THE LUMINOSITY PROFILE AND STRUCTURAL PARAMETERS OF THE ANDROMEDA GALAXY

We have constructed an extended composite luminosity profile for the Andromeda galaxy, M31, and have decomposed it into three basic luminous structural components: a bulge, a disk, and a halo. The dust-free Spitzer/Infrared Array Camera (IRAC) imaging and extended spatial coverage of ground-based optical imaging and deep star counts allow us to map M31's structure from its center to 22 kpc along the major axis. We apply, and address the limitations of, different decomposition methods for the one-dimensional luminosity profiles and two-dimensional images. These methods include nonlinear least-squares and Bayesian Monte Carlo Markov chain analyses. The basic photometric model for M31 has a Sersic bulge with shape index n similar or equal to 2.2 +/- .3 and effective radius R-e = 1.0 +/- 0.2 kpc, and a dust-free exponential disk of scale length R-d = 5.3 +/- .5 kpc; the parameter errors reflect the range between different decomposition methods. Despite model covariances, the convergence of solutions based on different methods and current data suggests a stable set of structural parameters. The ellipticities (epsilon = 1 - b/a) of the bulge and the disk from the IRAC image are 0.37 +/- 0.03 and 0.73 +/- 0.03, respectively. The bulge parameter n is rather insensitive to bandpass effects and its value (2.2) suggests a first rapid formation via mergers followed by secular growth from the disk. The M31 halo has a two-dimensional power-law index similar or equal to -2.5 +/- 0.2 (or -3.5 in three-dimensional), comparable to that of the Milky Way. We find that the M31 bulge light is mostly dominant over the range R-min less than or similar to 1.2 kpc. The disk takes over in the range 1.2 kpc less than or similar to R-min less than or similar to 9 kpc, whereas the halo dominates at R-min greater than or similar to 9 kpc. The stellar nucleus, bulge, disk, and halo components each contribute roughly 0.05%, 23%, 73%, and 4% of the total light of M31 out to 200 kpc along the minor axis. Nominal errors for the structural parameters of the M31 bulge, disk, and halo amount to 20%. If M31 and the Milky Way are at all typical, faint stellar halos should be routinely detected in galaxy surveys reaching below mu(i) similar or equal to 27 mag arcsec(-2). We stress that our results rely on this photometric analysis alone. Structural parameters may change when other fundamental constraints, such as those provided by abundance gradients and stellar kinematics, are considered simultaneously.