, CA 94035, USA Department of Physics, Villanova University, 800 E. Lancaster Ave., Villanova, PA 19085, USA Harvard-Smithsonian Center for Astrophysics, 60 Garden Street MS-15, Cambridge, MA 02138, USA USRA, 7178 Columbia Gateway Drive, Columbia, MD 21046, USA
Submitted to ApJABSTRACTGalactic outflows driven by starbursts can modify the galactic magnetic fields and drive them away from thegalactic planes. Here, we quantify how these fields may magnetize the intergalactic medium. We estimate thestrength and structure of the fields in the starburst galaxy M82 using thermal polarized emission observationsfrom SOFIA/HAWC+ and a potential field extrapolation. We modified the Davis-Chandrasekhar-Fermi methodto account for the large-scale flow and the turbulent field. Results show that the observed magnetic fields arisefrom the combination of a large-scale ordered potential field associated with the outflow and a small-scaleturbulent field associated with bow-shock-like features. Within the central pc radius, the potential fieldaccounts for ± % of the observed turbulent magnetic energy with a median field strength of ± µ G,while small-scale turbulent magnetic fields account for the remaining ± % with a median field strength of ± µ G. We estimate that the turbulent kinetic and turbulent magnetic energies are in close equipartitionup to ∼ kpc (measured), while the turbulent kinetic energy dominates at ∼ kpc (extrapolated). We concludethat the fields are frozen into the ionized outflowing medium and driven away kinetically. This indicates that themagnetic field lines in the galactic wind of M82 are ‘open,’ providing a direct channel between the starburst coreand the intergalactic medium. Our novel approach offers the tools needed to quantify the effects of outflowson galactic magnetic fields as well as their influence on the intergalactic medium and evolution of energeticparticles. Keywords: infrared: galaxies - techniques: polarimetric - galaxies: individual (M82) - galaxies: magnetic fields INTRODUCTIONMessier 82 (M82) is a canonical starburst galaxy at adistance of . ± . Mpc (20 pc/arcsec, Vacca et al.2015, using SNIa 2014J). Observations reveal a bipolar su-perwind that originates in the core and extends perpendic-ular to the galactic plane out into the halo and intergalac-tic medium (IGM) (e.g. Shopbell & Bland-Hawthorn 1998;Ohyama et al. 2002; Engelbracht et al. 2006; Heckman &Thompson 2017). The geometry of the magnetic fields inthe core of the galaxy and the superwind has been investi-gated with various techniques. Results from optical and near-infrared interstellar polarization observations suggest that thefield geometry is perpendicular to the plane of this edge-onspiral galaxy, in line with the superwind, rather than parallel
Corresponding author: Lopez-Rodriguez, [email protected] as might be expected for spiral spirals (see e.g. Jones 2000,and references therein).Non-thermal radio emission from the central region ex-tends normal to the plane of M82, suggesting that the syn-chrotron emitting plasma is part of the outflow (Reuter et al.1992). These results were obtained with the Very Large Ar-ray (VLA) from 3.6 cm to 90 cm at an angular resolutionin the range of − (cid:48)(cid:48) . Subsequent observations with theVLA at 6.2 and 3.6 cm at a resolution of (cid:48)(cid:48) found evidencefor a poloidal magnetic field at heights of up to 400 pc fromthe plane, consistent with an outflowing plasma with veloci-ties high enough to drag the field along with it (Reuter et al.1994). These data from the VLA archive were later com-bined with complementary 18 cm and 22 cm data at a resolu-tion of (cid:48)(cid:48) from the Westerbork Synthesis Radio Telescope(WSRT) by Adebahr et al. (2017). The analysis reveals polar-ized emission with a planar geometry in the inner part of thegalaxy, which they interpret as a magnetized bar. The longerwavelength data show polarized emission up to a distance of a r X i v : . [ a s t r o - ph . GA ] F e b L OPEZ -R ODRIGUEZ ET AL .2 kpc from the disk, which could be described as large-scalemagnetic loops in the halo.Polarimetry at optical and near-infrared wavelengths isstrongly contaminated by the scattering of light from the nu-clear starburst, and the relativistic electrons that give rise tothe radio synchrotron emission may not sample the same vol-ume of gas as polarization. Fortunately, the magnetic fieldstructure can also be obtained using observations of polar-ized thermal emission from the aligned dust grains in thecentral region of M82. The field lines in the 850 µ m polariza-tion map with an angular resolution of (cid:48)(cid:48) from the Submil-limetre Common-User Bolometer Array (SCUBA) cameraon the James Clerk Maxwell Telescope (JCMT) formed a gi-ant magnetic loop or bubble with a diameter of at least 1 kpc.Greaves et al. (2000) speculated that this bubble was possi-bly blown out by the superwind. However, a map createdfrom reprocessed data with an angular resolution of (cid:48)(cid:48) didto show a clear bubble (Matthews et al. 2009).Jones et al. (2019) analyzed far-infrared polarimetry ob-servations of M82 at and µ m with angular reso-lutions of . (cid:48)(cid:48) and . (cid:48)(cid:48) , respectively, taken with High-resolution Airborne Wideband Camera-plus (HAWC+; Vail-lancourt et al. 2007; Dowell et al. 2010; Harper et al. 2018)on the Stratospheric Observatory for Infrared Astronomy(SOFIA). The polarization data at both wavelengths reveala magnetic field geometry that is perpendicular to the disknear the core and extends up to 350 pc above and below thegalactic plane. The 154 µ m data add a component that ismore parallel to the disk further from the nucleus. These re-sults are consistent with the interpretation that the superwindoutflow is dragging the field along with it.The somewhat controversial nature of the magnetic bubbledetected by Greaves et al. (2000) but not by Matthews et al.(2009) using the same data inspired us to draw upon a solarphysics analogy. Would the HAWC + field lines describedby Jones et al. (2019) extend towards the IGM (galactic out-flow), like the magnetic environment in the solar wind, orturn over to the galactic plane (galactic fountain), similar tocoronal loops? To extend the HAWC + data to greater heightsabove and below the galactic plane, we turn to a standardand well-tested technique used in heliophysics − the poten-tial field extrapolation. With only rare exceptions (see e.g.Schmelz et al. 1994, and references therein), the magneticfield in the solar corona, a magnetically dominant environ-ment, cannot be measured directly. Therefore, significanteffort has been invested by the community into extrapolat-ing the field measured at the surface via the Zeeman Effectup into the solar atmosphere. The simplest of these approxi-mations assumes that the electrical currents are negligible sothe magnetic field has a scalar potential that satisfies Laplaceequation and two boundary conditions: it reduces to zero atinfinity and generates the normal field measured at the pho-tosphere. The pioneering work by Schmidt (1964) assumeda flat photospheric boundary. Sakurai (1982) later expandedthis technique to include a spherical boundary surface in acode that was available and widely used. In this paper, we have quantified the magnetic fieldstrength and strucuture in the starburst region of M82. Wehave also modified the solar potential field approximationto work with the HAWC + data in order to extrapolate themagnetic field observed by Jones et al. (2019) and investi-gate the magnetic structures in the halo of M82. The paperis organized as follows: Section 2 describes the estimationof the averaged magnetic field strength in the starburst re-gion, which we use to compute a two-dimensional map ofthe energies in Section 3. The potential field extrapolation isdeveloped in Section 4. We discuss the results in Section 5and conclusions in Section 6. THE MAGNETIC FIELD STRENGTH OF M822.1.
