An alternative possibility relying on Newtonian physics, is that some of the observed dSph satellites may not be in virial equilibrium and may not be spherical but with non-isotropic velocity dispersions, in which case the observed (M/L)obs ratios may not be physical. That such systems may exist is shown by the simulations of the long-term evolution of initially spherical satellite galaxies with masses of 107 Msun, initial Plummer radii of 300 pc on eccentric orbits in an extended Galactic dark halo with a circular velocity of 200 km s-1 (Kroupa 1997). The finding is that after about 99 per cent of the mass is lost from the satellites through repetitive tidal modification, remnants with (M/L)obs>10 remain that survive for a few orbital periods. This study is extended by Klessen & Kroupa (1998) covering more orbits and Galactic halo masses using two different numerical codes.
A shortcoming common to these remnants is that they have a central surface brightness too faint by about one order of magnitude, if (M/L)true = 3 is the mass-to-light ratio of the stellar population. One possible solution to this problem is to postulate that (M/L)true≅0.3 (Kroupa 1997). However, this implies an unusual initial mass function. Another possibility is to scale the satellite up in mass and size so that each particle carries a larger mass (for simulations with the same number of particles) and thus light, while keeping the binding energy of the satellite roughly unaffected (Klessen & Kroupa 1998). This, however, leads to remnants that have too large half-light radii.
It is thus clear that the simulations mentioned above, as well as other observational evidence summarised in Kroupa (1997) and Klessen & Kroupa (1998), give a strong hint that some of the Galactic dSph satellites may not be dark matter dominated but that they may be significantly affected by tides. However, much work remains to be done to establish if models can be produced that fit all the observational properties of at least some of the known dSph satellites.
It is the purpose of this contribution to give a preliminary account of the extensive parameter survey under way in Heidelberg that aims at constraining the possible region in (initial satellite binding-energy, mass and extend of the Galactic dark matter halo, and orbit) parameter space in which viable ``dSph solutions'' exist in the tidal scenario. If none such region can be found then the conclusion that all of the dSph satellites are dark matter dominated is strengthened.
The problem under investigation here is reduced to the interaction of a low-mass satellite galaxy with a massive Galactic dark halo. The details of setting up the satellite and Galactic halo models can be found in Kroupa (1997). The dark halo is assumed to be an isothermal mass distribution with a circular velocity of 200 km s-1 and a cutoff radius of Rc. The satellite is defined by its initial mass, Msat, and its initial Plummer radius, RPl. The satellite is placed into the Galactic dark halo at apo-galactic distance Rapo and with a tangential velocity vt. The resulting orbit has an eccentricity e=(Rapo-Rperi)/(Rapo+Rperi), where Rperi is the peri-galactic distance.
The satellite is observed as an observer from Earth sees a dSph satellite. It's projected brightness profile is measured. The central surface brightness and half-light radius are computed through profile fitting, and the line-of sight velocity dispersion is determined. The hypothetical observer thus estimates (M/L)obs as a function of time.
Typically, (M/L)obs remains constant at its initial low value until disruption time, when the satellite looses most of its remaining mass during passage through peri-galacticon. Thereafter, a remnant with roughly 1 per cent of the initial satellite mass remains. It has properties rather similar to typical dSph satellites, with large (M/L)obs. Evolution curves for (M/L)obs(t) and other satellite parameters are presented in Kroupa (1997) and Klessen & Kroupa (1998).
A particularly noteworthy result obtained by Klessen & Kroupa (1998) is that a remnant has a line-of-sight velocity dispersion σ>6 km s-1 if e>0.5. This suggests a useful observational criterion, for if e<0.5 for σ>6 km s-1 then the respective system is probably dark matter dominated. Here, preliminary additional results are presented for this satellite, with some discussion of other models as well.
The time when (M/L)obs≥50 occurs is denoted by τ50; it increases for increasing e, as is evident from Fig. 1.
From the figure it is apparent that τ50 is primarily a function of e and Rapo. Two observational constraints are plotted: The dSph satellite Ursa Minor contains only old stars with ages τ≅15 Gyr (van den Bergh 1994). It's preliminary proper motion (without an uncertainty) is reported by Olszewski (1998), from which the orbital eccentricity is estimated. The dSph satellite Sculptor has stars with ages in the range τ≅5-15 Gyr (van den Bergh 1994), and the proper motion has been estimated by Schweitzer et al. (1995). Both satellites are at a distance of 60-70 kpc. It is interesting to note that UMi has (M/L)obs=95±43, while Scl has (M/L)obs=10.9±7.5 (Irwin & Hatzidimitriou 1995).
The application of Fig. 1 is as follows: If the entire satellite was assembled a few Gyr ago then this would imply some recent merger event strong enough to lead to the formation of tidal tail dwarfs (e.g. Kroupa 1998). It is not clear if there is any other evidence for such an event. The present masses of the stellar components (assuming (M/L)true = 3) of UMi and Scl are, respectively, about 6·105 Msun and 4·106 Msun (Irwin & Hatzidimitriou 1995), which may be too low to accrete gas from a hypothetical gas cloud on a similar orbit (c.f. Magellanic or similar stream), or let alone retain gas over time-spans of many Gyr. Any stars with nuclear ages of a few Gyr were probably born from some gas-accretion event during a more massive past. Perhaps one may identify the nuclear age, τ, of the youngest stars as being the time when the satellite was massive enough for the last time to accrete some gas. The precursor satellite galaxies will have been two orders of magnitudes more massive than the dSph satellites, if the tidal scenario is applicable. Thus, τ50<τ if the respective dSph satellite is in the remnant phase with artificially inflated (M/L)obs.
Unfortunately the observational constraints are too weak to allow any definitive conclusions. But it is clear that if a dSph with (M/L)obs>10 containing relatively young stars (a few Gyr old, e.g. Scl) can be shown with high confidence to be on a low eccentricity (e<0.3) orbit, then the case for dark matter in this system would be rather strong.
Ultimately, the parameter study will allow constraining that region in (Msat,RPl) space that may lead, within a Hubble time, to a remnant phase that agrees with the observational properties of at least some of the dSph satellites. Figure 2 demonstrates this schematically.
In this figure, the thick (D = 100 kpc) and thin (D = 50 kpc) short-dashed lines are the tidal radii, log10 rt = -3.51 + (1/3) log10 Msat + (2/3) log10 D in kpc, where Msat is in Msun and D is the distance from the Galactic centre in kpc. Satellites that lie initially to the right of these (RPl>rt) are more or less immediately destroyed on injection into the dark halo. The long-dashed line, log10 Msat = 8.3 + (1/2) log10 RPl (units as above), is the binding energy, Eb = (G Msat2) / RPl, of the satellite. Satellites that initially lie above this line do not enter the remnant phase within a Hubble time. The filled dot is the satellite mentioned above, and the open circle represents a series of simulations that barely lead to any solutions, irrespective of e.
Once the solution region is delineated in this diagram, inferences can be drawn about the physical properties of the progenitors of those dSph satellites that are not dark matter dominated. This in turn may allow conclusions about the physical conditions that lead to the birth of such systems.
There exists in (Msat,RPl) space a region that leads within a Hubble time to remnants of satellites that appear tantalisingly similar to the dSph satellites (Kroupa 1997). Predictions of correlations between observable parameters can be arrived at (Klessen & Kroupa 1998, Fig. 1). Also, information as to the possible initial state of the progenitors of those dSph satellites that may not be dark matter dominated is emerging (Fig. 2).
| First version: | 14th | July, | 1998 |
| Last update: | 08th | October, | 1998 |