The Odd Offset between the Galactic Disk and Its Bar in NGC 3906
Bonita de Swardt, Kartik Sheth, Taehyun Kim, Stephen Pardy, Elena D'Onghia, Eric Wilcots, Joannah Hinz, Juan-Carlos Munoz-Mateos, Michael W. Regan, E. Athanassoula, Albert Bosma, Ronald J. Buta, Mauricio Cisternas, S ebastien Comeron, Dimitri A. Gadotti, Armando Gil de Paz, Thomas H. Jarrett, Bruce G. Elmegreen, Santiago Erroz-Ferrer, Luis C. Ho, Johan H. Knapen, Jarkko Laine, Eija Laurikainen, Barry F. Madore, Sharon Meidt, Karin Menendez-Delmestre, Chien Y. Peng, Heikki Salo, Eva Schinnerer, Dennis Zaritsky
tto be submitted to ApJ
The Odd Offset between the Galactic Disk and Its Bar in NGC 3906
Bonita de Swardt , , Kartik Sheth , Taehyun Kim , Stephen Pardy , Elena D’ Onghia , , EricWilcots , Joannah Hinz , Juan-Carlos Mu˜noz-Mateos , , Michael W. Regan E. Athanassoula ,Albert Bosma , Ronald J. Buta , Mauricio Cisternas , , S´ebastien Comer´on , , Dimitri A.Gadotti , Armando Gil de Paz , Thomas H. Jarrett , Bruce G. Elmegreen , SantiagoErroz-Ferrer , , Luis C. Ho , , Johan H. Knapen , , Jarkko Laine , , Eija Laurikainen , ,Barry F. Madore , Sharon Meidt Kar´ın Men´endez-Delmestre Chien Y. Peng , Heikki Salo ,Eva Schinnerer Dennis Zaritsky , a r X i v : . [ a s t r o - ph . GA ] J un ABSTRACT
We use mid-infrared 3.6 and 4.5 µ m imaging of NGC 3906 from the Spitzer
Surveyof Stellar Structure in Galaxies (S G) to understand the nature of an unusual offsetbetween its stellar bar and the photometric center of an otherwise regular, circular outerstellar disk. We measure an offset of ∼
720 pc between the center of the stellar barand photometric center of the stellar disk; the bar center coincides with the kinematiccenter of the disk determined from previous HI observations. Although the undisturbedshape of the disk suggests that NGC 3906 has not undergone a significant mergerevent in its recent history, the most plausible explanation for the observed offset is an South African Astronomical Observatory, Observatory, 7935 Cape Town, South Africa SKA South Africa, 3rd Floor, The Park, Park Road, Pinelands, South Africa National Radio Astronomy Observatory / NAASC, 520 Edgemont Road, Charlottesville, VA 22903, USA Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI, 53706, USA Alfred P. Sloan Fellow MMTO, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA European Southern Observatory, Casilla 19001, Santiago 19, Chile Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA Aix Marseille Universit´e, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille,France Department of Physics and Astronomy, University of Alabama, Box 870324, Tuscaloosa, AL 35487, USA Instituto de Astrof´ısica de Canarias, E-38200 La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna, E-38205 La Laguna, Tenerife, Spain Division of Astronomy, Department of Physical Sciences, University of Oulu, Oulu, FIN-90014, Finland Finnish Centre of Astronomy with ESO (FINCA), University of Turku, V¨ais¨al¨antie 20, FI-21500, Piikki¨o, Finland Departamento de Astrof´ısica, Universidad Complutense de Madrid, Madrid 28040, Spain Astronomy Department, University of Cape Town, Rondebosch 7701, South Africa IBM Research Division, T.J. Watson Research Center, Yorktown Hts., NY 10598, USA The Observatories of the Carnegie Institution of Washington, 813 Santa Barbara Street, Pasadena, CA 91101,USA Kavli Institute for Astronomy and Astrophysics, Peking University 5 Yi He Yuan Road, Haidian District, Beijing100871, P. R. China Max-Planck-Institut f¨ur Astronomie/K¨onigstuhl 17 D-69117 Heidelberg, Germany Universidade Federal do Rio de Janeiro, Observat´orio do Valongo, Ladeira Pedro Antˆonio, 43, CEP 20080-090,Rio de Janeiro, Brazil University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA
Subject headings: galaxies: evolution — galaxies: formation — galaxies: structure
1. Introduction
