Made-to-measure (M2M) Particle Method NMAGIC

A high level flowchart describing NMAGIC. The main Χ2M2M algorithm is contained in the dashed block, the remainder is an optional potential solver and code for moving the particles, both of which are exchangeable. In our tests, Χ2M2M is generally applied only after a number of position/velocity updates. — A high level flowchart describing NMAGIC. The main Χ²M2M algorithm is contained in the dashed block, the remainder is an optional potential solver and code for moving the particles, both of which are exchangeable. In our tests, Χ²M2M is generally applied only after a number of position/velocity updates.

A high level flowchart describing NMAGIC. The main Χ²M2M algorithm is contained in the dashed block, the remainder is an optional potential solver and code for moving the particles, both of which are exchangeable. In our tests, Χ²M2M is generally applied only after a number of position/velocity updates.

The goal of dynamical modeling is to recover from observational data the distribution of orbits for the galaxy's stars, and the gravitational potential in which they move. Through dynamical modeling, one can determine the mass of the supermassive black hole in the galaxy's center, or the amount of dark matter in its outskirts. (more on dynamical modelling here)

The idea of the made-to-measure (M2M) method is to find a particle model that faithfully represents the galaxy observations (see Syer & Tremaine, 1996, De Lorenzi, Debattista, Gerhard & Sambhus, 2007) i.e., when the particle model is "observed" in the same way as the galaxy, its surface density distribution and projected kinematics should match those of the galaxy. Once this is achieved, the model can be used to learn about the intrinsic structure of the galaxy. The parallel code NMAGIC is an implementation of a made-to-measure technique suitable for finding such a model from a given set of observational data, starting from an initial particle distribution. (more on the M2M method here)

Evolution of an an initially spherical model consisting of 1.8 million particles towards a triaxial target galaxy. The panels show contour plots of the surface brightness distribution. The black solid lines represent the particle model and the red solid lines correspond to the triaxial target galaxy. The left panel compares the initial model with the target galaxy and the right panel shows the final model. The match is excellent.

Evolution of an an initially spherical model consisting of 1.8 million particles towards a triaxial target galaxy. The panels show contour plots of the surface brightness distribution. The black solid lines represent the particle model and the red solid lines correspond to the triaxial target galaxy. The left panel compares the initial model with the target galaxy and the right panel shows the final model. The match is excellent.

We have used the M2M method for modelling the dynamics of elliptical galaxy halos and, more recently, the galactic bulge and bar.

We are still updating this section. You can access the old NMAGIC pages here

Regularizing made-to-measure particle models of galaxies

Lucia Morganti & Ortwin Gerhard, 2012, MNRAS, 422, 1571

Typical particle weight distribution after a classical entropy regularization fit (black) and after Moving Priors entropy Regularization (red). MPR method avoid trails of extremely increased or decreased weights.

Typical particle weight distribution after a classical entropy regularization fit (black) and after Moving Priors entropy Regularization (red). MPR method avoid trails of extremely increased or decreased weights.

Made-to-measure methods such as the parallel code NMAGIC have to solve underdetermined problems, where the number of constraints (photometric of kinematic observables) are usually much lower than the number of particle weights to define. A regularization method is therefore needed to make the method converge. Here we introduce a Moving Prior entropy Regularization method (MPR). The basic idea is to update the prior distribution needed by standard entropy regularization in parallel of the weight adaptation. The prior distribution is determined from the distribution of particles in phase-space. This allows one to construct smooth models from noisy data without erasing global phase-space gradients.

Full paper on ADS

Publications

Blaña Díaz, M., Gerhard, O., Wegg, C., Portail, M., Opitsch, M., Saglia, R., et al., 2018, MNRAS, 481, 3210,
Sculpting Andromeda - made-to-measure models for M31's bar and composite bulge: dynamics, stellar and dark matter mass. 2018MNRAS.481.3210B

Portail M., Wegg C., Gerhard O., Ness M., 2017, MNRAS, 470, 1233
Chemodynamical Modelling of the Galactic Bulge and Bar 2017MNRAS.470.1233P

Portail M., Gerhard O., Wegg C., Ness M., 2017, MNRAS, 465, 1621
Dynamical Modelling of the Galactic Bulge and Bar: Pattern Speed, Stellar, and Dark Matter Mass Distributions. 2017MNRAS.465.1621P

Portail, M., Wegg, C., Gerhard, O., Martinez-Valpuesta, I., 2015, MNRAS, 448, 713,
Made-to-measure models of the Galactic box/peanut bulge: stellar and total mass in the bulge region. 2015MNRAS.448..713P

Morganti, L., Gerhard, O., Coccato, L., Martinez-Valpuesta, I., Arnaboldi, M., 2013, MNRAS, 431, 3570,
Elliptical galaxies with rapidly decreasing velocity dispersion profiles: NMAGIC models and dark halo parameter estimates for NGC 4494.
2013MNRAS.431.3570M

De Lorenzi, F., Hartmann, M., Debattista, V. P., Seth, A. C., Gerhard, O., 2013, MNRAS, 429, 2974,
Three-integral multicomponent dynamical models and simulations of the nuclear star cluster in NGC 4244. 2013MNRAS.429.2974D

Morganti, L., Gerhard, O., 2012, MNRAS, 422, 1571,
Regularizing made-to-measure particle models of galaxies. 2012MNRAS.422.1571M

Das, P., Gerhard, O., Mendez, R. H., Teodorescu, A. M., de Lorenzi, F., 2011, MNRAS, 415, 1244,
Using NMAGIC to probe the dark matter halo and orbital structure of the X-ray bright, massive elliptical galaxy, NGC 4649. 2011MNRAS.415.1244D

de Lorenzi, F., Gerhard, O., Coccato, L., Arnaboldi, M., Capaccioli, M., Douglas, N. G., et al., 2009, MNRAS, 395, 76,
Dearth of dark matter or massive dark halo? Mass-shape-anisotropy degeneracies revealed by NMAGIC dynamical models of the elliptical galaxy NGC
3379. 2009MNRAS.395...76D

de Lorenzi, F., Gerhard, O., Saglia, R. P., Sambhus, N., Debattista, V. P., Pannella, M., et al., 2008, MNRAS, 385, 1729,
Dark matter content and internal dynamics of NGC 4697: NMAGIC particle models from slit data and planetary nebula velocities. 2008MNRAS.385.1729D

de Lorenzi, F., Debattista, V. P., Gerhard, O., Sambhus, N., 2007, MNRAS, 376, 71,
NMAGIC: a fast parallel implementation of a χ²-made-to-measure algorithm for modelling observational data. 2007MNRAS.376...71D