On the origin of the clumpy streams of Palomar 5
Alessandra Mastrobuono-Battisti, Paola Di Matteo, Marco Montuori, Misha Haywood
aa r X i v : . [ a s t r o - ph . GA ] A p r Mem. S.A.It. Vol. 75, 282 c (cid:13) SAIt 2008
Memorie della
On the origin of the clumpy streams ofPalomar 5
Alessandra Mastrobuono-Battisti , Paola Di Matteo , Marco Montuori ,Misha Haywood Physics Department, Technion - Israel Institute of Technology, Haifa, Israel 32000e-mail: [email protected] GEPI, Observatoire de Paris, CNRS, Universit´e Paris Diderot, 5 place Jules Janssen,92190 Meudon, France ISC-CNR & Dipartimento di Fisica, Universit`a di Roma La Sapienza, Piazzale AldoMoro 2, 00185 Rome, Italy
Abstract.
In this paper we report a study (see Mastrobuono-Battisti et al., 2012) about theformation and characteristics of the tidal tails around Palomar 5 along its orbit in the MilkyWay potential, by means of direct N-body simulations and simplified numerical models.Unlike previous findings, we are able to reproduce the substructures observed in the stellarstreams of this cluster, without including any lumpiness in the dark matter halo. We showthat overdensities similar to those observed in Palomar 5 can be reproduced by the epicyclicmotion of stars along its tails, i.e. a simple local accumulation of orbits of stars that escapedfrom the cluster with very similar positions and velocities. This process is able to formstellar clumps at distances of several kiloparsecs from the cluster, so it is not a phenomenonconfined to the inner part of Palomar 5’s tails, as previously suggested.
Key words.
Galaxy: halo – (Galaxy:) globular clusters: individual: Palomar 5 – Galaxy:evolution – Galaxy: kinematics and dynamics – Methods: numerical
1. Introduction
Palomar 5 (Pal 5) is an outer Milky Way glob-ular cluster (GC) which presents some pecu-liar characteristics: a very low mass, M tot = × M ⊙ , a large core radius, r c = . c = Send o ff print requests to : A. Mastrobuono-Battisti Dionatos , 2006; Jordi & Grebel, 2010). Withan overall detected extension of 22 ◦ on the sky,corresponding to a projected spatial length ofmore than 10 kpc, Pal 5’s tails are so elon-gated and massive that they contain more stel-lar mass than the one currently estimated to bein the system itself (Odenkirchen et al., 2003).Pal 5’s streams are characterized by the pres-ence of inhomogeneities: stellar density gaps(underdense regions) and clumps (overdenseregions) are particularly visible in the trail-ing stream, with the most evident and massiveoverdensities found between 100 and 120 ar-cmin from the cluster center (Odenkirchen et astrobuono-Battisti et al.: Substructures in Pal 5’s tidal tails 283 al., 2003). As Capuzzo-Dolcetta et al. (2005)and Di Matteo al. (2005) showed, the presenceof similar substructures in globular cluster tidaltails can be related to kinematic e ff ects and lo-cal decelerations in the motion of stars, lateridentified by K¨upper et al. (2008, 2010, 2012)and Lane et al. (2012) as “epicyclic cusps”,i.e. regions where stars escaping from the clus-ter slow down in their epicyclic motion, asseen in the cluster reference frame. However,while all these works were successful in show-ing that complex morphological substructurescan be formed in the tidal streams of globu-lar clusters, until now no simulation or modelhas been able to reproduce convincingly theonly stellar clumps robustly observed in thetails of a Galactic GC: those of Pal 5. Evenin the most complete numerical study of Pal5’s stellar streams realized in the last years,Dehnen al. (2004) have not succeeded in re-producing the clumpy nature of the stream.This lead them to propose that the observedclumps may be the e ff ect of Galactic substruc-tures (as giant molecular clouds or dark mattersubhalos) not accounted to in their simulations.The hypothesis that the gravitational e ff ects ofdark subhalos can generate a complex mor-phology in tidal tails, with overdensities andgaps, has been recently confirmed by Yoon etal. (2011). However, in the results presented byMastrobuono-Battisti et al. (2012) and summa-rized in this paper, we show that the inhomo-geneous tails of Pal 5 can be reproduced alsowithout invoking any lumpy dark halo, just asan e ff ect of epicyclic motion of stars.
2. Models and initial conditions
We used N-body, direct summation simula-tions to investigate the formation and charac-teristics of Pal 5’s tidal tails (see Mastrobuono-Battisti et al., 2012, for more details). To runthe simulations we used a modified version ofNBSymple (Capuzzo-Dolcetta et al., 2011), ahigh performance direct N -body code imple-mented on a hybrid CPU + GPU platform. Inthis code, the e ff ect of the external galactic field is taken into account by mean of an ana-lytical representation of its gravitational poten-tial (see Sect. 2.2). To smooth the mutual in-teraction between particles we adopted a soft-ening length, ε = .
