A tidally induced global corrugation pattern in an external disc galaxy similar to the Milky Way
Facundo A. Gómez, Sergio Torres-Flores, Catalina Mora-Urrejola, Antonela Monachesi, Simon D. M. White, Nicolas P. Maffione, Robert J. J. Grand, Federico Marinacci, Rüdiger Pakmor, Volker Springel, Carlos S. Frenk, Philippe Amram, Benoît Epinat, Claudia Mendes de Oliveira
DD RAFT VERSION N OVEMBER
26, 2020
Preprint typeset using L A TEX style emulateapj v. 08/22/09
A TIDALLY INDUCED GLOBAL CORRUGATION PATTERN IN AN EXTERNAL DISC GALAXY SIMILAR TO THEMILKY WAY F ACUNDO
A. G
ÓMEZ , S
ERGIO T ORRES -F LORES , C
ATALINA M ORA -U RREJOLA , A NTONELA M ONACHESI , S
IMON
D. M.W
HITE , N ICOLAS
P. M
AFFIONE , R
OBERT
J. J. G
RAND , F EDERICO M ARINACCI , R ÜDIGER P AKMOR , V OLKER S PRINGEL ,C ARLOS
S. F
RENK , P HILIPPE A MRAM , B ENOÎT E PINAT , AND C LAUDIA M ENDES DE O LIVEIRA Draft version November 26, 2020
ABSTRACTWe study the two dimensional (2D) line-of-sight velocity ( V los ) field of the low-inclination, late-type galaxyVV304a. The resulting 2D kinematic map reveals a global, coherent and extended perturbation that is likelyassociated with a recent interaction with the massive companion VV304b. We use multi-band imaging and asuite of test particle simulations to quantify the plausible strength of in-plane flows due to non-axisymmetricperturbations and show that the observed velocity flows are much too large to be driven either by spiral structurenor by a bar. We use fully cosmological hydrodynamical simulations to characterize the contribution from in-and off-plane velocity flows to the V los field of recently interacting galaxy pairs like the VV304 system. Weshow that, for recently perturbed low-inclination galactic discs, the structure of the residual velocity field, aftersubtraction of an axisymmetric rotation model, can be dominated by vertical flows. Our results indicate thatthe V los perturbations in VV304a are consistent with a corrugation pattern. Its V los map suggests the presenceof a structure similar to the Monoceros ring seen in the Milky Way. Our study highlights the possibility ofaddressing important questions regarding the nature and origin of vertical perturbations by measuring the line-of-sight velocities in low-inclination nearby galaxies. Subject headings: galaxies: stellar discs – methods: numerical – galaxies: stellar content INTRODUCTION
Over the last decade a significant number of observationalstudies have provided strong evidence of an oscillating verti-cal asymmetry in our own Galactic disc (e.g. Widrow et al.2012; Xu et al. 2015). Well-known features observed in theMilky Way, such as the Monoceros Ring (Newberg et al.2002; Yanny et al. 2003), the TriAnd clouds (Price-Whelanet al. 2015), and the recently discovered A13 overdensity(Sheffield et al. 2018), can be naturally accounted for by thisasymmetry, best described as a corrugation pattern (Laporteet al. 2018b). With the recent arrival of the
Gaia data release2 (Gaia Collaboration et al. 2018), we have had direct confir-mation that our own Galactic disc is undergoing phase mixingof a non-equilibrium perturbation (Antoja et al. 2018). Mostsuccessful models to describe the origin of this perturbationrely on the interaction between the Galaxy and the Sagittariusdwarf spheroidal galaxy, together with a recent boost fromthe Magellanic Clouds system (e.g. Gómez et al. 2012, 2013;Laporte et al. 2018a,b, 2019; Bland-Hawthorn et al. 2018).A corrugation pattern is manifested by an extended andoscillatory vertical displacement of the disc with respect to Instituto de Investigación Multidisciplinar en Ciencia y Tecnología, Uni-versidad de La Serena, Raúl Bitrán 1305, La Serena, Chile Departamento de Física y Astronomía, Universidad de La Serena, Av.Juan Cisternas 1200 Norte, La Serena, Chile Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748Garching, Germany Universidad Nacional de Río Negro. Río Negro, Argentina Consejo Nacional de Investigaciones Científicas y Técnicas. Argentina Department of Physics & Astronomy, University of Bologna, via Gobetti93/2, 40129 Bologna, Italy Institute for Computational Cosmology, Department of Physics, Univer-sity of Durham, South Road, Durham DH1 3LE, UK Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France Departamento de Astronomia, Instituto de Astronomia, Geofísica e Ciên-cias Atmosféricas da USP, Cidade Universitaria, CEP: 05508-900, São Paulo,SP, Brazil the overall disc mid-plane. Studies that have assessed thefrequency with which corrugation patterns arise in late-typegalaxies, based on cosmological simulations, have shown thatsuch patterns are expected to be common (Gómez et al. 2016,2017). Large observational samples of nearly edge-on discgalaxies have revealed that ∼
70 per cent show perturbedvertical structure (e.g. Reshetnikov & Combes 1998; Ann &Park 2006), typically displaying S-shaped warps. However,evidence for more complex corrugation patterns in externalgalaxies is still extremely limited (Fridman et al. 1998; Alfaroet al. 2001; Sánchez-Gil et al. 2015), and no full two dimen-sional (2D) maps of coherent and global features, similar tothose observed in the Milky Way, have been reported. Mor-phological signatures of these vertical perturbations in exter-nal galaxies are washed out due to projection effects, indepen-dently of the inclination of the galactic disc. Thus, they cannotbe detected through classical imaging. Instead, thanks to theexpected 90 ◦ difference in oscillation phase between the lo-cal disc’s mean-height, (cid:104) Z (cid:105) , and mean vertical velocity, (cid:104) V Z (cid:105) (e.g. Gómez et al. 2013), a corrugation pattern can be revealedthrough line-of-sight velocity fields, V los , of low-inclinationdiscs (e.g. Gómez et al. 2017). In traditional long-lit spec-troscopic observations, such patterns can be easily confusedwith the effects of local perturbations such as fountain flows(Sánchez-Gil et al. 2015). Therefore, full 2D kinematic mapsare preferable to search for global and coherent patterns. Lowinclination angles are also required to avoid significant con-tamination from in-plane flows in the resulting V los maps (e.g.Grand et al. 2016b).Here, we present a full 2D kinematic map of a Milky Way-type galaxy, namely VV304a, that shows a global, coherentand extended perturbation consistent with a corrugation pat-tern, likely associated with the recent interaction with its mas-sive companion, VV304b. THE PERTURBED VELOCITY FIELD OF VV304A a r X i v : . [ a s t r o - ph . GA ] N ov Gómez et al.
