arXiv:astro-ph/0205100v1 7 May 2002 G 92adNC10:acoeecutrbtenopen between Oliveira de encounter M.R. close a 1907: ? NGC clusters and 1912 NGC cto fpyia trcutrpisi h aay with , the identi- in the of pairs However, Grebel exception cluster 2000b). & the al. Dieball physical et 1998, of Oliveira fication al. 1988, de et Hatzidimitriou Vallenari and & 1992, 2000 (Bhatia al. decade et au- last Bica several the by in extensively thors investigated been have Clouds capture. without encounter most with spatial in ages encounter a different (iii) have spatial binary cases; to a expected (ii) are from which age; capture, arising star-forming comparable systems a with physical in binary origin necessarily (i) common as: complex, with classified systems basically phys- be physical cluster can star effects, interactions projection ical simple to contrast In Introduction 1. 1 ais aais trclusters star : namics; words: Key and Galaxy the the fly-by. of that a regions experience different suggest presently in approach born Detailed were their model. clusters of potential clus- simulations Galactic the a of N-body in motions retrieved orbital are past and ters the velocities Spatial and radial interaction. motions, available proper from possible derived the study are detail present velocities the more and in distances, physi- similar explores a on NGC suggested based and studies pair 38) cal Previous (M investigated. 1912 is NGC 1907 clusters open projected sely Abstract. Accepted / Received 2 bu %o hi aacudb hsclsses Sub- systems. physical that be suggested could and data pc their of 20 with 8% than pairs cata- about cluster less cluster probable separations open 18 of Subra- spatial identify use by could the proposed they With was logues (1995). Galaxy al. the et in maniam phys- for pairs candidates of cluster distances list As ical A cluster account. effects. the into inside taken projection from be should Galaxy of the possibility seeing are strong we the to owing edopitrqet to requests offprint Send 11.13.1,11.19.4 are: codes thesaurus later) Your hand by inserted be (will no. manuscript A&A EM,Osraor ePrs 1A.d ’bevtie F-7 l’Observatoire, de Av. 61 Paris, de Observatoire LERMA, nttt eFsc-FG,C 55,CP95190PA-RS, - POA 91501-970 CEP 15051, CP Fisica-UFRGS, de Instituto h xsec fsa lse ar nteMagellanic the in pairs cluster star of existence The h osbepyia eainbtenteclo- the between relation physical possible The aay pncutr,knmtc n dy- and kinematics clusters, open Galaxy: h + 1 , 2 χ .Fausti A. , [email protected] : esi a o ena aytask easy an been not has Persei, 2 .Bica E. , 2 n .Dottori H. and , 04Prs France Paris, 5014 ednn;()poetdsprto;()dsac othe to distance (7) centre. separation; Galactic projected (6) reddening; lse ae 2 J2000 (2) name; Cluster 1. Table itneo 30p n ednn fEBV=03 for 0.38 derived E(B-V)= SS99 of a recently, reddening More obtained a 1907. (1966) and NGC Hoag pc 1380 SS99). of (Subramaniam hereafter distance pc 1999, 18.8 of Sagar separation & projected a with 38) a for the values. candidate on age based good similar possibility resulting this a the advanced was that They pair. 1907 suggested physical and 1912/NGC pairs NGC pos- cluster pair two open for photom- reddening Galactic CCD and sible of distances use ages, the obtained with etry, (1999), Sagar & ramaniam oiywsrtivdb eno -oysmltosi a ve- in spatial simulations in N-body bar of mean error by the retrieved by The was allowed locity motions. orbits proper of and bundle velocities radial available from SS99. by compiled as show pair we cluster star-forming 1 this Table for same In information the some 1997). Kumai in and origin (Fujimoto common complex a the of with face consistent hypothesis at marginally Taken only is uncertainties. difference within this range values assert, this to in difficult differences 1907 are NGC Age for respectively. Myr 1912, 250 NGC and and 400 isochrone complex, of of ages derived dust means SS99 By Taurus- fitting variable. highly the is are extinction of clusters where the background that the fact the in from arise probably ferences d 16)motie,wt h s fpoolcrcphotom- photoelectric Applequist of etry, use & the Hoag with 1912, obtained, NGC (1965)Km For E(B-V)=0.40. and pc ⊙ 1 2 3 4 5 6 (7) (6) (5) (4) (3) (2) (1) G11 52:33:11 5 .39.8 9.8 18.8 0.23 0.40 250 400 35:51:18 35:19:30 05:28:43 05:28:06 NGC1912 NGC1907 Name 11 pc =1810 Brazil G 97i lse rjce erNC11 (M 1912 NGC near projected cluster a is 1907 NGC ntepeetsuyw siaetesailvelocities spatial the estimate we study present the In 2 d ⊙ 7 cadEBV=.7 hl S9obtained SS99 while E(B-V)=0.27, and pc 870 = ai aafrNC11 n G 97 (1) 1907. NGC and 1912 NGC for data Basic ± s : m : h 6 cadEBV=02.Rdeigdif- Reddening 0.23. E(B-V)= and pc 265 δ α o α ckpc pc ” : ’ : 3 J2000 (3) ; ASTROPHYSICS ASTRONOMY g (-)separ. E(B-V) Age δ 4 g Mr;(5) (Myr); age (4) ; AND d ⊙ =1785 ± 260 R g 2 M.R. de Oliveira et al.: NGC 1912 and NGC 1907