The long unsolved problem of asymmetries in Magellanic type spirals has come under increasedscrutiny due to recent kinematic studies of the Large and Small Magellanic Clouds (LMC and SMC).These studies also showed that an interaction with the SMC passing close to the center of the LMCis the most probable cause of the off centered stellar bar (Besla et al. 2012). Off-center or ”offsetbars” are a characteristic feature in late-type spiral galaxies and in particular Magellanic types (deVaucouleurs & Freeman 1972; Odewahn 1996; Elmegreen & Elmegreen 1980) – the usual definitionof an offset bar is a stellar bar whose photometric center is offset from the photometric center ofthe outer isophotes of a galaxy disk.Off-centered stellar bars coupled with remnant spiral structure could contribute to asymmetriesin a stellar disk – asymmetrical stellar disks are often referred to as “lopsided” disks. However,a recent study of lopsidedness in 167 galaxies by Zaritsky et al. (2013) from the
Spitzer
Surveyof Stellar Structure in Galaxies (S G) (Sheth et al. 2010), found that lopsidedness is a genericfeature of disks. While the lopsidedness is correlated with the strength of the spiral pattern it is not correlated with the presence of a stellar bar. Zaritsky et al. (2013) specifically note that astellar bar is neither the cause of lopsidedness nor is the lopsidedness giving rise to the formationof a stellar bar.Numerical simulations of barred galaxies have shown that a bar may become off-centeredthrough from its disk via an interaction of a small companion (Athanassoula 1996; Athanassoula,Puerari & Bosma 1997; Berentzen et al. 2010). Bekki (2009) investigated possible evolutionaryscenarios that show that an off-center bar with some degree of spiral structure can form in theLMC if a galaxy collides with a low-mass Galactic subhalo corresponding to only a few per centof the total mass of the LMC. These subhaloes were referred to as ‘dark satellites’ since they mayhave no or little visible matter. Bekki (2009) claimed that dark satellites with masses in the rangeof 10 − M (cid:12) can strongly disturb the disk of low mass galaxies such as the LMC.However there are many isolated Magellanic galaxies. In a VLA study, Wilcots & Prescott(2004) found only two of thirteen Magellanics were clearly interacting with their neighbor. Theyargued that in most cases the asymmetry in barred Magellanic spirals cannot be explained by 4 –on-going interactions with a companion galaxy or by environment. This earlier result was put onsolid ground with the larger S G study by Zaritsky et al. (2013). So the offset bars, which are acommon feature of Magellanics, may be a long lived feature that is caused by some other process.de Vaucouleurs & Freeman (1970) suggested that the asymmetry in a disk may suggest that it is a”protogalaxy” that might be forming a bar as well.NGC 3906 is an ideal case to study these odd properties of a disk and an offset bar in detail.Classified as a Magellanic type face-on spiral, NGC 3906 hosts a displaced stellar bar from whatappears to be an otherwise undisturbed circular stellar disk, showing no signature of any tidalinteraction at ultra-violet and optical wavelengths. A search with NASA’s Extragalactic Databasereveals that the closest companions to NGC 3906 are located 14-16 (cid:48) ( 50kpc) away. Watson et al.(2010) mapped the distribution of neutral hydrogen gas in NGC 3906 and found a very circular HIdisk similar to that seen at the other wavelengths. There was no evidence of tidal tails or streamswhich suggests that the off-centered bar in NGC 3906 is likely not from any on-going interactionof the galaxy with any nearby galaxies.In this paper, we investigate the origin of the off-centered bar in NGC 3906 using 3.6 and 4 . µ mimaging from the Spitzer
Survey of Stellar Structure in Galaxies (S G)(Sheth et al. 2010). Theseobservations allow us to peer through the layers of dust so that we are looking at the dominantolder stellar population in the galaxy. The observations and basic properties of the galaxy aredescribed in §
2. More clues to the structure of NGC 3906 are obtained from the photometry of the
Spitzer . µ m images. These results are presented in §
2. Observations and Archival Data
The
Spitzer
Survey of Stellar Structure in Galaxies (S G) is a volume-, magnitude-, and size-limited (d <
