Made-to-measure models of the Galactic box/peanut bulge: stellar and total mass in the bulge region

MNRAS 448, 713–731 (2015) doi:10.1093/mnras/stv058 Made-to-measure models of the Galactic box/peanut bulge: stellar and total mass in the bulge region M. Portail,1‹ C. Wegg,1 O. Gerhard1 and I. Martinez-Valpuesta2,3 1 Max-Planck-Institüt für Extraterrestrische Physik, Gießenbachstraße, D-85741 Garching, Germany de Astrofı́sica de Canarias, E-38205 La Laguna, Tenerife, Spain 3 Universidad de La Laguna, Department Astrofı́sica, E-38206 La Laguna, Tenerife, Spain 2 Instituto Accepted 2015 January 9. Received 2014 December 12; in original form 2014 August 23 We construct dynamical models of the Milky Way’s box/peanut (B/P) bulge, using the recently measured 3D density of red clump giants (RCGs) as well as kinematic data from the Bulge Radial Velocity Assay (BRAVA) survey. We match these data using the NMAGIC made-tomeasure method, starting with N-body models for barred discs in different dark matter haloes. We determine the total mass in the bulge volume of the RCGs measurement (±2.2 × ±1.4 × ±1.2 kpc) with unprecedented accuracy and robustness to be 1.84 ± 0.07 × 1010 M . The stellar mass in this volume varies between 1.25 and 1.6 × 1010 M , depending on the amount of dark matter in the bulge. We evaluate the mass-to-light and mass-to-clump ratios in the bulge and compare them to theoretical predictions from population synthesis models. We find a mass-to-light ratio in the K band in the range 0.8–1.1. The models are consistent with a Kroupa or Chabrier initial mass function (IMF), but a Salpeter IMF is ruled out for stellar ages of 10 Gyr. To match predictions from the Zoccali IMF derived from the bulge stellar luminosity function requires ∼40 per cent or ∼0.7 × 1010 M dark matter in the bulge region. The BRAVA data together with the RCGs 3D density imply a low pattern speed for the Galactic B/P bulge of p = 25-30 km s−1 kpc−1 . This would place the Galaxy among the slow rotators (R ≥ 1.5). Finally, we show that the Milky Way’s B/P bulge has an off-centred X structure, and that the stellar mass involved in the peanut shape accounts for at least 20 per cent of the stellar mass of the bulge, significantly larger than previously thought. Key words: methods: numerical – Galaxy: bulge – Galaxy: centre – Galaxy: kinematics and dynamics – Galaxy: structure. 1 I N T RO D U C T I O N Observations of external disc galaxies have shown that about half of all disc galaxies have strong bars (Eskridge et al. 2000). The Milky Way (MW) Galaxy has been considered for many years as one of them. The Galactic bar/bulge causes the non-circular motions in the gas flow seen in H I and CO (Peters 1975; Binney et al. 1991; Englmaier & Gerhard 1999; Fux 1999) and is the origin of the asymmetries seen in the near-infrared light distribution (Blitz & Spergel 1991; Weiland et al. 1994; Binney, Gerhard & Spergel 1997) and star counts (Nakada et al. 1991; Stanek et al. 1997; LópezCorredoira, Cabrera-Lavers & Gerhard 2005). The Galactic bulge (GB) is regarded as the 3D part of the bar seen nearly end-on (Shen et al. 2010; Martinez-Valpuesta & Gerhard 2011) with a semimajor axis of about 2 kpc (Gerhard 2002; Wegg & Gerhard 2013), as is  E-mail: also indicated by the near-cylindrical rotation of the bulge stars (Beaulieu et al. 2000; Kunder et al. 2012; Ness et al. 2013). In the last decade, stellar surveys of the GB such as 2MASS (Skrutskie et al. 2006), VVV (Saito et al. 2012), OGLE (Sumi et al. 2004), Bulge Radial Velocity Assay (BRAVA; Rich et al. 2007) and Argos (Freeman et al. 2013) have released unprecedented data sets which allow us to study the GB star by star. The triaxial bulge of the MW is now believed to be a so-called box/peanut bulge (B/P bulge) or X-shaped bulge as indicated by its bimodal distribution of red clump giants (RCGs). This was first reported from the 2MASS catalogue by McWilliam & Zoccali (2010) and from the OGLE-III survey by Nataf et al. (2010). Ness et al. (2012) showed that this split red clump is seen for stars with metallicity [Fe/H] > −0.5. The peanut shape was mapped last year in three dimensions by Wegg & Gerhard (2013) using public data from the VVV survey. Star counts and infrared observations have revealed a long and flat bar component, located mostly in the Galactic plane and extending up to l ∼ 27◦ (Hammersley et al. 2000; Benjamin et al. 2005;  C 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society ABSTRACT 714 M. Portail et al. 2 PA RT I C L E M O D E L S O F BA R R E D D I S C S 2.1 N-body models in different dark matter haloes Our M2M modelling of the GB relies on reasonable initial particle models of barred discs. These initial models were created by evolving near-equilibrium stellar discs embedded in live dark matter haloes. Near-equilibrium models are constructed using the program MAGALIE (Boily, Kroupa & Peñarrubia Garrido 2001) and evolved MNRAS 448, 713–731 (2015) with the tree-code GYRFALCON (Dehnen 2000), all distributed with the publicly available NEMO toolbox (Teuben 1995). During the evolution, the disc naturally forms a bar which rapidly buckles out of the Galactic plane and creates a B/P bulge (Combes & Sanders 1981; Raha et al. 1991). As we want to address the question of the total mass of the GB including the amount of dark matter in the bulge, we generated a set of five disc+halo N-body models using the same disc component and varying the halo properties. The disc is exponential with scalelength of 1 internal units (iu), scaleheight of 0.14 iu, unit total disc mass, and Q parameters of 1.4 at R = 3.07 iu. Haloes have a Hernquist density profile with flattening of 0.8 and a sharp cutoff at 20 iu. All models contain two million particles, one million each for disc and halo. With these settings fixed only two free parameters remain: the halo mass inside the cutoff, Mh , and the halo break radius of the Hernquist profile, ah . They were fixed considering the total rotation curve of a model. Following the language of Sackett (1997), we call the degree of maximality of a disc the proportion of the disc contribution to the total velocity curve, at the radius where the disc velocity curve is maximal. Assuming a flat rotation curve at large radii, we build a one parameter family of models parametrized by the degree of maximality of the disc. We make five models of this family, called M80, M82.5, M85, M87.5 and M90 which have different degree of maximality ranging from 80 to 90 per cent. As we show later this allows us to build models of barred galaxy which span all kind of rotators, from slow to fast. The halo parameters used to construct these models are summarized in Table 1. For each model, we select a snapshot of a late evolutionary stage, where the bar is fully grown. The circular velocity curves obtained from the azimuthally averaged potential of this set of models are plotted in Fig. 1, before any evolution (top) and, for the selected snapshot after bar and B/P bulge format (...truncated)