Free Access
Volume 546, October 2012
Article Number L7
Number of page(s) 6
Section Letters
DOI https://doi.org/10.1051/0004-6361/201219563
Published online 16 October 2012

Online material

Appendix A: Dependency on the orbital parameters

In Sect. 3, we have seen that epicyclic motion of stars in the tails generate overdensities mostly in the trailing tail of Pal 5, at distances of few degrees from the cluster center. Here we show how sensitive this finding is to a change in the orbital parameters. To this aim, we have run several N-body simulations changing both the radial, vr, and tangential, vt, velocities with respect to those of the standard orbit (we recall the reader that, for the standard orbit, vr = −44.3 km s-1 and vt = 90 km s-1). In particular, for the tangential velocity, we adopted the extreme values, 80 km s-1 and 110 km s-1, beyond which the orbit fails to give a good representation of the observations, as shown by Odenkirchen et al. (2003), and also two intermediate values similar to those of the standard orbit, vt = 89 km s-1 and vt = 91 km s-1. For the radial velocity we arbitrarily varied the best fit parameter by  ± 2 km s-1, since the error on this value is smaller than the one affecting the tangential velocity (Odenkirchen et al. 2003). In all the models presented in this section, the position angle PA has been kept fixed to  = 231° and the internal parameters of the cluster have not been changed. In Figs. A.1 and A.2 the results of this analysis are presented. The orbits with vr = −44.3 km s-1 and vt = 110 km s-1 or vt = 80 km s-1 are significantly different from the standard orbit. On the first orbit (which has a pericenter  ~1.2 kpc greater than that of the standard orbit) the cluster loses a small percentage of its mass, and the tails are characterized by a low density and a nearly flat stellar distribution, with density variations within the error bars. On the other hand, although the cluster with vr = −44.3 km s-1 and vt = 80 km s-1 is destroyed by the tidal interaction with the Galactic field (the pericenter of the orbit is 4.7 kpc, a factor  ~1.3 smaller than that of the standard orbit), clumps are clearly visible between 229° and 231°. Thus, for variation of the tangential velocity of the order of 10 km s-1 the density of the tails changes significantly. For smaller changes of the tangential and radial velocities the mass loss rate is closer to that of the standard orbit and stellar overdensities are present in the trailing tail, with similar positions and amplitudes. This also confirms that the overdensities found for the standard orbit are not due to random fluctuations, but rather robust characteristics of this portion of the tail, since for small changes around the standard values they are still present, and generate a profile that closely resembles that of the standard orbit.

thumbnail Fig. A.1

Upper panel: linear density of the trailing tail, as a function of the distance from the cluster center, for different orbits having the same radial velocity of the standard orbit (S.O., black line), i.e. −44.3 km s-1, and vt = 80 km s-1 (blue line), vt = 89 km s-1 (magenta line), vt = 91 km s-1 (green line), or vt = 110 km s-1 (red line). Lower panel: the same but for orbits having the same tangential velocity of the standard orbit (S.O., black line), i.e. 90 km s-1, and vr = −42 km s-1 (blue line) or vr = −46 km s-1 (red line). The typical Poisson’s uncertainty is shown.

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thumbnail Fig. A.2

Isodensity contour plots for the trailing tail of the cluster for different N-body simulations having orbits with vr = −44.3 km s-1 and vt = 80 km s-1 (upper left panel), vr = −44.3 km s-1 and vt = 89 km s-1 (upper right panel), vr = −44.3 km s-1 and vt = 91 km s-1 (middle left panel), vr = −44.3 km s-1 and vt = 110 km s-1 (middle right panel), vr = −42 km s-1 and vt = 90 km s-1 (bottom left panel), vr = −46 km s-1 and vt = 90 km s-1 (bottom right panel). See upper panel of Fig. 2 for a comparison with the isodensity contours of the standard orbit

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thumbnail Fig. A.3

Time, tloss, at which escaped stars crossed the tidal boundary of the cluster as a function of the right ascension α of stars in Pal 5’s tails. The right ascension has been evaluated at the current epoch (see Fig. 1 for comparison). tloss is zero for stars lost from the GC at the current epoch, and attends the lowest values for stars escaped from the GC at the beginning of the simulation. Each color in the plot corresponds to stars lost at different pericenter passages, while grey points correspond to stars lost between two consecutive pericenter passages.

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Appendix B: Why are clumps not caused by an episodic mass loss?

In their modeling of Pal 5’s tidal tails, Dehnen et al. (2004) have already shown that at any given distance from the cluster center, stars lost from the cluster at different times can be found. We confirm this finding in Fig. A.3, where we plot the time stars escape from the tidal boundary3 as a function of the right ascension α, which describes the spatial extension of the streams. At any given value of α corresponds many different values of tloss: this is especially the case for particles in the inner part of the tails, at distances of 3°−4° from the cluster center. Moreover, the distribution in the plane α − tloss resembles a tree, with branches

and trunk corresponding, respectively, to stars lost at each pericenter passage (plotted in Fig. A.3 with different colors), and in between two consecutive pericenter passages. Due to their higher velocity dispersion when they escape the cluster, stars lost at the pericenter passage are rapidly spread over a larger extension of the tidal tails than stars lost in between consecutive pericenter passages, which are systematically, for every tloss, closer to the cluster center than stars lost at pericenters. This behavior in the redistribution of stars lost in different phases of the cluster orbit clearly demonstrates that any temporary accumulation outside the tidal boundary of stars lost at the pericenter passage is rapidly cleaned out and thus cannot be a mechanism able to produce stellar overdensities in tidal streams at several degrees of distance from the cluster center.

© ESO, 2012

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