40 Mpc, | b | > ◦ , m Bcorr < . D > (cid:48) ) imaging survey of over 2300 galaxiesusing the Infrared Array Camera (IRAC) at 3.6 and 4.5 µ m. The basic properties of the galaxy arelisted in Table 1. The apparent optical diameter of NGC 3906 is D ∼ . (cid:48) and with the 5 (cid:48) fieldof view of Spitzer , the galaxy is mapped well beyond a radial extent of 1 . × D within a singlepointing. The S G survey and data analysis are described in detail in Sheth et al. (2010).The 3.6 µ m S G image of NGC 3906 is shown in Fig. 1, alongside images from near-ultravioletto radio wavelengths (GALEX, HST-ACS (F606W), VLA-HI). The HST image was retrieved fromthe Multimission Archive at STScI under the program ID 10829 (PI: Martini, P.). An undisturbed,circular stellar disk is evident at all wavelengths while the spiral features in the galaxy can most http://archive.stsci.edu/index.html . DEC (J2000) +48:25:33.0 Morphological Type SB(r’l)dm Distance 13.5 (Mpc) m B (mag) 13.5 M B (mag) -17.8 D (arcsec) 112 Inclination (deg) 3 ± PA (deg) 13.5 v sys (km s − ) 959 . ± . M H I ( × M (cid:12) ) 3.76 Physical Scale 1 (cid:48)(cid:48) = 65 pc
Note. — References: de Vaucouleurs et al. (1991); Buta et al. (2010); Distance (in Mpc) calculated from the measured recession velocity from de Vaucouleurs et al. (1991) and correctedfor Virgo-centric infall assuming H = 71 km s − Mpc − ; Apparent B -band magnitude corrected for Galactic and internal extinction from de Vaucouleurs et al. (1991); Absolute B -band magnitude using the apparent magnitude and distance above Systemic velocity and H I mass measured by Watson et al. (2010). clearly be distinguished in the F606W HST image. The galaxy is face-on with an inclination of < G data.Narrow-band H α and Johnson R -band imaging was obtained by James et al. (2004) using the1.0m Jacobus Kapteyn Telescope (JKT) at La Palma. The H α contours are over-plotted on the R -band image of the galaxy in Fig. 2. These contours together with the near-ultraviolet imagefrom GALEX indicate that massive star formation occurs at the bar ends, a result commonly seenin Magellanic type (e.g. 30 Dor in the LMC) and strongly-barred galaxies (e.g., Sheth et al. 2000,2002; James et al. 2004). Smaller knots of star formation are also observed in the galaxy disk whichappear to be associated with the dominant spiral arm. James et al. (2004) have determined a starformation rate of 0 . (cid:12) yr − using the H α imaging of NGC 3906 shown in Fig. 2 and assuminga Kennicutt et al. (1994) star formation rate calibration for disk galaxies. The low star formationrate detected in NGC 3906 is typical of Magellanic spirals, which are believed to be on the vergeof exhausting their reservoirs of cold gas. The contours of neutral hydrogen H I gas are overplottedon the 3.6 µ m image of NGC 3906 in Fig. 1. The gaseous disk appears circular and unperturbed,however there is a small extension to the east of the disk which may indicate that NGC 3906 isexperiencing an interaction. 6 –Fig. 1.— Imaging of NGC 3906 at different wavelenths: near-ultraviolet imaging with GALEX ( topleft ); at 6060˚A with HST /ACS using the F606W filter ( top right ); 3.6 µ m S G image with IRAConboard
Spitzer ( bottom left ); and H I contours are overlayed on the 3.6 µ m image ( bottom right ). Ascale of 1 arcmin (correspnding to a physical scale of 65 pc) is indicated on the left of each image.North is up and East is left. 7 –
3. Photometric Characterization from Mid-infrared Imaging3.1. Structure of NGC 3906
We carried out a detailed photometric analysis of NGC 3906 using both the 3.6 and 4.5 µ mS G images to characterize the underlying structure of the galaxy (see details of the method inSheth et al. 2010; Munoz-Mateos et al. 2015) . The radial profiles of surface brightness, ellipticityand position angle were determined in both bands using the IRAF task ELLIPSE and are shownin Fig. 3. The galaxy center, ellipticity ( (cid:15) ) and position angle were allowed to vary when derivingthe radial profiles. The elliptical isophotes corresponding to each fit with radius are illustrated inFig. 4. Here it can be seen that the inner isophotes are more elliptical and map the structure ofthe bar, whereas the outer isophotes trace the circular geometry of the stellar disk.The radial profiles shown in Fig. 3 were constructed using a 2 arcsec interval between the suc-cessive elliptical fits. The high spatial sampling of these profiles allows us to accurately measure thegeometry of the outer stellar disk down to the detection limit of µ . µm ( AB )(1 σ )= 27 mag arcsec − . The surface brightness profile shows that NGC 3906 hosts an exponential disk whereas a more dom-inant contribution to the light profile from the stellar bar is seen at smaller radii of r ≤
