The moving groups as the origin of the vertical phase space spiral
Tatiana A. Michtchenko, Douglas A. Barros, Angeles Pérez-Villegas, Jacques R. D. Lépine
DDraft version March 21, 2019
Preprint typeset using L A TEX style emulateapj v. 12/16/11
THE MOVING GROUPS AS THE ORIGIN OF THE VERTICAL PHASE SPACE SPIRAL
Tatiana A. Michtchenko , Douglas A. Barros , Angeles P´erez-Villegas , and Jacques R. D. L´epine Universidade de S˜ao Paulo, IAG, Rua do Mat˜ao, 1226, Cidade Universit´aria, 05508-090 S˜ao Paulo, Brazil Rua Sessenta e Trˆes, 125, Olinda, 53090-393 Pernambuco, Brazil (Dated: March 21, 2019)
Draft version March 21, 2019
ABSTRACTUsing the
Gaia data release 2 (DR2), we analyzed the distribution of stars in the close vicinity ofthe Sun in the full 3D position-velocity space. We have found no evidence of incomplete phase mixingin the vertical direction of the disk, which could be originated by some external events. We show thatthe vertical phase space spiral Z – V z is produced by the well-known moving groups (MGs), mainlyby Coma-Berenices, Pleiades-Hyades and Sirius, when the statistical characteristics (mean, median,or mode) of the azimuthal velocity V ϕ are used to analyze the distribution in the vertical position-velocity plane. This result does not invoke external perturbations and is independent on the internaldynamical mechanisms that originate the MGs. Our conclusions counterbalance current argumentsin favor of short-lived (between 300 and 900 Myr) structures in the solar neighborhood. Contrarily,they support the hypothesis of a longer formation time scale (around a few Gyr) for the MGs. Subject headings:
Galaxy: kinematics and dynamics—solar neighborhood—Galaxy: structure—Galaxies: spiral INTRODUCTION
The
Gaia data release 2 (DR2) has brought many newresults and interpretations for the observed phenomenarelated to the dynamics of the stars in the Solar neigh-borhood (SN). One result in particular came as a sur-prise, the detection by Antoja et al. (2018) of spiral-like structure in the Z -direction (perpendicular to theGalactic plane). This structure extends in the ranges of-1 kpc < Z < − < V z <
60 km s − . Theauthors interpret it as an evidence of incomplete phasemixing in the vertical direction of the Galactic disk, thatrequires to assume some hypothesis on the origin for thisphenomenon. Several works have already proposed ex-planations, like the influence of a satellite galaxy (Antojaet al. 2018; Binney & Sch¨onrich 2018; Bland-Hawthornet al. 2018; Laporte et al. 2019), the buckling instabilityof the bar (Khoperskov et al. 2019) and the vertical bend-ing waves in a stellar disk (Darling & Widrow 2019).Antoja et al. (2018) also claim that there is ”a strongcorrelation between the vertical and the in-plane motionsof the stars”. Since it is generally accepted that the domi-nant structures in the phase-space distribution of the SNare the moving groups (MGs) (e.g. Antoja et al. 2008;Quillen et al. 2018), that statement prompted us to in-vestigate the connection between the vertical structuresand the MGs.We provide a short description of the MGs in theGalactic plane in Sect. 3. The MGs have widely beenattributed to Galactic resonances, associated with thebar and/or spiral arms, such as the inner and outer Lind-blad resonances (ILRs and OLRs) and corotation (P´erez-Villegas et al. 2017; Michtchenko et al. 2018; Hattoriet al. 2018).The distribution of stars in the Galactic plane is com- e-mail: [email protected]: [email protected]: [email protected]: [email protected] pared with the distribution of stars in the Z –directionin Sect. 4. Our approach is to focus on the arrangementof stars in the phase-space as they are observed, withoutusing any dynamical model to explain the observed dis-tribution. In Sect. 5, starting from the known distribu-tion of stars associated with the MGs, we verify that, in astatistical representation of V ϕ (the velocity in the direc-tion of Galactic rotation) on the Z – V z plane, a spiral-likestructure appears more pronounced in the median/modevalues than in the mean values. We associate this be-havior to the inhomogeneous distribution of the data inthe bins with fixed Z and V z related to the existing MGs.The MGs pull the median/mode towards themselves thatproduces V ϕ -oscillations between the bins and, conse-quently, the spiral-like feature on the Z – V z plane. Oncontrary to the incomplete vertical phase mixing, whichrequires a number of assumptions on its origin, our in-terpretation is based on the well-known fact of existingMGs. There is no need for any external mechanism, butonly the known MGs, to explain the observed spiral onthe Z – V z plane.An interesting consequence of our finding concerns thelifetime of the structures in the SN. If we assume thatMGs are formed by action of diverse resonances of thespiral arms and/or bar, we can conjecture about the life-time of these structures. Indeed, the establishment ofresonance zones, that are filled with captured stars, isnot a fast process. For instance, the azimuthal periodof the orbits close to the corotation zone is about 1 Gyr.Therefore, our result reinforces the idea of longer forma-tion time scales for the structures in the SN, such as theMGs. Consequently, this conclusion not only brings anargument against that the spiral structure in the Z − V z plane is an evidence of the incomplete phase mixing,which is in favor of short-lived structures (between 300and 900 Myr, see Antoja et al. 2018), but it also rein-forces the idea of longer formation time scales for thestructures in the SN, such as the MGs. a r X i v : . [ a s t r o - ph . GA ] M a r Fig. 1.—