The Davis-Chandrasekhar-Fermi Method
The plane-of-the-sky (POS) magnetic field strength hasbeen estimated from polarimetric data in Galactic (i.e.Wentzel 1963; Schmidt 1970; Gonatas et al. 1990; Zweibel1990; Leach et al. 1991; Shapiro et al. 1992; Morris et al.1992; Chrysostomou et al. 1994; Minchin & Murray 1994;Aitken et al. 1998; Davis et al. 2000; Henning et al. 2001;Attard et al. 2009; Cortes et al. 2010; Chapman et al. 2011;Stephens et al. 2013; Cashman & Clemens 2014; Zielinskiet al. 2020, Li et al., in prep.) and extragalactic sources(i.e. Lopez-Rodriguez et al. 2013, 2015, 2020) by using theclassical Davis-Chandrasekhar-Fermi (DCF) method (Davis1951; Chandrasekhar & Fermi 1953). This method relatesthe line-of-sight velocity dispersion and the plane-of-sky po-larization angle dispersion. It assumes an isotropically turbu-lent medium, whose turbulent kinetic and turbulent magneticenergy components are in equipartition.For a steady state with no large-scale flows, the DCFmethod establishes that the velocity of a transverse magne-tohydrodynamical (MHD; Alfv´en) wave, V A = B √ πρ , (1)is related to the observed dispersion of polarization angleswhere B is the magnetic field strength and ρ is the mass den-sity. This relation is derived from the wave equation with thepropagation velocity found to be V = V A = σ v σ φ , (2)where σ v is the amplitude of the time variation ( i.e. , velocitydispersion) and σ φ is the spatial amplitude (i.e. angular dis-persion). Combining Eqs. 1 and 2, gives us the well-knownDCF approximation: B DCF = ξ (cid:112) πρ σ v σ φ . (3)The angular dispersion σ φ is the standard deviation of thedistribution of polarization angles. When σ φ ≤ ◦ , ξ ∼ . accounts for the projection of the magnetic field and densitydistributions on the POS (Ostriker et al. 2001). HE STRENGTH AND MORPHOLOGY OF THE MAGNETIC FIELD IN THE GALACTIC OUTFLOW OF
M82 3Figure 1 shows the magnetic field orientations of M82 in-ferred from the 53 µ m observations with HAWC+ (Joneset al. 2019). Polarization measurements with P/σ P ≥ areshown, where σ P is the uncertainty of the polarization frac-tion, P . Polarization measurements have been normalizedand rotated by ◦ to show the B-field orientation. To applythe DCF approximation, the velocity dispersion, mass den-sity, and angular dispersion have to be estimated in the sameregion. The FIR spectroscopic analysis of Contursi et al.(2013) separated the kinematics of M82 into four regions − the disk, the starburst, the north outflow, and the southoutflow − based on several emission lines ([CII], [OI] and[OIII]) using PACS/ Herschel data. We find that only the star-burst region provides sufficient polarization measurements toperform the dispersion analysis used for this work. The star-burst mask, with a size of × pc at a PA of ∼ ◦ inthe east of north direction, the region of focus for this work,is shown in Figure 1. h m s m s s s s D e c ( J ) M82
53 m HAWC+/SOFIANormalized B-field
Starburst Mask l o g ( I [ J y / s q a r c s e c ]) Figure 1.
Inferred magnetic field orientation (white) of M82 usingthe 53 µ m polarimetric observations with HAWC+/SOFIA (Joneset al. 2019). All polarization measurements are normalized, andonly those with p/σ p ≥ are shown. The color scale shows thetotal intensity at 53 µ m. Contours start at σ with increments of nσ , where n = 2 . , . , . , . . . and σ = 2 . mJy/sqarcsec. Thestarburst mask (yellow solid line) taken from Contursi et al. (2013)is used for the parameter estimations of the magnetic field strengths.Beam size (red circle) is shown. Figure 2-top shows the maps of the several empirical quan-tities necessary to estimate the magnetic field strength withinthe starburst mask. Figure 2-bottom shows the distributionsof each quantity with the estimated median (solid line) and σ uncertainties (dashed lines). The first is the column den-sity, N H + H , from Jones et al. (2019). The N H + H map hasbeen smoothed using a Gaussian profile with a full-width- at-half-maximum (FWHM) equal to the beam size of theHAWC+ observations and projected to the HAWC+ obser-vations. We estimate the median column density within thestarburst mask to be N H + H = (2 . ± . × cm − .To convert N H + H to mass density ( ρ ), we need to knowthe extend of the gas and dust in the line-of-sight (LOS)direction. An estimate of this dimension is the effectivedepth of the starburst region, ∆ (cid:48) , which can be calculatedfollowing Houde et al. (2011). Specifically, we calculatethe normalized autocorrelation function of the polarized fluxof M82 using polarization measurements with P/σ P ≥ .This cut ensures that the same polarization measurements areused through the data analysis. Then, the half-width-at-half-maximum (HWHM) of the distribution is taken as the valueof ∆ (cid:48) , which is estimated to be ∆ (cid:48) = 0 . (cid:48) ( . pc).We interpret ∆ (cid:48) as the depth of the starburst region that con-tains ≥ % of the polarized flux, which assumes that thegas and dust distribution in the starburst of M82 is isotropic.Note that this result is in good agreement with that of Ade-bahr et al. (2017), who estimated a width of the polarizedemitting region of ∼ pc using and cm data and as-suming a cylindrical symmetry. Finally, using ∆ (cid:48) , we canestimate the mass density within the starburst mask to be ρ = m H µN H + H / ∆ (cid:48) = (1 . ± . × − g cm − ,where m H is the hydrogen mass and µ = 2 . is the meanmolecular mass.Multiple authors have measured the velocity dispersion forthe central disk of M82 within similar physical scales as ourmask. Emission lines, e.g. [ArIII] 8.99 µ m, H µ m,[FeII] 25.98 µ m, and [SiII] 34.815 µ m, in the mid-infraredobserved with the Infrared Space Observatory (ISO) and anangular resolution of (cid:48)(cid:48) (180 pc) show velocities within arange of 71 −
114 km s − (Sohn et al. 2001). CO(1-0) ob-servations made with the Nobeyama Millimeter Array at aresolution of . (cid:48)(cid:48) (50 pc) show a velocity dispersion of km s − (Chisholm & Matsushita 2016). Tadaki et al. (2018)measured the velocity dispersion of individual clumps in thedisk of M82 to be ∼ km s − using 0 . (cid:48)(cid:48) ± km s − for the CO-emitting gas within adisk of ∼ kpc radius. Understanding that the velocity dis-persion of the disk shows a very complex structure, we findthat the most complementary observations for our analysiscome from Leroy et al. (2015). They show that the molecu-lar gas, CO(2-1), traces the high-density regions of M82,which is spatially coincident with the dust emission fromour FIR observations. We use their CO(2-1) emission linewithin our mask to estimate a median velocity dispersion of σ v, CO(1 − = 66 . ± . km s − . The σ v, CO(1 − maphas been smoothed using a Gaussian profile with a FWHMequal to the beam size of the HAWC+ observations and pro-jected to the HAWC+ observations.The final variable required to estimate B DCF is σ φ , whichcorresponds to the standard deviation of the polarization an-gle distribution. Here, we use the polarization angle of theinferred B-field orientation from the 53 µ m HAWC+ obser-vations (Jones et al. 2019) within our mask to estimate a me- L OPEZ -R ODRIGUEZ ET AL . H + H (cm ) 1e22010203040506070 O cc u r e n c e N H + H = 2.27 ± 0.57 × 10 cm
50 55 60 65 70 v , CO (2 1) (km s )020406080 O cc u r e n c e v , CO (2 1) = 66.0 ± 6.6 km s
80 60 40 20 0 20 40 60PA B ( )020406080100120 O cc u r e n c e PA B = 15.3 ± 17.1 h m s s s s D e c ( J ) h m s s s s RA (J2000) 9 h m s s s s RA (J2000)1.52.02.53.03.5 N H + H ( c m ) v , C O ( ) ( k m s ) P A B () Figure 2.
