The formation of ultra-compact dwarf galaxies and nucleated dwarf galaxies

Ultra compact dwarf galaxies (UCDs) have similar properties as massive globular clusters or the nuclei of nucleated galaxies. Recent observations suggesting a high dark matter content and a steep spatial distribution within groups and clusters provide new clues as to their origins. We perform high-resolution N-body / smoothed particle hydrodynamics simulations designed to elucidate two possible formation mechanisms for these systems: the merging of globular clusters in the centre of a dark matter halo, or the massively stripped remnant of a nucleated galaxy. Both models produce density profiles as well as the half light radii that can fit the observational constraints. However, we show that the first scenario results to UCDs that are underluminous and contain no dark matter. This is because the sinking process ejects most of the dark matter particles from the halo centre. Stripped nuclei give a more promising explanation, especially if the nuclei form via the sinking of gas, funneled down inner galactic bars, since this process enhances the central dark matter content. Even when the entire disk is tidally stripped away, the nucleus stays intact and can remain dark matter dominated even after severe stripping. Total galaxy disruption beyond the nuclei only occurs on certain orbits and depends on the amount of dissipation during nuclei formation. By comparing the total disruption of CDM subhaloes in a cluster potential we demonstrate that this model also leads to the observed spatial distribution of UCDs which can be tested in more detail with larger data sets.Comment: 8 pages, 8 figures, final version accepted for publication in MNRA

Resolving the timing problem of the globular clusters orbiting the Fornax dwarf galaxy

We re-investigate the old problem of the survival of the five globular clusters orbiting the Fornax dwarf galaxy in both standard and modified Newtonian dynamics. For the first time in the history of the topic, we use accurate mass models for the Fornax dwarf, obtained through Jeans modelling of the recently published line of sight velocity dispersion data, and we are also not resigned to circular orbits for the globular clusters. Previously conceived problems stem from fixing the starting distances of the globulars to be less than half the tidal radius. We relax this constraint since there is absolutely no evidence for it and show that the dark matter paradigm, with either cusped or cored dark matter profiles, has no trouble sustaining the orbits of the two least massive globular clusters for a Hubble time almost regardless of their initial distance from Fornax. The three most massive globulars can remain in orbit as long as their starting distances are marginally outside the tidal radius. The outlook for modified Newtonian dynamics is also not nearly as bleak as previously reported. Although dynamical friction inside the tidal radius is far stronger in MOND, outside dynamical friction is negligible due to the absence of stars. This allows highly radial orbits to survive, but more importantly circular orbits at distances more than 85% of Fornax's tidal radius to survive indefinitely. The probability of the globular clusters being on circular orbits at this distance compared with their current projected distances is discussed and shown to be plausible. Finally, if we ignore the presence of the most massive globular (giving it a large line of sight distance) we demonstrate that the remaining four globulars can survive within the tidal radius for the Hubble time with perfectly sensible orbits.Comment: 8 pages, 10 figures, 1 table, MNRAS in pres

Homo- and Heterotypic Cell Contacts in Malignant Melanoma Cells and Desmoglein 2 as a Novel Solitary Surface Glycoprotein

During progression of melanomas, a crucial role has been attributed to alterations of cell–cell adhesions, specifically, to a “cadherin switch” from E- to N-cadherin (cad). We have examined the adhesion of melanoma cells to each other and to keratinocytes. When different human melanoma cell lines were studied by protein analysis and immunofluorescence microscopy, six of eight lines contained N-cad, three E-cad, and five P-cad, and some lines had more than one cad. Surprisingly, two N-cad-positive lines, MeWo and C32, also contained desmoglein 2 (Dsg2), a desmosomal cad previously not reported for melanomas, whereas other desmosome-specific proteins were absent. This finding was confirmed by reverse transcriptase–PCR, immunoprecipitation, and matrix-assisted laser desorption ionization–time of flight analyses. Double-label confocal and immunoelectron microscopy showed N-cad, α- and β-catenin in plaque-bearing puncta adhaerentia, whereas Dsg2 was distributed rather diffusely over the cell surface. In cocultures with HaCaT keratinocytes Dsg2 was found in heterotypic cell contact regions. Correspondingly, immunohistochemistry revealed Dsg2 in five of 10 melanoma metastases. Together, we show that melanoma cell adhesions are more heterogeneous than expected and that certain cells devoid of desmosomes contain Dsg2 in a non-junction-restricted form. Future studies will have to clarify the diagnostic and prognostic significance of these different adhesion protein subtypes

