The enigmatic pair of dwarf galaxies Leo IV and Leo V: coincidence or common origin?
Jelte T. A. de Jong, Nicolas F. Martin, Hans-Walter Rix, Kester W. Smith, Shoko Jin, Andrea V. Maccio'
aa r X i v : . [ a s t r o - ph . C O ] J a n Draft version November 4, 2018
Preprint typeset using L A TEX style emulateapj v. 08/13/06
THE ENIGMATIC PAIR OF DWARF GALAXIES LEO IV AND LEO V: COINCIDENCE OR COMMONORIGIN?
Jelte T. A. de Jong , Nicolas F. Martin , Hans-Walter Rix , Kester W. Smith , Shoko Jin , Andrea V.Macci`o Draft version November 4, 2018
ABSTRACTWe have obtained deep photometry in two 1 ◦ × ◦ fields covering the close pair of dwarf spheroidalgalaxies Leo IV and Leo V and part of the area in between. From the distribution of likely red giantbranch and horizontal branch stars in the data set, we find that both Leo IV and Leo V are significantlylarger than indicated by previous measurements based on shallower data. With a half-light radius of r h =4 . ′ ± . ′ ±
36 pc) and r h =2 . ′ ± . ′ ±
31 pc), respectively, both systems are now well withinthe physical size bracket of typical dwarf spheroidal Milky Way satellites. Both are also found to besignificantly elongated with an ellipticity of ǫ ≃ .
5, a characteristic shared by many of the fainter( M V > −
8) Milky Way dwarf spheroidals. The large spatial extent of our survey allows us to searchfor extra-tidal features in the area between the two dwarf galaxies with unprecedented sensitivity. Thespatial distribution of candidate red giant branch and horizontal branch stars in this region is foundto be non-uniform at the ∼ σ level. Interestingly, this substructure is aligned along the directionconnecting the two systems, indicative of a possible ‘bridge’ of extra-tidal material. Fitting the stellardistribution with a linear Gaussian model yields a significance of 4 σ for this overdensity, a most likelyFWHM of ∼
16 arcmin and a central surface brightness of ≃
32 mag arcsec − . We investigate differentscenarios to explain the close proximity of Leo IV and Leo V and the possible tidal bridge betweenthem. Orbit calculations demonstrate that the two systems cannot share the exact same orbit, whilea compromise orbit does not approach the Galactic center more than ∼
160 kpc, rendering it unlikelythat they are remnants of a single disrupted progenitor. A comparison with cosmological simulationsshows that a chance collision between unrelated subhalos is negligibly small. Given their relativedistance and velocity, Leo IV and Leo V could be a bound ‘tumbling pair’, if their combined massexceeds 8 ± × M ⊙ . The scenario of an internally interacting pair that fell into the Milky Waytogether appears to be the most viable explanation for this close celestial companionship. Subject headings: galaxies: individual (Leo IV dSph, Leo V dSph) – Local Group INTRODUCTIONIn the past four years, the Sloan Digital Sky Survey(SDSS) has revealed satellite galaxies of the Milky Way(MW) that are up to 100 times fainter than those knownbefore, more than doubling the number of known satel-lites. Most of these new discoveries are dwarf spheroidalgalaxies (dSph) that are dark-matter dominated objects(Martin et al. 2007; Simon & Geha 2007), yet have sur-prisingly complex star formation histories (de Jong et al.2008a) and/or morphologies (e.g. Coleman et al. 2007a;Martin et al. 2008a; de Jong et al. 2008b). Thanks tothese new objects and the uniform sky coverage pro-vided by SDSS, it is now possible to probe the faintend of the satellite galaxy luminosity function (e.g.Koposov et al. 2008). This extended data set has en-abled a detailed comparison with galaxy formation mod-els, leading to better agreement between models andobservation, thereby largely solving the ‘missing satel-lite problem’, one of the stumbling blocks for currentcosmological models on small scales (e.g. Koposov et al.2009; Macci`o et al. 2009). Recent studies of the struc-
