The kinematical and space structures of IC 2391 open cluster and moving group with Gaia-DR2
E. S. Postnikova, W. H. Elsanhoury, Devesh P. Sariya, N. V. Chupina, S. V. Vereshchagin, Ing-Guey Jiang
aa r X i v : . [ a s t r o - ph . GA ] A ug Research in Astron. Astrophys. Vol.0 (200x) No.0, 000–000 R esearch in A stronomy and A strophysics The kinematical and space structures of IC 2391 opencluster and moving group with Gaia-DR2
E. S. Postnikova, W. H. Elsanhoury, , Devesh P. Sariya, N. V. Chupina, S. V.Vereshchagin, and Ing-Guey Jiang Institute of Astronomy of Russian Academy of Sciences (INASAN), 48 Pyatnitskaya st.,Moscow, Russia; Astronomy Department, National Research Institute of Astronomy and Geophysics(NRIAG) 11421, Helwan, Cairo, Egypt (Affiliation ID: 60030681); Physics Department, Faculty of Science, Northern Border University, Rafha Branch, SaudiArabia; Department of Physics and Institute of Astronomy, National Tsing Hua University,Hsin-Chu, Taiwan, [email protected] ; Abstract
The kinematical parameters, spatial shape and structure of the opencluster IC 2391 and the associated stellar stream are studied here using Gaia-DR2(GDR2) astrometry data. The apex positions are determined for the open clusterIC 2391 (data taken from Cantat-Gaudin et al.) and for the kinematical stream’sstars mentioned in Montes et al. using both convergent point and AD-diagrammethods. The values of apex coordinates are: (
A, D ) CP =(6 . h ± . h , − . ◦ ± . ◦ . h ± . h − . ◦ ± . ◦ A , D )= (6 . h ± . h − . ◦ ± . ◦
3; cluster) & (6 . h ± . h − . ◦ ± . ◦ Key words:
Stars: kinematics and dynamics, Galaxy: stellar content, (Galaxy:)open clusters and associations: individual: IC 2391
Stellar moving groups are ensembles of gravitationally unbound stars moving with almost iden-tical space motions (Montes et al. 2001, Chumak & Rastorguev 2006). IC 2391 is an interestingtarget which represents an open cluster as well as a stellar moving group (a.k.a. stream, flow, orsupercluster). The young moving group IC 2391 was discovered by Eggen (1991). In the Gaiaera, with the availability of extremely precise data, moving groups are seeing new limelight tounderstand the Galactic disk in the solar neighborhood. Also, young clusters like IC 2391 in the
E. S. Postnikova et al. solar vicinity enable us to characterize the abundance of our immediate portion of the Galacticdisk (D’Orazi & Randich 2009).IC 2391 (other names: MWSC 1529, Cl VDBH 42, omi Vel Cluster, C 0838-528, Escorial 31)is a nearby young open star cluster located in south of the Galactic plane ( α = 08 h m . s δ = − ◦ m s ) with Galactic coordinates ( l, b ) = (270 . ◦ , − . ◦ m − M ) =5.84. Using Hipparcos data for 11 stars, Robichon et al. (1999) obtained a distance of 146 +48 − pc.Dodd (2004) evaluated the cluster’s distance as 147 ± . E ( B − V ) = 0 .
01 (Randich et al. 2001).The proper motion of the cluster was given by Loktin (2003) as ( µ α cos δ, µ δ = − . ± . , . ± .
28 mas yr − ), while Dodd (2004) gave mean proper motion components= − . ± .
53 and 23 . ± .
23 mas yr − . Both of these works used Tycho-2 catalogue (Høg etal. 2000). Dias et al. (2002) listed the value of the proper motion components as − . ± . . ± .
30 mas yr − . The radial velocity of IC 2391 is 12 . ± .
533 km s − as given byConrad et al. (2014) and about 14 . ± .
14 km s − according to Dias et al. (2002).In the 3D velocity space, a kinematical stream (or, moving group) of several dozens of starsis associated with IC 2391 open cluster. Eggen (1991) discovered the stream and used the term“supercluster” for it. Montes et al. (2001) prepared a modern list of the member stars of IC 2391stream. The visible dimensions of the stream (in V ) are 60’ . × .