Top:
Maps of the N H + H (left) from Jones et al. (2019), σ v, CO(1 − (middle) from Leroy et al. (2015), and PA of the inferredB-field orientation, P A B , (right) using the 53 µ m polarimetric observations from Jones et al. (2019). Contours start at N H + H = 1 . × cm − and σ v, CO(1 − = 48 km s − , and increase in steps of . × cm − , and km s − , respectively. The contours of P A B aredisplayed in the range of [ − , ◦ in intervals of ◦ . Bottom:
Histograms of the measurements for each map. The median (solid line) and σ uncertainties (dashed lines) are shown. dian value of − . ◦ with an angular dispersion (std. devia-tion) of σ φ = 17 . ◦ . Therefore, using σ φ = 0.29 rad (17.1 ◦ ),we find B DCF = 0 . ± . mG.2.2. The Angular Dispersion Function
In the starburst region of M82, the dominant driver of theturbulence is the supernova explosions. The observed pat-terns of the B-field orientation are the results of two contri-butions: 1) one from the morphology of the large-scale reg-ular magnetic field, which is larger than the turbulent scale( δ ) driven by supernova explosions at scales of − pcin nearby galaxies (i.e. Ruzmaikin et al. 1988; Brandenburg& Subramanian 2005; Elmegreen & Scalo 2004; Haverkornet al. 2008); and 2) another contribution from the small-scale( i.e., turbulent or random) magnetic field, which relies on tur-bulent gas motions at scales compared to or smaller than δ .Because the DCF method relies on the speed of an Alfv´enwave to measure the magnetic field strength, only the per-turbed ( i.e., turbulent or random) component provides the correct value of B . Therefore, it is important to extract theturbulent component from the measured dispersion.Hildebrand et al. (2009) and Houde et al. (2009, 2011)have been able to separate the regular and turbulent compo-nents using a careful analysis of the dispersion of polariza-tion angles obtained from dust continuum polarization ob-servations. This technique has been applied to FIR-sub-mmpolarimetric observations of Galactic sources (i.e. Chapmanet al. 2011; Crutcher 2012; Girart et al. 2013; Pattle et al.2017; Soam et al. 2019; Chuss et al. 2019; Redaelli et al.2019; Wang et al. 2020; Guerra et al. 2020; Michail et al.2021, Li et al. in prep.), as well as sub-mm polarimetric ob-servations of external galaxies, like M51 (Houde et al. 2013).Specifically, an isotropic two-point structure function ( i.e., dispersion function) is computed to describe the dispersionas a function of angular scale. Then, the dispersion func-tion separates the large-scale field from that of the turbulence(Houde et al. 2016, eq. 13), HE STRENGTH AND MORPHOLOGY OF THE MAGNETIC FIELD IN THE GALACTIC OUTFLOW OF
M82 5 − (cid:104) cos[∆ φ ( l )] (cid:105) = 11 + N (cid:104) (cid:104) B t (cid:105)(cid:104) B (cid:105) (cid:105) − (cid:26) − exp (cid:18) − l δ + 2 W ) (cid:19)(cid:27) + a l (4)where the first term on the right accounts for the small-scale turbulent contribution to the dispersion, and the sec-ond term accounts for the large-scale regular (ordered) fieldcontribution. l is the distance between pairs of measure-ments with angle difference ∆ φ . W is the standard deviationof the beam size assumed to be a Gaussian function W = FWHM / .
355 = 2 . (cid:48)(cid:48) , where FWHM = . (cid:48)(cid:48) for our 53 µ mHAWC+ observations (Harper et al. 2018). (cid:104) B t (cid:105) / (cid:104) B (cid:105) isthe turbulent-to-large-scale energy ratio, δ is the correlationlength for the turbulent field, a is the large-scale coefficient,and N is the number of independent turbulent cells in thecolumn of dust probed observationally given by N = ( δ + 2 W )∆ (cid:48) √ πδ (5)(Houde et al. 2016, eq. 14), where ∆ (cid:48) is the effective thick-ness of the starburst region, which was already estimated inSection 2.1.We evaluate the left-hand side of Eq. 4 within the star-burst mask using the 53 µ m polarization data of M82 ob-served with HAWC+ (Jones et al. 2019). Using ∆ (cid:48) = 0 . (cid:48) ( . pc), this leaves three free parameters to be determined: (cid:104) B t (cid:105) / (cid:104) B (cid:105) , δ , and a . We use a Markov Chain Monte Carlo(MCMC) solver for fitting the non-linear model of Eq. 4to the dispersion functions as implemented by Chuss et al.(2019). This fitting routine infer the optimal model parame-ters and its associated uncertainties from the posterior distri-butions of the MCMC chains. Figure 3-left shows the mea-sured dispersion function − (cid:104) cos[∆ φ ( l )] (cid:105) (blue circles ina and b panels) with the best-fit for the large-scale compo-nent (red solid line). In panel c, the autocorrelated turbu-lent component (blue circles), its best fit (dashed red line)and the beam profile (grey solid line) are displayed. Cor-rectly resolving the turbulence in the gas depends on theturbulent part (blue symbols and dashed red line in Figure3c) having a wider shape than the observations’ autocor-related beam (solid grey line). This is evident in Figure3c. Figure 3-right shows the posterior distributions obtainedwith the MCMC solver, which statistics provide the best-fit model parameter values for the dispersion function with a = 406 . +5 . − . × − arcmin − .We infer a coherent length of the turbulent magnetic fieldto be δ = 3 . (cid:48)(cid:48) +0 . − . ( . +5 . − . pc). The coherent length islarger than the beam size of our observations (Figure 3c), √ W = 2 . (cid:48)(cid:48)