10 kpc
B-band I-bandVV304b VV304a F IG . 1.— Top panel: Optical image of the interacting pair VV304. Bothgalaxies show clear indications of recent interaction. The u’, g’ and r’-bandfalse colour image was obtained with the GMOS instrument at the Gem-ini South Observatory, under the scientific program GS-2013B-Q-27. Blue,green and red colours are associated with each filter, respectively. The inset(white square) allows to visually inspect inner galactic regions with signif-icant more detail. Note that, unlike VV304b, VV304a does not posses awell-defined bar. Bottom panels: The left and right panels show structuremaps in the B- and I-band, respectively. The maps were obtained from thepublicly available database of the The Carnegie-Irvine Galaxy Survey, andpresented by Ho et al. (2011). Structure maps, originally developed by Pogge& Martini (2002), are a powerful method to enhance fine structural featuresin single-filter images. The structure maps obtained in both filters clearlyshow the absence of a strong bar in the galaxy VV304a. In addition, theyalso highlight the lack of a dominant bisymmetric spiral structure. Interest-ingly, one can clearly observe the double strong barred nature of VV304b,demonstrating the strength of this method. VV304a: General properties
VV304a is a late-type galaxy that has recently interactedwith its closest companion, VV304b (Torres-Flores et al.2014, hereafter TF14). VV304a is located at a distance of ∼
54 Mpc, has an optical radius of R opt ≈
18 kpc and a ro-tational velocity curve that peaks at ∼
245 km s − (TF14).Based on the observed circular velocity profile, obtained using H α Fabry-Perot observations (see Sec 2.2), TF14 estimateda total VV304a dynamical mass within R opt of M ( < R opt ) ≈ . × M (cid:12) . These broad properties are similar to those ofthe Milky Way (McMillan 2017; Liu et al. 2017; Cautun et al.2020). Its companion, VV304b, also a late-type galaxy, has anoptical radius of 18 kpc and a peak circular rotational velocityof ∼
200 km s − . The top panel of Figure 1 shows a u (cid:48) , g (cid:48) and r (cid:48) -band Gemini/GMOS false colour image of the VV304 pair.The pair shows clear signatures of recent interaction, whichmakes VV304a an ideal candidate to search for a corrugatedvertical structure. Visual inspection of this panel reveals that,unlike VV304b which shows a clear double barred structureand well defined grand design spiral arms, VV304a does notpossess any clear strong m = 2 perturbation. This is particu-larly relevant for our study since strong m = 2 modes coulddrive large in-plane velocity flows that could contribute sig- F IG . 2.— Mulitband image of the VV304 galactic pair, with isophotalcontours. This image contains observations from Wise 22 microns (red),FUV GALEX (1530 Å, Blue) and the r’-band optical image (Gemini/GMOS,green). The isophotes were derived from the r’-band image. nificantly to, or even dominate, perturbations in the V los fieldof VV304a.To better characterize the morphological structure ofVV304a we show, on the left and right bottom panels ofFig. 1, structure maps in the B- and I-band, respectively.Structure maps, originally developed by Pogge & Martini(2002), are a powerful method to enhance fine structural fea-tures in single-filter images. The maps were obtained from thepublicly available database of the The Carnegie-Irvine GalaxySurvey, and presented by Ho et al. (2011). The structure mapsobtained in both filters clearly show the absence of a strongbar in VV304a. In addition, they also highlight the lack ofa dominant bisymmetric spiral structure. Interestingly, onecan clearly see the strongly double barred nature of VV304b,demonstrating the strength of this method.In Figure 2 we show a multiband image of the VV304galactic pair. To create this image we have used observationsfrom:• Red: Wise 22 microns, (heated dust by UV photons).• Blue: FUV GALEX (1530 Å), UV photons associatedwith massive (young) stars.• Green: r’-band optical image (Gemini/GMOS). Red-dest optical band we have available.The lack of any strong bar in the inner regions of VV304ais also evident from this image. The iso-contour curves high-light the very round shape of the inner regions, only distortedby the presence of a foreground star. In the outer regions, theiso-contours are distorted, reflecting the recent tidal interac-tion with VV304b. H α Fabry-Perot observations
In this work we analyze the 2D kinematic field of VV304a’s H α distribution, obtained from Fabry-Perot observations pub-lished by TF14. The data were obtained with the instrumentCInématique des GALaxiEs (CIGALE) mounted on the Euro-pean Southern Observatory (ESO) 3.6 m telescope at La Silla(Chile). These types of observations are ideal to derive 2Dkinematic maps due to their large field-of-view (207 × ), high spectral resolution ( R ∼ ∼ F IG . 3.— Left panel: Observed line-of-sight velocity field, V los , of VV304a, derived from its H α emission. The smooth coloured background shows the modeledaxisymmetric velocity field in regions without observable H α . The black lines show iso-velocity contours of this axisymmetric field. Middle panel: Residualvelocity field, V res , obtained from the difference between the observed and modeled V los field. The transitions from positive to negative velocities along a giveniso-velocity line are consistent with a corrugation pattern. These velocity fluctuations could indicate a significant displacement of the disc’s (cid:104) Z (cid:105) with respect toits overall mid-plane. Right panel: Residual velocity field including isophotal contours obtained from r’-band optical image (Gemini/GMOS). The H α
3D data cube of VV304a was reduced using a pub-licly available package, which is described in detail in Daigleet al. (2006) . The package provides the velocity momentmaps of the H α
3D data cube and it has been used by differentauthors during the last years (e.g. Boselli et al. 2018; Muñoz-Elgueta et al. 2018; Gómez-López et al. 2019). The mainadvantage of the techniques implemented in this package isthe use of adaptive spatial binning, based on a 2D Voronoitessellation method, applied to the spatial dimensions of the3D data cubes. As a result, it allows one to obtain high spa-tial resolution in high signal-to-noise regions and large spatialcoverage in low signal-to-noise regions. Here we demandeda uniform Signal-to-Noise ratio (SNR) over the whole field ofview. This was achieved by binning neighboring pixels, untila signal-to-noise target (SNRt) is reached. For each bin, thenoise is determined from the ratio between the H α line fluxand the root mean square of the continuum. Note that regionsof initial SNR higher than SNRt are not binned, thus keepingthe angular resolution as high as possible. In this work, SNRt= 6 was used. To remove the OH sky lines, the reduction pro-cess of the Fabry-Perot data produces a sky-cube, which isremoved from the observed cube. In practice, the sky cubeis derived from sky dominated regions as follows. Consider-ing that the H α emission line of a galaxy displays small shiftsin frequency due to the rotation of the gas, the sky emissionlines correspond to the ones that appear always in the samefrequency across the cube. Based on this, the reduction pro-cess applies a spatial binning on the data cube, in order toreach a desired signal-to-noise ratio on the sky lines. At thesame time it creates a median spectrum of the cube. A crosscorrelation between the median spectrum and the spatially-binned sky regions allow us to determine the sky dominatedregions, which are used to produce a sky cube. Finally, thesky cube is subtracted from the original observed data cube.We refer the reader to TF14 for more details. VV304a residual V los field