00. The member stars ofthe stream occupy a broad area of the sky, with its stars being scattered almost throughout thenorthern hemisphere. Eggen (1991, 1995) suggested an age spread among the stream’s stars.Montes et al. (2001) provided an age estimate of 35 Myr for the stream.With its unprecedented high accuracy, the Gaia data allows us to address the questionof the reliability of the joint origin and the possible spatial-kinematic connection of the starstream and cluster. In this paper, we used two lists of stars: cluster members of IC 2391 listedin Cantat-Gaudin et al. (2018) and another list of stars belonging to the stream from Monteset al. (2001). Data for the cluster and the stream’s stars can be found in Table 1 and Table 2,respectively. We will use these parameters to determine apex positions (example, Vereshchaginet al. 2014; Elsanhoury et al. 2016, 2018) for the cluster and the stream using both convergentpoint method (CP) and AD-diagram method. We also study the space motion, the velocityellipsoids, the shape in the space and birthplaces for both cluster and the stream.The structure of this article is as follows: Section 2 explains the data used in this study.Section 3 deals with the kinematical properties. The next Section shows velocity ellipsoid pa-rameters. In Section 5, we discuss the cluster’s shape in space. Section 6 gives the birthplacesof the IC 2391 cluster and the stream. The conclusions of this work are presented in Section 7.
Using Gaia Data Release 2 (GDR2, Gaia Collaboration et al., 2016, 2018) data, Cantat-Gaudinet al. (2018) provided a list of 224 probable members of IC 2391. Out of those, 39 stars have he structure of IC 2391 3
Table 1
Data for 39 stars of IC 2391 cluster. The star list is taken from Cantat-Gaudinet al. (2018). Apex positions and distance mentioned in the table are determined inthis paper.
GDR2 α J . δ J . π σ π µ α σ µ α µ δ σ µ δ V r σ V r A D ddeg deg mas mas yr − mas yr − km s − deg deg pc5317423293481147264 131.89258 -54.48348 6.55 0.02 -25.28 0.05 23.66 0.04 12.86 2.16 91.38 -1.04 151.655317884439832479872 130.75151 -53.90202 6.38 0.03 -23.29 0.06 22.85 0.06 16.48 4.82 94.29 -6.48 155.075317887321743547264 130.57572 -53.90217 6.64 0.04 -24.63 0.06 23.31 0.06 16.12 0.68 93.10 -6.34 148.845317906155187202176 130.34457 -53.63577 6.53 0.02 -24.91 0.04 23.20 0.05 16.51 1.32 92.58 -6.38 152.005318059532750974720 129.84384 -53.91815 6.48 0.05 -24.45 0.10 23.44 0.11 16.94 0.94 92.95 -6.86 151.615318069604459639552 129.10085 -54.01815 6.47 0.02 -23.69 0.04 23.38 0.05 14.11 2.21 91.02 -2.74 153.435318077507199948672 129.46469 -53.76262 6.68 0.02 -24.73 0.04 23.76 0.04 14.86 0.80 91.36 -4.04 148.635318093243960659456 130.20441 -53.62916 6.71 0.02 -24.04 0.04 23.80 0.04 13.55 0.61 91.99 -1.96 147.955318097916884923520 130.07602 -53.50790 6.60 0.02 -23.75 0.04 22.46 0.04 14.52 2.49 91.78 -4.32 150.345318150349846655488 128.93185 -53.35554 6.34 0.28 -24.26 0.53 23.51 0.50 17.61 7.77 92.55 -6.79 141.985318162238316886528 129.74460 -53.32008 6.60 0.02 -24.90 0.04 23.00 0.04 16.87 11.83 92.27 -7.11 150.205318170828251553792 129.31320 -53.33834 6.58 0.01 -24.02 0.03 23.07 0.03 9.66 12.47 87.13 4.84 151.295318176875565072768 129.22895 -53.14275 6.71 0.02 -23.96 0.05 23.78 0.04 16.20 1.52 93.07 -5.74 147.955318185667356683392 129.48414 -52.95143 6.66 0.03 -23.73 0.05 23.74 0.05 11.05 5.75 89.51 2.94 148.525318186221414047104 129.59528 -52.94657 6.66 0.02 -25.24 0.05 24.23 0.04 15.43 0.71 91.67 -3.76 148.915318229274167094656 131.56346 -53.75616 6.65 0.03 -24.66 0.05 22.92 0.04 16.00 0.83 93.73 -6.46 149.005318267653995965568 131.04233 -53.72592 6.68 0.03 -25.05 0.05 23.87 0.05 12.63 1.28 90.96 -0.33 148.435318296275658773888 131.44960 -53.43063 6.71 0.03 -26.09 0.05 23.48 0.05 15.83 8.73 92.44 -5.54 147.705318328676892604800 131.36203 -52.86715 6.65 