Star-galaxy classification in multi-band optical imaging

Ground-based optical surveys such as PanSTARRS, DES, and LSST will produce large catalogs to limiting magnitudes of r ≳ 24. Star-galaxy separation poses a major challenge to such surveys because galaxies - even very compact galaxies - outnumber halo stars at these depths. We investigate photometric classification techniques on stars and galaxies with intrinsic FWHM <0.2 arcsec. We consider unsupervised spectral energy distribution template fitting and supervised, data-driven support vector machines (SVMs). For template fitting, we use a maximum likelihood (ML) method and a new hierarchical Bayesian (HB) method, which learns the prior distribution of template probabilities from the data. SVM requires training data to classify unknown sources; ML and HB do not. We consider (1) a best-case scenario (SVM_best) where the training data are (unrealistically) a random sampling of the data in both signal-to-noise and demographics and (2) a more realistic scenario where training is done on higher signal-to-noise data (SVM_real) at brighter apparent magnitudes. Testing with COSMOS ugriz data, we find that HB outperforms ML, delivering ∼80% completeness, with purity of ∼60%-90% for both stars and galaxies. We find that no algorithm delivers perfect performance and that studies of metal-poor main-sequence turnoff stars may be challenged by poor star-galaxy separation. Using the Receiver Operating Characteristic curve, we find a best-to-worst ranking of SVM_best, HB, ML, and SVM_real. We conclude, therefore, that a well-trained SVM will outperform template-fitting methods. However, a normally trained SVM performs worse. Thus, HB template fitting may prove to be the optimal classification method in future surveys.