In the top panel of Figure 3 we show the V los field ofVV304a, derived from the H α data cube. Note that H α emis-sion in this galaxy can be detected up to its optical radius (seeFigure B1 of T14). Thus it can be used to map the kinemat-ics of the disc’s outskirts. The kinematic position angle PA = 104 ◦ ± ◦ , inclination angle i = 39 ◦ ± ◦ , systemic velocity V sys = 3811 ± − , and rotation curve were estimated byfitting an axisymmetric velocity field model to the observeddata and minimizing the residual velocity dispersion. Thiswas performed by applying the fitting method developed byEpinat et al. (2008, E08). We refer the reader to E08 for moredetails about the fitting procedure. The axisymmetric modelfor the velocity field is also shown in this panel by the smoothcoloured background in regions without observable H α .The observed V los field contains contributions from the threedifferent velocity components: the distributions within thedisc plane, radial V R and rotational, V φ ; and the perpendic-ular velocity to the disc plane, V Z . To remove the modelledunperturbed V φ velocity field from the observed V los distribu-tion, we subtract the axisymmetric kinematic model from thedata. The residual velocity map, V res , is shown in the bottompanel of Figure 3. The map shows a strong, global and co-herent pattern extending all the way to the disc outskirts, with V res values that can be as large as 50 km s − .The structure of the residual map is consistent with whatis expected for the V Z field of a corrugated disc galaxy. Asshown by several previous studies (see e.g. Gómez et al.2016; D’Onghia et al. 2016; Gómez et al. 2017; Laporte et al.2018b) vertical velocity flows both in the disc stellar and gascomponents, caused by a recent interaction with an externalperturber, are common and can reach these large amplitudes.These studies have also shown that vertical patterns in thecold star-forming gas and stellar components of a disc canremain coincident for more than 1 Gyr (Gómez et al. 2017).Given the large amplitudes of the perturbations observed inthe VV304a V res field ( ∼
50 km s − ) a significant contributionfrom off-plane velocity flows, V Z , induced by the recent in-teraction with VV304b, can thus be expected. The upper halfof the V res map shown in the middle panel of Figure 3 showsa particularly interesting feature, which covers approximately180 ◦ of the galactic disc, extends to the outskirts of the disc,and has an amplitude of ∼
40 km s − . Note how the disc’s V res sharply transitions from large positive to negative values.Such behaviour could indicate a significant displacement ofthe disc’s (cid:104) Z (cid:105) with respect to its overall mid-plane. A similardisplacement has been observed in the outer Milky Way disc.Known as the Monoceros ring, this large and complex stellarstructure exhibits a north-south asymmetry in (cid:104) Z (cid:105) , with thesouthern and northern parts dominating the regions closer and Gómez et al.farther from the Sun, respectively (e.g. Slater et al. 2014).However, as previously discussed, due to the non-negligibleinclination of the VV304a disc and to the presence of spi-ral structure and a possible weak bar, the resulting V res couldcontain significant contributions from in-plane velocity flows.Monari et al. (2016) studied the effects of bar-spiral couplingon stellar kinematics considering bars and spiral structure,similar to those observed in the Milky Way. They find thatthe in-plane velocity perturbations associated with these m=2patterns are <
20 km s − (see also Canzian 1993).It is worth recalling that VV304a does not possess anystrong m = 2 bar perturbation (see Sec. 2.1). However, itdoes show a flocculent-like spiral structure. To quantify thestrength of this spiral structure, we generate a 2D model ofthe galaxy’s light distribution. We fit elliptical isophotes to theGemini/GMOS r’-band image of the galaxy using the IRAFtask ELLIPSE with a fixed ellipticity of 0.2. The 2D modelis obtained using the isophotal results. Once the model is ob-tained, we generate a residual overdensity map by assuminga constant mass-to-light ratio across the disc. This is done bycomputing ∆ ρ = image − modelmodel . Note that, in this photometric band, departures from a con-stant mass-to-light ratio across the disc are expected to besmall (see appendix A for more details.)The results of this procedure are shown in Figure 4, wherethe color coding indicates the value of ∆ ρ . The overdense re-gion in the bottom left area of this figure is likely the resultof the recent tidal interaction with VV304b, and can also beappreciated in the top panel of Fig. 1. On the other hand,the underdense region in the top right area is the result ofsignificant dust extinction (see also top panel of Fig. 1). Ingeneral, we find that the spiral structure of VV304a shows adensity contrast with respect to the background disc of the or-der ∆ ρ (cid:46)
30 per cent, similar to that observed in the MW (seeMonari et al. 2016, and references therein). In the followingSection we will use this information to further characterizethe contribution from in-plane velocity flows that could arisefrom bars or bi-symmetric spiral structure to the V res field of alow-inclination disc. ANALYTIC MODELS OF PERTURBED VELOCITY FIELDS
It is well known that radial and tangential flows can arisefrom the dynamical influence of a bar or spiral structure ona disc (Siebert et al. 2012; Grand et al. 2016b; Monari et al.2016), and that the amplitudes of such flows vary with thestrength of these m = 2 modes. To characterize the contribu-tion from in-plane velocity flows driven by the VV304a non-axisymmetric structure, we have run and analyzed a suite oftest particle simulations using a MW-like galactic potential.The model parameters were chosen to reasonably reproducethe properties of VV304a listed in Sec. 2.1.The analytic galactic model considers a Hernquist profilefor the bulge component, Φ bulge = − GM bulge (cid:112) x + y + z + (cid:15) bulge , (1)with M bulge = 0 . × M (cid:12) y (cid:15) bulge = 0 . F IG . 4.— Estimated overdensity map of VV304a. Tho color bar indicatesthe value of ∆ ρ = (image - model)/model. The light distribution model wasobtained by fitting elliptical isophotes to the galaxy’s Gemini/GMOS r’-bandimage. The spiral structure of VV304a shows a density contrast with respectto the background disc of the order ∆ ρ (cid:46)