Electronic address: [email protected] Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, D-69117Heidelberg, Germany Astronomisches Rechen-Institut, Zentrum f¨ur Astronomie derUniversit¨at Heidelberg, M¨onchhofstraße 12-14, D-69120 Heidel-berg, Germany Alexander von Humboldt research fellow tural properties of these newly discovered dwarf galaxiesbased on SDSS data have revealed that they are, as aclass, more elongated than their brighter counterparts(Martin et al. 2008b), indicating that some systems maybe tidally disrupted by the MW. It is as yet unclearwhether these objects represent a lower mass limit to thegalaxy formation process, or whether their stellar bodiesare remnants of originally larger systems.In this context, the recently discovered systems LeoIV (Belokurov et al. 2007) and Leo V (Belokurov et al.2008) are particularly interesting, as they are separatedby less than 3 . ◦ on the sky with fairly similar distances(154 ± ∼
180 kpc, respectively; Moretti et al.2009; Belokurov et al. 2008) and radial velocities (10 . ± . − and 60 . ± . − , respectively, with re-spect to the Galactic Standard of Rest; Simon & Geha2007; Belokurov et al. 2008), implying that they mightbe related to a single disrupting or disrupted progeni-tor. Belokurov et al. (2008) also found the distribution ofblue horizontal branch (BHB) stars in Leo V to be elon-gated and even detected two candidate red giant branch(RGB) stars at ∼ ′ North of the system, well beyond theestimated tidal radius. Futhermore, with its estimatedhalf-light radius of ∼
40 pc (Belokurov et al. 2008), Leo Vappears to fall in the ‘size gap’ between globular clustersand classical dwarf spheroidal galaxies (cf. Gilmore et al.2007).We have obtained deep photometry in two 1 ◦ × ◦ de Jong et al. Fig. 1.—
Layout of observed fields and color-magnitude diagrams.
Left:
Black solid lines outline the two 1 ◦ × ◦ fields that wereobtained, with the gray lines showing the individual chips. The dashed square outlines the third field that was lost to bad weather. Thelocations of Leo IV and Leo V are indicated. Middle:
Color-magnitude diagram of Leo IV within 3 ′ from the center. Overplotted is a 14Gyr isochrone with [Fe/H]= − m − M =20.94. Two selection boxes to select HB and RGB stars are shown with solid outlines, whilea third selection box used for the maximum-likelihood fitting procedure is indicated with a dashed outline. Right:
As the middle panel,but for Leo V. Here the isochrone has m − M =21.23. In both cases the isochrones are from Dotter et al. (2008). fields, covering both Leo IV and V as well as much ofthe area in between them. These new data enable are-determination of the structural parameters for bothgalaxies, as well as a sensitive search for possible extra-tidal material connecting the two systems. The remain-der of this paper is structured as follows. In § §
3. The different ways in which we search for evidence ofextra-tidal stars in between the two systems is describedin §
4, and in § § DATADeep, wide-field photometry in the Johnson B and V filters was obtained for two 1 ◦ × ◦ fields, using theLAICA imager on the 3.5m telescope at the Calar Altoobservatory. Four 4k ×
4k CCDs with a pixel size of 0 . ′′ ◦ × ◦ field of view. Observations were carried outduring the nights of February 24th and 25th 2009, underphotometric conditions with seeing ranging from 1 . ′′ . ′′
8. Total exposure times in B and V were 1950s and2600s, divided over single exposures of 650s. The loca-tions of the fields are shown in the left panel of Figure 1;a planned central field could not be obtained due to badweather.After bias subtraction and flatfielding, the data fromthe individual chips were astrometrically corrected andstacked using the SCAMP (Bertin 2006) and
SWARP software , developed by Terapix. A chip-by-chip analy-sis of the data was necessary because of seeing differencesbetween different pointings and PSF distortions. Objectdetection was done using SExtractor (Bertin & Arnouts1996) and subsequent PSF-fitting photometry with the daophot package in IRAF. By cross-matching objectswith SDSS DR7 (Abazajian et al. 2009) and convertingSDSS magnitudes to B and V using the transformations SCAMP and
SWARP can be obtained fromhttp://terapix.iap.fr from Jester et al. (2005), the photometry was calibratedto SDSS. The photometry of all stars is made availablein Table 1, which contains the coordinates, magnitudesand their uncertainties, and the extinction at the posi-tion of each star interpolated from the extinction mapsof Schlegel et al. (1998). Using these extinction values,all stars were individually corrected for the limited fore-ground extinction towards these fields ( E ( B − V ) ∼ . B and V . Color-magnitudediagrams (CMD) of Leo IV and V within radii of 3 ′ arepresented in Figure 1. Artificial star tests to assess thecompleteness in all CCDs were done by placing 4 500sources spread over a magnitude range of 17 to 25 ineach CCD and for each filter and analysing them fol-lowing the exact same procedure. The completenessesderived are shown in Figure 2 for the Leo IV field and inFigure 3 for the Leo V field. Seeing variations cause thecompleteness to be non-uniform, but ∼