Density of stars in the SN in the V R – V ϕ plane, ina logarithmic scale, calculated in a grid of 2.0 × − . The V R – V ϕ plane is divided into six zones (see text for details). Thelocation of the main MGs is indicated as: 1 - Pleiades-Hyades, 2 -Coma-Berenices, 3 - Sirius, 4 - Hercules. SAMPLE
Our sample consists of stars from the
Gaia
DR2 (GaiaCollaboration et al. 2018), which provides positions, par-allaxes (cid:36) , proper motions (Lindegren et al. 2018), andradial line-of-sight velocities (Katz et al. 2018) for starswith
G <
13 mag. The sample was restricted to objectswith parallax errors smaller than 20%. In order to con-vert the positions, parallaxes, proper motions on thesky, and radial velocities of the selected stars into Carte-sian Galactic positions and velocities, we used the galpy python tool (Bovy 2015).Following Antoja et al. (2018), we also transformedthe heliocentric rectangular coordinates to the Galacto-centric cylindrical coordinates for the stellar positions( R , ϕ , Z ) and velocities ( V R , V ϕ , V z ). We consider thatthe Sun is placed at the Galactocentric and vertical dis-tances of R = 8 . Z = 0 .
027 kpc, respec-tively, with a circular velocity of V ( R ) = 230 km s − ;these parameters are slightly different from those usedin Antoja et al. (2018). We assume the solar pecu-liar motion with respect to the Local Standard of Restas (11 . , . , .
25) km s − (Sch¨onrich et al. 2010). Tocompare our results to those presented in Antoja et al.(2018), we limit the Galactocentric radii to the range of7.9 kpc < R < | ϕ | < ◦ from theSun, and in the vertical position and velocity to | z | < . | V z | <
60 km s − , respectively. As result, ourfinal catalog contains 838,883 stars. SAMPLE ON THE V R – V ϕ PLANE AND MGS
Figure 1 shows the velocity distribution in the V R – V ϕ plane. The well-known MGs are easily identified inthe figure as streams extended along the horizontal axis, V R . They appear delimited along the V ϕ -axis, producinga ridge-like pattern. These features were analyzed anddescribed in detail in our previous work (Michtchenkoet al. 2018), where we associated them to the action of thecorotation and the near-by high-order ILRs and OLRs ofthe spiral arms. Briefly, we summarize below our mainresults, roughly delimiting in Fig. 1 the zones of actionof these dynamical mechanisms. There are: • zone I - stars coming from the inner part of theGalaxy and evolving in the 6/1 ILR; • zone II - Hercules stream ( • zone III - a weak stream associated with the 12/1and higher-order ILRs, close to the corotation zone; • zone IV - corotation zone harboring the Sun, theMGs of Coma-Berenices( • zone V - Sirius group ( • zone VI - the objects involved in the strong 4/1OLR.This zone list is one example of interpretation of thepossible nature of the MGs. There are several other onesin the literature; we note that the interpretation is notrelevant in the present work. The contour around regions1, 2 and 3 encompasses partially Pleiades-Hyades, Coma-Berenices, and Sirius, respectively, and represents 90%of the maximal density of the sample. This contour isused to select stars that clearly belong to each group:Pleiades-Hyades with 114,565 members, Coma-Bereniceswith 47,722 members, and Sirius with 30,954 members. MGS IN THE VERTICAL POSITION-VELOCITYDIRECTION
Knowing the stellar velocity distribution in the Galac-tic plane, we now can study the phase and velocity spacesof the MGs outside of the plane. For this, we plot thedensity of stars in the vertical position-velocity direc-tion as a function of the azimuthal ( V ϕ ) and radial ( V R )velocities in Fig. 2. Since the MGs are associated withdifferent ranges of V ϕ , their respective zones, from I toVI, are easily identified on the planes V ϕ – Z and V ϕ – V z (left column). The Hercules stream (zone II) is moreevident, since this group is clearly separated from theothers. The Hercules members are nearly symmetricallydistributed in the vertical direction. The same behavioris observed for the III- and V-zones, which both are stuckto the main component located in the IV-zone. There isno observed correlation between azimuthal and verticalvelocities on these density maps (Fig. 2), at least, in alarge scale (analysis of possible local alterations is out ofthe scope of this paper).The