0.02 -25.58 0.05 23.42 0.04 11.48 1.97 89.35 1.93 149.085318474941990522368 130.35768 -53.37808 6.65 0.03 -25.04 0.05 25.06 0.04 20.72 11.17 96.58 -10.53 149.085318504426950057728 130.49085 -52.87044 6.58 0.03 -25.73 0.05 22.70 0.05 17.12 2.11 92.07 -7.22 150.465318521671232021632 131.10882 -52.70888 6.58 0.03 -24.87 0.05 23.38 0.04 13.84 2.47 91.66 -1.62 150.785318532189619619328 130.98653 -52.68479 6.68 0.09 -22.95 0.16 22.84 0.14 14.84 3.70 94.33 -4.13 145.825318536999982933248 130.82442 -52.60302 6.52 0.03 -24.65 0.05 22.76 0.05 14.15 1.45 91.32 -2.43 151.655318541982138813824 129.99375 -53.05061 6.61 0.04 -25.30 0.07 24.69 0.07 17.24 0.83 93.48 -5.86 149.035318545521198976000 129.97087 -52.96569 6.56 0.02 -24.35 0.04 23.90 0.04 16.85 1.66 93.65 -5.87 151.255318546139674245888 129.92918 -52.96414 6.64 0.03 -25.44 0.05 22.48 0.05 16.78 2.79 91.52 -7.25 149.375318546822567826944 130.06753 -52.94134 6.54 0.03 -23.22 0.04 23.23 0.04 7.14 5.52 86.58 10.31 151.575318549678727766656 130.29139 -52.90283 6.58 0.03 -25.68 0.05 22.85 0.06 11.52 13.40 87.63 1.57 150.765318565656005527936 129.76157 -52.71059 6.50 0.02 -23.71 0.05 23.82 0.05 11.82 3.91 90.27 2.36 152.495318567958108066944 130.00665 -52.70338 6.64 0.03 -24.57 0.06 23.38 0.05 15.65 0.49 92.38 -4.63 149.215318647466543875584 131.91069 -52.26934 6.95 0.09 -25.41 0.16 24.42 0.18 16.68 2.97 95.37 -5.90 139.455321176205843037440 128.55421 -52.97214 6.70 0.02 -24.41 0.04 24.29 0.04 15.12 1.26 91.44 -3.43 148.145321188953307253760 129.35248 -52.90294 6.54 0.02 -23.94 0.05 22.51 0.05 15.50 4.71 91.55 -5.11 151.525321275295028390912 128.57546 -52.26594 6.44 0.02 -23.47 0.04 23.07 0.04 14.90 0.59 91.11 -2.80 153.805321280728169745536 128.75480 -52.23363 6.83 0.02 -24.52 0.04 24.36 0.04 17.26 2.55 93.34 -6.39 145.365321517672922567040 127.18998 -52.09067 6.42 0.02 -23.03 0.04 23.05 0.04 12.65 1.79 88.45 1.00 154.605321600445535344000 129.65022 -52.11067 6.63 0.03 -24.97 0.05 23.59 0.04 11.74 6.47 88.62 2.30 149.665321723109802924416 130.91001 -51.50794 6.54 0.05 -25.61 0.06 23.41 0.06 16.05 1.57 92.33 -3.85 150.41 the availability of radial velocity information. This list of 39 stars is used in this paper for theanalysis of IC 2391 cluster’s kinematics. The data used for cluster stars are listed in Table 1.The distances to the stars are determined by the parallaxes ( π ) from GDR2. For eachmeasurement of π , the Monte Carlo method generated N random variables in the range of( π ± σ π ). The resulting distribution is Gaussian with a maximum at a point with an argumentvalue of π . Artificially modeled parallax values are transferred to distances according to theformula 1 /π , where π is specified in arc seconds. The distribution of the obtained distancesis not normal. By the method of least squares, it is approximated by a curve representingthe Maxwell distribution. The argument values giving the maximum of this curve (maximumprobability density) are taken as the most likely distance values.The list of stream stars was taken from Montes et al. (2001) and is shown in Table 2. Theastrometric data (parallaxes and proper motions values) were taken from GDR2 for most ofthe stars. For two stars (HIP IDs 11072 and 62686), the astrometric data were taken from vanLeeuwen (2007).Table 1 and Table 2 are compiled in a slightly different format: in Table 1 the first col-umn gives GDR2 number, while the first two columns in Table 2 represent Hipparcos (HIP)and GDR2 numbers. Then, the tables contain parallaxes ( π ) and their errors; proper motioncomponents ( µ α , µ δ ) and their errors. The next columns show radial velocities ( V r ) and theirerrors. The references for the radial velocity data are mentioned in the “Ref.” column (Table 2only). For Table 1, all the values of radial velocity are taken from Cantat-Gaudin et al. (2018). E. S. Postnikova et al.
