EDP Sciences
Open Access
Volume 535, November 2011
Article Number A70
Number of page(s) 13
Section Galactic structure, stellar clusters and populations
DOI https://doi.org/10.1051/0004-6361/201117474
Published online 10 November 2011

Online material

Appendix A: Estimating the maximum energy gain

In this section we briefly describe the process of how we obtained estimates for the velocities Vperi and vesc(Rtidal), which we need to evaluate Eq. (12). The ingredients for this are

  • the radial mass profile of the host galaxy;

  • the radial dark matter and baryonic mass profile of the satellite galaxy;

  • the parameters of the satellite orbit, namely the initial angular momentum Lsat and the initial orbital energy Esat.

As a first step we estimate the minimum distance to which the satellite approaches the host center, i.e. the pericenter distance Rperi. For this we use the effective potential + Φhost(r), exploiting (A.1)where we compute the energy loss from dynamical friction ΔEDF using Eq. (14). Furthermore we compute the satellite velocity in the perigalacticon via (A.2)To compute the escape velocity vesc(Rtidal) from the satellite system we first have to determine the tidal radius Rtidal which we assume to be equal to the Jacobi radius at the distance Rperi: (A.3)However, we do not take the total satellite mass Msat for the final radius. We also take into account that due to its much larger extension the dark matter halo of the satellite is stripped much earlier the the baryonic component. Consequently we compute the tidal radius using the total satellite mass Msat and assume that all material outside this “dark matter tidal radius” Rtidal,DM is lost. We then compute the “baryonic tidal radius” using Eq. (A.3) with the mass . Finally we obtain the escape speed: (A.4)The tidal radius computed in this two-step process also allows a very good estimate of the baryonic mass loss of the satellite when it is assumed that all mass outside this tidal radius is lost, i.e., (A.5)This was used in Sect. 6 to estimate the fraction of satellite mass expelled as HVSs into intergalactic space.

Appendix B: Scaling tests

thumbnail Fig. B.1

Comparison of the energy distributions obtained from corresponding high and low resolution runs. The dashed lines indicate the mass resolution limits of the simulations, i.e. the mass of a single star particle.

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To assess the influence of the numerical resolution on our results, we ran a set of simulations with the number of particles in the satellite system reduced by a factor of 10. This was done by taking the initial snapshot file of one of our high-resolution runs and randomly removing 90 percent of the satellite particles. Then the masses of the remaining particles increased by a factor of 10. In this way we obtain an equilibrium configuration of a satellite system with exactly the same properties as the high-resolution one.

In Fig. B.1 we show the resulting energy distributions, together with those of the corresponding high-resolution runs with the same initial conditions. The shapes of the distributions show no significant differences. The width of the corresponding distributions, ϵw, obtained by fitting Eq. (17) also differ by less than 10 percent. As could be expected, the low-resolution distribution does not reach as high an energy as the high-resolution one. However, the maximum energies do not differ by much, due to the steep slope in the outer tails of the distribution.

We also repeated one simulation run using a five times longer softening length for the star particles. For all quantities measured for this study the outcome changed by less than 1 percent. Especially the maximum energies reached by satellite particles differ only by 0.1 percent. This shows that our results are not affected by artificial heating by two-body encounters.

Appendix C: Other host galaxy potentials

thumbnail Fig. C.1

Radial gravitational potential profiles of the four alternative host galaxy representation and for the N-body live host galaxy (black). The alternative models cover a variety of central and outer slopes allow testing of the influence of those on satellite tidal tails. The varying thickness of the profile lines reflects the nonspherical symmetry of the potentials.

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To test the influence of the shape of the Milky Way-host potential, we performed a small number of test simulations with different rigid potentials representing the host galaxy. Four different models were applied: three of them (potentials 1–3) share the same parametrization of the baryonic disk and spheriod components. In three of the models the baryonic component of the Galaxy is modeled as a Miyamoto & Nagai (1975) disk with mass 1011M, radial and vertical scale length of 6.5 and 0.26 kpc, respectively and a Hernquist (1990) bulge component of mass 3.4 × 1010M and a scale length of 0.7 kpc. The dark halos are modeled with

  • potential 1: a logarithmic potential with vh = 128 km s-1 and rh = 12 kpc. This potential has already been often used by other studies to mimick a Milky Way (e.g. Johnston 1998; Helmi & White 2001);

  • potential 2: a Plummer (1911) sphere with mass 6 × 1011M and scale radius 25.7 kpc;

  • potential 3: an NFW sphere (Navarro et al. 1997) with central density 1.523 × 106Mkpc-3 and scale radius 36 kpc.

All three potentials were chosen such that Vcirc(8.5kpc) = 220 km s-1 and Vesc(8.5kpc) = 550 km s-1. As a fourth option we used the model potential number 4 of Dehnen & Binney (1998), which we implemented in Gadget-2 using a C++ routine prepared by Walter Dehnen and distributed with the NEMO Stellar Dynamics Toolbox (Teuben 1995).

thumbnail Fig. C.2

Comparison of the energy distributions of the tidal tail particle stripped from identical satellite galaxies with identical initial phase space positions evolving in different host potentials.

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Figure C.1 shows a comparison of the radial profiles of the four potentials with the radial profile of the live halo used in the main part of the simulations. All potentials have a steeper slope in the inner regions. The virtually flat part of the live potential is due to the gravitational softening becoming significant on these scales.

Figure C.2 plots the energy tidal tail distributions (cf. Fig. 6) obtained with the different host representations but otherwise identical initial conditions. While the distribution changes strongly in regions with small  | ΔE | , the tail of the distribution remains virtually unchanged. We thus conclude that the actual shape of the Galactic potential has no major influence on our results. The variations around the central minimum are most likely due to the different evolutions of the Roche radius of the satellite during its orbits thereby determining whether particles with low  | ΔE |  that stay near the satellite for longer periods are recaptured.

Appendix D: Initial conditions

Table D.1

Initial parameters of the satellite systems (plus some results)

© ESO, 2011

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