80% completenessis reached to at least B = V ≃ REVISED PROPERTIES OF LEO IV AND LEO VAn accurate distance to Leo IV has been determinedby Moretti et al. (2009) using RR Lyrae stars. Althoughthe absolute calibration of our photometry would intro-duce uncertainties in the determination of the distanceto Leo V, the luminosity of its HB stars can be com-pared to the luminosity of the HB in Leo IV, providinga distance offset with respect to the latter. The stars onthe horizontal part of the horizontal branch (HB) of LeoIV have a mean B =21.78 ± B =22.06 ± ± ± ± ± TABLE 1Photometric data
Chip ID ∗ α δ B σ B V σ V E(B-V)( ◦ J2000.0) ( ◦ J2000.0) (mag) (mag) (mag) (mag) (mag)0 11 173.33533 2.05084 23.302 0.042 21.902 0.014 0.0280 11 173.23705 2.05027 23.603 0.048 22.295 0.021 0.0280 11 173.28453 2.05040 23.531 0.042 23.185 0.047 0.0280 11 173.29111 2.04999 24.160 0.071 23.551 0.074 0.0280 11 173.27151 2.05098 23.059 0.028 22.804 0.032 0.028
Note . — The complete table is available online. ∗ The first digit of the chip ID indicates the field, where a ‘0’ stands for the Northernfield containing Leo V and a ‘1’ for the Southern field containing Leo IV; the integersfollowing the underscore signify the exposure and the chip number, respectively, bothrunning from 1 to 4.
Fig. 2.—
Completeness as a function of magnitude for all CCDsin the 1 ◦ × ◦ field containing Leo IV. The solid line is for the B -band, and the dashed line for the V -band. Gray vertical lines indi-cate the magnitude limits used for the maximum-likelihood analy-sis of the stellar spatial distribution: 23.9 for B (solid) and 23.4for V (dashed). Fig. 3.—
As Fig. 2 but for the field containing Leo V. members of a dwarf galaxy (selected by a rough color-magnitude cut) to determine the best elliptical, expo-nential surface density profile of the satellite, and fit forthe fore/background stars at the same time. Given thepositions of Leo IV and V near the edge of the observedfields, we use the adapted version of the algorithm pre-sented in § − . M V = − . ± . − . ± . TABLE 2Structural parameters of Leo IV and Leo V
Parameter Leo IV Leo V α (J2000) 11 32 58.6 ± ± δ (J2000) −
00 33 06 ±
54 +02 12 57 ± θ (deg) − ± − ± ǫ ± ± r h (arcmin) 4.6 +0 . − . ± r h (pc) 206 +36 − ± D (kpc) 154 ± a ) ± m − M (mag) 20.94 ± a ) ± − ± a ) − ± b ) M V − ± − ± L V ( L ⊙ ) 1 . ± . × . ± . × µ V (mag/arcsec ) 27 . ± . . ± . v GSR ( km s − ) 10 . ± . c ) . ± . d ) Note . — a ) Moretti et al. (2009); b ) Walker et al.(2009); c ) Simon & Geha (2007); d ) Belokurov et al. (2008);all other values based on this publication. from Martin et al. (2008b), but they agree to within 1 σ .It is also statistically equivalent to the value measuredby Sand et al. (2009) from their deeper data. The differ-ence is due to the fact that the deeper data reveal thatLeo IV is actually more elongated and has a larger half-light radius than that measured from SDSS data. LeoV is found to be almost a magnitude brighter than thelower limit given by Belokurov et al. (2008), who onlytook into account the light inside an aperture of 3 ′ . A BRIDGE OF STARS BETWEEN LEO IV ANDLEO V?At the Galactic latitudes where Leo IV and V are lo-cated, b ∼ ◦ , the Galactic stellar populations do notvary significantly. Hence, in the absence of tidal featuresrelated to Leo IV and/or Leo V the spatial distributionof stars, in any region of the color-magnitude plane, isexpected to be very close to uniform in the area betweenthe two galaxies. We define a coordinate system ( X, Y ),rotated with respect to ( α , δ ), such that Leo IV is lo-cated at the origin and Leo V lies along the Y -axis. Us-ing the color-magnitude selection boxes overplotted onthe CMDs in Figure 1, candidate HB and RGB stars atthe distance of Leo IV and V are selected. Their spatialdistributions in the ( X , Y ) coordinate system are shownin Figure 4. The magnitude limit of B < . ◦ -wide bins along the X -axis. In thefollowing analysis we exclude all data within 5 half-lightradii