60 80 100 120
A, deg −40−30 −20−100102030 D , d e g Fig. 1
The AD-diagram for IC 2391 open cluster and stream. Black crosses representdata for 39 cluster stars from Cantat-Gaudin et al. (2018) and the data for stellarstream from Montes et al. (2001) is presented by gray crosses. The data for the streamcontains 56 entries considering that some stars could be double or binary stars.The tables also present the values of apex (determined from AD-method) for individual starsdetermined in this work (
A, D ) and heliocentric distances ( d ).Montes et al. (2001) originally presented a list of 53 stars for the stream associated withIC 2391. But, while cross-matching the data with Gaia DR2, it gave us two entries in GDR2for some stars. This is why Table 2 has 57 entries of stars. In the case of these stars, for thesame HIP IDs, there were different GDR2 IDs. The fact that both the entries for these starshave approximately the same astrometric parameters give support to the notion in the favorof them being likely double or binary stars. The double star with two entries HIP 99803 waspreviously known. While the stars with Hipparcos IDs HIP 10175, 12326, 15058, 42253 are newlikely double or binary stars. For the star with HIP ID 15058, one of the entries had no availablemeasurement for the radial velocity and its error. This limited our calculations for apex to 56entries.Owing to its better spatial resolution and overall superior characteristics, Gaia results areovertaking the Hipparcos ones in their scientific significance. This also means that in the regionswhere HIP could discover one star, Gaia may discover multiple stars. Although we are using thestars with multiple entries as likely double or binary stars but we are not absolutely claimingabout their status as double stars. The close values of astrometric parameters made us includethese stars into our list rather than discarding that star entirely or choosing one of the twoentries. he structure of IC 2391 5 −30 −20 −10 0 10 V, km/s −40−30−20−10 U , k m / s −30 −20 −10 0 10 V, km/s −20−10010 W , k m / s Fig. 2
Comparison of the spatial velocities of the stars of the cluster and the stream.The velocities are given in km s − . Cluster stars are shown in black color and thestream stars are shown in gray. It is known that a moving cluster is a group of stars whose parallel motions on the celestialsphere and its direction of proper motion will direct towards a virtual point called convergentpoint or apex of this group. This method has been used by our group to determine apex andother kinematical parameters for open clusters M67, NGC 188 and Pleiades (Vereshchagin etal. 2014, Elsanhoury et al. 2016, 2018).Here, we calculate the apex for both cluster and stream represented by IC 2391 with theclassical convergent point (CP) and the AD-diagram methods.