90, which allow the characterization of the tur-bulent magnetic field (Houde et al. 2011). It is worth notic-ing that our coherent length of the turbulent magnetic field isin agreement with the typical scale length of turbulent fieldsin galaxies of order − pc, which is driven by super-nova explosions (i.e. Haverkorn et al. 2008). Adebahr et al.(2017) estimated a coherent length of the magnetic field of ∼ pc using radio polarimetric observations in the cen-tral ∼ × . kpc of M82, in agreement with our results.Using isotropic Kolmogorov turbulence ( P ( k ) ∝ k / ), weestimate a coherent length (L´opez-Coto & Giacinti 2018) of L c = δ/ . pc, where δ is considered to be the maxi-mum coherent length, L max , within the starburst region. Weconclude that our observations are able to resolve the turbu-lent magnetic field in the central × pc starburst ofM82 and therefore, further detailed analysis of the magneticfield strengths can be performed.We infer a turbulent-to-large-scale energy of (cid:104) B t (cid:105) / (cid:104) B (cid:105) =0 . +0 . − . . This result implies that the central starburst re-gion of M82 is dominated by a large-scale regular magneticfield since the turbulent magnetic energy is small ( ≈ B ADF = (cid:112) πρσ v (cid:20) (cid:104) B t (cid:105)(cid:104) B (cid:105) (cid:21) − / (6)(Houde et al. 2009). The values of ρ , the mass density, and σ v , the velocity dispersion, are those previously estimated inSection 2.1 and Fig. 2. Using these parameters, we estimatethe magnetic field strength within the starburst mask of M82to be B ADF = 1 . ± . mG.2.3. The Effect of Galactic Outflows
In this section, we investigate how both values of the mag-netic field, B DCF and B ADF , are affected by the M82 out-flow. Assuming there is a steady, large-scale velocity field (cid:126)U = U ˆ z in the same direction as the magnetic field (cid:126)B , thewave equation for this case – after several steps – reduces to(Eq. 10 by Nakariakov et al. 1998): (cid:20) ∂∂t + ( U − V A ) ∂∂z (cid:21) (cid:20) ∂∂t + ( U + V A ) ∂∂z (cid:21) V = 0 . (7)This means there are two standing waves with velocities V − = U − V A and V + = U + V A . However, these twovelocities are associated with the same observed spatial dis-turbance ( i.e , polarization-angle dispersion). Replacing thismodified velocity into Eq. 2, ( V ± ) = ( U ± V A ) = σ v σ φ , (8)results in ± V A = σ v σ φ − U , (9) L OPEZ -R ODRIGUEZ ET AL . .
000 0 .
025 0 .
050 0 .
075 0 .
100 0 .
125 0 .
150 0 . ‘ (arcmin ) . . - h c o s ( ∆ φ ) i a .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 .
30 0 .
35 0 . ‘ (arcmin) . . - h c o s ( ∆ φ ) i b Large scale field .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 .
30 0 .
35 0 . ‘ (arcmin) . . T u r b . C o m p . c δ = 3.67 arcsec BeamCorr. Turb. a [ − arcmin − ] = . +5 . − . . . . . δ [ a r c s ec ] δ [arcsec] = . +0 . − .
400 405 410 415 a [ − arcmin − ] . . . . . h B t i / h B i .
25 3 .
50 3 .
75 4 . δ [arcsec] .
056 0 .
064 0 .
072 0 .
080 0 . h B t i / h B ih B t i / h B i = . +0 . − . Figure 3.
Left:
Dispersion function (a,b) within the starburst mask of M82 at 53 µ m. Data points (blue circles) and fits (red solid line) of thelarge-scale field are shown. (c) The best fit (red dashed-line) of the turbulent component and the beam (grey solid line) of the observations areshown. The fits represent the best inferred results using Eq. 4. Right:
Posterior distributions of the large-scale field ( a ), turbulent correlationlength ( δ ), and turbulent-to-large-scale field ratio ( (cid:104) B t (cid:105) / (cid:104) B (cid:105) ). Using the definition of Alfv´en wave (Eq. 1), ± B √ πρ = σ v σ φ − U , (10)which indicates that two Alfv´en waves with the same speedtravel in opposite directions, due to the same magnetic fieldstrength and the same non-zero, steady-state large scale ve-locity. Therefore, we can take the absolute value of Eq. 10and re-arrange the terms, B = (cid:112) πρ (cid:12)(cid:12)(cid:12)(cid:12) σ v σ φ − U (cid:12)(cid:12)(cid:12)(cid:12) , (11)where B is the absolute value of the field strength. Finally,using the definition of B DCF (including the adjustment factor ξ ), we define the modified B (cid:48) DCF as B (cid:48) DCF = B DCF (cid:12)(cid:12)(cid:12)(cid:12) − σ φ U σ v (cid:12)(cid:12)(cid:12)(cid:12) . (12)Equation 12 reduces to the well-known DCF approximation(Eq. 3) when U = 0 . Assuming, of course, that σ φ is non-zero, the modification to the DCF value is proportional to U /σ v — the ratio of large-scale velocity to the velocity dis-persion.From Eq. 12 we now have two possible regimes:• B (cid:48) DCF < B
DCF , which means σ φ U σ v < and (cid:54) = B (cid:48) DCF > B
DCF , which means σ φ U σ v > . Therefore the correction to the DCF value (Eq. 12) in-creases the strength of the magnetic field when the ratioof dispersion-to-large-scale velocities is lower than half the measured angle dispersion ( . σ φ > σ v /U ) — the large-scale velocity field dominates. On the other hand, the correc-tion lowers the magnetic field strength when the turbulencedominates the velocity field ( . σ φ < σ v /U ).Using the median velocity of the σ v, CO(1 − molecularoutflow within the starburst mask of U = 396 ± km s − (Leroy et al. 2015), the σ φ = σ v = ± . km s − from Section 2.1, we estimate the modifying factorto be: σ φ U σ v = 1 . ± . (13)since this factor is <
2, we conclude that the large-scale ve-locity field from the galactic outflow dominates over the tur-bulent magnetic field within the starburst mask. This resultis in agreement with that the large-scale regular magneticfield dominates over the turbulent magnetic energy withinthe starburst region. These results imply that the B DCF and B ADF are overestimated. We can now calculate the cor-rected strength of the magnetic field within the starburst maskfor both the classical DCF method, B (cid:48) DCF = 0 . ± . mG, and the angular dispersion analysis method, B (cid:48) ADF =0 . ± . mG.Both estimates of the magnetic field, B (cid:48) DCF and B (cid:48) ADF ,agree within the uncertainties when galactic outflow com-ponent is taking into account. The separation of turbulent-to-large-scale fields, as described in Houde et al. (2009),does take into account some influence of the large-scale ve-locities present in the starburst mask. However, the ADFmethod still requires a correction of ∼ %. As the cor-rected ADF method is now dominated by the turbulent field,we use B (cid:48) ADF hereafter.