of the dwarf galaxies (the ellipses in Fig. 4). Thecombined density of RGB and HB stars in each bin isplotted in panels (a) to (c) of Figure 5 with filled cir-cles for the individual mosaics and the complete dataset. The same is done for MW foreground M dwarf stars(selected in the color-magnitude region 21.0 < B < < B − V < . ◦ -wide bins are defined along the δ -axis and theirstellar densities are shown in panel (d). The distributionof MW foreground stars is consistent with being uniform,both in X and in δ . In contrast, the RGB and HB starsare uniformly distributed in δ , but not in X , where inboth fields substructure is visible that resembles a bumpor overdensity at X ∼ − . ◦ . Based on basic Poissonstatistics the significance of this bump is approximately3.5 σ . Kolmogorov-Smirnov (KS) tests (Press et al. 1992)indicate that the probability of the distribution of RGBand HB stars along the X -axis being drawn from a uni-form distribution is only 0.4%, thus rejecting this nullhypothesis at the ∼ σ level. Along the δ -axis this prob-ability is 56%, and for the MW foreground stars the prob-abilities are 87% and 62% respectively, thus all consistentwith a uniform distribution. Both tests therefore indicatethe presence of substructure only in the distribution ofRGB and HB stars and only along the direction parallelto a line connecting Leo IV and V. In addition, the KStest also shows that the distributions of RGB and HBstars along the X -axis in the individual fields are consis-tent with being drawn from the same distribution, witha probability of 59%. The substructure is therefore notisolated to a single field.To estimate the significance of this overdensity rigor-ously, we performed a ML fit similar to the one used todetermine the structural parameters of the galaxies. Thedensity at any point ( X, Y ) of the field of view, Σ(
X, Y ),is here modeled by a flat background, Σ b , with an ad-ditional linear enhancement that is constant along theLeo IV/V axis (the Y -axis of Fig. 4) and of Gaussianform G ( X | A, X , σ ) along the X -axis:Σ( X, Y | A, X , σ ) = G ( X | A, X , σ ) + Σ b (1)= A √ πσ exp − (cid:18) X − X σ (cid:19) ! + Σ b .A denotes the amplitude of the Gaussian, X its centeralong the X -axis and σ its standard deviation, also alongthe X -axis. The probability of the model parameters( A, X , σ ), given the location ( X i , Y i ) of all consideredstars in the data set, is then p ( A, X , σ | X i , Y i , ∀ stars i ) ∝L ( X i , Y i , ∀ stars i | A, X , σ ) p ( A, X , σ ) , (2)where L ( X i , Y i , ∀ stars i | A, X , σ ) is the likelihood of themodel given the data points and p ( A, X , σ ) is the priorprobability distribution for the model’s parameters. Thelikelihood itself is the product, over all stars, of the modeldefined in equation (1), taken on the stellar positions.Henceforth L ( X i , Y i , ∀ stars i | A, X , σ ) = Y star i Σ( X i , Y i | A, X , σ )= Y star i A √ πσ exp − (cid:18) X i − X σ (cid:19) ! + Σ b ! . (3)The background density, Σ b can also be expressed as afunction of the model parameters by requiring that N ∗ ,the total number of stars in the data set, corresponds tothe integral of the density, Σ, over the field of view, ofarea A :Σ b = (cid:16) N ∗ − Z FoV G ( X | A, X , σ ) dXdY (cid:17) A − . (4)he enigmatic pair of dSphs Leo IV and Leo V 5 Fig. 4.—
Spatial distribution of HB (blue dots) and RGB(black dots) stars around Leo IV and V, selected using the color-magnitude boxes drawn in Figure 1. The coordinates are rotatedso that Leo IV and V are both at X = 0 and Leo IV lies at theorigin. Red contours show the RGB star density, and correspondto densities exceeding 1.5 σ , 3 σ , 4 σ , and 5 σ over the backgrounddensity. The gray ellipses indicate the regions that are neglectedwhen looking for extra-tidal material, and the dotted vertical linesoutline the bins used for the histograms in panels (a) to (c) of Fig.5. The ML fits benefit from a larger sample of stars thanprovided by the selection boxes in Figure 1 to constrainthe fit parameters optimally. Here we therefore use adifferent selection box (the dashed box in Figure 1) con-taining 5 891 stars in the surveyed area but more than5 r h from the center either of the two dwarf galaxies. Theprior probability distributions for the model’s parameterswere chosen to be uniform over ranges that are physicallymotivated by a stream of stars originating from the dwarfgalaxies: the probability on σ is uniformly distributed be-tween 3 ′ (the typical size of the dwarf galaxies) and 12 ′ ,whereas X and A are uniformly chosen between ± . ◦ (the width of the data set), and ± X = − . ± . ◦ , σ = 0 . ± . ◦ ,and A = 172 +50 − stars/deg . This corresponds to a back- ground density of Σ b = 3224 stars/deg for the chosenselection box and a total of 275 stars in the overden-sity for the selection box and footprint used. Comparingthe peak amplitude of the overdensity to the number ofRGB and BHB stars in Leo IV yields a central surfacebrightness of µ V ≃