It is a classical method which depends on the proper motion vectors components (i.e. µ α cos δ and µ δ in mas yr − ). Also, using the well-known formulae given by Smart (1968), we canestimate the velocity components ( V x , V y , V z ) along x, y, and z-axes in the coordinate systemcentered at the Sun for a group of N cluster member stars with coordinates ( α, δ ), at distance r i (pc), and with radial velocity V r (km s − ). i.e. V x = − . r i µ α cos δ sin α − . r i µ δ sin δ cos α + V r cos δ cos α , V y = +4 . r i µ α cos δ cos α − . r i µ δ sin δ sin α + V r cos δ sin α , V z = +4 . r i µ δ cos δ + V r sin δ .From the above equations and letting ξ = V x V z , η = V y V z , we get a i ξ + b i η = c i , where the coefficients a i = µ ( i ) α sin δ i cos α i cos δ i − µ ( i ) δ sin α i , b i = µ ( i ) α sin δ i sin α i cos δ i + µ ( i ) δ cos α i , c i = µ ( i ) α cos δ i , E. S. Postnikova et al. and the index i varies from 1 to N which is the number of the cluster members. Sotan A CP = ηξ , (1)tan D CP = ( η + ξ ) − / . (2)The coordinates ( A CP , D CP ) of the cluster apex are derived from the Equations (1) and (2).The results on the apex position of both the cluster and the stream are presented in Table 3. The formulae to construct the AD-diagram can be seen in Chupina et al. (2001, 2006). Thevalue of the apex coordinates for the IC 2391 cluster using data from Table 1 is ( A , D ) =(6 . h ± . h , − . ◦ ± . ◦ A , D ) = (6 . h ± . h , − . ◦ ± . ◦ U, V, W ) In order to compute the space velocity components U , V and W , we used an equatorial-Galactic transformation explained in Liu et al. (2011). They determined the position of theGalactic plane using recent catalogs like Two-Micron All-Sky Survey (2MASS, Skrutskie et al.2006) and defined the optimal Galactic coordinate system by adopting the ICRS position ofthe compact radio source Sagittarius A ∗ at the Galactic center (Liu et al. 2011).The values of space velocity components along the three axes are given by: U = − . V x − . V y − . V z , V = +0 . V x − . V y +0 . V z , W = − . V x − . V y +0 . V z .Figure 2 shows the components ( U , V , W ) of the spatial velocities of the cluster stars and thestream stars, for which the input data were taken from Tables 1 and 2. As can be seen in Figure 2,the components of space velocities of all the stars do not show much different orientation. Thus,it can be concluded that both the cluster and the stream move in approximately the samedirection. To compute the velocity ellipsoid and its parameters for IC 2391 open cluster and the stream, wefollowed the computational algorithm mentioned in Elsanhoury et al. (2015). A brief explanationof the algorithm is given here.The coordinates of the i th , star with respect to axes parallel to the original axes, but shiftedto the center of the distribution i.e. towards average velocities ( U , V and W ), will be ( U i − U );( V i − V ); ( W i − W ). The average velocities U , V and W are defined as: U = N P i =1 U i N , V = N P i =1 V i N , W = N P i =1 W i N . (3)N being the total number of stars. he structure of IC 2391 7
Let ξ be an arbitrary axis, its zero point coincident with the center of the distribution andlet l , m and n be the direction cosines of the axis with respect to the shifted ones, then thecoordinates Q i of the point i , with respect to the ξ -axis is given by: Q i = l ( U i − U ) + m ( V i − V ) + n ( W i − W ) . (4)If the measured scatter components are Q i , a generalization of the mean square deviationcan be defined as σ = 1 N N X i =1 Q i . (5)From equations (3), (4) and (5) we deduce that σ = x T Bx , where x is the (3 ×
1) directioncosines vector and B is (3 ×
3) symmetric matrix with elements µ ij : µ = N N P i =1 U i − ( U ) ; µ = N N P i =1 U i V i − U V ; µ = N N P i =1 U i W i − U W ; µ = N N P i =1 V i − ( V ) ; µ = N N P i =1 V i W i − V W ; µ = N N P i =1 W i − ( W ) .The necessary conditions for an extremum are now( B − λI ) x = 0 . (6)These are three homogeneous equations in three unknowns, which have a nontrivial solution ifand only if D ( λ ) = | B − λI | = 0 , (7)where λ is the eigenvalue, and x and B are given as: x = lmn and B = µ µ µ µ µ µ µ µ µ Equation (7) is the characteristic equation for the matrix B . The required roots (i.e. eigen-values) are λ = 2 ρ cos φ − k ; λ = − ρ (cid:16) cos φ + √ φ (cid:17) − k ; λ = − ρ (cid:16) cos φ − √ φ (cid:17) − k ,where k = − ( µ + µ + µ ); k = µ µ + µ µ + µ µ − (cid:0) µ + µ + µ (cid:1) ; k = µ µ + µ µ + µ µ − µ µ µ − µ µ µ ; q = k − k ; r = ( k k − k ) − k ; ρ = p − q ; x = ρ − r ; φ = tan − (cid:16) √ xr (cid:17) .Depending on the matrix that controls the eigenvalue problem (Equation 6) for the velocityellipsoid, we establish analytical expressions of some parameters for the correlations studiesin terms of the matrix elements µ ij of the eigenvalue problem for the velocity ellipsoid (i.e.Velocity Ellipsoid Parameters, VEPs). E. S. Postnikova et al.