03 pc. The time integra-tion of the particles trajectories was done usingthe second-order leapfrog method. The averagerelative error per time step was less than 10 − for the cluster both isolated or in the Galacticpotential. The result of the N-body simulationswere compared to simplified, restricted three-body models, where we used the same initialconditions adopted to run the simulation but, ateach time step, instead of considering the mu-tual interactions, we evaluated the interactionwith the global gravitational potential of thecluster and with the Galactic potential for eachparticle. Finally, similar to Lane et al. (2012),we produced streaklines to visualize in a moreclear way the spatial distribution, at the presenttime, of stars that have escaped from Pal 5 inthe last Gyrs. To do so, we integrated the orbitof a point mass representing Pal 5 barycenter,and, at each time step, released two particles atdistance r max =
120 pc from it, along the in-stantaneous Galactic center and anticenter di-rections, and with a velocity equal to that ofthe cluster. The motion of these escapers is in-tegrated in time, taking both the e ff ects of theGC and Galactic potential into account. The Galactic potential is from Allen &Santillan (1991), whose model consists of aspherical central bulge and a flattened disk,plus a massive smooth spherical halo. For theGC we adopted the parameters of the “modelA” described by Dehnen al. (2004) which con-sists of a single-mass King model (King, 1966)with tidal radius r t =
56 pc, W = .
75, and M = × M ⊙ ; we used N = .
95 Gyr, in the Galactic potential.Then we translated the positions and velocitiesof the King model to coincide with those of
84 Mastrobuono-Battisti et al.: Substructures in Pal 5’s tidal tails
229 230 231 232 233 234 235 α (deg)-0.5 0 0.5 1 1.5 2 2.5 3 3.5 δ ( deg ) Λ ( deg - ) α (deg) Fig. 1.
Upper panel: The trailing tail at the endof the N-body simulation. The contour lines inthe tails refer to 740, 2200, 4800, 6300 and7400 M ⊙ / deg . Bottom panel: Linear densityof the trailing tail shown in the upper panel, asa function of the right ascension α . The clus-ter is on the right of the panel. Error bars arePoisson errors. From Mastrobuono-Battisti etal. (2012).the cluster barycenter 2 .
95 Gyr ago, and we in-tegrated the whole cluster 2 .
95 Gyr forward intime.
3. Results and discussion
During its evolution, the simulated cluster haslost the most of its initial mass (88%), nowredistributed into two long and narrow tidaltails. This tails are only apparently smooth: asit becomes evident plotting the cluster isoden-sity contours, their structure is actually com-plex and the stellar distribution is clearly inho-mogeneous. In particular, as shown in the up-per panel of Fig. 1, the densest substructuresare all localized in the trailing tail. In this tail,our N-body simulation predicts there are two
229 230 231 232 233 234 235 α (deg)-0.5 0 0.5 1 1.5 2 2.5 3 3.5 δ ( deg ) Fig. 2.
The trailing tail of the cluster in the re-stricted three-body model. The contour linesin the tails refer to 470, 940, 1410, 1970,2500 and 3300 M ⊙ / deg . From Mastrobuono-Battisti et al. (2012).prominent density enhancements: the first lo-cated very close to the cluster ( α < ◦ ) andthe second starting at α = ◦ and ending at α = ◦ . The second region shows an under-dense region in it, whose extension is ∼ ◦ .All these characteristics, at the same location,are also found in the observed streams (seeFig. 3 in Odenkirchen et al., 2003). Not onlydoes the position of these clumps closely re-semble the location of those observed in Pal5’s tails, but their linear densities (bottom panelof Fig. 1) – 2–3 times above the density ofthe surrounding streams – and the presenceof underdense regions, with sizes of 0.5 ◦ -1 ◦ ,also agree with those measured for Pal 5 (seeFig. 4, Odenkirchen et al., 2003). As shownin Fig. 2, these substructures are also visiblein the isodensity contours of the simplified nu-merical model, at few degrees from the clustercenter. These regions of over- and underden-sities are due to the epicyclic motion of starsescaping from the cluster: stars lost at di ff er-ent times redistribute along the tail followinga complex path, as shown by the streaklines inFig. 3. This kinematic process, described andstudied in a number of papers (K¨upper et al.,2008, 2010, 2012; Lane et al., 2012), is ap-plied here for the first time to reproduce ob-served stellar streams, including both the po-sition and the intensity of the observed stellar astrobuono-Battisti et al.: Substructures in Pal 5’s tidal tails 285 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 229 230 231 232 233 234 235 δ ( deg ) α (deg) Fig. 3.
Streaklines which show the positions,at the present time, of stars that have escapedfrom Pal 5 in the last 2 .
95 Gyrs. Di ff erent col-ors correspond to stars lost during di ff erenttime intervals of 0 . ∼
4. Conclusions
We have studied the formation and character-istics of the tidal tails of the GC Pal 5 alongits orbit in a smooth Milky Way potential bymeans of N-body simulations and simplifiednumerical models. For the first time, we wereable to reproduce the observed inhomogeneousstructure of Pal5’s tidal tails using N-body sim-ulations, without including any lumpiness inthe Galactic halo. The epicyclic motion of starsalong the tails is the main mechanism respon-sible for the formation of clumps. This resultmust be taken into account when using streamsinhomogeneities to evaluate the granularity ofthe Milky Way dark halo.
Acknowledgments
This work was carried out under the HPC-EUROPA2 project (project number: 228398)with the support of the European CommissionCapacities Area-Research InfrastructuresInitiative.
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