vertical position/velocity distribution of the MGsshown in Fig. 2 (left column) suggests that the motion ofstars out of the Galactic plane can be approximated bya one-dimensional oscillator model (Binney & Tremaine2008). It is expected that the observed vertical scat-tering of the groups is correlated with the size of theirpopulation, which seems to be correct in the case of thelow-density Hercules group. However, Sirius has approx-imately only one quarter of the Pleiades-Hyades’ popu-lation, but the vertical extensions of the correspondingzones IV and V are quite similar. We analyzed the dis-tributions of the heights from the Galactic plane of thestars from Pleiades-Hyades, Coma-Berenices, and Sirius,and we found that the scale-heights of the distributionsvary in the narrow range from 127 pc (Pleiades-Hyades)to 140 pc (Sirius). This suggests that the vertical excur-sions of objects can be originated, at least partially, by Fig. 2.—
Left column: Density of stars in the SN on the V ϕ – Z (top) and V ϕ – V z planes (bottom), in the logarithmic scale, calculatedon a 2.0 km s − × × − grid, respectively. Right column: The same as left panels, except for V R along thehorizontal axis. the Galactic resonances. Indeed, the resonances excitethe motion of the group’s members and this excitationshould be related to the force of the resonance and itschaotic region. The corotation (zone IV) is the strongestresonance, while the chaotic phenomena are stronger inthe Sirius zone (zone V), where the 8/1 and higher-orderOLRs overlap.Contrarily to what happens along the azimuthal ve-locity V ϕ , the MGs have no well-defined characteristicvalues of the radial velocity V R . Indeed, as shown inFig. 1, the MGs are extended along the V R -axis, overlap-ping in the range between approximately -20 km s − and20 km s − . Due to this fact, the distribution of the starson the V R – Z and V R – V z planes (right column in Fig. 2)is more homogeneous and the MGs are not detectable.This difference contributes to the distinct appearances ofthe azimuthal and radial velocities on the Z – V z plane, asshown in the next section. MODES OF V R AND V ϕ IN THE VERTICAL DIRECTION
Figure 3 clarifies the mechanisms that contribute tothe formation of a spiral on the Z – V z plane, and, at thesame time, provides a comparison between the propertiesof the azimuthal velocity V ϕ (left column) and the radialvelocity V R (right column). At the top row, the modesof these velocities, obtained in bins of ∆ Z =0.02 kpc and∆ V z =1.0 km s − , are shown in a linear color scale on the Z – V z plane. These panels reproduce similar informationto that one shown by Antoja et al. (2018) in their Fig. 2,(b) and (c), although they used the medians, not themodes as done here. Several authors prefer to present means and/or medians versions of those figures. Wechoose to use the modes because this emphasizes the ef-fect of groups present in the sample. A spiral is clearlyvisible in the V ϕ representation (top-left panel in Fig. 3),while, in the V R representation (top-right panel), its pres-ence is just marginal, if existent.The middle row in Fig. 3 presents the stellar densityon the V ϕ – Z (left) and V R – Z (right) planes. Theseplanes are the same of Fig. 2 (top row), except thatnow we consider the stars confined to a narrow inter-val of -1 km s − < V z < − . These planes areuseful to analyze the structures located along the x –axis on the planes Z – V z (top row), inside the bins of0.02 kpc × − . Using this reduced sample of stars,we calculated the modes of the velocities as functions of Z in bins of 0.02 kpc, and plotted them on the correspond-ing planes in Fig. 3 (middle row) by black symbols. Sincethe mode values are signicantly spread, we apply a low-pass filter, in order to cut off the numerical noise. Thesmoothed red curves obtained show clearly an oscilla-tory behavior, which must produce spiral-like structureswhen calculated for all velocity values and projected onthe Z – V z plane.Black horizontal lines on the middle panels in Fig. 3illustrate the position of bins with fixed Z , from whichwe extract the histograms of objects along the V ϕ and V R directions (bottom row). On the V ϕ – Z plane, wechoose two Z –values, which correspond to the minimumvalue of the V ϕ –mode, at 0.23 kpc, and the maximumof the V ϕ –mode, at 0.35 kpc. The V ϕ –mode along thefirst line (corresponding to the blue-colored histogram on Fig. 3.—
Top row: Mode values of the azimuthal velocity V ϕ (left) and the radial velocity V R (right) calculated in bins of0.02 kpc × − on the Z – V z planes. Middle row: Same as the top row in Fig. 3, considering stars within − . < V z < . − .The crosses show mode values of the azimuthal velocity V ϕ (left) and the radial velocity V R (right) as functions of Z . The red curves arethe same functions, with noise filtered by applying a low-pass filter. Bottom row: Normalized frequencies of the stars from the intervals:left - Z = 0 . ± .
