Michele Cappellari IDL Programs

The following software is freely available. However, if you use it for published research, I would appreciate an acknowledgement. You are not allowed to re-distribute any of these programs (modified or not) without explicit permission from the author.

1. The MGE_FIT_SECTORS package: to fit Multi-Gaussian Expansion (MGE) models to galaxy images, to be used as a parameterization for galaxy photometry
2. The JAM modelling package: to construct Jeans Anisotropic MGE dynamical models for the stellar kinematics of axisymmetric galaxies
3. VORONOI_2D_BINNING: to perform adaptive spatial binning of Integral-Field Spectroscopy, X-ray or imaging data, to reach a chosen constant signal-to-noise ratio per bin
4. Penalized Pixel-Fitting (pPXF): to extract the galaxy stellar kinematics from absorption-line spectra
5. FIT_KINEMATIC_PA: to measure the global galaxy kinematical axis from integral field observations

1. The MGE_FIT_SECTORS package

MGE profiles NGC 4342

MGE contours NGC 4342

This software efficiently obtains an accurate Multi-Gaussian Expansion (MGE) parameterization for a galaxy surface brightness, with the fitting method of Cappellari (2002, MNRAS, 333, 400).

See Cappellari et al. (2006) for a large scale application of this software to the study of the M/L ratio and the Fundamental Plane of early-type galaxies. The MGE parameterization (Emsellem et al. 1994) is useful in the construction of realistic dynamical models of galaxies (see JAM modelling below), for PSF deconvolution of images, for the correction and estimation of dust absorption effects, or for galaxy photometry.

The source code

The source code of the IDL package MGE_FIT_SECTORS, with examples and instructions, can be downloaded here in ZIP format (178 KB). This version was last updated on the 14 October 2009 and the changes are documented in the program file. Optionally the FITS files of the five images that are required to run the examples routine can be downloaded here in ZIP format (19 MB!).

I would appreciate if you drop me an e-mail (address at the bottom) when you download MGE_FIT_SECTORS.

Also required is the following IDL routine, which must be downloaded separately:

• The Bounded-Variables Least-Squares (BVLS) algorithm by Lawson & Hanson (1995). This is a generalization of the Non-Negative Least-Squares (NNLS) algorithm by the same authors. My IDL routine bvls.pro can be found here;

And if you just started using IDL and still do not have the IDL Astronomy User's Library installed, or if you have an old version, you should immediately get it from here.

	2. The JAM modelling method
	Jeans Anisotropic MGE dynamical models of stellar kinematics of axisymmetric galaxies

Figure 1: Examples of JAM data-model comparisons. The bi-symmetrized state-of-the-art SAURON stellar kinematics of 20 fast-rotator early-type galaxies is compared to the predictions of the anisotropic Jeans models with JAM. The kinematics varies widely for different galaxies, yet these two-parameters models are able to correctly predict the shape of a pair of two-dimensional functions (V and Vrms), once the observed surface brightness is given. In many cases χν2 ≈ 1 and the models describe the original un-symmetrized data within the errors. This shows that most of the information on the dynamics of these galaxies is contained in the photometry alone! (Cappellari 2008)

Figure 3: JAM models examples of kinematically decoupled components. (a) Three-parameters JAM description of the SAURON stellar kinematics of the early-type galaxy NGC4550, which contains two counter-rotating stellar disks (Cappellari et al. 2007). To reproduce the observed velocity field, the flattest (q' < 0.25) Gaussians of the MGE model were assigned opposite rotation (κ < 0). (b) Same as in [a] but with the model orbits all rotating in the same direction. (c) Best fitting JAM model of NGC5308, with constant anisotropy (βz = 0.28 and κ = 1.02) (Cappellari 2008). (d) Same as in [c], but with a non-rotating bulge (κ = 0). (e) Same as in [c] but with an isotropic bulge (βz = 0) and an anisotropic disk (βz = 0.28). The best model has an oblate velocity ellipsoid, with the same strong anisotropy and the same rotation for both the bulge and the disk!

The software in this section implements a solution of the Jeans equations which allows for orbital anisotropy (three-integrals distribution function). It was introduced in Cappellari (2008, MNRAS, 390, 71) and we call it the Jeans Anisotropic MGE (JAM) modelling method.

The simple and user-friendly JAM method gives a dramatic improvement over the less general but widely used two-integral Jeans models. The JAM models provide good descriptions of state-of-the-art integral-field stellar kinematics of real galaxies (Figure 1). This makes the technique well suited to measure the inclination, the dynamical M/L and angular momenta of early-type fast-rotators and spiral galaxies.