HE STRENGTH AND MORPHOLOGY OF THE MAGNETIC FIELD IN THE GALACTIC OUTFLOW OF
M82 7 THE TWO-DIMENSIONAL MAP OF THEMAGNETIC FIELD STRENGTHIn Section 2, we estimated the average turbulent magneticfield strength in the starburst region of M82 using the mean ofthe mass density, velocity dispersion, and angular dispersion.Here, we here estimate a pixel-by-pixel turbulent magneticfield strength measurements using the full maps of the massdensity and velocity dispersion. A similar approach has suc-cessfully been applied to OMC-1 by Guerra et al. (2020). Wehere present a novel approach using the energy budget to es-timate the two-dimensional turbulent magnetic field strengthof M82.Contursi et al. (2013) suggested that the cold clouds fromthe disk are entrained into the outflows by the galactic wing,where small, dense clouds may remain intact during the out-flow process. Jones et al. (2019) proposed a scenario wherethe magnetic field is entrained with the gas and dust, anddragged by the outflow away from the galactic disk to thegalactic wind. This entrainment is generally quantified bythe plasma β parameter, defined as the ratio of thermal gaspressure, U G , to magnetic pressure, U B . β traditionally de-termines whether an environment is dominated by thermal ormagnetic forces: β = U G U B = n H k B T g B / π (14)where n H is the gas density, k B is the Boltzmann constant,and T g is the gas temperature.Turbulent energy densities are generally larger than ther-mal energy densities in galaxies (Beck & Krause 2005).Thus, a β − like parameter that takes both the turbulent kineticand hydrostatic energies of the outflow of M82 into accountis required. We here define a β (cid:48) parameter: β (cid:48) = U H + U K U B (15)where U H , U K , and U B are the hydrostatic, turbulent kinetic,and turbulent magnetic energies, respectively.Let the hydrostatic energy, U H , be U H = πG Σ g = πG ( N H m H µ ) (16)where G is the gravitational constant, Σ g is the gas density, N H is the gas column density, m H is the hydrogen mass, and µ = 2 . is the mean molecular mass per H molecule.Let the turbulent kinetic energy, U K , and magnetic energy, U B , be U K = 12 ρσ v (17) U B = B π (18)where σ v is the three-dimensional dispersion velocity definedas √ σ v, CO (2 − .Using β (cid:48) (Eq. 15), the two-dimensional magnetic fieldstrength map can be estimated such as B = (cid:20) π (cid:18) U K + U H β (cid:48) (cid:19)(cid:21) / = (cid:20) πβ (cid:48) ( πGN H m H µ + 12 ρσ V ) (cid:21) / (19)where we impose the condition that β (cid:48) is equal to the meanvalue of the energies within the starburst mask.We use the mean values within the starburst mask fromSection 2, and estimate a β (cid:48) = 0 . ± . . Impos-ing this condition satisfies that the estimated mean turbu-lent magnetic field strength within the starburst mask is (cid:104) B (cid:105) = B (cid:48) ADF = 0 . mG. In combination with the mapsof N H + H , σ v, CO(2 − from Section 2, we compute thetwo-dimensional maps of the energies and turbulent magneticfield strength of M82. Figure 4-A-D shows the resulting two-dimensional maps of the hydrostatic, turbulent kinetic, andturbulent magnetic energies as well as the turbulent magneticfield strength, each (cid:48)(cid:48) × (cid:48)(cid:48) ( . × . kpc ) in size. Fig-ure 4-E-F shows the radial profiles of the energies and turbu-lent magnetic field strength. We estimated the median andstandard deviation of the median (1 σ ) for annulus of widthequal to the Nyqvist sampling ( . (cid:48)(cid:48) , . pc) of the HAWC+observations.We find that the turbulent kinetic and turbulent magneticenergies are in close, within 1 σ , equipartition across thegalactic outflow at radius ∼ − pc. At radius ≤ pc, the turbulent magnetic energy appears to be higher thatthe turbulent kinetic energy. We note that this result withinthe starburst mask may imply that 1) the observed turbulentmagnetic energy may be larger than the combined turbulentkinetic and hydrostatic energy in the compact star-formingregions, or 2) there may be several magnetic field compo-nents that may be overestimating the median turbulent mag-netic field strength. A decomposition of the turbulent mag-netic field strength is required to disentangle the several com-ponents within the starburst mask (see Section 5.1). At radius > pc, the turbulent kinetic energy shows a steeper dropthan the turbulent magnetic energy, however both energiesstill remain close to equipartition, within σ uncertainties. POTENTIAL FIELD EXTRAPOLATIONWe are interested in quantifying the influence of the galac-tic outflow in the magnetic field towards the intergalacticmedium. This study requires the knowledge of the mag-netic and kinetic energies at distances of several kiloparsecsfrom the galaxy plane. Although the kinetic energy can beestimated up to tens of kpc, there are no empirical measure-ments to compute the magnetic energies at these distances inM82. Our magnetic field results of M82 obtained in Section3 provide an observational boundary condition required toperform a potential field extrapolation and estimate the fieldstrength and morphology at several kpc above and below thegalactic plane.We employ a standard, well-tested technique that has beenused in solar physics for decades to determine the magnetic L
OPEZ -R ODRIGUEZ ET AL . Figure 4.
Hydrostatic (A), turbulent kinetic (B), and magnetic (C) energy maps within a (cid:48)(cid:48) × (cid:48)(cid:48) ( . × . kpc ) region. Contours startat − and increases in steps of . in logarithmic scale. (D) Turbulent magnetic field strength map. Contours start at . mG and increase insteps of . mG. Radial profiles of the energies (E) and turbulent magnetic field strength (F) showing the median (lines) and 1 σ uncertainties(shaded region). field in the solar corona, a region where the magnetic field(with rare exceptions) cannot be measured directly. In thesolar physics case, the LOS magnetic field is measured in thephotosphere using the Zeeman Effect. This observation pro-vides the first required boundary condition; the second con-dition assumes the field reduces to zero at infinity (see e.g. ,Sakurai 1982). For a comprehensive review of magnetic fieldextrapolation techniques in solar physics please see Wiegel-mann & Sakurai (2012). Potential field extrapolation has alsobeen employed to study the magnetic field in slow-rotatingand cool stars (Donati 2001; Hussain et al. 2001) such as τ Sco (Donati et al. 2006). Here, we have modified the so-lar physics method to work with POS polarization data fromHAWC + . 4.1. Solving Laplace’s Equation
The simplest of these extrapolation approximations as-sumes that the electrical currents are negligible. In thiscase, the magnetic field, B = −∇ φ , has a scalar potential, φ ( x, y, z ) , that satisfies Laplace equation (see e.g. Neukirch2005) ∇ Φ = 0 . (20)Here, the plane x − y is parallel to the galaxy’s disk and ourextrapolation will be limited to the x − z plane, above and be-low the galactic plane. This two-dimensional Cartesian ge-ometry requires one boundary condition from the magnetic field map (Section 3) along the plane of the galaxy’s disk at xz = ( x, B z ( x,