Table 2. Input parameters for the simulations. (1) Model; cillations which occur at 15 trx (Cohn 1980, Makino (2) number of particles of the cluster; (3) cluster total 1996). The present objective≃ is trying to detect any tidal mass; (4) half-mass radius; (5) maximum radius of the effect in the outskirts of the clusters, and thus we neglected cluster; (6) mean velocity of the particles (modulus); (7) the effects of primordial binaries as they have little effect softening parameter. on the overall evaporation rate of the clusters (McMillan & Hut 1994). N M R R V ǫ Model part T h max md As we are simulating the evolution of the clusters since (M⊙) (pc) (pc) (km/s) (pc) T= -200 Myr we have to take into account the mass loss M1907 3072 3000 2.0 4.0 1.5 0.03 due to stellar evolution. To do this we calculated how M1912 4096 4200 3.1 6.0 1.5 0.03 the Salpeter mass function evolves back in time. Approx- imately 10% of the mass is lost for both clusters in the time interval T= -200 Myr (initial condition) to T= 0 Galactic potential model over 200 Myr. The simulation (present condition). Also, we calculated the mass loss due time is comparable to the ages and relaxation times of the to the dynamical evolution of the cluster in the presence clusters. of an external gratitational field, which causes evapora- In Sect. 2 we present the initial conditions of the sim- tion of cluster . We assumed a typical value of mass ulations. In Sect. 3 we present the results and discussion. loss by evaporation of 3% per relaxation time, according Finally, the concluding remarks are given in Sect. 4. The to Gnedin & Ostriker (1997). During the simulation the present simulations are part of a series of N-body simula- stellar evolution has not been included since it is expected tions to be fully explored in a coming paper. to be more important for the very early evolution of the clusters (Terlevich 1987). The initial values for our models are presented in Table 2. 2. The method and initial conditions

The N-body code used is the TREECODE algorithm 2.1. The Galaxy Model (Hernquist 1987, Hernquist & Katz, 1989) where the force calculation between two particles is done by a softened The Galaxy potential was modeled by means of three com- Keplerian potential. We performed the simulations in a ponents, disk, bulge and halo, combined to reproduce the CRAY-T94 computer of the CESUP Laboratory of the rotation curve compiled by Allen & Martos (1986). Universidade Federal do Rio Grande do Sul. The units The disk model is that of Kuzmin & Kutuzov (1962). used in the simulation are pc, km/s, Myr and G=1. The Hernquist & Katz’s (1989) TREECODE works with The models are represented by a density distribution a triaxial generalization of the Kuzmin-Kutuzov model. that follows a Plummer truncated polytrope (Aarseth et The potential for this model is al. 1974) and have been generated in the same way as in de Oliveira et al. (1998) - hereafter ODB98. Cluster GMd w,z 1 Φd( )= 2 2 2 2 2 2 2 2 2 2 model dimensions were based on estimates for the real −(w + z + a + b +2 √a b + b w + a z ) 2 clusters (Lyng˚a1987). The cluster masses were estimated from the best statistics absolute magnitude (MV) interval where w and z are the radius and height in cylindrical in common with the Hyades (-0.3 < MV < 1.2), using coordinates. Md is the total mass of the disk component, colour magnitude diagrams (CMD) from SS99 and the a is the length scale in w and b is the scale in z. WEBDA database (Mermilliod 1996), in the web page The bulge model (Hernquist 1990) has the following obswww.unige.ch/webda. The masses were estimated by potential expression: scaling the number of members in the fiducial MV inter- val, assuming comparable mass functions. Adopting for GM Φ (r)= the Hyades a total mass of 1000M⊙ (Perryman et al. b −r + c ≃ 1998), we obtained masses of 3400M⊙ and 2500M⊙ for NGC 1912 and NGC 1907, respectively.≃ In contrast to the where r = √w2 + z2 is the radius in spherical coordinates equal mass models of ODB98 we introduced a mass spec- and c the length scale. trum that follows the Salpeter mass function, i.e. dN/dm The halo was modeled with a logarithmic potential m−2.35, and adopted a mass spectrum ranging from 0.5 (Binney & Tremaine 1987), ∝ to 3.0 M⊙ for NGC1912 and 0.5 to 2.4 M⊙ for NGC1907 2 according to the turnoff mass and age relation of Renzini 1 2 2 2 z Φ (w,z)= v0 ln(d + w + 2 )+ constant & Buzzoni (1986). As we search here for a possible cluster h 2 qΦ encounter that occurred in a recent epoch, we simulated our models in time scales of the order of the relaxation where v0 is the asymptotic halo velocity, d is the length time trx of the clusters, thus avoiding complications of scale of the model and the constant is adjusted so that Φh long-term effects like core collapse and gravothermal os- is zero at rc, the cutoff radius of the model. We assume a M.R. de Oliveira et al.: NGC 1912 and NGC 1907 3