32 mag arcsec − . The 2-D probabilitydistribution functions are shown in Figure 6 for all pa-rameters. The significance of the peak in the probabilitydistribution function is just over 4 σ in all cases, leadingus to conclude that the data show evidence of a 4 σ over-density of stars that coincides with the bump visible inFigure 5. DISCUSSIONAll tests — the histograms in Figure 5, the KS testsand the ML fits — indicate that there is structure inthe distribution of stars consistent with being Leo IV orLeo V members in the area between the systems. Thestrongest case is provided by the last test, which indicatesa significance of the overdensity of & σ . Aside from thepreferred model, there is another local maximum visiblein Figure 6 that corresponds to an underdensity in thedata set. This coincides with the drop in density visibleat X ≃ +0 . ◦ in panels (b) and (c) of Figure 5. Thelimited extent of our survey perpendicular to the possi-ble bridge of stars implies that an overdensity can also befit as a region with high background, with an adjacentunderdensity. However, marginalizing over all parame-ters but A (top panel of Fig. 6) makes it clear that theprobability of this ‘underdensity’ is only 2%, whereas theprobability of an overdensity corresponds to 98%. Thisshows that the structure in the field is more likely causedby an overdensity than by an underdensity. This infer-ence is based purely on statistics, not taking into accountthat it is not clear what could cause an underdensity ofstars in the field.In their recent analysis, Sand et al. (2009) find no ev-idence for extra-tidal features emanating from Leo IV.Due to their much smaller field-of-view their analysisis, however, considerably less sensitive to the presenceof a possible tidal stream, despite deeper photometry.In the region between Leo IV and Leo V, where anyputative bridge would be found, our survey covers anarea seven times larger than that available to Sand et al.(2009). At a given depth, this leads to a seven-fold in-crease in the number of stellar tracers, in our case RGBand BHB stars, that can be found. The higher sensitivityof the Sand et al. (2009) data only partly compensatesfor this, and only adds fainter stars in a region of theCMD where contamination by faint galaxies is high. Thedetection limit of Sand et al. (2009) for tidal streams of µ g . − is insufficient to detect the stellarbridge, which has an estimated central surface brightnessof µ V ∼
32 mag arcsec − . It is, however, interesting tonote that one of the significant ‘nuggets’ of stars seen bySand et al. (2009) to the north-west of Leo IV lies exactlyon top of the location of the stellar bridge, as indicatedby our ML fits.The spatial proximity of Leo IV and Leo V and the in-triguing possibility of extra-tidal material between themelicits the question of whether these two systems aresomehow related and/or interacting with each other.Here we consider the following different scenarios: de Jong et al. Fig. 5.—
Stellar densities in 0 . ◦ -wide strips. In panels ( a ), ( b ) and ( c ), the strips are at constant X , parallel to the straight lineconnecting Leo IV and V. From left to right, the panels correspond to the field containing Leo IV, the field containing Leo V, and thesum of both fields. Elliptical regions corresponding to 5 half-light radii around Leo IV and Leo V are avoided (Fig. 4). In all panels, filledcircles are for stars selected with the RGB and HB color-magnitude selection boxes (Fig. 1) and open squares for foreground M dwarf stars.Vertical error bars show the Poisson errors and the horizontal error bars the width of each strip. In panel ( d ) the strips are at constantdeclination δ , almost perpendicular to the straight line connecting Leo IV and V. • Leo IV and Leo V might be condensations of starsin a much larger stellar stream, even though thedensity contrast between the condensations and theunderlying stream would be very high. The appar-ent width of the extra-tidal substructure in the can-didate RGB and HB stars of ∼