0) = F ( x ) (21)and a second boundary condition at infinity, B z → as | z | →∞ . Using separation of variables Φ( x, z ) = X ( x ) Z ( z ) . (22)Substituting Eq. 22 into Eq. 20 gives X (cid:48)(cid:48) Z + XZ (cid:48)(cid:48) = 0 . (23)A particular solution with wavenumber k has X (cid:48)(cid:48) = − k X and Z (cid:48)(cid:48) = k Z , so X ( x ) = A cos( kx ) + B sin( kx ) , (24) Z ( z ) = Ce − k | z | + De k | z | , (25)where A , B , C , and D are constants. We now have B z = ∂ Φ ∂z = X ( x )( − Cke − k | z | + Dke k | z | ) , (26)As B z → when z → ∞ , the constant D = 0 . We can alsoset C = 1 as the constants can be set by the values of A and B . Then Z ( z ) = e − k | z | , X ( x ) = − F ( x ) /k , and HE STRENGTH AND MORPHOLOGY OF THE MAGNETIC FIELD IN THE GALACTIC OUTFLOW OF
M82 9 Φ k = − k F ( x ) e − k | z | . (27)We will assume that the source of (cid:126)B is finite, so that B z ( x,
0) = F ( x ) = 0 for | x | > (cid:96)/ for some length (cid:96) .We will also assume that the net flux into the upper halfplane is zero, i.e. (cid:90) (cid:96)/ − (cid:96)/ F ( x ) dx = 0 . (28)Expansion into a Fourier series gives F ( x ) = n = ∞ (cid:88) n =1 ( a n cos k n x + b n sin k n x ) , k n = 2 πn(cid:96) . (29)We now have B x ( x, z ) = n = ∞ (cid:88) n =1 ( a n sin k n x − b n cos k n x ) e − k n | z | (30) B z ( x, z ) = n = ∞ (cid:88) n =1 ( a n cos k n x + b n sin k n x ) e − k n | z | . (31)The coefficients are given by a n = 2 (cid:96) (cid:90) (cid:96)/ − (cid:96)/ F ( x ) cos( k n x ) dx, (32) b n = 2 (cid:96) (cid:90) (cid:96)/ − (cid:96)/ F ( x ) sin( k n x ) dx. (33)Finally, the potential field orientations in the POS are esti-mate as φ = arctan (cid:18) B z B x (cid:19) , (34)where the magnetic field components require to be projectedon the observer’s view given the inclination and tilt angle ofthe galaxy on the POS.4.2. Potential Field Solutions
The boundary condition, F ( x ) , corresponds to the normal-to-plane component of the magnetic field ( B Norm ), so the ob-served POS magnetic field ( (cid:126)B
POS ) needs to be reprojected.We define the galaxy’s plane by its tilt angle of θ = 64 o mea-sured as positive in the East from North direction (Mayyaet al. 2005); this is designated by the black solid line inFigure 5. (cid:126)B POS corresponds to the measurements of the magnetic field strength (Figure 4-D) and orientation (pseudo-vectors in Figure 5) along this line. We use Euler rota-tions around the x-axis, R x [ i ] , and the z-axis, R z [ θ ] , to com-pute B Norm = R x [ i ] R z [ θ ] (cid:126)B POS using an inclination angleof i = 76 ◦ (Mayya et al. 2005) with respect to the LOS. B Norm is displayed in Figure 5 as vectors along the galaxy’splane with lengths and color corresponding to their repro-jected strength. In Figure 5 both B POS and B Norm are seenas a function of the offset radius from the maximum of StokesI intensity along the galaxy’s plane.It is important to recall here that magnetic field orienta-tions determined by FIR polarimetric data suffer from the180 ◦ ambiguity (Hildebrand et al. 2000) – that is all vec-tors in Figure 5- Top have the same likelihood to be pointinginto the galaxy’s plane. This angular ambiguity does not af-fect the shape or strength of the magnetic field lines, just thedirection. Thus, we choose to calculate the potential field so-lution with this choice of direction for B Norm and only workwith the orientation of the potential solutions. D ec li n a t i o n
200 0 200 400
O↵set [pc] . . . [ G a u ss ] B POS B norm . . . . . . B n o r m [ G a u ss ] Figure 5.
Top:
Boundary values B Norm for the potential fieldextrapolation in M82. B Norm vectors length and color correspondto the B POS strength. The solid black line represents the plane ofthe galaxy defined at tilt angle 64 ◦ (Mayya et al. 2005). HAWC+rotated polarization orientations (black) and arrows correspondingto the normal-to-plane component of the magnetic field (red) areshown along the galaxy’s plane. Background corresponds to theStokes I intensity. Bottom: B POS (solid) and B Norm (dashed) profileas a function of the offset position from the maximum I intensityalong the galaxy’s plane. Using the values of B Norm displayed in Figure 5 for theboundary condition F ( x ) , we can calculate the coefficients a n and b n in Eqs. 32, 33 for n = 1 . . . , (cid:96) = 1 . kpc (theextent of F ( x ) ) using a trapezoidal method to evaluate theintegral. Subsequently, we evaluate the potential field com-ponents in Eqs. 30, 31 for x, z = − . to . kpc. The0 L OPEZ -R ODRIGUEZ ET AL . Figure 6.
Potential magnetic field lines of M82 inferred using the µ m polarimetric observations with HAWC+/SOFIA. The potentialmagnetic field is calculated by extrapolation of the magnetic field at the galaxy’s plane. Magnetic field lines are visualized in a field of view ∼ centered at M82. The potential field strength is seen larger in the bulk of the galaxy, ∼ resulting potential magnetic field lines are shown in Figure 6within a . × . kpc region centered at M82. Magneticfield lines are displayed in a grey scale that matches the po-tential field strength. Note that some lines appear truncatedas an artifact of the line integration process performed bythe python package MATPLOTLIB . We display the potentialfield lines that originate from the empirical measurements us-ing the µ m polarimetric observations with HAWC+. Themaximum magnetic field strength of ∼ + data (Section 4.2). Themagnetic field strength decreases to 100 µ G at a radius of1500 pc.Figure 7 displays a comparison between the orientationscalculated with the potential field ( | φ | , Eq. 34; red) and themeasured with the HAWC+ instrument (black) for the cen-tral ∼ ×
700 pc region of M82 where the total intensity I > . Jy/arcec and polarization fraction P/σ P > (theChauvenet criteria). We measure an absolute angular differ-ence (or misalignment) with a mean value of 16.3 ± ◦ ,where the maximum of occurrence is at ∼ ◦ . Smaller an-gular differences ( < ◦ ) are located within the central ∼ DISCUSSION5.1.
The magnetic fields in the starburst region
As noted in Section 3, the observed turbulent magnetic en-ergy ( U B ), is larger than the turbulent kinetic and hydrostaticenergy ( U K + U H ) within the starburst mask (Fig. 4). Toinvestigate additional components in the observed turbulentmagnetic energy within the central . × . kpc region,we subtract the potential field magnetic energy from the ob-served turbulent magnetic energy (Fig. 8). The resulting mapis labeled ‘non-potential’ field, U B NPF = U B − U B PF , whichcan be interpreted as a ‘residual’ map of the observed mi-nus model magnetic field energies. The ‘non-potential’ map, U B NPF , has a ‘bow-shock-like’ arc structure along the south-
HE STRENGTH AND MORPHOLOGY OF THE MAGNETIC FIELD IN THE GALACTIC OUTFLOW OF
M82 11 h m s s s s s D e c li n a t i o n Potential AngleHAWC+ PA
Figure 7.
