Recovering 3D structural properties of galaxies from SDSS-like photometry

Because of the 3D nature of galaxies, an algorithm for constructing spatial density distribution models of galaxies on the basis of galaxy images has many advan- tages over approximations of the surface density distribution. We present a method for deriving the spatial structure and overall parameters of galaxies from images and estimate its accuracy and derived parameter degeneracies on a sample of idealised model galaxies. The test galaxies consist component with varying proportions and of a disc-like component and a spheroidal properties. Both components are assumed to be axially symmetric and coplanar. We simulate these test galaxies as if they had been observed in the SDSS project through ugriz filters, thus gaining a set of realis- tically imperfect images of galaxies with known intrinsic properties. These artificial SDSS galaxies were thereafter remodelled by approximating the surface brightness distribution with a 2D projection of a bulge＋disc spatial distribution model and the restored parameters were compared to the initial ones. Down to the r-band limiting magnitude of 18, errors in the restored integral luminosities and colour indices re- main within 0.05 mag and errors in the luminosities of individual components within 0.2 mag. Accuracy of the restored bulge-to-disc luminosity ratio （B/D） is within 40% in most cases, and becomes worse for galaxies with low B/D, but the general balance between bulges and discs is not shifted systematically. Assuming that the intrinsic disc axial ratio is ≤ 0.3, then the inclination angles can be estimated with errors 〈 5° for most of the galaxies with B/D 〈 2 and with errors 〈 15° up to B/D = 6. Errors in the recovered sizes of the galactic components are below 10% in most cases. The axial ratios and the shape parameter N of Einasto＇s distribution （similar to the Sersic index） are relatively inaccurate, but can provide statistical estimates for large samples. In general, models of disc components are more accurate than models of spheroidal components for geometrical reasons.

Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies

We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve （or vice versa）. For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-tolight ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the ＂galactic rotation number＂ that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerial solution. Through a systematic computational analysis, we have illustrated that the galactic rotation number remains within 4-10% of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to V02 Rg, with V0 denoting the characteristic rotation velocity （such as the ＂flat＂ value in a typical ro- tation curve） and Rg the radius of the galactic disk. The predicted total galactic mass of the Milky Way is in good agreement with the star-count data.

Made-to-measure galaxy modelling utilising absorption line strength data

We enhance the Syer ＆ Tremaine made-to-measure （M2M） particle method of stellar dynamical modelling to model simultaneously both kinematic data and absorption line strength data, thus creating a ＇chemo-M2M＇ modelling scheme. We apply the enhanced method to four galaxies （NGC 1248, NGC 3838, NGC 4452, NGC 4551） observed using the SAURON integral-field spectrograph as part of the ATLAS3D programme. We are able to reproduce successfully the 2D line strength data achieving mean X2 per bin values of ≈ 1 with 〉 95% of particles having converged weights. Because M2M uses a 3D particle system, we are also able to examine the underlying 3D line strength distributions. The extent to which these dis- tributions are plausible representations of real galaxies requires further consideration. Overall, we consider the modelling exercise to be a promising first step in developing a ＇chemo-M2M＇ modelling system and in understanding some of the issues to be addressed. While the made-to-measure techniques developed have been applied to absorption line strength data, they are in fact general and may be of value in modelling other aspects of galaxies.