The JAM routines are designed for axisymmetric or spherical geometry, they allow for (i) the inclusion of dark matter, (ii) variable stellar M/L, (iii) supermassive black holes (Figure 2), (iv) spatially varying anisotropy, and (v) multiple kinematic components (Figure 3). The JAM package also includes a routine to compute the circular velocity from the MGE models. Some sample applications of the JAM method are given below:

• The stellar orbital distribution near the BH in Centaurus A (Cappellari et al. 2009)
• Comparison of 25 BH mass determinations with JAM and Schwarzschild method (Cappellari et al. 2010)
• Dynamical M/L of a sample of 48 early-type galaxies, from integral-field stellar kinematics (Scott et al. 2009)
• Dark matter profiles from stellar kinematics of a sample of 28 spiral and S0 galaxies (Williams et al. 2009)
• Dark matter from integral-field stellar kinematics up to 5 R_e (Weijmans 2009, Chapter 4)
• Dynamical masses for a sample of 9 passive early-type galaxies at z~2 (Cappellari et al. 2009)
• Dark matter from stellar dynamics and gravitational lensing (van de Ven et al., submitted to ApJ)

To construct dynamical models with the JAM method one needs to describe the galaxies surface brightness via the Multi-Gaussian Expansion parametrization (Emsellem et al. 1994) using my MGE_FIT_SECTORS package above.

The source code

The source code of the JAM modelling package in IDL, with documentation and examples, can be downloaded here in ZIP format (41 KB). This version was last updated on 08 February 2010 and the changes are documented in the program files.

I would appreciate if you drop me an e-mail (address at the bottom) when you download the JAM package.

Also required are the generic plotting routines SAURON_COLORMAP and PLOT_VELFIELD which can be found in this ZIP file.

And if you just started using IDL and still do not have the IDL Astronomy User's Library installed, or if you have an old version, you should immediately get it from here.

Figure 2: Example of estimation of the mass of a supermassive black (BH) with the JAM method. Top Panels: The PSF-convolved model predictions for Vrms, for a range of BH and anisotropy βz, are compared to the observed integral-field nuclear OASIS stellar kinematics of the fast-rotator early-type galaxy NGC4660. Bottom Panel: Contours of the χ2 describing the agreement between the data and the models. The observations are well reproduced by a significantly anisotropic model with BH∼4×108 solar masses. Models without a BH are strongly excluded. For another example see Cappellari et al. (2010).

3. The Voronoi binning method

Four-coloring of Voronoi binning.

Unbinned versus Voronoi binned IFS.

Voronoi binning of X-ray data.

The Voronoi Binning method of Cappellari & Copin (2003, MNRAS, 342, 345) optimally solves the problem of preserving the maximum spatial resolution of general two-dimensional data, given a constraint on the minimum signal-to-noise ratio.

The Voronoi binning method has been applied to a variety of types of data. A review of the concepts and applications to (i) X-ray data, (ii) integral-field spectroscopy, (iii) Fabry-Perot interferometry, (iv) N-body simulations, (v) standard images and (vi) other regularly or irregularly sampled data is given in Cappellari (2009).

The source code

The source code of the IDL program VORONOI_2D_BINNING, with examples and instructions, can be downloaded here in ZIP format (41 KB). This version was last updated on 3 December 2007 and the changes are documented in the program file. Some minor adaptations of the routine may be required to optimally use the method with different types of data. Please ask for suggestions if needed.

I would appreciate if you drop me an e-mail (address at the bottom) when you download VORONOI_2D_BINNING.

This optional ZIP file contains the routines DISPLAY_BINS, DISPLAY_PIXELS, PLOT_VELFIELD and SAURON_COLORMAP which can be used to visualize Voronoi 2D-binned or unbinned data, either using interpolation, or by showing the actual bins like in the figures above.

4. Penalized Pixel-Fitting (pPXF)

pPXF fit to SAURON spectrum of NGC 3379

NGC 4150

NGC 4278

NGC 4459

This software implements the Penalized Pixel-Fitting method (pPXF) developed by Cappellari & Emsellem (2004, PASP, 116, 138) to extract the stellar kinematics from absorption-line spectra of galaxies, using a maximum penalized likelihood approach. The following key features are also implemented in the pPXF routine:

• Optimal template: Fitted together with the kinematics to minimize template-mismatch errors. Also useful to extract gas kinematics or derive emission-corrected line-strengths indexes;
• Regularization of templates weights: To reduce the noise and try to attach a physical meaning to the output weights e.g. in term of the star formation history of a galaxy;
• Iterative sigma clipping: To clean the spectra from residual bad pixels or cosmic rays;
• Two-sided LOSVD fitting: To reduce systematic errors in the kinematics, using two spectra taken at the opposite sides of the galaxy nucleus;
• Additive/multiplicative polynomials: To correct low frequency continuum variations. Also useful for calibration purposes;
• Inclusion of sky spectrum: To deal with spectra heavily contaminated by the sky spectrum (Weijmans et al. 2009)
• Reddening fit: To determine the reddening of the spectrum using the exctinction curve of Calzetti et al. (2000)

See e.g. Emsellem et al. (2004) for a large-scale application of the pPXF method to the measurement of the stellar kinematics of galaxies. Falcon-Barroso et al. (2004) present an example of using the optimal template generated by pPXF to extract the gas kinematics from galaxy spectra and to measure emission-corrected line-strength indexes. McDermid et al. (2006; their Fig. 3) use pPXF for spectral flux calibration, and extract the kinematics of a large galaxy sample.