Cores and Cusps in the Dwarf Spheroidals

We consider the problem of determining the structure of the dark halo of nearby dwarf spheroidal galaxies (dSphs) from the spherical Jeans equations. Whether the dark halos are cusped or cored at the centre is an important strategic problem in modern astronomy. The observational data comprise the line-of-sight velocity dispersion of a luminous tracer population. We show that when such data are analysed to find the dark matter density with the spherical Poisson and Jeans equations, then the generic solution is a dark halo density that is cusped like an isothermal. Although milder cusps (like the Navarro-Frenk-White 1/r cusp and even cores are possible, they are not generic. Such solutions exist only if the anisotropy parameter beta and the logarithmic slope of the stellar density gamma satisfy the constraint gamma = 2 x beta at the centre or if the radial velocity dispersion falls to zero at the centre. This surprisingly strong statement is really a consequence of the assumption of spherical symmetry, and the consequent coordinate singularity at the origin. So, for example, a dSph with an exponential light profile can exist in Navarro-Frenk- White halo and have a flat velocity dispersion, but anisotropy in general drives the dark halo solution to an isothermal cusp. The identified cusp or core is therefore a consequence of the assumptions (particularly of spherical symmetry and isotropy), and not the data.Comment: MNRAS, in pres

Search for the light dark matter with an X-ray spectrometer

Sterile neutrinos with the mass in the keV range are interesting warm dark matter (WDM) candidates. The restrictions on their parameters (mass and mixing angle) obtained by current X-ray missions (XMM-Newton or Chandra) can only be improved by less than an order of magnitude in the near future. Therefore the new strategy of search is needed. We compare the sensitivities of existing and planned X-ray missions for the detection of WDM particles with the mass ~1-20 keV. We show that existing technology allows an improvement in sensitivity by a factor of 100. Namely, two different designs can achieve such an improvement: [A] a spectrometer with the high spectral resolving power of 0.1%, wide (steradian) field of view, with small effective area of about cm^2 (which can be achieved without focusing optics) or [B] the same type of spectrometer with a smaller (degree) field of view but with a much larger effective area of 10^3 cm^2 (achieved with the help of focusing optics). To illustrate the use of the "type A" design we present the bounds on parameters of the sterile neutrino obtained from analysis of the data taken by an X-ray microcalorimeter. In spite of the very short exposure time (100 sec) the derived bound is comparable to the one found from long XMM-Newton observation.Comment: 9pp, revtex

Statistical mechanics of the random K-SAT model

The Random K-Satisfiability Problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M=alpha N random logical clauses containing K variables each, is studied using the replica symmetric framework of diluted disordered systems. We present an exact iterative scheme for the replica symmetric functional order parameter together for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to predict a first order jump at the threshold where the Boolean expressions become unsatisfiable with probability one, is thoroughly displayed. In the case K=2, the (rigorously known) critical value (alpha=1) of the number of clauses per Boolean variable is recovered while for K>=3 we show that the system exhibits a replica symmetry breaking transition. The annealed approximation is proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section added and references update

The Nature of UCDs: Internal Dynamics from an Expanded Sample and Homogeneous Database

We have obtained high-resolution spectra of 23 ultra-compact dwarf galaxies (UCDs) in the Fornax cluster with -10.4>M_V>-13.5 mag (10^6<M/M_*<10^8), using FLAMES/Giraffe at the VLT. This is the largest homogeneous data set of UCD internal dynamics assembled to date. We derive dynamical M/L ratios for 15 UCDs covered by HST imaging. In the M_V-sigma plane, UCDs with M_V<-12 mag are consistent with the extrapolated Faber-Jackson relation for luminous ellipticals, while fainter UCDs are closer to the extrapolated globular cluster (GC) relation. At a given metallicity, Fornax UCDs have on average 30-40% lower M/L ratios than Virgo UCDs, suggesting possible differences in age or dark matter content between Fornax and Virgo UCDs. For our sample of Fornax UCDs we find no significant correlation between M/L ratio and mass. We combine our data with available M/L ratio measurements of compact stellar systems with 10^4<M/M_*<10^8, and normalise all M/L estimates to solar metallicity. We find that UCDs (M > 2*10^6 M_*) have M/L ratios twice as large as GCs (M < 2*10^6 M_*). We show that stellar population models tend to under-predict dynamical M/L ratios of UCDs and over-predict those of GCs. Considering the scaling relations of stellar spheroids, UCDs align well along the 'Fundamental Manifold', constituting the small-scale end of the galaxy sequence. The alignment for UCDs is especially clear for r_e >~ 7 pc, which corresponds to dynamical relaxation times that exceed a Hubble time. In contrast, GCs exhibit a broader scatter and do not appear to align along the manifold. We argue that UCDs are the smallest dynamically un-relaxed stellar systems, with M > 2*10^6 M_* and 7<r_e<100 pc. Future studies should aim at explaining the elevated M/L ratios of UCDs and the environmental dependence of their properties.Comment: 17 pages, 14 figures, accepted for publication in A&A. V3 taking into account proof corrections: Table 3 radial velocity entries corrected by heliocentric correction, updated sigma entries in Table 5 for a few CenA sources, updated references for G1 and omega Ce