Fig. 3
The Galactic XY plane distribution is shown here for the stream stars (Table 2,gray crosses) – left panel; and for the cluster stars of IC 2391 (Table 1, black crosses)– right panel. In the left panel, the stars of the cluster are also visible as a small pileof black crosses at the lower side from the center of the stream stars’ distribution.Contours of equal stellar flux density are drawn in the both panels. σ j , j = 1 , , parameters The σ j , j = 1 , , σ j = p λ j . l j , m j and n j parameters The l j , m j and n j are the direction cosines for eigenvalue problem. We have the followingexpressions for l j , m j and n j as l j = µ µ − σ i ( µ + µ − σ i ) − µ D j , j = 1 , , m j = µ µ − µ µ + σ j µ D j , j = 1 , , n j = µ µ − µ µ + σ j µ D j , j = 1 , , , where D j = (cid:0) µ µ − µ (cid:1) + ( µ µ − µ µ ) +( µ µ − µ µ ) +2[( µ + µ ) (cid:0) µ − µ µ (cid:1) + µ ( µ µ − µ µ )+ µ ( µ µ − µ µ )] σ j + (cid:0) µ + 4 µ µ + µ − µ + µ + µ (cid:1) σ j − µ + µ ) σ j + σ j .Considering ( x c , y c , z c ; pc) is the center of the cluster, it can be estimated as the equatorialcoordinates of the center of mass for N number of discrete objects as given below: x c = N P i =1 ( r i cos α i cos δ i ) N , he structure of IC 2391 9 X , p c −300−200−1000 100200300 Y , p c −300−200−100 0 100 200 300 Z , p c −300−200−1000100200300 Fig. 4
The 3D picture of the cluster and stream stars in the rectangular Galacticcoordinate system. The black points are star cluster stars, while the gray points arethe stream stars. y c = N P i =1 ( r i sin α i cos δ i ) N , z c = N P i =1 ( r i sin δ i ) N . L j and B j Parameters
Let L j and B j , j = 1 , , L j = tan − (cid:18) − m j l j (cid:19) , B j = sin − ( − n j ) . The Solar motion can be defined as the absolute value of the Sun’s velocity relative to the groupof stars under consideration, i.e. S ⊙ = (cid:16) U + V + W (cid:17) / , km s − . The Galactic longitude l A and Galactic latitude b A of the Solar apex are l A = tan − (cid:18) − VU (cid:19) , b A = sin − (cid:18) − WS ⊙ (cid:19) . −6000 −5500 −5000 X, pc −6500−6000−5500−5000−4500−4000−3500−3000 Y , p c −6000 −5500 −5000 X, pc −800−600−400−2000200400600800 Z , p c Fig. 5
Places of star formation for the cluster stars (black crosses, data from Table 1)and for the stream stars (gray crosses, Table 2).
We have a distribution of residual velocities of stars inside the cluster and moving group. InTable 3 we present the results of our calculations.