Minimizing Template Mismatch

The ability of the pPXF method to fit a large set of stellar templates together with the kinematics allows the template mismatch problem to be virtually eliminated. This is particularly useful given the current availability of large stellar libraries spanning wide ranges of physical parameters and having good spectral resolution. Excellent results have been obtained by using a few hundred template stars with pPXF, from which generally about 10-20 are selected by the program to provide detailed fits to high S/N galaxy spectra (e.g. the four Figures on the right show pPXF fits to SAURON spectra using the full MILES stellar library). An extensive account of the available stellar libraries is maintained by David Montes. An incomplete list of useful libraries for the kinematics extraction in the visual and near-infrared K-band region is given below:

• Jones Coudé Feed Spectral Library : 684 stars covering the region from 3820 - 4500 Å and 4780 - 5460 Å at a spectral resolution of 1.8 Å (FWHM), σ~50 km/s. From Jones (1998)
• Indo-U.S. Coudé Feed Spectral Library: 1273 stars covering the region from 3460 - 9464 Å at a spectral resolution of 1.0 Å (FWHM), σ~22 km/s. From Valdes et al. (2004)
• Ca II triplet : 706 stars covering the region from 8348 - 9020 Å at a spectral resolution of 1.5 Å (FWHM), σ~22 km/s. From Cenarro et al. (2001)
• ELODIE : 1388 stars covering the region from 4000 - 6800 Å at a spectral resolution of 0.5 Å (FWHM), σ~12 km/s. From Prugniel and Soubiran (2001)
• MILES Library of Stellar Spectra: 985 well-calibrated stars covering the region from 3525 - 7500 Å at a spectral resolution of 2.3 Å (FWHM), σ~57 km/s. From Sánchez-Blázquez, et al. (2006)
• GNIRS library of late spectral templates: 29 stars with a range of CO equivalent widths, covering the K-band region from 2.18 - 2.43 μm at a spectral resolution of 3.4 Å (FWHM), σ~19 km/s. From Winge et al. (2009)

The source code

The source code of the IDL program PPXF, with examples and instructions, can be downloaded here in ZIP format (107 KB). This version was last updated on 18 September 2009 and the changes are documented in the program file. See the important note in the README file for a proper usage of pPXF! Also required are the following two IDL routines, which must be downloaded separately:

• The Bounded-Variables Least-Squares (BVLS) algorithm by Lawson & Hanson (1995). This is a generalization of the Non-Negative Least-Squares (NNLS) algorithm by the same authors. My IDL routine bvls.pro can be found here;
• The MINPACK (Moré, Garbow & Hillstrom, 1980) Levenberg-Marquardt nonlinear least-squares optimization algorithm. The IDL routine mpfit.pro (Markwardt 2009) can be found here.

I would appreciate if you drop me an e-mail (address at the bottom) when you download pPXF.

And if you just started using IDL and still do not have the IDL Astronomy User's Library installed, or if you have an old version, you should immediately get it from here.

5. Fit kinematic PA

Best fitting symmetrized kinematics of NGC 2974

This software implements the method presented in Appendix C of Krajnovic et al. (2006, MNRAS, 366, 787) to measure the global kinematic position-angle (PA) from integral field observations of a galaxy stellar or gas kinematics.

See Cappellari et al. (2007) for a large scale application of this software to the study of the stellar kinematical misalignment of 66 early-type galaxies. See Davor's Krajnovic page for the related Kinemetry package.

The source code

The source code of the IDL program FIT_KINEMATIC_PA, with examples and instructions, can be downloaded here in ZIP format (9 KB). This version was last updated on 14 October 2009 and the changes are documented in the program file. Also required are the generic routines SAURON_COLORMAP and PLOT_VELFIELD which can be found in this ZIP file.

I would appreciate if you drop me an e-mail (address at the bottom) when you download FIT_KINEMATIC_PA.

And if you just started using IDL and still do not have the IDL Astronomy User's Library installed, or if you have an old version, you should immediately get it from here.

Comments and suggestions are welcome to the address

Latest changes: 04/FEB/2010 Go back to Michele Cappellari Homepage