30 per cent. (Miyamoto & Nagai 1975). Smith et al. (2015) provides auser-friendly online web-form that computes the best-fittingparameters for an exponential disc , ρ ( R , z ) = ρ exp( − R /(cid:15) sdisc ) exp( − | z | /(cid:15) hdisc ) , (2)with ρ ( R , z ) the axysimmetric density, R = √ r − z the pro-jected galactocentric distance, ρ the central density. Our re-sulting disc model has a total mass M disc = 5 . × M (cid:12) ,scalelength (cid:15) sdisc = 3 . (cid:15) hdisc = 0 . Φ NFW = − Ar ln (cid:20) + rr s (cid:21) , (3)where A = GM ln(1 + c NFW ) − c NFW + c NFW , with M = 1 . × M (cid:12) , r = 234 . r s = 14 . ≈ . × M (cid:12) and peak circularvelocity of 250 km/s, in good agreement with VV304a.Following Monari et al. (2016, hereafter M16) we includea 3D bar potential, described by Φ bar ( R , φ, z , t ) = α v (cid:18) R R b (cid:19) U ( r ) R r cos( γ b ) , (4)where R b is the length of the bar, v is the circular velocity at R , γ b ( φ, t ) ≡ φ − φ b − Ω b t ), and U ( r ) ≡ (cid:26) − ( r / R b ) − for r ≥ R b , ( r / R b ) − r < R b . (5)The amplitude α is the ratio between the bar’s and axisymmet-ric contribution to the radial force along the bar’s long axis at( R , z ) = ( R , http://astronomy.swin.edu.au/~cflynn/expmaker.php V304a corrugation pattern 5 F IG . 5.— V los maps from our suite of test particle simulations, obtained after rotating the models to emulate the orientation of VV304a, ( i = 35 ◦ , PA = 105 ◦ ).The top left corner of each panel indicates the value of the density contrast at R of the spiral structure, ∆ ρ , with respect to the background disc surface density.The third panel also includes the contribution from a galactic bar with similar parameters to those of the MW bar. The color bar in the top panels is scaled to thecorresponding maximum V los value. For comparison, the color bars in the bottom panels have been scaled as in the bottom panel of Fig. 3. Note that even ourour strongest spiral model, ∆ ρ = 1000, cannot generate in-plane velocity perturbations as large as those seen in VV304a. that of the MW. This is α = 0 .
01 , Ω b = − . − kpc − ,and R b = 3 . Φ spiral ( R , φ, z , t ) = − AR s KD · e − ( R − Rs ) R sd cos( γ s ) (cid:20) sech (cid:18) Kz β (cid:19)(cid:21) β , (6)where K ( R ) = 2 R sin( p ) ,β ( R ) = K ( R ) h s [1 + . K ( R ) h s ] , D ( R ) = 1 + K ( R ) h s + . K ( R ) h s ] + . K ( R ) h s ,γ s ( R , φ, t ) = 2 (cid:104) φ − φ s − Ω s t − ln( R / R s )tan p (cid:105) . (7)Here, p is the pitch angle, A the amplitude of the spiral po-tential, h s controls the scale–height of the spiral, and R s is thereference radius for the angle of the spirals. We choose R s =1 kpc, R sd = 3 . Ω s = − . − kpc − and p = 9 . ◦ .For our study, the most relevant parameter is A , which setsthe strength of the perturbation. When modelling the MWM16 considered two values of A . The first, A = 341 . s − and referred to as ‘reference spirals’, corresponds to a 30per cent density contrast of the spiral arms with respect to thebackground disc surface density at R = R = 8 kpc. A secondmodel, referenced to as ‘strong spirals’, considers A = 683 . s − ; i.e. a 60 per cent density contrast. These values of A result on a maximum radial force exerted by the spiral arms of0.5 per cent and 1 per cent of the force due to the axisymmet-ric background at R , and introduced velocity perturbation in V R and V φ <
15 km/s. As previously discussed in Section 2.3, the strength of VV304a spiral structure lies in between theM16 reference and strong models. Nonetheless, in this workwe are interested in exploring how strong a spiral perturba-tion should be in order to induce perturbation in the V los fieldas large as those observed in VV304a (i.e. ∼
50 km/s). Forthis purpose, we also explore significantly larger values of A ,namely a 100, 200, 600 and 1000 per cent density contrast, ∆ ρ , with respect to the background disc surface density at R .The later model translate into a maximum radial force exertedby the spiral arms of ∼
17% of the force due to the axisym-metric background at R .For each model a set of ∼ × test particles, samplingof the phase-space distribution of the unperturbed stellar disc,were initialized in equilibrium using the publicly availablecode MAGI (Miki & Umemura 2018). The initial condi-tions were integrated using another publicly available code,the LP-VIcode (Carpintero et al. 2014) to make themevolve for 9.6 Gyr to allow the system to relax. This inte-gration time was chosen so that any spurious substructure onthe disc density field, arising due to the unrelaxed set of initialconditions, are well mixed within the inner 20 kpc. After thatperiod of time, the non-axisymmetric perturbations to the po-tential were slowly introduced by linearly increasing in timetheir amplitude to the desired value. Following Monari et al.(2016), this was done within a period of 3 Gyr, which repre-sents ≈
15 full rotations of non-axisymmetric perturbations.Finally, each model was allowed to evolve under the influ-ence of the perturbed potential for an additional period of 3Gyr.In Figure 5 we show the resulting V los map for each model,after rotating them into an inclination of 35 ◦ and a position an-gle of 105 ◦ to emulate VV304a orientation. To compute the V los we subtracted from each particle’s V φ the circular veloc-ity at the corresponding galactocentric radii. To highlight theeffect of the non-axysimmetric perturbation, the colorbars inthe top panels have been scaled based the maximum V los valueobtained on each map. The left most panel shows the results https://bitbucket.org/ymiki/magi http://lp-vicode.fcaglp.unlp.edu.ar/ Gómez et al. F IG . 6.— Present-day stellar distribution of the Aq-C4 disc. The imageswere constructed by mapping the K-, B- and U-band luminosities to the red,green and blue channels of a full colour composite image. Younger (older)star particles are therefore represented by bluer (redder) colours. The leftand right panels show the edge-on and face-on views, respectively. Note thesimulated disc shows a weak bar and multi-arm spiral structure, similar towhat is observed in VV304a disc. Figure from Marinacci et al. (2014). obtained for the ∆ ρ = 100% model, similar to the strong spi-ral model of M16 ( ∆ ρ = 60%). As expected, our results arein good agreement with those of M16 (see their Fig. 5). Af-ter inclining the disc to i = 35 ◦ , the resulting perturbation inthe V los field is of the order of only 1 km/s. As we increasethe strength of the spiral perturbation, the magnitude of thein-plane flows significantly increases, reaching values of 10km/s for our most extreme model, i.e. ∆ ρ = 1000%. Thesecond and third panels show a comparison between modelswithout and with bars, respectively. Both models include aspiral perturbation with ∆ ρ = 200%. Note that the bar en-hances the magnitude of the in-plane flows in the very innerdisc regions, doubling its amplitude with respect to the barlessmodel. Yet, even with the bar included, the V los perturbationsreach values < i = 35 ◦ , neither a bar asstrong as the one of the MW nor spiral structure with a ∆ ρ aslarge as 1000 per cent can secularly introduce perturbationsin the V los field with amplitudes as large as those observed inVV304a. We recall that VV304a does not show a bar and thatthe ∆ ρ of its spiral structure is <