Table 3. A non-linear curve fitting function was used to optimize the parameters of the galaxy model a, b, Md, c, Mb and d with precision 0.01. The data intervals are quoted in Col. 3.

Parameters Fit results Constraints Disk length scale in w: a = 4.61 kpc (4000

1.2 Bulge Disc 250 Halo

0.6 200

150 0 kpc Vr(km/s)

100

−0.6 50

0 0 2 4 6 8 10 12 14 16 18 20 −1.2 radius(kpc) −12 −6 0 6 12 Fig. 1. Rotation curve resulting from the choice of the kpc three mass components compared to the data points for Fig. 2. Centre of mass orbit projected on the XZ plane for the Galaxy, as compiled by Allen & Martos (1986). -200 < T (Myr) < 0. Dashed line is N-body model M1912 representing the NGC 1912, and solid line is Table 4. Position and velocity components of the clusters M1907 representing NGC 1907. in the Galactocentric inertial system for the present epoch.

Object X Y Z V U W [pc] [pc] [pc] [km/s] [km/s] [km/s] NGC1907 9783 231 9 6.16 212.29 -19.74 2 Catalogue (Hog et al. 2000). From Tycho-2 we have NGC1912 9781 242 22 10.90 213.87 41.97 considered five stars with magnitudes V < 12.4, which are not non-members according to WEBDA. We used the weighted average of these values to obtain the mean proper motions for NGC 1907. The radial velocities and available spherical halo (qΦ = 1). The parameters of the three com- errors for NGC 1912 and NGC 1907 are Vr = -1.00 0.58 ± ponents that fit the data, together with the data intervals km/s and Vr = 0.10 1.80 km/s respectively. The proper ± used in the fits are listed in the Table 3. motion values for NGC 1912 are µα = 3.60 0.50 mas/yr ± and µδ = 1.90 0.50 mas/yr, and for NGC 1907 are µα = The rotation curve resulting from the potential Φ = ± -0.81 0.73 mas/yr and µδ = -4.51 0.76 mas/yr. Φd +Φb +Φh is plotted in Figure 1. ± ± Using Johnson & Soderblom’s (1987) method, we ob- x0 y0 2.2. Orbital Initial Conditions tained the present day set of vector components , , z0, U0, V0, W0 (Table 4), which refer to a right-handed The kinematical initial conditions were derived from Cartesian Galactocentric inertial system where the Sun is proper motions and radial velocities. Heliocentric radial at X⊙ = 8 kpc, Y⊙ = 0, Z⊙ = 0 and the z axis points velocities and mean proper motions have been obtained towards the− North Galactic Pole. In order to correct for from the WEBDA open cluster database (Mermilliod the solar motion we used U⊙ = 10 km/s, V⊙ = 240 km/s, 1996). For NGC 1907, the mean proper motions have been W⊙ = 7.5 km/s with ULSR = 0, VLSR = 225 km/s, calculated from two sources, namely WEBDA and Tycho- WLSR = 0. 4 M.R. de Oliveira et al.: NGC 1912 and NGC 1907

2 120

Orb_1 Orb_2 100 Orb_3 1 Orb_4 Orb_5 80 Orb_6 Orb_7 0 Orb_8 kpc Orb_9 V (km/s) ∆ 60

−1 40

20 −2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 −12 −6 0 6 12 ∆R (kpc) kpc

Fig. 3. Centre of mass orbit projected on the XZ plane Fig. 5. Probing, within parameter uncertainties, other for -200 < T (Myr) < 0 for three possible orbital models possible orbital solutions similar to that of Fig. 1. We plot for NGC 1912. Dotted line is N-body model M1912 with the relative velocity against separation (modulus) for al- the mean velocity values prsented in the text. The solid ternative models in the time interval T= -10 Myr to T= line is the model with velocity values corresponding to the 0. error lower limits, while the dashed line corresponds to the 1 upper limits.