20 arcsec.The circular geometry of the stellar disk is evident for radii r (cid:38)
40 arcsec where the outer isophotesare seen to be nearly circular ( (cid:15) (cid:39) µ . µm = 25 . − in surface brightness (at a radius of r = 54 (cid:48)(cid:48) ) as thecenter of the stellar disk (see Table 2).The influence of the stellar bar on the luminosity profile of the galaxy is seen as an increase inthe ellipticity for radii r <
40 arcsec. The geometrical parameters of the bar were determined fromthe elliptical fits in the radial range of r = 7 to r = 21 arcsec. Small variations in the ellipticity(∆ (cid:15) (cid:46) .
06) are observed in this radial range so that the structure of bar itself is revealed. Thegeometrical parameters of the bar as measured in this radial range are given in Table 2. Theserepresent the mean values in the ellipticity, position angle and central coordinates. The outer radiusdefines the length of the bar which is 21 (cid:48)(cid:48) (or ∼ . µ m image of NGC 3906 in Fig. 5. These positionshave a maximum error of 1.2 (cid:48)(cid:48) which accounts for the error in fitting the elliptical isophotes. Thedisplacement of the center of the bar relative to the center of the stellar disk is about ∼
11 arcsec.The location of the dynamical center from H I observations (Watson et al. 2010) as well as theerror associated with this center are shown with a open circle and a dashed error circle respectively IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association ofUniversities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation. α contours are over-plotted on the R -band image of NGC 3906 to indicate where massivestar formation occurs in the galaxy.in Fig. 5. The dynamical center overlaps with the photometric center of the bar within the errorsof the fit to the HI data (∆ r = 7 (cid:48)(cid:48) ). These initial results suggest that the HI gas and underlyingstellar component are rotating about a common point which lies close to the photometric center ofthe bar.The H I dynamical center has an angular separation of ∼ (cid:48)(cid:48) (or ∼
720 pc) from the photo-metric center of the stellar disk. This result is in contrast to what is observed for the LMC wherethe H I dynamical center is offset by ∼ I distribution isfound to be highly disturbed in the gaseous disk of the galaxy due to its on-going tidal interactionwith the Milky Way (Kim et al. 1998; Staveley-Smith et al. 2003). NGC 3906 does not, on theother hand, show a highly disturbed gaseous disk so that the H I dynamical center likely correspondswith the dynamical center of the stellar disk. Salo et al. (2014) have found NGC 3906 to host avery strong bar (bar strength parameter Q b = 0 .
74 following the method described in Salo et al.(2010) with the force maximum located within the bar region. This provides further evidence thatthe dynamical center of the stellar disk is found within the bar such that the gaseous and stellardisks have a common center in the bar. It is therefore very likely that we are observing an offset inthe galaxy disk rather than an offset bar in NGC 3906. More clues to the structure of the galaxywill be revealed in the next section when carrying out a two-dimensional decomposition of the S Gimages. 9 –
20 22 24 26 28 30 µ λ ( AB m ag / a r cs e c ) NGC39063.6 µ m4.5 µ m + 1 0 0.2 0.4 0.6 0.8 1 E lli p t i c i t y E lli p t i c i t y µ m4.5 µ m + 0.1-75-50-25 0 25 50 75 100 125 0 10 20 30 40 50 60 70 80 PA ( deg ) sma (arcsec)-75-50-25 0 25 50 75 100 125 0 10 20 30 40 50 60 70 80 PA ( deg ) sma (arcsec)3.6 µ m4.5 µ m + 10 -12-10-8-6-4-2 0 ∆ R A ( a r cs e c ) µ m4.5 µ m-12-10-8-6-4-2 0 2 0 10 20 30 40 50 60 70 80 ∆ D E C ( a r cs e c ) sma (arcsec)3.6 µ m4.5 µ m Fig. 3.— Radial profiles for NGC 3906 obtained from the surface photometry of the 3 . . µ mS G images. An offset has been applied to the 4 . µ m profile for the sake of clarity. Top Left : Surfacebrightness profiles from the 3 . µ m (black filled circles) and 4 . µ m-bands (grey filled circles). MiddleLeft : Variation of the ellipticity of the best-fitting isophote with the radius.