15 arcmin is similarto the sizes of Leo IV and V, and is therefore con-sistent with this scenario. In this case they wouldbe expected to closely follow the same orbit, whichshould come close enough to the Galactic center tocause the tidal disruption of a common progenitor. • Leo IV and Leo V might have fallen into theMilky Way together as members of a group ofdwarf galaxies, a process expected to be com-mon in a ΛCDM cosmology (e.g. D’Onghia & Lake2008; Li & Helmi 2008), or as satellites of a largerhalo, as has been suggested for Segue 1 and 2(Belokurov et al. 2009). Regarding the latter case,it should be noted that the revised half-light radiiof Leo IV ( ∼
200 pc) and Leo V ( ∼
130 pc) makethem much larger systems than Segue 1 and 2 and,in terms of size, clearly more similar to other dSphs.If they do constitute a pair with a common origin,they would still follow the same orbit around theMilky Way, but with a possibly large velocity dis-persion, as they orbit a common center of mass.In this scenario, extra-tidal stars might be the re-sult of interactions between the two galaxies, ratherthan with the Milky Way. • A final option would be that Leo IV and Leo V wereoriginally unrelated satellites of the Milky Way, buthad a chance encounter. A near head-on collisionmight be able to cause an interaction strong enoughto disrupt their stellar bodies.5.1.
A common orbit
If Leo IV and Leo V are tied together and follow thesame orbit around the Milky Way, their common orbitshould be easily determinable from simple physical ar-guments. In the following, we assume that the Galac-tocentric properties of the galaxies are interchangeablewith their heliocentric properties, a reasonable assump-tion given the large distances to the systems compared to the solar radius around the Milky Way. If the two dwarfgalaxies lie along the same orbit, they should actuallyshare the same orbital energy and angular momentum.The latter requirement can first be used to link togetherthe tangential velocities of the two galaxies in the planeof the sky, v t, and v t, , and their distances, r and r ,respectively for Leo IV and Leo V: v t, = v t, r /r . Wethen invoke energy conservation along the Leo IV/V or-bit to obtain( v tot , ) − ( v esc , ) = ( v tot , ) − ( v esc , ) , (5)where v tot ,i = p ( v t,i ) + ( v r,i ) is the total velocity ofLeo i , v r,i its radial velocity with respect to the GalacticStandard of Rest, and v esc ,i the escape velocity in the as-sumed model of the Milky Way potential, at the locationof Leo i . For Leo IV, the tangential motion of the orbitthat links Leo IV and Leo V is therefore defined by: v t, = vuut(cid:16) ( v r, ) − ( v r, ) + ( v esc , ) − ( v esc , ) (cid:17) − (cid:18) r r (cid:19) ! − . (6)In order to determine v t, and v t, with their associ-ated uncertainties, we follow a Monte Carlo scheme andrandomly generate the distances and radial velocities foreach of the two dwarf galaxies from Gaussian distribu-tions defined by their observed properties, as listed in Ta-ble 2. We then determine the escape velocities requiredby equation (6) for the Milky Way model adopted byPaczy´nski (1990), after removing unphysical cases whereone of the two galaxies is not bound to the Milky Way.The median and central 68.3% of the resulting distribu-tions after 10 000 trials yield v t, = 239 +19 − km s − and v t, = 211 +30 − km s − .These large values, combined with the small radial ve-locities of the dwarf galaxies, make it impossible to finda viable orbit that reproduces the observed propertiesof both systems at the same time. None of the orbitsdrawn in Figure 7 goes through both points in all pan-els, demonstrating that, whether Leo IV or Leo V is usedas a starting point, neither the velocity nor the distancealong the orbit has a strong enough gradient to replicatethe observed properties of the other dwarf galaxy. Thishe enigmatic pair of dSphs Leo IV and Leo V 7 Fig. 6.—
Probability distribution functions from maximum-likelihood fits of a linear Gaussian to the stellar distribution between LeoIV and Leo V.