In Figure 3, the curves show contours of equal flux star density. The kernel-density estimationwas done considering Gaussian kernels (Scott, 2015) using scipy python package (Jones et al.2001) to make the isodensity plot. At the periphery of the stream as well as the cluster too,stars are so few that it is not possible to determine a significant value of density. As can beseen in Figure 3 (left panel), the stars of the stream occupy a region stretched roughly along(at a small angle not exceeding 40 degree) the axis OY. The axis OY represents the directionof Galactic rotation. The reason behind this orientation is the process leading to the decay ofclusters (from the associations containing multiple clusters) with their gradual stretching (due todifferential rotation) along the direction of rotation of the Galactic disk. This causes the gradualtransformation of clusters into streams with their transformation into ordered ring structuresstretched around the Galactic center (Perottoni et al. 2019, Wang et al. 2019). Interestingly, asimilar distribution of stellar flows/streams is observed in other galaxies (Pearson et al. 2019).The fact that the stream’s stars are scattered over a wide area of the sky and there are greateruncertainties in their selection, makes the distribution of stream stars much more scatteredthan the cluster stars in Figure 3. As for the IC 2391 cluster itself, represented by a handful ofstars (from Table 1) in Figure 3 (right panel), its spatial outlines shows the same pattern witha stretching along the OY direction. Since the number of stars in the sample used here is small,the structure is not defined in fine details.Figure 4 shows the 3D distribution of stars of the cluster and stream under consideration. Itis noticeable from Figure 4 that the stars of the cluster and the stream are located in separateregions in space. he structure of IC 2391 11
Figure 5 shows the position of the stars of the cluster and the stream approximately at thetime of their formation, determined by trial calculations of orbits back in time, up to 70 millionyears ago. The galpy program was used to calculate the orbits (Bovy 2015). Note that similarcalculations carried out using another method are available in Kharchenko et al (2009) andChumak & Rastorguev (2006). Gravitational interactions among the stars of the stream werenot taken into account. For the cluster, the effect of irregular forces was not taken into account(the dispersion of the peculiar velocities of stars, is a negligible value compared with the spatialvelocity). In addition, the calculations did not take into account the effect of spiral arms. Assuggested by Figure 5, we conclude that the birthplaces of the stars of the cluster and thestream are in the same region of the disk.
In this work, we have determined various kinematical parameters of the open cluster IC 2391( n = 39 stars) and the associated stream ( n = 57 stars). A computational routine using the“Mathematica” software has been developed to compute the kinematical structure.We calculated the apex positions by two independent methods: convergent point methodand AD-diagram using the two data presented in Table 1 and Table 2. We have determinedthe apex position with convergent point method ( A, D ) CP =(6 . h ± . h , − . ◦ ± . ◦ . h ± . h − . ◦ ± . ◦ A , D ) = (6 . h ± . h − . ◦ ± . ◦
3) and (6 . h ± . h − . ◦ ± . ◦ σ j ), direction cosines l j , m j and n j , Galactic longitudeand latitude ( L j , B j ) with (j = 1, 2, 3), and the Solar elements S ⊙ , l A and b A . The parametersof the ellipsoids of residual velocities (VEPs) of the stars of the cluster and the stream are alsodetermined.It is evident from the two-dimensional Figure 3 and the 3D structure of the cluster andthe stream shown in Figure 4 that the cluster and the stream are not spherically symmetricstructures in the Galactic space. They are elongated in shape and directed along the directionof Galactic rotation. In general, all of this is consistent with the theoretical ideas regarding thetidal forces of the Galaxy acting on a stellar system, stretching the system towards the Galacticcenter and the differential rotation of the Galactic disk, turning the system in the directionof rotation. In addition, we obtained the evidence of the genetic connection between the starcluster IC 2391 and the stream back in time, leading to the time of their formation in theGalactic disk. Acknowledgements