Comparison between the HAWC+-inferred magnetic fieldorientation (black) and the potential orientation (red) in locations ofM82 with
I > . Jy/arcsec and p > σ p . Above a below the cen-ter of the galaxy’s plane (where the outflow is observed) both ori-entations coincide, hinting that the poloidal-type of magnetic fieldis near a force- free configuration. Near the FIR edges orientationsdiffer suggesting a non-potential configuration of the field. Greycontours in the background correspond to M82’s FIR intensity val-ues from HAWC+. east and north-west regions of the outflow with an extensionup to ∼ pc from the core. Shopbell & Bland-Hawthorn(1998) found a bow-shock arc at ∼ pc in the south-eastregion of the outflow using [OIII] and H α emission lines.We find that the morphology of the ‘non-potential’ field issimilar to the morphology of the CO(2-1) velocity disper-sion. The increase of velocity dispersion corresponds to ahigher ‘non-potential’ magnetic energy. The south-east re-gion has a higher contribution to the magnetic energy than thenorth-west region. From our LOS, the north-west is viewedthrough the galactic disk, so this region of the outflow maybe highly extinguished. The bow-shock-like structure maybe the wave front of the galactic outflow expanding throughthe intergalactic medium. This result represents the first di-rect detection of the turbulent magnetic energy generated bya bow-shock in the galactic outflow of M82.We conclude that the observed turbulent magnetic field en-ergy within the starburst region is composed of two magneticfield components. A potential, large-scale ordered (turbu-lent or random) magnetic field from the galactic outflow, anda small-scale turbulent magnetic field (i.e. ‘non-potential’field) from a bow-shock-like region. The large-scale ordered(turbulent or random) B-field is thought to be generated bythe galactic wind at scales equal to or larger than the turbu-lent coherent length ( δ = 73 . ± . pc). The small-scaleturbulent B-field is thought to be generated by the turbulentor random fields in the the bow-shock-like structure at scalessmaller than δ .The observed turbulent magnetic energy has potential andnon-potential components, U B = U B PF + U B NPF . Fig. 8-D shows the radial profiles of U K + U H , U BP F , and U B NPF .Note that the non-potential magnetic energy (yellow) dropsprecipitously at a radius of pc. The magnetic fields asso-ciated to these energies are shown in Fig. 8-E. We estimatethat the non-potential and potential magnetic energies con-tribute ± % and ± % to the observed turbulent mag-netic energy, respectively. Using these relative contributions,we estimate a median magnetic field strength of ± µ G and ± µ G for the potential field and non-potentialmagnetic field strength components, respectively.Radio polarimetric observations using VLA and WSRT es-timated a turbulent magnetic field strength in the range of − µ G in the central × . kpc of M82 (Adebahret al. 2017). To explain such a high magnetic field strengthat radio wavelengths, Adebahr et al. (2013, 2017) suggestedthat there may be a superposition of at least two differentphases of the magnetized medium at the core of M82 – Astrong mG field arising from the compact star-forming re-gions, and a weak diffuse µ G component surrounding it.Lacki & Beck (2013) estimated a B-field strength of − µ G using a revised equipartition due to strong energylosses in the dense cores of starburst galaxies. This revisionwas suggested by Thompson et al. (2006), who estimateda maximum B-field strength of . mG for the starburst ofM82 from an equipartition analysis between the magneticenergy density and the hydrostatic ISM pressure. This sce-nario is similar to that measured in dense molecular cloudstowards the Galactic center, where Zeeman splitting obser-vations of OH masers indicate strong magnetic fields up tofew mG (e.g. Yusef-Zadeh et al. 1996), while radio polari-metric observations reveal lower values of − µ G (e.g.Crocker et al. 2010). Current FIR polarimetric observationsat µ m from HAWC+ of the Galactic center region using anapproach similar to the one presented here estimate magneticfield strengths of ∼ mG (Dowell et al., in preparation). Fromtheoretical developments of the evolution of particles in theoutflow of M82, Yoast-Hull et al. (2013) estimated a B-fieldstrength in the range of − µ G, while Paglione &Abrahams (2012) found a best-fit model with magnetic fieldstrengths of µ G. The difference resides in the mean gasdensities of − cm − for the former and − cm − for the latter. Our results show that the mG componentarises from the star forming region (potential field) and thesmall-scale anisotropic turbulent field from the bow-shock-like feature (non-potential field) within the central pc ofM82. Further models would require detail analysis of bothcomponents to explain the production of high energy parti-cles, formation of galactic winds, and generation of galacticshocks. 5.2. ‘Open’ vs. ‘Closed’ magnetic field lines We investigate whether the potential magnetic field linesof M82 are ‘open’ (i.e. galactic outflows) or ‘closed’ (i.e.galactic fountains). We have revised the definitions from so-lar physics (i.e. Levine et al. 1977; Fisk & Schwadron 2001)to apply to galactic winds. ‘Open’ magnetic field lines re-main attached to the central starburst and extend to large dis-2 L
OPEZ -R ODRIGUEZ ET AL . Figure 8.
The observed magnetic energy ( U B ; A) is composed of a potential ( U B PF ; B) and a no-potential ( U B NPF ; C) field components. Allenergy maps with contours and FOV as Fig. 4. The no-potential field magnetic energy, U B NPF = U B − U B PF , with overlaid CO (2 − velocity dispersion (white contours) is shown. The contours start at km s − and increases in steps of 5 km s − . (D) The radial profiles of U K + U H , U B NPF , and corrected potential field, U B PF , energies with their associated magnetic field strengths in (E). The median (lines) and1 σ uncertainties are shown. tances from the galactic plane. The turbulent kinetic energyof the outflowing wind exceeds the restoring turbulent mag-netic energy. Field lines reaching these distances are draggedradially outward by the outflowing wind. ‘Open’ field linesthus provide the missing link between the galaxies and in-tergalactic medium. ‘Closed’ field lines remain attached tothe central starburst and loop back to the plane of the galaxy.‘Closed’ field lines provide a feedback channel from the cen-tral starburst back to the host galaxy.We have shown that the turbulent kinetic and turbulentmagnetic energies are in close equipartition up to ∼ kpc(Fig. 4 and Section 3). It is important to note that the fieldlines may have a complex morphology within the starburstregion at higher angular resolution that those from our obser-vations. The averaged orientation of the turbulent magneticfield appears as ordered and fairly parallel to the outflowlines, but there may be many reversals or loops at smallerscales. From observational results, however, the field linesappear to remain ‘open’ up to ∼ kpc. The outflow of M82 extends at least ∼ kpc from thegalactic plane (i.e. Devine & Bally 1999), at which distancesome potential field lines may turn over and reconnect withthe galactic plane. A magnetic field line will only serve asa channel for feedback if its strength is large enough to con-fine the ionized material to move along it. We find a strik-ing similarity between the orientation of the observed B-fieldand potential field extrapolation, and the gas streams in MHDsimulations using TNG50 (see fig. 12 by Nelson et al. 2019)or galactic outflows driven by supernovae. This result im-plies that the potential magnetic field is frozen in where thefield lines are aligned with the outflowing wind. So do themagnetic field lines remain ‘open’ at ∼ kpc or do theyturn over at a height above ∼ kpc?We can answer this question by comparing the kinetic andmagnetic energies at such distances. To estimate the tur-bulent kinetic energy at distances of several kpc, the mea-surements of the dispersion velocity and mass density are re-quired. HI observations of the M81 triplet covering an areaof ◦ × ◦ at a resolution of (cid:48)(cid:48) ( pc) provides a velocity HE STRENGTH AND MORPHOLOGY OF THE MAGNETIC FIELD IN THE GALACTIC OUTFLOW OF
M82 13
Figure 9.