Bottom Left : PositionAngle (PA) of the best-fitting isophote as a function of radius.
Right : Change in the centroid ofthe best fit rllipse in right ascension and declination.
A multiple component fitting algorithm was implemented in Python which uses GALFIT (Peng et al. 2002) in modeling the light distribution of the galaxy. The algorithm, called “Multi-GALFIT” ( private communication , C.Y. Peng), allows for up to six components to be fitted withoutmaking any assumptions of the number of components needed to model the galaxy. An initial guessfor the center of the galaxy is the only parameter required to begin the fitting process. The multi-ple component fit was carried out on the binned 3.6 µ m image of NGC 3906. Figure 6 shows thatNGC 3906 is best modeled (goodness of fit χ ν = 0 . r eff = 5 . (cid:48)(cid:48) , n = 0 .
41) models the bar in the galaxy, while the stellarcomponent surrounding the bar, an inner disk, was suitably modeled with a S´ersic law having aneffective radius of r eff = 7 . (cid:48)(cid:48) and structural index of n = 0 .
23. The low sersic indices are typical for http://users.obs.carnegiescience.edu/peng/work/galfit/galfit.html
10 –Fig. 4.— The elliptical fits at each radius are displayed on the 3.6 µ m image of NGC 3906. Thebar isophotes are indicated in purple. The darker ellipse indicates the µ . µm = 25 . − isophote which was used to determine the photometric center of the galaxy disk.Table 2: Geometrical parameters of the stellar disk and bar from surface photometry.Photometric CentersRA DEC Error(J2000) (arcsec)Disk 11 49 39.9 +48 25 25.2 0.06Bar 11 49 40.6 +48 25 33.5 0.75HI center 11 49 40.4 48 25 36 7late type galaxies as these disks are not centrally concentrated (e.g. Macarthur et al. 2003) Thefaint outer disk is displaced from both these components as can be clearly seen in Fig. 6.The extended stellar disk of the galaxy is best modeled using a S´ersic function with an effectiveradius of r eff = 14 . (cid:48)(cid:48) and index n = 0 .
23. Perturbations were introduced in to the model in theform of the azimuthal m = 1 Fourier mode to obtain a measure of the asymmetry of the stellar disk.In face-on systems (inclinations of i (cid:46)
25 deg) such as NGC 3906, the amplitude of the Fourier m = 1 mode ( A ) is an excellent indicator of lopsidedness of the disk (Rix & Zaritsky 1995). Theprojection effects are minimized in these low inclination galaxies so that the apparent structure ofthe disk is revealed. The 3.6 µ m image of NGC 3906 allows for the measurement of the Fourier A amplitude in the extended stellar disk out to at least three times the effective radius of thedisk. An amplitude of A = 0 . ± .