We are thankful to the referee of this paper for useful and constructivecomments. Devesh P. Sariya and Ing-Guey Jiang are supported by the grant from the Ministryof Science and Technology (MOST), Taiwan. The grant numbers are MOST 105-2811-M-007-038, MOST 105-2119-M-007 -029 -MY3, MOST 106-2112-M-007 -006 -MY3 and MOST 106-2811-M-007 -051. This work has made use of data from the European Space Agency (ESA)mission
Gaia , processed by the Gaia
Data Processing and Analysis Consortium (DPAC ).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia
Multilateral Agreement. This research has made use of the SIMBADdatabase, operated at CDS , Strasbourg, France, Wenger et al. (2000). References
Cool stars, StellarSystems and the Sun : 15 th Cambridge Workshop, edited by E. Stemples, 1094, 951 http://simbad.u-strasbg.fr/simbad/ he structure of IC 2391 13 Parker, S. R., Tinney, C. G., 2013, MNRAS, 430, 1208Pearson, S., Starkenburg, T. K., Johnston, K. V., Williams, B. F., Ibata, R. A., 2019,arXiv:1906.03264Platais, I., Melo, C., Mermilliod, J.-C. et al. 2007, A&A, 461, 509Randich, S., Pallavicini, R., Meola, G. et al. 2001, A&A, 372, 862Robichon, N., Arenou, F., Mermilliod, J.-C., Turon, C., 1999, A&A, 345, 471Scott, D.W., Multivariate Density Estimation: Theory, Practice, and Visualization, 2ndEdition, John Wiley & Sons Inc., New York, Chicester, 2015, 384 pp.Siegler, N., Muzerolle, J., Young, E. T. et al. 2007, AJ, 654, 580Skrutskie, M. F., et al., 2006, AJ, 131, 1163Smart, W. M., 1968, Stellar kinematics. ”Longmans”Tokovinin, A., 2013, AJ, 145, 76Vereshchagin, S.V., Chupina, N.V., Sariya, Devesh P., Yadav, R.K.S., Kumar, B., 2014. NewAstron. 31, 43Wang, H.-F., Huang, Y., Carlin, J.L. et al., 2019, arXiv:1905.11944Wenger, M., et al., 2000, A&AS, 143, 9White, R. J., Gabor, J. M., Hillenbrand, L. A., 2007, AJ, 133, 2524Wilson, R. E., 1963, General Catalogue of stellar radial velocities (1963 reprint), Washington:Carnegie Institutevan Leeuwen, F., 2007, A&A, 474, 653
Table 2
Data listed for star stream in Montes et al. (2001) cross-matched withother data sources to obtain astrometric parameters and radial velocity. Apex posi-tions mentioned in the table are determined in this paper. This table has 57 entries(see, Section 2). The values of parallaxes ( π ) and proper motions with their errorsare taken from GDR2. For the stars with no entries in GDR2 (with HIP numbers11072 and 62686), the values and errors of π and proper motions are taken from vanLeeuwen (2007). Pairs of stars marked with an asterisk (*) near HIP number are con-sidered likely double or binary stars. The “Ref.” column contains the references for V r and σ V r according to: a – GDR2, b – Gontcharov (2006), c – Wilson(1963), d –Tokovinin(2013), e – Famaey et al.(2005) and f – White et al. (2007). HIP GDR2 π σ π µ α σ µ α µ δ σ µ δ V r σ V r Ref.
A D dmas mas mas yr − mas yr − km s − deg deg pc4979 2538159890494125184 16.95 0.07 122.91 0.15 -40.36 0.07 5.6 2.90 b 96.27 -17.73 58.446869 2593154747696080640 19.39 0.06 112.68 0.11 -33.45 0.12 8.61 0.16 a 91.00 -10.16 51.1910175 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ he structure of IC 2391 15 Table 3
Kinematical parameters determined in this study for the IC 2391 clusterand the star stream.
Parameters Results Reference N
39 Table 1 N
56 Table 2(
A, D ) CP . h ± . h − . ◦ ± . ◦
381 Table 16 . h ± . h − . ◦ ± . ◦
447 Table 2( A , D ) 6 . h ± . h − . ◦ ± . ◦ . h ± . h − . ◦ ± . ◦
290 Table 25 . h , − . ◦
44 Montes et al. (2001)5 . h , − . ◦
44 Eggen (1991) (cid:0)
U, V , W (cid:1) km s − − . , − . , − .
525 Table 1 − . , − . , − .
653 Table 2 − . , − . , − . x c , y c , z c ) pc − . , . , − .
66 Table 14 . , − . , .
287 Table 2Space velocity (km s − ) 28 . ± .
19 Table 1= (cid:16) U + V + W (cid:17) / . ± .
21 Table 227 . ± .
24 Montes et al. (2001)30 .
00 Eggen (1991)( λ , λ , λ ) km s − . , . , .
19 Table 1590 . , . , .
16 Table 2( σ , σ , σ ) km s − . , . , .
44 Table 124 . , . , .
19 Table 2Dispersion velocity (km s − ) 28 . ± .
18 Table 125 . ± .
20 Table 2( l , m , n ) deg 0 . , . , .
20 Table 10 . , . , .
30 Table 2( l , m , n ) deg − . , . , .
01 Table 1 − . , . , .
92 Table 2( l , m , n ) deg 0 . , . , − .
98 Table 10 . , − . , .
24 Table 2 L j , j = 1 , , − . ◦ , − . ◦ , . ◦
685 Table 1 − . ◦ , − . ◦ , − . ◦
453 Table 2 B j , j = 1 , , . ◦ , . ◦ , − . ◦
702 Table 117 . ◦ , . ◦ , . ◦
946 Table 2 S ⊙ , km s − . ± .
19 Table 123 . ± .
21 Table 2 l A − . ◦
439 Table 1 − . ◦
866 Table 2 b A . ◦
279 Table 116 . ◦◦