Brouwer’s satellite solution redux

Brouwer’s solution to the artificial satellite problem is revisited. We show that the complete Hamiltonian reduction is rather achieved in the plain Poincaré’s style, through a single canonical transformation, than using a sequence of partial reductions based on von Zeipel’s alternative for dealing with perturbed degenerate Hamiltonian systems. Beyond the theoretical interest of the new approach as regards the complete reduction of perturbed Keplerian motion, we also show that a solution based on a single set of corrections may yield computational benefits in the implementation of an analytic orbit propagator.

Abundance of dwarf galaxies around low-mass spiral galaxies in the Local Volume

The abundance of satellite dwarf galaxies has long been considered a crucial test for the current model of cosmology leading to the well-known missing satellite problem. Recent advances in simulations and observations have allowed the study of dwarf galaxies around host galaxies in more detail. Using the Dark Energy Camera we surveyed a 72 deg2 area of the nearby Sculptor group, also encompassing the two low-mass Local Volume galaxies NGC 24 and NGC 45 residing behind the group, to search for as yet undetected dwarf galaxies. Apart from the previously known dwarf galaxies we found only two new candidates down to a 3σ surface brightness detection limit of 27.4 r mag arcsec−2. Both systems are in projection close to NGC 24. However, one of these candidates could be an ultra-diffuse galaxy associated with a background galaxy. We compared the number of known dwarf galaxy candidates around NGC 24, NGC 45, and five other well-studied low-mass spiral galaxies (NGC 1156, NGC 2403, NGC 5023, M 33, and the LMC) with predictions from cosmological simulations, and found that for the stellar-to-halo mass models considered, the observed satellite numbers tend to be on the lower end of the expected range. This could mean either that there is an overprediction of luminous subhalos in ΛCDM or that we are missing some of the satellite members due to observational biases.

An Algorithm for the Numerical Integration of Perturbed and Damped Second-Order ODE Systems

A new method of numerical integration for a perturbed and damped systems of linear second-order differential equations is presented. This new method, under certain conditions, integrates, without truncation error, the IVPs (initial value problems) of the type: x″(t)+Ax′(t)+Cx(t)=εF(x(t),t), x(0)=x0, x′(0)=x0′, t∈[a,b]=I, which appear in structural dynamics, astrodynamics, and other fields of physics and engineering. In this article, a succession of real functions is constructed with values in the algebra of m×m matrices. Their properties are studied and we express the solution of the proposed IVP through a serial expansion of the same, whose coefficients are calculated by means of recurrences involving the perturbation function. This expression of the solution is used for the construction of the new numerical method. Three problems are solved by means of the new series method; we contrast the results obtained with the exact solution of the problem and with its first integral. In the first problem, a quasi-periodic orbit is integrated; in the second, a problem of structural dynamics associated with an earthquake is studied; in the third, an equatorial satellite problem when the perturbation comes from zonal harmonics J2 is solved. The good behavior of the series method is shown by comparing the results obtained against other integrators.

Boötes. IV. A new Milky Way satellite discovered in the Subaru Hyper Suprime-Cam Survey and implications for the missing satellite problem

We report on the discovery of a new Milky Way (MW) satellite in Boötes based on data from the ongoing Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP). This satellite, named Boötes IV, is the third ultra-faint dwarf that we have discovered in the HSC-SSP. We have identified a statistically significant (32.3σ) overdensity of stars with characteristics of a metal-poor, old stellar population. The distance to this stellar system is $D_{\odot }=209^{+20}_{-18}\:$kpc with a V-band absolute magnitude of $M_V=-4.53^{+0.23}_{-0.21}\:$mag. Boötes IV has a half-light radius of $r_{\rm h}=462^{+98}_{-84}\:$pc and an ellipticity of $0.64^{+0.05}_{-0.05}$, which clearly suggests that this is a dwarf satellite galaxy. We also found another overdensity that appears to be a faint globular cluster with $M_V=-0.20^{+0.59}_{-0.83}\:$mag and $r_{\rm h}=5.9^{+1.5}_{-1.3}\:$pc located at $D_{\odot }=46^{+4}_{-4}\:$kpc. Adopting the recent prediction for the total population of satellites in a MW-sized halo by Newton et al. (2018, MNRAS, 479, 2853), which combined the characteristics of the satellites observed by the Sloan Digital Sky Survey and the Dark Energy Survey with the subhalos obtained in ΛCDM models, we estimate that there should be about two MW satellites at MV ≤ 0 in the ∼676 deg2 covered by HSC-SSP, whereas that area includes six satellites (Sextans, Leo IV, Pegasus III, Cetus III, Virgo I, and Boötes IV). Thus, the observed number of satellites is larger than the theoretical prediction. On the face of it, we have a problem of too many satellites, instead of the well-known missing satellites problem whereby the ΛCDM theory overpredicts the number of satellites in a MW-sized halo. This may imply that the models need more refinement for the assignment of subhalos to satellites, such as considering those found by the current deeper survey. More statistically robust constraints on this issue will be brought by further surveys of HSC-SSP over the planned ∼1400 deg2 area.

Gaia DR2 proper motions of dwarf galaxies within 420 kpc

A proper understanding of the Milky Way (MW) dwarf galaxies in a cosmological context requires knowledge of their 3D velocities and orbits. However, proper motion (PM) measurements have generally been of limited accuracy and are available only for more massive dwarfs. We therefore present a new study of the kinematics of the MW dwarf galaxies. We use the Gaia DR2 for those dwarfs that have been spectroscopically observed in the literature. We derive systemic PMs for 39 galaxies and galaxy candidates out to 420 kpc, and generally find good consistency for the subset with measurements available from other studies. We derive the implied Galactocentric velocities, and calculate orbits in canonical MW halo potentials of low (0.8 × 1012 M⊙) and high mass (1.6 × 1012 M⊙). Comparison of the distributions of orbital apocenters and 3D velocities to the halo virial radius and escape velocity, respectively, suggests that the satellite kinematics are best explained in the high-mass halo. Tuc III, Crater II, and additional candidates have orbital pericenters small enough to imply significant tidal influences. Relevant to the missing satellite problem, the fact that fewer galaxies are observed to be near apocenter than near pericenter implies that there must be a population of distant dwarf galaxies yet to be discovered. Of the 39 dwarfs: 12 have orbital poles that do not align with the MW plane of satellites (given reasonable assumptions about its intrinsic thickness); 10 have insufficient PM accuracy to establish whether they align; and 17 satellites align, of which 11 are co-orbiting and (somewhat surprisingly, in view of prior knowledge) 6 are counter-orbiting. Group infall might have contributed to this, but no definitive association is found for the members of the Crater-Leo group.

On the central configurations of the n-body problem

We present a brief survey on some classes of central configurations of then-body problem. We put special emphasis on the central configurations of the 1+n-body problem also called the coorbital satellite problem, and on the nested central configurations formed by either regularn-gons, or regular polyhedra. We also present some conjectures.