01 was measured for the disk component using MultiGALFIT, 11 –consistent with the Zaritsky et al. (2013) measurement in the outer disk as shown in their Figure 6.Bournaud et al. (2005) measured a mean Fourier m = 1 amplitude of 0.1 for a sample of 149 spiralgalaxies in the near-infrared with values above this threshold indicating lopsidedness. Zaritsky etal. (2013) have done the same for 167 face-on galaxies from S Gas noted earlier. Compared toother disks, NGC 3906 shows a modest amount of lopsidedness in its outer disk but as Zaritsky etal. (2013) note the lopsidedness is typically uncorrelated with the presence of the bar.By making a cut perpendicular to the bar and through the photometric center of the galaxy(given in Table 2) the symmetry of the disk could be further investigated. The opposite sides of theone-dimensional cut about the photometric center are plotted in Fig. 7 where the strongest peakin the intensity distribution corresponds to the bar itself on the northern side of the galaxy. Theintensity peak at a radius of r ∼ (cid:48)(cid:48) coincides with the spiral arm feature in the northern part ofthe stellar disk.The technique of unsharp masking (Malin 1977) was applied to the 3 . µ m S G image to revealunderlying structure in the stellar disk. The features are detected by dividing the original galaxyimage by a smoothed image of the galaxy. The unsharp mask for NGC 3906 was produced bysmoothing the 3 . µ m galaxy image with an elliptical Gaussian of kernel size σ kernel = 15 pixels.Figure 8 shows the residual image of NGC 3906 after carrying out the unsharp masking. The stellarbar and inner disk can be clearly seen in the residual image. A single bright dominant spiral armis seen to originate from the east side of the bar and winds in a clockwise direction in the disk.Fainter arms can be seen extending from the bar edges from both the east and west regions of thebar. The fainter arms eventually merge with the dominant spiral form. The asymmetric spiralstructure is seen as the unsharp mask makes prominent the single, bright spiral arm (as opposed tosymmetric grand design spiral arms). This is characteristic in late-type spirals and Magellanic-typegalaxies (de Vaucouleurs & Freeman 1970). However it is unclear what phenomenon gives rise tothese types of spiral features typical in late-type Magellanic systems. The mass of the individual stellar components were calculated from the total fluxes measuredfrom MultiGALFIT. The luminosity of each stellar component was determined using the zeroTable 3: Derived parameters for stellar component fits using multiGALFIT.S´ersic ParametersStellar r eff M . µ m Component (arcsec) n ( M (cid:12) )Bar 5.9 0.41 2 . ± . × Inner disk 7.7 0.23 5 . ± . × Outer disk 14.4 0.23 1 . ± . ×
12 –point flux of 280.9 Jy for IRAC channel 1 (Reach et al. 2005) and an absolute magnitude of M . µ m (cid:12) = 3 .
24 mag for the Sun in the IRAC 3 . µ m-band (Oh et al. 2008). Both the LMC andNGC 3906 are late-type disk galaxies having similar morphology and stellar populations. The mass-to-light ( M/L . ) ratio obtained for the LMC was therefore adopted when transforming luminosityin to mass in NGC 3906. The M/L . of 0.5 for the LMC from Eskew et al. (2012) was used toderive the mass for the stellar components listed in Table 3. These results show that NGC 3906has a massive disk in which the bar and inner disk contribute to less than 50% to the mass of theextended stellar disk. Adding the mass estimates of the three stellar components and the H I massin Table 1 gives a total baryonic mass of ∼ × M (cid:12) for NGC 3906 which is comparable to themass estimates obtained for the LMC and other barred Magellanic spirals in Wilcots & Prescott(2004).
4. Discussion
Tidal interactions remain as the most likely explanation for the offset between the kinematicand photometric centers of NGC 3906. New numerical simulations from our team are finding thatan interaction with a body at least 1/10th the mass of the main galaxy is needed to create theobserved offset (Pardy et al. 2015, in preparation), consistent with previous studies (Athanassoula1996; Athanassoula, Puerari & Bosma 1997; Berentzen et al. 2010). However the main problemfor NGC 3906 is that observations in a wide range of wavelengths rule out a nearby companions.This is also the case for many other Magellanics with offset bars (Wilcots & Prescott 2004). Aninteraction with a dark companion such as a dark matter sub-halos could explain the offset assuggested by Bekki (2009) but the constraints on the type of collision required may be that thecompanion galaxy has to pass close to the center of the main galaxy (e.g. (Besla et al. 2012)).We are currently studying the precise range of interaction / merger parameters that can lead to anoffset bar to constrain the nature of the dark matter substructure. We are also investigating howlong the observed offset can last in different types of collisions to better constrain the evolution ofthis system.NGC 3906 is also a lopsided disk with the strongest asymmetry in the inner parts evidentlyfrom the offset between the bar and the disk. (Zaritsky et al. 2013) have already shown that thegeneral class of asymmetries (m=1 Fourier modes) is too common to exist from purely interactionevents. The asymmetry must also be long lived since it is commonly observed. Noordemeer etal (2001) and Levine & Sparke (1998) have argued that long-lived lopsidedness may occur if thestellar disk is off-center from a galaxy’s dark matter halo. However, they do not provide any reasonor mechanism which would cause the disk to be displaced in the first place. Secular and internalprocesses such as gas accretion can also lead to lopsidedness in the disk (Bournaud et al. 2005). 13 –