100 per cent of the back-ground density of its disc.In this Section we have analyzed the secular response of adisc to a bar and spiral perturbation using test particle simula-tions of an isolated galaxy. In what follows we use highlyresolved fully cosmological self-consistent hydrodynamicalsimulations to characterize the impact that in-plane velocityflows, associated with both strong and mild m = 2 modes, canhave on the V res field of a galactic disc that has recently inter-acted with an external perturber. SELF CONSISTENT MODELS OF PERTURBED VELOCITYFIELDS
In the previous section we used a suite of test particles sim-ulations to show that the VV304a spiral structure can notsecularly drive in-plane flows sufficiently large to accountfor the velocity perturbation observed in its V res field. Inthis section we further study the impact that in-plane flowsmay have on the V res field of this low-inclination interactinggalaxy by analyzing fully self-consistent cosmological simu-lation of VV304a like models. We have focused on modelsthat have recently interacted with an external companions and F IG . 7.— The moment of closest approach between the simulated Aurigagalaxy, Au25, and its massive companion. The images were created as inFig.6. The face-on (left) and edge-on (right) views are oriented with respectto the Au25 disc. The disc shows a strong bar and a grand design spiralstructure. that present i) weak and ii) very strong m = 2 modes.The main advantage of using fully cosmological simula-tions, as opposed to tailored simulations of interacting galax-ies set in isolation, is that the former self-consistently includemechanisms that can significantly perturb an otherwise ini-tially relaxed disc, such as previous close encounters withsatellites, distant flybys of massive objects, and accretion ofmisaligned cold gas from halo infall or from mergers. Thusa realistic representation of possible sources of confusion isincluded in our study. The Auriga models
The Auriga project (Marinacci et al. 2014; Grand et al.2017, 2019) consists of ∼
40 high-resolution cosmologicalzoom-in simulations of the formation of late-type galaxieswithin Milky Way-sized halos, performed with the N-body,magneto-hydrodynamics code AREPO (Springel 2010). Thecode includes modelling of a wide range of critical physi-cal processes that govern galaxy formation (Marinacci et al.2014) such as gas cooling/heating, star formation, mass returnand metal enrichment from stellar evolution, the growth of asupermassive black hole, and feedback from stellar sourcesand from black hole accretion. The halos were selected froma lower resolution dark matter only simulation from the Ea-gle Project, a periodic cube of side length 100 comoving Mpc(Schaye et al. 2015). Each halo was chosen to have, at z = 0,a virial mass in the range of 0 . − × M (cid:12) and to be moredistant than nine times the virial radius from any other haloof mass more than 3% of its own mass. The dark matter par-ticle and gas cell mass for the simulation considered here are ∼ × M (cid:12) and ∼ × M (cid:12) , respectively. The gravi-tational softening length of the stars and dark matter growswith scale factor up to a maximum of 369 pc, after whichit is kept constant in physical units. The softening length ofgas cells scales with the mean radius of the cell, but is neverallowed to drop below the stellar softening length. A studyacross three resolution levels shows that many galaxy prop-erties, such as surface density profiles, orbital circularity dis-tributions, star formation histories and disc vertical structuresare already well-converged at the resolution level consideredin this work.Previous studies based on the same simulations have shownthat vertical patterns in the cold star-forming gas and stellarcomponents of a disc can remain coincident for more than 1Gyr (Gómez et al. 2017). Thus, we focus on the stellar com-ponents which have much better spatial resolution comparedto the cold gas discs. Nevertheless, it is worth noticing that theV304a corrugation pattern 7 Time [Gyr] < A / A > Au25Aq-C4 F IG . 8.— The time evolution of the amplitudes of the m = 2 Fourier modeof the simulated stellar discs analyzed in this work. The green and blue linesshow results for the Aq-C4 and Au25 discs, respectively. vertical pattern in the two models considered here can also berecovered from the cold star-forming gas distribution. Weak m = 2 model
We first analyze the Aq-C4 model, first introduced in Mari-nacci et al. (2014). Aq-C4 has the property of being onethe most similar models to the Milky Way within the sam-ple. It has a flat rotation curve that peaks at 250 km s − at ∼ M tot ∼ . × M (cid:12) , baryonic disc + bulge mass M ∗ ∼ . × M (cid:12) and a disc optical radius of ∼
20 kpc.Here we define the optical radius as the radius where µ B = 25mag arcsec − (cf. Pranav & Jog 2010). Note that these prop-erties make Aq-C4 a very reasonable model of VV304a (seeSec. 2.1). Aq-C4 shows a quiet formation history since z ≈ M sat / M host = 1 /
40. The most significant perturber is alow-velocity fly-by with a pericentre passage of 80 kpc at alookback time of t look ≈ . ∼ × M (cid:12) ( M sat / M host ≈ / m = 2 mode in Aq-C4’s disc, computedwithin the inner 20 kpc following the approach of Grand et al.(2016a). Strong m = 2 model
Among the Auriga models, Au25 is the one that mostclosely resembles the VV304 system in terms of its global F IG . 9.— First row: Aq-C4 line-of-sight velocity field, V los , obtained forthree different inclination angles. From left to right we show the maps aftertilting the disc by i = 0 ◦ , ◦ and 35 ◦ , respectively. The second row showsresidual velocity maps, V res , obtained after subtracting from every stellar par-ticle the mean rotation velocity at the corresponding radial position. The thirdand fourth rows show the contributions from vertical and in-plane motions tothe V res fields, respectively. Note that even at i = 35 ◦ V res is dominated byvertical motions, V Z . properties. Furthermore, as discussed below, it has thestrongest m = 2 close to z = 0. The host galaxy has, at thepresent-day, a total mass of M tot ∼ . × M (cid:12) , a bary-onic disc + bulge mass of M ∗ ∼ . × M (cid:12) , a peak cir-cular velocity of ∼