2 0.5

1 0 Z (kpc)

0 kpc −0.5

−1 −1 −12 −6 0 6 12 Y (kpc)

−2 Fig. 6. XZ plane projection of closest approach model −12 −6 0 6 12 kpc Orb-9 (Fig. 2) for -200 < T(Myr) < 0. Line symbols as in Fig. 2. Fig. 4. Same as Fig. 3 for a set of possible orbit models for NGC 1907. 3. Results and Discussion Around the orbital solution of Fig.2 we probed a grid of We left a point mass at x0, y0, z0, U0, V0, W0, radial velocities and proper motion values within uncer- to evolve in the Galactic potential, to get− x ,−y , z −, U , i i i i tainties in these quantities, trying to find out which one V , W at an earlier time. Then, by reversing again− the i i provided the smallest relative velocity and separation be- −velocity− components we obtained the initial conditions of tween the clusters. In Figs. 3 and 4 we show the orbital our simulations x , y , z , U , V , W . i i i i i i results for the NGC 1912 and NGC 1907 models. Each In Fig. 2 we plot the orbit of both clusters from T= figure has three possible orbits, one corresponding to the -200 Myr up till now, according to the values obtained mean values for the orbit in Fig. 2 and the other two to the above. extreme values derived by means of the upper and lower limits for the errors of the velocity components. M.R. de Oliveira et al.: NGC 1912 and NGC 1907 5

XZ XZ XZ

40 40 40

20 20 20

0 0 0

-20 -20 -20

-40 -40 -40

40 20 0 -20 -40 40 20 0 -20 -40 40 20 0 -20 -40

Fig. 8. XZ plane projection of the cluster encounter according to orbit model Orb-9 at three different times. From left to right: orbit model at T=-1.2 Myr, at present time (T=0) and in the near future (T = +0.8 Myr).

Fig. 9. Left panel: surface density map for the encounter of the N-body cluster models NGC 1912 (top) and NGC 1907 (bottom). Right panel: surface density map of the open clusters NGC 1912 (top) and NGC 1907 (bottom), as derived from the Digitized Sky Survey.

In Fig. 5 we show the relative velocity against separa- which is corroborated by their differing ages (Fujimoto tion (modulus) for all the possible orbital model combina- and Kumai 1997). We can also estimate, as first approxi- tions of Figs. 3 and 4 in the interval T= -10 Myr to T= mation, that the limiting velocity for a close orbit between 0. The best model is Orb-9 which gives a relative velocity the clusters is around one order of magnitude smaller than ∆V= 41.9 km/s for a centre to centre separation of 2.7 pc the relative velocity obtained for model Orb-9 at T= -0.4 at T= -0.4 Myr. The orbits for both clusters are plotted Myr. The results suggest that a fast fly-by with transpass- in Fig. 6. ing occurred in the near past. Since the radial velocity of NGC 1912 was based on For isophotal analysis purposes we extracted digitized one star (Sect. 2.1), we also tested other orbits including images of the pair NGC 1912/NGC 1907 from the DSS. the measures of three more stars presented by Glushkova The plate is a Palomar blue one. The PDS pixel values cor- & Rastorguev (1981). Despite a high membership proba- respond to photographic density measures from the origi- bility, these authors have classified them as non-members nal plates, and are not calibrated. The method used here based on proper motions. In Fig. 7 we show the relative to obtain the isophotal contours is identical to de Oliveira velocity against separation (modulus) for variations of the et al. (2000a). Orb-9 model taking into account the possibility of differ- In Fig. 9 we compare the model clusters isodensity map ent values for the NGC 1912 radial velocity based on these on the sky at the present epoch with the NGC 1907 and additional stars. We conclude that the orbit is not much NGC1912 isophotal contours. dependent on this uncertainty. Apparently there is no evidence of a bridge linking In Fig. 8 we show the encounter according to the Orb- the clusters, neither for the N-body models nor for the 9 orbit model for T= -1.2 Myr, T= 0 (present time) and open clusters themselves (Fig. 9). In a multi-mass system, T= +0.8 Myr. The possible orbit (Fig. 6) suggest that due to mass segregation, low mass stars are preferentially the clusters were formed in different parts of the Galaxy, stripped out by the external tidal galactic field, so one 6 M.R. de Oliveira et al.: NGC 1912 and NGC 1907

