We present new optical long-slit data along six position angles of the bulge region of M 31. We derive accurate stellar and gas kinematics reaching 5 arcmin from the center, where the disk light contribution is always less than 30%, and out to 8 arcmin along the major axis, where the disk provides 55% of the total light. We show that the velocity dispersions of McElroy (1983) are severely underestimated (by up to 50 km s −1 ). As a consequence, previous dynamical models have underestimated the stellar mass of M 31's bulge by a factor of 2. As a further consequence, the light-weighted velocity dispersion of the galaxy grows to 166 km s −1 and to 170 km s −1 if rotation is also taken into account, thus reducing the discrepancy between the predicted and measured mass of the black hole at the center of M 31 from a factor of 3 to a factor of 2. The kinematic position angle varies with distance, pointing to triaxiality, but a quantitative conclusion can be reached only after simultaneous proper dynamical modeling of the bulge and disk components is performed. We detect gas counterrotation near the bulge minor axis. We measure eight emission-corrected Lick indices. They are approximately constant on circles. Using simple stellar population models we derive the age, metallicity and α-element overabundance profiles. Except for the region in the inner arcsecs of the galaxy, the bulge of M 31 is uniformly old (≥12 Gyr, with many best-fit ages at the model grid limit of 15 Gyr), slightly α-elements overabundant ([α/Fe] ≈ 0.2) and of solar metallicity, in agreement with studies of the resolved stellar components. The predicted u − g, g − r and r − i Sloan color profiles match the dust-corrected observations reasonably well, within the known limitations of current simple stellar population models. The stellar populations have approximately radially constant mass-to-light ratios (M/L R ≈ 4−4.5 M /L for a Kroupa IMF), which is in agreement with the stellar dynamical estimates based on our new velocity dispersions. In the inner arcsecs the luminosity-weighted age drops to 4-8 Gyr, while the metallicity increases to above three times the solar value. Starting from 6 arcmin from the center along the major axis, the mean age drops to ≤8 Gyr with slight supersolar metallicity (≈+0.1 dex) and α-element overabundance (≈+0.2 dex) for a mass-to-light ratio M/L R ≤ 3 M /L . Diagnostic diagrams based on the [OIII]/Hβ and [NI]/Hβ emission line equivalent widths (EWs) ratios indicate that the gas is ionized by shocks outside 10 arcsec, but an AGN-like ionizing source could be present near the center. We speculate that a gas-rich minor merger happened some 100 Myr ago, causing the observed minor axis gas counterrotation, the recent star formation event and possibly some nuclear activity.

NGC 4494 is one of several intermediate-luminosity elliptical galaxies inferred to have an unusually diffuse dark matter halo. We use the χ 2 -made-to-measure particle code NMAGIC to construct axisymmetric models of NGC 4494 from photometric and various kinematic data. The extended kinematics include light spectra in multiple slitlets out to 3.5R e , and hundreds of planetary nebulae velocities out to ≃ 7R e , thus allowing us to probe the dark matter content and orbital structure in the halo.We use Monte Carlo simulations to estimate confidence boundaries for the halo parameters, given our data and modelling set-up. We find that the true potential of the dark matter halo is recovered within ∆G(merit function) ∼ < 26 (∆χ 2 ∼ < 59) at 70% confidence level (C.L.), and within ∆G ∼ < 32 (∆χ 2 ∼ < 70) at 90% C.L.. These numbers are much larger than the usually assumed ∆χ 2 = 2.3(4.6) for 70% (90%) C.L. for two free parameters, perhaps case-dependent, but calling into question the general validity of the standard assumptions used for halo and black hole mass determinations.The best-fitting models for NGC 4494 have a dark matter fraction of about 0.6±0.1 at 5R e (70% C.L.), and are embedded in a dark matter halo with circular velocity ∼ 200kms −1 . The total circular velocity curve (CVC) is approximately flat at v c = 220kms −1 outside ∼ 0.5R e . The orbital anisotropy of the stars is moderately radial. These results are independent of the assumed inclination of the galaxy, and edge-on models are preferred. Comparing with the halos of NGC 3379 and NGC 4697, whose velocity dispersion profiles also decrease rapidly from the center outwards, the outer CVCs and dark matter halos are quite similar. NGC 4494 shows a particularly high dark matter fraction inside ∼ 3R e , and a strong concentration of baryons in the center.

Made‐to‐measure methods such as the parallel code nmagic are powerful tools to build galaxy models reproducing observational data. They work by adapting the particle weights in an N‐body system until the target observables are well matched. Here we introduce a moving prior entropy regularization (MPR) method for such particle models. It is based on determining from the particles a distribution of priors in phase space, which are updated in parallel with the weight adaptation. This method allows one to construct smooth models from noisy data without erasing global phase‐space gradients. We first apply MPR to a spherical system for which the distribution function can in theory be uniquely recovered from idealized data. We show that nmagic with MPR indeed converges to the true solution with very good accuracy, independent of the initial particle model. Compared to the standard weight entropy regularization, biases in the anisotropy structure are removed and local fluctuations in the intrinsic distribution function are reduced. We then investigate how the uncertainties in the inferred dynamical structure increase with less complete and noisier kinematic data, and how the dependence on the initial particle model also increases. Finally, we apply the MPR technique to the two intermediate‐luminosity elliptical galaxies NGC 4697 and NGC 3379, obtaining smoother dynamical models in luminous and dark matter potentials.

Following the seminal result of An & Evans, known as the central density slope-anisotropy theorem, successive investigations unexpectedly revealed that the density slope-anisotropy inequality holds not only at the center, but at all radii in a very large class of spherical systems whenever the phase-space distribution function is positive. In this paper we derive a criterion that holds for all spherical systems in which the augmented density is a separable function of radius and potential: this new finding allows to unify all the previous results in a very elegant way, and opens the way for more general investigations. As a first application, we prove that the global density slope-anisotropy inequality is also satisfied by all the explored additional families of multi-component stellar systems. The present results, and the absence of known counter-examples, lead us to conjecture that the global density slope-anisotropy inequality could actually be a universal property of spherical systems with positive distribution function.Comment: 6 pages, MNRAS accepte