180 km s − , and a disc optical radius thatazimuthally varies between 21 and 30 kpc. Even though Au25is slightly less massive than VV304a, it had a close encounterwith a massive satellite 0.9 Gyr ago whose total mass at infallwas M sat ∼ × M (cid:12) and whose orbit reached the host’sinner 40 kpc. This configuration is reminiscent of the recentinteraction in VV304a and b. Figure 12 highlights the momentof closest approach. During the interaction, the host galaxyis strongly tidally perturbed and develops a significant mis-alignment of its outer dark matter halo regions. The interac-tion also induces the formation of two tidal arms and triggersstrong vertical patterns whose signatures can still be detectedclearly at the present-day (Gómez et al. 2017). Note the 1:4host to satellite mass ratio, which can be classified as a mas-sive interaction. In Figure 8 we show the time evolution ofits m = 2 mode, measured as in Sec. 4.1.1. The interactionwith its massive companion triggers the development a strong m = 2 signal associated with both a galactic bar and grand de-sign spiral structure (see Fig. 12). Grand et al. (2016a) studiedthe time evolution of the m = 2 modes on a large sample of theAuriga models. Figure 4 of that work shows that Au25 has Gómez et al.the strongest m = 2 mode during the last 3 Gyr of evolution. Simulated residual V los fields
To investigate whether our simulated discs develop similarvelocity patterns to those observed in VV304a, we first rotatethe main host discs to an inclination of i = 35 ◦ and PA = 100 ◦ ,similar to the values estimated for VV304a. We then computemaps of mean V los across the disc plane for all snapshots afterthe interactions. The top rightmost panels of Figures 9 and10 show an example of the V los map obtained from the Aq-C4 and Au25 discs, respectively. The snapshot correspondsto z = 0 for Aq-C4, 2.4 Gyr after the flyby closest approach,and ∼ .
75 Gyr after the strong interaction suffered by Au25,just one snapshot before z = 0. Although some interestingdepartures from perfectly rotating discs can be observed, inboth cases the resulting maps are clearly dominated by the V φ velocity component.To obtain the V res velocity field for the simulated stellardiscs, we subtract from every stellar particle the mean rota-tion velocity at the corresponding radial position. The result-ing maps are shown on the second row rightmost panels ofFigs. 9 and 10. As in the VV304a case, the V res maps showstrong and coherent velocity patterns that can reach ampli-tudes as large as 50 km s − . Note that both maps show sim-ilarly strong flows, despite the differing strength of their in-plane disc m = 2 modes. The morphology of the coherentflows show very similar features to those in the observationaldata, with sharp transitions between positive and negative V res velocities. Such transitions are associated with extrema in thedisplacement of the mid-plane of the discs if the V res fields areindeed dominated by off-plane motions, V Z . To explore this,we show on the second row of Figs 9 and 10 the V res maps ob-tained after inclining the disc by only 15 ◦ (second panel) and0 ◦ (first panel). Note that in a perfectly face-on configuration,i.e. i = 0 ◦ , the resulting V los and V res maps are equivalent to thedisc’s mean vertical velocity distribution, V Z . Thus, coherentand extended departures from 0 km s − on these maps are adirect indication of a corrugation in the simulated host discs.It is clear in both cases that the patterns seen in the V res fieldare preserved as we tilt the discs towards lower inclinations.In the case of Aq-C4, these are not only preserved but the am-plitude of the patterns increases for lower inclination angles.This indicates a negligible contribution from in-plane flowsto the V res field, even at i = 35 ◦ . This is not surprising since,as in the case of VV304a, the simulated disc shows a verymild m = 2 pattern. A similar result is found for Au25 (seeFig. 10). The global morphology of the V res field is preservedas we decrease the inclination. The i = 0 ◦ map reveals verystrong vertical flows, with amplitudes larger than 40 km s − ,that are the result of a disc corrugation. Note the trailing na-ture of this corrugation pattern. Contrary to the Aq-C4 case,where leading patterns develop over time due to the inner disctorque (Shen & Sellwood 2006; Gómez et al. 2016), the ver-tical structure of the Au25 disc traces the trailing structure ofthe tidal arms created during the recent interaction.It is clear that vertical flows dominate the i = 35 ◦ V res field inAu25 disc. However the amplitudes of some of these featuresdecrease for lower inclination, indicating a non-negligiblecontribution from in-plane flows. To further characterize thecontribution from the different velocity components, we showin Figs 9 and 10 velocity maps in which only vertical (thirdrow) and in-plane (fourth row) motions are included. For Aq-C4 (weak m = 2 mode) it is clear that the contribution from F IG . 10.— As in Figure 9, for Au25. in-plane flows is negligible, even at i = 35 ◦ . In the Au25 case(strong m = 2), even though significant in-plane flows can befound at certain locations, the off-plane flows dominate thetotal residual velocity patterns over most of the disc, even at i = 35 ◦ . This shows that the velocity perturbations seen in theinclined simulated disc are indeed primarily associated with acorrugation pattern.Clearly, features in the V res map of a low-inclination discthat has recently interacted with a companion can be domi-nated by flows in the direction perpendicular to the disc plane.We recall that this is true even for Au25 which shows thestrongest in-plane m = 2 pattern in the Auriga sample closeto z = 0. The disc of VV304a shows neither a strong bar nor agrand design spiral and thus more closely resembles the struc-ture seen in Aq-C4. This suggests that the global and coherentvelocity patterns seen in VV304a could indeed be associatedwith vertical flows.In Figure 11 we show the time evolution of the mean height, (cid:104) Z (cid:105) (top), and mean vertical velocity, (cid:104) V Z (cid:105) (bottom) of thestellar disc in Au25. A similar figure for Aq-C4 can be foundin Gómez et al. (2016, fig. 3). This period of time covers thesatellite’s closest approach and the snapshot used for data tomodel comparison, indicated with a magenta star. The linkbetween the onset of the disc vertical perturbation and closetapproach of the most massive companion, at t ∼ m = 1pattern that winds-up as time goes by. The counterparts of theextended and coherent structures seen in the (cid:104) V Z (cid:105) and inclined V res fields at t = 0 .