01 kpc (blue) and Z = 0 . ± .
01 kpc (white); right - Z = 0 . ± .
01 kpc (blue) and Z = − . ± .
01 kpc (white). Themain MGs are indicated. the bottom-left panel) gets its major contribution fromPleiades-Hyades, at V ϕ around 220 km s − , which is inagreement with Fig. 1. The second black line crosses Sir-ius at V ϕ around 240 km s − , which gives the majorcontribution in the white-colored histogram. It also hasa minor contribution from Coma-Berenices.On the middle-right panel in Fig. 3, we choose two bins,at Z = -0.10 and Z = +0.13 kpc. We see that the cor-responding histograms (bottom-right panel) have severalcomparable peaks, due to the contribution of the over-lapping MGs. As a consequence, the V R –mode does notshow well-defined variations when we vary Z (middle-right panel). Thus, the large amplitude mode oscillationof V ϕ gives rise to the spiral on the Z – V z plane, whilethe lower amplitude mode oscillation of V R produces apractically non-existent spiral.The discussion above allows us to identify, at leastin a first approximation, the MGs that give main con-tributions to different parts of the vertical phase spacespiral-like structure. The white-color histogram inFig. 3 (bottom-left panel) shows that the Sirius groupmust be responsible for the outer ’loop’ of the spiral-like structure in Fig. 3 (top-left). This result is sup-ported by the observational evidence that metal-poorstars ([Fe/H] < -0.2) are dominating in the external partof the vertical spiral (Bland-Hawthorn et al. 2018), to-gether with our interpretation (see Sect.3), according towhich the Sirius group comes from the outer Galacticdisk.Coma-Berenices, located between Pleiades-Hyades andSirius, have typical V ϕ -values of around 225–230 km s − and their main contribution to the spiral-like structureis limited around the origin on the Z – V z plane. Thepeculiar location of this group, deeply inside the coro-tation zone, can explain the metal-richness ([Fe/H] > V ϕ around 220 km s − is dominating in population in the SN. We deduce thatthe valleys corresponding to the lower values of the V ϕ -mode in the spiral-like distribution in Fig. 3 top-left isoriginated by this group. A spiral-like structure produced by three MGs
Here we perform a detailed analysis of the groupsPleiades-Hyades, Coma-Berenices, and Sirius, whosemembers were selected as described in Sect.3. Our pur-pose is to show how a spiral feature in the vertical phasespace can be produced by the sum of the MGs. In Fig. 4,we present the Z – V z plane for each group, with distinctvalues of the V ϕ –median, given by the color scales besideeach panel, from (a) to (c). The panel (d) is the same ofthe others, obtained by merging the samples of the threegroups and then computing the medians in each bin.Figure 4 shows that the spiral-like feature is onlymarginally present in any of the groups on the pan-els (a)–(c). The remaining spiral-like features are dueto the ’contamination’ of one group by the membersof others; this effect is vanishing for the Sirius group,which is well-separated from Pleiades-Hyades and Coma-Berenices (see Fig. 1). However, the spiral-like structureappears clearly in the sum of the three samples on thepanel (d). This result shows that, to obtain a spiral, nothing else except the well established MGs are needed. TESTING THE CORRELATION BETWEEN THEVERTICAL AND IN-PLANE MOTIONS