Composite image of M82 displaying the potential magnetic field lines. The starburst activity is seen in white light and the high-speedgalactic outflow (red) in H α emission, both by the HST . In dark yellow, dust observed with
Spitzer . Potential field lines, in white, are seenvanished at r ≈ dispersion of ± km s − at . kpc from M82 (de Bloket al. 2018). Martini et al. (2018) estimated that dusty cloudsin the outflow are embedded in an ambient medium. Thecloud particle density is n cH = 10 cm − ( ρ = 1 . × − g cm − ), while the ambient particle density is n aH = 0 . cm − ( ρ = 7 . × − g cm − ). Using Eq. 17, we esti-mate turbulent kinetic energies of U cK = 3 . × − g s − cm − and U aK = 1 . × − g s − cm − for the cloudsand ambient medium, respectively. Using the results of the potential field extrapolation, weestimate a magnetic field strength at radius ≥ . kpc of B P F ≤ µ G, yielding U B PF ≤ . × − g s − cm − .Magnetic field strengths up to µ G at scales of ∼ kpcin M82 has been measured using radio polarimetric obser-vations and justified in terms of magnetized galactic winds(i.e. Kronberg et al. 1999). Basu & Roy (2013) used ra-dio polarimetric observations to estimate B-field strengths of ∼ µ G at a distance of ∼ kpc in several nearby nor-mal spiral galaxies assuming equipartition of energy between4 L OPEZ -R ODRIGUEZ ET AL .cosmic ray particles and magnetic fields. We estimate that U B PF ∼ U aK < U cK in the outflow at scales up to . kpc.We find that the dusty clouds are dominated by the kineticenergy in the outflowing wind, while the ambient mediumis in close equipartition with the magnetic energy. Since theturbulent kinetic energy dominate the dusty medium, we con-clude that the field lines are ‘open’ at distances up to . kpcfrom the plane of M82, channeling magnetic energy and mat-ter into the intergalactic medium.Magnetic field strengths in the range of − µ G havebeen measured in clusters on scales of − kpc throughFaraday rotation measurements (i.e. Dreher et al. 1987; Kimet al. 1990; Taylor & Perley 1993; Clarke et al. 2001). Thesemagnetic fields may be primordial, seeded in the intergalacticmedium from shock waves or linked with the formation andevolution of galaxies (Subramanian 2019, i.e.). Using semi-analytic simulations of magnetized galactic winds, (Bertoneet al. 2006; Samui et al. 2018) suggested that galactic out-flows may be able to seed a fraction of the magnetic field inthe intracluster medium. CONCLUSIONSWe used the HAWC+ polarimetric data as well as meanvalues of the mass density, ρ , and the velocity dispersion, σ v, CO(2 − , from the literature to estimate the averageplane-of-the-sky magnetic field strength in the starburst re-gion of M82 to be B = 1 . ± . mG.We described a novel approach to quantify the turbulentmagnetic field when large-scale flows are present (Section2.3). We modified the DCF method to account for galacticsuperwind by adding a steady-flow term to the wave equa-tion, which reverts to the traditional approach when large-scale flows are negligible. After we accounted for the large-scale flow, the average magnetic field within the starburst re-gion is reduced to B = 0 . ± . mG.We defined the turbulent plasma beta, β (cid:48) , as the ratio ofhydrostatic-plus-turbulent-kinetic pressure to magnetic pres-sure and, using mean values within the starburst mask fromSection 2, estimate β (cid:48) = 0 . ± . . We can then use thepixel-by-pixel values of the density and velocity dispersionto construct, for the first time, a two-dimensional map of theturbulent magnetic field strength within the central . × . kpc region of M82 (Figure 4-D).We modified the solar potential field method to work withgalactic outflows using HAWC+ polarization data. We ex-trapolated the magnetic field from the core using the Laplaceequation, ∇ Φ = 0 , and investigate the potential magneticstructures along the galactic outflow of M82. The two-dimensional Cartesian set up places the center of M82 at ( x, z ) = (0 , and the galactic plane along the x-axis. Thefirst boundary condition involves the B-field values deter-mined from the map at B ( x, and the second assumes that B ( x, ∞ ) = 0 . The resulting potential magnetic field struc-ture is shown in Figure 6.These results indicate that the observed turbulent magneticfield energy within the starburst region is composed of twocomponents: a potential field arising from the galactic out-flow and a small-scale turbulent field arising from a bow-shock-like region. This result represents the first detection ofthe magnetic energy from a bow shock in the galactic outflowof M82.The results of the potential field extrapolation allow us todetermine, for the first time, if the field lines are ‘open’ (i.e.galactic outflow) or ‘closed’ (i.e. galactic fountain). We showthat the turbulent kinetic and turbulent magnetic energies arein close equipartition up to ∼ kpc (measured), while theturbulent kinetic energy dominates at ∼ kpc (extrapolated).We conclude that the magnetic field lines associated with thegalactic superwind of M82 are ‘open’, channeling matter intothe galactic halo and beyond. These observations indicatethat the powerful winds associated with the starburst phe-nomenon could be responsible for injecting material enrichedwith elements like carbon and oxygen into the intergalacticmedium.We demonstrated that FIR polarization observations are apowerful tool to study the B-field morphology in the coldISM of galactic outflows. Ongoing efforts like the SOFIALegacy Program (PIs: Lopez-Rodriguez & Mao) focused onstudying extragalactic magnetism will provide deeper obser-vations at µ m to analyze the large-scale magnetic field inthe disk of M82 as well as other nearby galaxies. The resultspresented here can also be used to investigate the high en-ergy particles production from starburst galaxies. This workserves as a strong reminder of the potential importance ofmagnetic fields, often completely overlooked, in the forma-tion and evolution of galaxies.Based on observations made with the NASA/DLR Strato-spheric Observatory for Infrared Astronomy (SOFIA).SOFIA is jointly operated by the Universities Space Re-search Association, Inc. (USRA), under NASA contractNAS2-97001, and the Deutsches SOFIA Institut (DSI) underDLR contract 50 OK 0901 to the University of Stuttgart. Facilities:
SOFIA (HAWC+),
Herschel (PACS, SPIRE),
HST (WFPC2, ACS)
Software:
ASTROPY (Astropy Collaboration et al. 2013,2018), APL PY (Robitaille & Bressert 2012), MATPLOTLIB (Hunter 2007), P
YTHON (Van Rossum & Drake 2009),N
UMPY (Harris et al. 2020),
PANDAS (pandas developmentteam 2020).REFERENCES
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HE STRENGTH AND MORPHOLOGY OF THE MAGNETIC FIELD IN THE GALACTIC OUTFLOW OF