17 and 0 Gyr are clearly associated with avertical displacement of the disc with respect to the overallV304a corrugation pattern 9 F IG . 11.— Time evolution of the vertical structure of the disc in Au25 over a period of ∼ (cid:104) Z (cid:105) . Thebottom panels show maps of the mass-weighted (cid:104) V Z (cid:105) . The onset-time of the vertical perturbation is 1 (cid:47) t onset (cid:47) . m = 1 mode that winds-up in time. The snapshot used for comparison with the VV304a data is highlightedwith the magenta stars(second from the right. In this projection the galactic disc rotates counterclockwise. mid-plane. These structures resemble one of the largest ver-tical asymmetries of our own Galactic disc: the Monocerosring. A similar feature is seen in the V res field of VV304a (bot-tom panel of Fig. 3), which strongly suggests the presence ofa Monoceros ring-like feature in this external late-type galaxy.The origin of the Monoceros ring has been a puzzle formany years and it has been debated whether its constituentstars are the debris of a disrupted satellite galaxy or whetherthe structure is the projection of a corrugation pattern in ourown disc (see Laporte et al. 2018b; Guglielmo et al. 2018, andreferences therein). CONCLUSIONS
In this work we have analyzed the 2D V los field of the late-type galaxy VV304a, obtained through H α Fabry-Perot ob-servations. In many aspects, VV304a can be considered aMilky Way analogue which is currently interacting with amassive companion, VV304b. After subtracting an axisym-metric kinematic model from the observed V los field, we findthat the residuals show strong, global and coherent motionswhich are consistent with a corrugation pattern. The contribu-tion from in-plane flows to the V res field cannot be subtractedwith the available data. However, non-axisymmetric featuressuch as spiral arms and/or a bar are much too weak in VV304ato generate line-of-sight perturbations as large as those mea-sured. We have demonstrated this by analysing multi-bandimages of VV304a, and comparing to a suite of test-particlesimulations of non-axisymmetric galaxies with bars and m=2spiral structure but no extraplanar perturbations. Even spi-ral spiral arms an order of magnitude stronger than those ob-served in VV304a do not induce velocity flows strong enoughto explain the perturbations seen in its V res field. Based onthese results, we analysed fully cosmological models withstrong and weak m = 2 patterns to explore whether the V res field of a galaxy that recently interacted with an external per-turber could still be dominated by signatures of a corrugationpattern, even for a disc as inclined as VV304a. Our resultsshow that this can indeed be the case. The VV304a V res map hints at a structure that resemblesthe Monoceros ring, an extended low latitude stellar overden-sity in our own Galaxy which may therefore be associatedto a global disc corrugation pattern. Several recent studieshave linked this structure to interactions with the Sgr dwarfgalaxy (Purcell et al. 2011; Gómez et al. 2013; Laporte et al.2018b), even though its origin is still being debated. Note thatalthough Sgr was likely less massive at infall than VV304b,several different arguments suggest a total infall mass of theorder of (cid:38) M (cid:12) (e.g. Purcell et al. 2011); this could thusbe a 1:10 interaction. As shown in Gómez et al. (2017), strongglobal corrugation patterns can be induced during such inter-actions.Our results demonstrate that it is possible to address impor-tant questions regarding the nature and origin of vertical per-turbations by measuring the velocity distribution of nearbynearly face-on galaxies. What is the prevalence of verticalcorrugation patterns in the Local Universe? What are the mainphysical mechanisms behind the formation of such patterns?And what can they tell us about the recent interaction historyof their host galaxies? The tidal origin of VV304a’s perturba-tion is very clear: a close interaction with VV304b. However,the presence of a corrugation pattern could also be used toconstrain the asymmetries of the host dark matter halo and tostudy unseen structure in the outskirts of galaxies (Vesperini& Weinberg 2000; Gómez et al. 2016). Our study opens anew window to investigating whether the corrugation patternobserved in the Milky Way disc is a rare or common featureof late-type galaxies. ACKNOWLEDGEMENTS
FAG acknowledges financial support from FONDECYTRegular 1181264. FAG, AM and CM acknowledge fundingfrom the Max Planck Society through a Partner Group grant.AM acknowledges financial support from FONDECYT Reg-ular 1181797. FM acknowledges support through the Pro-gram ‘Rita Levi Montalcini’ of the Italian MIUR
REFERENCESAlfaro, E. J., Pérez, E., González Delgado, R. M., Martos, M. A., & Franco,J. 2001, ApJ, 550, 253Ann, H. B., & Park, J.-C. 2006, New Astron., 11, 293Antoja, T., et al. 2018, Nature, 561, 360 Bland-Hawthorn, J., et al. 2018, ArXiv e-printsBoselli, A., et al. 2018, A&A, 614, A56Canzian, B. 1993, ApJ, 414, 487