5. Conclusions
Images from S G of NGC 3906 reveal a strikingly odd offset between the stellar bar and theunderlying stellar disk. Analysis of the S G data and VLA HI data reveal that, unlike the LMC,the HI kinematic center is coincident with the bar, but is offset from the photometric center ofthe stellar disk by ∼
720 pc. Investigation of the bar structure using ellipse fits and a full 2-Ddecomposition using MultiGALFIT using a bar, inner and outer disk components reveals a strong1.4 kpc bar (Q b = 0.74) containing ∼
10% of the total baryonic mass (M t ∼ × M (cid:12) ) of thegalaxy. Residual images of the galaxy also show the presence of asymmetric spiral structure. Giventhe lack of any nearby companions, a likely explanation for the offset may be an interaction with adark matter sub halo. We are carrying out new simulations to create the observed offsets and findthat a companion with at least 1/10th the mass of the disk is needed. We are currently studyingthe lifetime of the offset to better constrain the likely evolution of this system. Other observationshave shown that many Magellanic systems with offset bars are also similarly isolated and thereforemay offer a unique probes for the structure of the dark matter halo if collisions with dark mattersub halos are responsible for offset bars.
6. Acknowledgements
We thank the anonymous referee for comments and feedback that greatly improved this pa-per. K. Sheth, J.C. Munoz-Mateos, T. Kim and B. de Swardt gratefully acknowledge support fromthe National Radio Astronomy Observatory which is a facility of the National Science Foundationoperated under cooperative agreement by Associated Universities, Inc. BdS would also like to ac-knowledge the South African National Research Foundation (NRF) for financial support providedfor the research presented in this paper. ED gratefully acknowledges the support of the Alfred P.Sloan Foundation and the Aspen Center for Physics for their hospitality and support under grantNo. PHYS-1066293. ED and SP acknowledge support provided by the University of Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate Education with funding fromthe Wisconsin Alumni Research Foundation and NSF Grant No. AST-1211258 and ATP-NASAGrant No. NNX14AP53G. EA, AB, AGdP, JHK, EL, ES and HS acknowledge financial supportfrom the People Programme (Marie Curie Actions) of the European Unions Seventh FrameworkProgramme FP7/2007-2013/ under REA grant agreement number PITN-GA-2011-289313 to theDAGAL network. EA and AB also ackowledge financial support from the CNES (Centre Na-tional dEtudes Spatiales - France) and from the Programme National de Cosmologie et Galaxies(PNCG) of CNRS/INSU, France. JHK acknowledges financial support from the Spanish Ministryof Economy and Competitiveness (MINECO) under grant number AYA2013-41243-P. 14 –
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16 –Fig. 5.— The location of the photometric centers and dynamical center are overlaid on the 3 . µ mimage of NGC 3906. The center of the stellar disk (yellow cross) is defined as the center of the µ . µm = 25 . − isophote (black solid circle). The dynamical center (open circle) andcenter of the bar (plus symbol) are indicated in grey. The error associated with the dynamicalcenter is shown by the dashed circle. 17 –Fig. 6.— The three component fit to the light distribution of NGC 3906 using MultiGALFIT. Left : The original 3.6 µ m image of the galaxy; Middle : best S´ersic profile fits to model the bar, aninner disk and outer disk components. An azimuthal m = 1 Fourier mode has been added to thedisk component; Right : residuals from the three component fit of the galaxy. The residuals areprimarily from hot dust around star forming regions that remains a contaminant for 3.6 µ m images(see Meidt et al. 2011)Fig. 7.— A one-dimensional (1D) profile cut which runs perpendicular to the bar and throughthe photometric center of the galaxy. The radius r = 0 (cid:48)(cid:48) corresponds to the photometric center ofNGC 3906. The 1D profiles on either side of the photometric center (top one is the northern side)are shown to emphasize the dramatically different light distribution due to the offset bar. 18 –Fig. 8.— Fine structure in NGC 3906 using unsharp masking. The original 3.6 µµ