On the freezing of variables in random constraint satisfaction problems

The set of solutions of random constraint satisfaction problems (zero energy groundstates of mean-field diluted spin glasses) undergoes several structural phase transitions as the amount of constraints is increased. This set first breaks down into a large number of well separated clusters. At the freezing transition, which is in general distinct from the clustering one, some variables (spins) take the same value in all solutions of a given cluster. In this paper we study the critical behavior around the freezing transition, which appears in the unfrozen phase as the divergence of the sizes of the rearrangements induced in response to the modification of a variable. The formalism is developed on generic constraint satisfaction problems and applied in particular to the random satisfiability of boolean formulas and to the coloring of random graphs. The computation is first performed in random tree ensembles, for which we underline a connection with percolation models and with the reconstruction problem of information theory. The validity of these results for the original random ensembles is then discussed in the framework of the cavity method.Comment: 32 pages, 7 figure

Sparser Random 3SAT Refutation Algorithms and the Interpolation Problem:Extended Abstract

We formalize a combinatorial principle, called the 3XOR principle, due to Feige, Kim and Ofek [12], as a family of unsatisfiable propositional formulas for which refutations of small size in any propo-sitional proof system that possesses the feasible interpolation property imply an efficient deterministic refutation algorithm for random 3SAT with n variables and Ω(n1.4) clauses. Such small size refutations would improve the state of the art (with respect to the clause density) efficient refutation algorithm, which works only for Ω(n1.5) many clauses [13]. We demonstrate polynomial-size refutations of the 3XOR principle in resolution operating with disjunctions of quadratic equations with small integer coefficients, denoted R(quad); this is a weak extension of cutting planes with small coefficients. We show that R(quad) is weakly autom-atizable iff R(lin) is weakly automatizable, where R(lin) is similar to R(quad) but with linear instead of quadratic equations (introduced in [25]). This reduces the problem of refuting random 3CNF with n vari-ables and Ω(n1.4) clauses to the interpolation problem of R(quad) and to the weak automatizability of R(lin)

Bridging the gap between low and high mass dwarf galaxies

While the dark matter content within the most massive giant and smallest dwarf galaxies has been probed -- spanning a range of over one million in mass -- an important observational gap remains for galaxies of intermediate mass. This gap covers K band magnitudes of approximately -16 > M_K > -18 (for which dwarf galaxies have B--K ~ 2). On the high mass side of the gap are dwarf elliptical (dE) galaxies, that are dominated by stars in their inner regions. While the low mass side includes dwarf spheroidal (dSph) galaxies that are dark matter-dominated and ultra compact dwarf (UCD) objects that are star-dominated. Evolutionary pathways across the gap have been suggested but remain largely untested because the `gap' galaxies are faint, making dynamical measurements very challenging. With long exposures on the Keck telescope using the ESI instrument we have succeeded in bridging this gap by measuring the dynamical mass for five dwarf galaxies with M_K ~ -17.5 (M_B ~ --15.5). With the exception of our brightest dwarf galaxy, they possess relatively flat velocity dispersion profiles of around 20 km/s. By examining their 2D scaling relations and 3D fundamental manifold, we found that the sizes and velocity dispersions of these gap galaxies reveal continuous trends from dE to dSph galaxies. We conclude that low-luminosity dwarf elliptical galaxies are dominated by stars, not by dark matter, within their half light radii. This finding can be understood if internal feedback processes are operating most efficiently in gap galaxies, gravitationally heating the centrally-located dark matter to larger radii. Whereas external environmental processes, which can strip away stars, have a greater influence on dSph galaxies resulting in their higher dark matter fractions. Abridged.Comment: 20 pages, includes 12 figures, accepted for publication in MNRA