Carpintero, D. D., Maffione, N., & Darriba, L. 2014, Astronomy andComputing, 5, 19Cautun, M., et al. 2020, MNRAS, 494, 4291Daigle, O., Carignan, C., Hernandez, O., Chemin, L., & Amram, P. 2006,MNRAS, 368, 1016D’Onghia, E., Madau, P., Vera-Ciro, C., Quillen, A., & Hernquist, L. 2016,ApJ, 823, 4Epinat, B., et al. 2008, MNRAS, 388, 500Fridman, A. M., et al. 1998, Astronomy Letters, 24, 764Gaia Collaboration et al. 2018, ArXiv e-printsGómez, F. A., Minchev, I., O’Shea, B. W., Beers, T. C., Bullock, J. S., &Purcell, C. W. 2013, MNRAS, 429, 159Gómez, F. A., White, S. D. M., Grand, R. J. J., Marinacci, F., Springel, V., &Pakmor, R. 2017, MNRAS, 465, 3446Gómez, F. A., White, S. D. M., Marinacci, F., Slater, C. T., Grand, R. J. J.,Springel, V., & Pakmor, R. 2016, MNRAS, 456, 2779Gómez, F. A., et al. 2012, MNRAS, 423, 3727Gómez-López, J. A., et al. 2019, A&A, 631, A71Grand, R. J. J., Springel, V., Gómez, F. A., Marinacci, F., Pakmor, R.,Campbell, D. J. R., & Jenkins, A. 2016a, MNRAS, 459, 199Grand, R. J. J., et al. 2016b, MNRAS, 460, L94—. 2017, MNRAS, 467, 179Grand, R. J. J., et al. 2019, MNRAS, 490, 4786Guglielmo, M., Lane, R. R., Conn, B. C., Ho, A. Y. Q., Ibata, R. A., &Lewis, G. F. 2018, MNRAS, 474, 4584Ho, L. C., Li, Z.-Y., Barth, A. J., Seigar, M. S., & Peng, C. Y. 2011, ApJS,197, 21Laporte, C. F. P., Gómez, F. A., Besla, G., Johnston, K. V., &Garavito-Camargo, N. 2018a, MNRAS, 473, 1218Laporte, C. F. P., Johnston, K. V., Gómez, F. A., Garavito-Camargo, N., &Besla, G. 2018b, MNRAS, 481, 286Laporte, C. F. P., Minchev, I., Johnston, K. V., & Gómez, F. A. 2019,MNRAS, 485, 3134Liu, C., et al. 2017, Research in Astronomy and Astrophysics, 17, 096Marinacci, F., Pakmor, R., & Springel, V. 2014, MNRAS, 437, 1750McMillan, P. J. 2017, MNRAS, 465, 76 Miki, Y., & Umemura, M. 2018, MNRAS, 475, 2269Miyamoto, M., & Nagai, R. 1975, PASJ, 27, 533Monari, G., Famaey, B., Siebert, A., Grand , R. J. J., Kawata, D., & Boily,C. 2016, MNRAS, 461, 3835Muñoz-Elgueta, N., Torres-Flores, S., Amram, P., Hernandez-Jimenez, J. A.,Urrutia-Viscarra, F., Mendes de Oliveira, C., & Gómez-López, J. A. 2018,MNRAS, 480, 3257Newberg, H. J., et al. 2002, ApJ, 569, 245Pogge, R. W., & Martini, P. 2002, ApJ, 569, 624Pranav, P., & Jog, C. J. 2010, MNRAS, 406, 576Price-Whelan, A. M., Johnston, K. V., Sheffield, A. A., Laporte, C. F. P., &Sesar, B. 2015, MNRAS, 452, 676Purcell, C. W., Bullock, J. S., Tollerud, E. J., Rocha, M., & Chakrabarti, S.2011, Nature, 477, 301Reshetnikov, V., & Combes, F. 1998, A&A, 337, 9Sánchez-Gil, M. C., Alfaro, E. J., & Pérez, E. 2015, MNRAS, 454, 3376Schaye, J., et al. 2015, MNRAS, 446, 521Sheffield, A. A., Price-Whelan, A. M., Tzanidakis, A., Johnston, K. V.,Laporte, C. F. P., & Sesar, B. 2018, ApJ, 854, 47Shen, J., & Sellwood, J. A. 2006, MNRAS, 370, 2Siebert, A., et al. 2012, MNRAS, 425, 2335Slater, C. T., et al. 2014, ApJ, 791, 9Smith, R., Flynn, C., Candlish, G. N., Fellhauer, M., & Gibson, B. K. 2015,MNRAS, 448, 2934Springel, V. 2010, MNRAS, 401, 791Torres-Flores, S., Amram, P., Mendes de Oliveira, C., Plana, H., Balkowski,C., Marcelin, M., & Olave-Rojas, D. 2014, MNRAS, 442, 2188Vesperini, E., & Weinberg, M. D. 2000, ApJ, 534, 598Widrow, L. M., Gardner, S., Yanny, B., Dodelson, S., & Chen, H.-Y. 2012,ApJL, 750, L41Xu, Y., Newberg, H. J., Carlin, J. L., Liu, C., Deng, L., Li, J., Schönrich, R.,& Yanny, B. 2015, ApJ, 801, 105Yanny, B., et al. 2003, ApJ, 588, 824APPENDIX A. M/L RATIOS ACROSS A SIMULATED DISC
In order to test whether the assumption of a mass-to-light (M/L) ratio across the disc is reasonable, we computed the M/L ratiomap for the galactic disc of the Au25 model. The map is shown in Figure 12. As in VV304a observations, we have focused on ther’-band. The reason behind this choice is that this band is a better tracer of the overall mass distribution than bluer photometricbands. As we can see from this Figure, our model indicates an average M/L of the order 1 throughout the disc, with values thatcan vary between 0.2 to 2.75. This indicates that assuming a constant M/L in the analysis shown in Section 2.3 is a reasonableapproximation in this case. Note that our goal in that Section is to estimate the strength of the spiral structure in terms of itsoverdensity pattern. Our study suggests that the spiral structure of VV304a is ∼
30 per cent denser than the background densityof the overall disc. However, in our analytic model, we have gone as far as considering spiral structures that are 1000% denserthan the background density. Thus, we expect small departures from a constant M/L to be covered by our most extreme models.V304a corrugation pattern 11 F IG . 12.— The color coding indicates the values of the simulated mass-to-light ratio in the r’-band, M/L, obtained across the disc of the cosmological simulationAu25. Values vary between M/L ∼ ..