Top panel: probability distribution function of the model parameter A marginalized over the two other parameters. Theregion of negative A , shown in grey, yields a small probability of only 2%, compared to 98% for the region of positive A ; the probabilityof the best model (indicated with a filled circle in all panels) is a factor ∼ higher than that of a uniform distribution ( A =0), whichcorresponds to a ∼ σ significance. Bottom panels: for all combinations of the three fit parameters ( A , X and σ ) the two-dimensionalprobability function is shown, marginalized over the third parameter. Here, contours represent drops of 50%, 90%, 99% and 99.9% of theprobability with respect to the best model. analysis thus shows that Leo IV and V cannot be follow-ing the exact same orbit. We can calculate a compromisesolution, with a starting point for the orbit integrationthat has the mean properties of the two galaxies (the cen-tral line in Figure 7). This orbit does not reproduce thevelocities and distances of the two systems and remainsat large Galactocentric distances, with an apocenter of244 kpc and a pericenter of 158 kpc. We conclude thatLeo IV and Leo V are very unlikely to be condensationsin a larger stellar stream, for two reasons: no viable singleorbit exists, and the compromise solution does not comeclose enough to the Galactic center for a single progenitorto have been tidally affected.5.2. A ‘tumbling pair’
Rather than being remnants of a progenitor disruptedby the gravitational tides of the Milky Way, the twodwarf galaxies could be a gravitationally bound pair in-teracting with each other. This means that they wouldfollow a ‘common’ orbit, but with a large velocity disper-sion, as they orbit their common center of mass. Such a‘tumbling pair’ of dwarf galaxies would be similar to the Large and Small Magellanic Clouds, albeit much morescaled-down. For the two systems to be gravitationallybound, the total kinematic energy of the system mustbe less than the total gravitational potential energy. Aspointed out by Davis et al. (1995), the two-body Newto-nian binding criterion can be written as M sys ≥ Rv los G sin α , (7)where M sys is the total mass of the system, R the dis-tance between the two objects, v los the line-of-sight rela-tive velocity, and α the angle between the axis of the two-body system and the sky. Inserting the values for theseparameters ( v los = 50 . ± . − , R = 22 ±
10 kpc, α = 70 ◦ +6 − ; see Table 2 and references therein) yields alower limit for the total mass of M sys ≥ ± × M ⊙ ,or half of that for each individual dwarf.Masses inferred from the stellar velocity dispersions infaint dSph galaxies are typically much lower, but onlyprobe the inner few hundred parsec of their dark mat-ter halos. Based on dynamical modeling of dSphs em-bedded in cosmologically motivated dark matter halos, de Jong et al. Fig. 7.—
Orbits for Leo IV and V, derived assuming commonenergy and angular momentum for the two dwarf galaxies. Thedotted, dashed and solid lines correspond to orbits with initial con-ditions determined using Leo IV, Leo V or their mean properties,respectively. The panels show the evolution of Galactic latitude(top), heliocentric distance (middle) and radial velocity with re-spect to the Galactic Standard of Rest (bottom) as functions ofGalactic longitude. Properties of Leo IV and V are indicated byfilled and open circles, respectively.
Fig. 8.—
Cumulative probability distribution for the distancebetween two dark matter subhalos (with a current mass larger than5 × M ⊙ ) in the last 3.4 Gyr (see text for details). Pe˜narrubia et al. (2008) derive masses of up to severaltimes 10 M ⊙ for Local Group dSphs. The masses re-quired for Leo IV and Leo V to be a bound pair aretherefore possible, but imply high mass-to-light ratios ofM/L V =10 in solar units.5.3. A close encounter
A third option would be that Leo IV and V are un-related systems that randomly collided in the MilkyWay halo, thus provoking an interaction. Given that the objects have a stellar extent of ∼
500 pc, we esti-mate that they would need to come to within a fewkiloparsecs of each other with a relative velocity of lessthan ∼
100 km s − for tides to affect their stellar com-ponents. We used results from N-body simulations inorder to compute the probability of such an encounter.We started from the four Milky Way-like dark matter(ΛCDM) halos presented in Macci`o et al. (2009) and, foreach subhalo within 250 kpc of the host galaxy’s centerand with a bound mass today M sub > × M ⊙ , wedetermined the distance to any other subhalo, D sub − sub ,in the last 3.4 Gyr. Figure 8 shows the cumulative prob-ability distribution for D sub − sub in the four Milky Wayanalogue simulations. The probability of two halos com-ing to within 5 kpc of one another is as low as a fewtimes 10 − . In addition, this number can only be anupper limit for a galaxy-galaxy interaction, since only ≈
