Inclinations and Position Angles for Disc Galaxies in the SGA sample

TL;DR

The paper introduces a data-driven Fourier-Laguerre framework to measure disc-galaxy orientation from imaging data by projecting light distributions onto a two-dimensional basis of radial Laguerre polynomials and azimuthal Fourier modes. A dimensionless metric $\eta$, derived from the $m=2$ and $m=0$ coefficients, provides a robust proxy for inclination, while the phase of the $m=2$ terms yields the position angle $\mathrm{PA}$; an empirical calibration maps $\eta$ to inclination. Validated on a golden sample and applied to 133{,}942 SGA disc galaxies across $grz$ bands, the method achieves typical scatters of $\sim10^\circ$ in inclination and $\sim5^\circ$ in PA, with negligible catastrophic failures and strong cross-band consistency. The approach is fast, morphology-agnostic, and suitable for next-generation surveys, with a Python package released for broad adoption.

Abstract

We present a data-driven method for determining the inclination and position angle (PA) of disc galaxies using a Fourier-Laguerre basis decomposition of imaging data. We define a dimensionless metric, $η$, that characterises the ratio of the quadrupole and monopole coefficients in the Fourier-Laguerre basis function expansion. This metric serves as a robust measure which is related to the inclination of a galaxy. We find an empirical relationship between $η$ and inclination which is agnostic to the galaxy morphology. The PA is derived directly from the phase of the quadrupolar Fourier-Laguerre functions. Across a benchmark sample of galaxies, the method reproduces published inclination and PA values to within a median of 10$^\circ$ and 5$^\circ$, respectively, while also demonstrating essentially zero catastrophic failures. Applying this pipeline to galaxies from the Siena Galaxy Atlas (SGA), we report measurements of $η$, scale length and PA for three different bands of 133,942 disc galaxies. Our computationally inexpensive technique automates parametrisation analysis and returns reproducible results for large surveys. We release a Python package ready for application to next generation surveys.

Figures (9)

• Figure 1: flex-derived metrics for the SGA disc dataset. (i) Distribution of $\eta$ values between 0 and 1 for each band (left). (ii) Distribution of PA for each band (right).
• Figure 2: (i) $grz$ image of NGC3067 via SGA (upper left), (ii) $\log_{10}$ of intensity of $g$-band masked image of galaxy NGC3067 (upper right), (iii) $\log_{10}$ of intensity of Fourier-Laguerre expansion of the image under the same colour map and mask (lower left) and (iv) $\log_{10}$ of intensity of galaxy with inclination of 68.6$^\circ$ and a PA of $104^\circ$ generated by discmodel (lower right).
• Figure 3: (i) flex-derived inclination value from $\eta$ against published inclinations (top). Each galaxy appears with two $x$-axis values: once with the inclination drawn from the HyperLEDA database (light markers) and once with the inclination drawn from GalaxyInclPaper (dark markers). (ii) Distribution of differences in literature inclination with flex-derived inclination (middle). (iii) flex-derived PA against HyperLEDA PA values (bottom).
• Figure 4: NGC4203 image ($grz$ composite) showing a nearly face-on galaxy ($i_{\rm flex}\approx0$), while literature values report $i_{\rm literature}=65-90^\circ$. Image from NERSC SGA portal: https://portal.nersc.gov/project/cosmo/data/sga/2020/data/183/NGC4203/NGC4203-largegalaxy-image-grz.jpg.
• Figure 5: Initial morphology distribution (dark bars) and quality flag reduced set morphology distribution (light bars) in the SGA sample of disc galaxies.