Exploring faint white dwarfs and the luminosity function with Subaru HSC and SDSS in Stripe 82

Abstract

We present 5,080 white dwarf (WD) candidates selected from stars matching between the multi-band imaging datasets of the Subaru Hyper Suprime-Cam (HSC) Survey and the Sloan Digital Sky Survey (SDSS) in the Stripe82 region covering about 165~deg$^2$. We select WD candidates from the ``reduced proper motion'' diagram by combining the apparent magnitude in the range $i=19$ -- 24 and the proper motion measured from the datasets among a baseline of $\sim$ 14~years. We refine the WD candidates by fitting blackbody and template WD atmosphere models to HSC photometries for each candidate, enabling the estimation of distance and tangential velocity ($v_{\rm t}$). The deep HSC data allow us to identify low-temperature ($<4000$~K) and faint WD candidates down to absolute magnitude, $M_{\rm bol}\simeq 17$. We evaluate the selection function of our WD candidates using a mock catalogue of spatial and kinematic distributions of WDs in the (thin and thick) disc and halo regions based on a Galactic model. We construct samples of disc and halo WD candidates by selecting WDs with tangential velocity, $40<v_{\rm t}/[{\rm km}~{\rm s}^{-1}]<80$ and $200<v_{\rm t}/[{\rm km}~{\rm s}^{-1}]<500$, respectively. The total number densities of the disc and halo WDs are $(9.33 \pm 0.89) \times 10^{-3}$~pc$^{-3}$ and $(6.34 \pm 2.90) \times 10^{-4}$~pc$^{-3}$. Our luminosity functions (LF) extend down to fainter absolute magnitudes compared with previous work. The faint WDs could represent the oldest generation of building blocks over the past $\sim$10 billion years of the assembly history of our Milky Way.