The claim made in Antoja et al. (2018), that theplane and vertical components of the stellar motion arestrongly correlated, can be tested on a basis of reci-procity: if the in-plane motion (particularly, the az-imuthal velocity V ϕ ) influences the vertical phase-spaceproducing the spiral-like feature (Fig. 3 top-left), the in-verse must be true and some structure should appear inthe equatorial phase-space also.We first analyze the distribution of the stars fromour sample on the equatorial plane R – V ϕ , plotting thestar density in bins of 0.004 kpc × − as shown inFig. 5 (top). Even if the R -range of the objects from oursample is small (7.9 kpc < R < R – V ϕ plane were explained in Michtchenkoet al. (2018) as footprints of the dynamical phenomena,corotation and near-by high-order Lindblad resonances(see Fig. 2 in that paper). In particular, Hercules, whichwe associated to the 8/1 ILR (zone II), is easily distin-guished in Fig. 5 top.However, the median values of the vertical velocity V z on the R – V ϕ plane (Fig. 5 bottom) show that there isno a clear feature, in such a way revealing that, if thecoupling between vertical and in-plane motions exists, itshould be weak. According to Khanna et al. (2019), de-creasing sufficiently the V z -range, we will probably findsome structures, formed by objects from the very closevicinity to the Galactic plane. These structures wouldbe due to asymmetries, clearly visible in the MGs distri-butions in Figs. 2 and 3. CONCLUSIONS
We re-examined the distribution of stars around theSun in the vertical position-velocity phase space. Wehave observed a spiral-like feature on the Z – V z plane,when the distribution of the mode of the azimuthal stel-lar velocity, V ϕ , was plotted. We attributed this behaviorto the use of the statistical presentation of V ϕ (mean, me-dian, or mode) and analyzed its properties in the Galacticplane. The kinematics in this plane shows a highly inho-mogeneous distribution for the velocities, characterizedby the presence of several massive MGs such as Coma-Berenices, Pleiades-Hyades and Sirius. On the otherhand, Hercules has no significant contribution to the ver-tical phase space spiral due to its low star density. Thegroups can be roughly separated in bands of specific val-ues of the azimuthal velocity: lower for Pleiades-Hyadesand higher for Sirius, with those of Coma-Berenices be-tween them. Plotted out of the Galactic plane, thesebands can be still distinguished in vertical positions andvelocities. We show that each of these bands shifts thevalues of the mean/median/mode in bins in its direction,producing oscillations that originates a spiral-like struc-ture in the Z – V z distribution. Thus, we could explainthe ’snail shell’ pattern as a kind of behavior producedby the use of the statistical V ϕ -component, which intro-duces the effects due to the MGs on the Z – V z plane.This result shows that there is no evidence of the in-complete phase mixing in the vertical direction of the Fig. 4.—
Median of V ϕ of Pleiades-Hyades (a), Coma-Berenices (b) and Sirius (c), calculated in bins of 0.02 kpc × − . Each panelis constructed in a linear color scale with stars of only one MG, selected within the contours of regions 1, 2, 3 of Fig. 1. The panel (d) isthe sum of the contributions of the three MGs of the previous panels. Galactic disk and, consequently, excludes the need forengaging external perturbations that would originate it.Moreover, it counterbalances any argument in favor ofshort-lived structures in the SN. Indeed, since it needs afew Gyr for stars in the SN to complete a few azimuthalperiods, the formation time scale of the MGs should beof the same order. However, this topic should be an issuefor a specific study.
ACKNOWLEDGEMENTS
We acknowledge our referee, Dr. James Binney, for thedetailed review and for the helpful suggestions, which al-lowed us to significantly improve the manuscript. Thiswork was supported by the Brazilian CNPq, FAPESP,and CAPES. APV acknowledges FAPESP for the post-doctoral fellowship 2017/15893-1. This work has madeuse of the facilities of the Laboratory of Astroinformatics(IAG/USP, NAT/Unicsul), funded by FAPESP (grant2009/54006-4) and INCT-A.
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Fig. 5.—
Top: Density of the stars from our sample onthe R – V ϕ plane, in logarithmic scale, calculated on a grid0.004 kpc × − . The zones of the MGs, from II to VI, areindicated by dashed lines. Bottom: Same as on the top panel,except that the median value of V zz