30% of dark matter halos with M sub > × M ⊙ areexpected to host stars (Macci`o et al. 2009). We concludethat a collision between Leo IV and Leo V is not a likelyexplanation for a possible interaction. CONCLUSIONSGiven that Leo IV and Leo V form a close pair on thesky, in distance, and in radial velocity, it has been arguedthat they might be interacting or even share the same or-bit (Belokurov et al. 2008). We have obtained new, deepphotometry in two 1 ◦ × ◦ fields containing both dwarfspheroidal galaxies, re-derived their structural proper-ties, and searched for extra-tidal stars. Both Leo IV andLeo V are considerably larger than previously thought,with sizes of 206 pc and 133 pc. These sizes are simi-lar to those of other recently discovered dSphs such asBo¨otes I or Ursa Major II (respectively 242 and 140 pc,Martin et al. 2008b) and the smaller ‘classical’ dSphs,for example Draco (221 pc, Martin et al. 2008b) or LeoII (185 pc, Coleman et al. 2007b). Both are also stronglyelongated, with axis ratios of 2:1, which is the case formany of the fainter ( M V > −
8) dSphs (Martin et al.2008b). We note, however, that the proximity of bothdwarf galaxies near the edge of our survey might havesome influence on these measurements.The combination of deep photometry and a large areacoverage of our survey provides an unprecedented sen-sitivity to low surface brightness features in the regionbetween Leo IV and Leo V. Analysis of the spatial dis-tribution of candidate RGB and HB stars using den-sity histograms and Kolmogorov-Smirnov tests revealsthe presence of a significant substructure in the observedfields. This substructure is detected at the ∼ σ level,but only along the direction connecting the two systems.Maximum-likelihood modeling of the stellar distributionwith a linear Gaussian confirms that the spatial struc-ture can be fit with an overdensity connecting the twosystems. With this method, the significance of the over-density is just over 4 σ , and has a peak surface brightnessof µ V ≃
32 mag arcsec − .The reason for the close proximity of Leo IV and Leo Vis still an enigma, and we have considered a few possibleexplanations. Orbits derived for the objects using theirpositions and velocities and by requiring the pair to sharecommon values for energy and angular momentum showthat it is not possible for both to be on the exact same or-bit under reasonable assumptions. Furthermore, a com-he enigmatic pair of dSphs Leo IV and Leo V 9promise orbit would not approach the Galactic centercloser than ∼
160 kpc, as also noted by Belokurov et al.(2008). Hence, it is highly unlikely that Leo IV and LeoV are condensations in a low surface brightness stellarstream resulting from the tidal disruption of a commonprogenitor. The fact that the elongations of the two sys-tems are not aligned might be a further indication of this.A large velocity dispersion around a mutual orbit, for ex-ample in the case of a ‘tumbling pair’ of dwarf galaxies,is only viable if Leo IV and Leo V have masses of atleast a few times 10 M ⊙ . This would imply extreme V -band mass-to-light ratios of & in solar units, butrecent dynamical simulations of dwarf spheroidal galaxies(Pe˜narrubia et al. 2008) show that the required massesare possible. If Leo IV and Leo V are indeed a bound andinternally interacting pair, this could account naturallyfor their unaligned elongations and the offset of the ap-parent ‘stellar bridge’ from the straight line connecting them. Finally, analysis of Milky Way-like ΛCDM halosreveals that the probability of two satellites colliding isnegligibly small. This is consistent with the findings ofBelokurov et al. (2008) who calculate a .
1% probabilityfor such a close association happening by chance. There-fore, the scenario in which Leo IV and Leo V are a boundpair of dwarf galaxies, orbiting and interacting with eachother, appears to be the most viable explanation for thisclose celestial companionship.The authors thank the anonymous referee for help-ful comments. Based on observations collected at theCentro Astron´omico Hispano Alem´an (CAHA) at CalarAlto, operated jointly by the Max-Planck Institut f¨ur As-tronomie and the Instituto de Astrof´ısica de Andaluc´ıa(CSIC). This research has made use of the VizieR cata-logue access tool, CDS, Strasbourg, France.
REFERENCESAbazajian, K. N., Adelman-McCarthy, J. K., Ag¨ueros, M. A.,Allam, S. S., Allende Prieto, C., et al. 2009, ApJS, 182, 543Belokurov, V., Zucker, D. B., Evans, N. W., Kleyna, J. T.,Koposov, S., et al. 2007, ApJ, 654, 897Belokurov, V., Walker, M. G., Evans, N. W., Faria, D. C., Gilmore,G., et al. 2008, ApJ, 686, L83Belokurov, V., Walker, M. G., Evans, N. W., Gilmore, G., Irwin,M. J., et al. 2009, arXiv:0903.0818Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393Bertin, E. 2006, in