43

Orb_9 Orb_9.1 Orb_9.2 42

41 V (km/s) ∆

40

39 Fig. 10. Surface density map for a parabolic encounter 0 100 200 300 400 of the cluster models NGC 1912 (top) and NGC 1907 ∆R (pc) (bottom) in the limiting case of a capture, showing the Fig. 7. Same as Fig. 5 for three different values for the formation of a prominent bridge. radial velocity of model M1912: -1.0 (solid), -5.0 (dashed) and -9.0 km/s (dot-dashed) respectively. body simulations of NGC 1912 and NGC 1907 encounter suggest a fly-by occurred in the near past. These simula- tions also shows that the faster the clusters approach the expect that tidal tails are mainly constituted by low mass weaker the tidal debris in the bridge region, which explain stars (Combes et al. 1999). So, in principle, these tidal why there is, apparently, no evidence of a material link be- bridges, arising in isolated clusters, would not be easily tween the clusters and why it should not be expected. It detectable. However, in a cluster pair encounter we can would be necessary deep wide field CCD photometry for a expect mass loss by one of the members up to 50% of more conclusive result about the apparent absence of tidal the initial cluster mass (Leon et al. 1999, de Oliveira et al. link between the clusters . 2000a). Also, according to the study of possible interacting clusters in the LMC Leon et al. (1999) have calculated that Acknowledgements. We made use of information stored at the star upper limit mass of these tails are comparable Centre de Donn´ees Stellaires (CDS, Strasbourg) and from the to the most massive stars in these clusters. So we would DSS (Digitized Sky Survey). We thank the CESUP-UFRGS for expect that in a cluster encounter some massive stars are alloted time on the CRAY-T94 computer. We are also grate- present in these tidal tails. ful to an anonymous referee for useful remarks. We acknowl- The simulations allow us to check how intense a bridge edge support from the Brazilian institutions CNPq, CAPES would appear in a near capture relative velocity. In order and FINEP. M.R.O. acknowledges financial support from the to test such scenario we simulated a parabolic encounter Brazilian CNPq (no. 200815/00-8), and wishes to thank the LERMA Department of Observatoire de Paris for its hospital- reducing the relative velocity to 10% of the original value, ity. which is beyond the error bar. In Fig. 10 we plot the on-the-sky model isodensity at T=0, after the closest ap- proach. The simulation shows that a strong bridge arises References in this case. Aarseth, S.J., H´enon & M., Wielen, R., 1974. A&A, 37, 183. Captures would require to lower the relative velocity Allen, C. & Martos, N.A., 1986. RMxAA, 13, 137. modulus in the last simulation which in turn would in- Bhatia R.K. & Hatzidimitriou D. , 1988. MNRAS, 230, 215. creases the bridge intensity. So, our model suggests that Bica E., Clari´aJ.J. & Dottori H., 1992. AJ, 103, 1859. we are witnessing a pair fly-by. Binney, J. & Tremaine, S., 1987. Galactic Dynamics, ed. J.P. Ostriker, (Princeton University Press. Cohn,H.N., 1980. ApJ, 242, 765. 4. Conclusions Combes, F., Leon, S. & Meylan, G., 1999. A&A, 352, 149. 358 In the present study we investigated if the closely pro- Dieball A.& Grebel E.K., 2000. A&A, , 897. de Oliveira, M.R., Dottori, H. & Bica, E., 1998. MNRAS, 295, jected open clusters NGC 1912 (M 38) and NGC 1907 are 921. a binary cluster. We derived spatial velocities from avail- de Oliveira, M.R., Bica, E. & Dottori, H., 2000a. MNRAS, 311, able radial velocities and proper motions, and the past or- 589. bital motions of the clusters are retrieved in a Galactic po- de Oliveira, M.R., Dutra, C.M., Bica, E. & Dottori, H., 2000b. tential model. According to our models, the clusters were A&AS, 146, 57. formed in different parts of the Galaxy. The detailed N- Fujimoto, M. & Kumai, Y., 1997. AJ, 113, 249. M.R. de Oliveira et al.: NGC 1912 and NGC 1907 7

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