Evaluation of the Vertical Scale Height of L dwarfs in the Galactic Thin Disk

Using the data release 1 of the Hyper Suprime-Cam Subaru Strategic Program covering about 130 square degrees at high galactic latitudes, we have obtained L dwarf counts based on the selection criteria on colors, limiting magnitude and PSF morphology using $i$, $z$, and $y$ bands. 3665 L dwarfs brighter than $z=24$ have been detected by these criteria. The surface number counts obtained differentially in $z$ magnitude are compared with predictions of an exponential disk model to estimate the thin-disk scale height in the vicinity of the Sun. In the exponential disk model, we first fix the local luminosity function (LLF) to the mean LLF of Cruz et al. (2007) and derive the best fit scale height of 260 pc. However this fit appears to be poor. We then allow the LLF to vary along with the scale height. We use the LLF of Cruz et al. as a starting point. The best-fit model is found for the vertical scale height of 380 pc. However the $\chi^2$ minimum is rather broad and the 90% confidence interval is between 320 and 520 pc. We investigate another model by varying the scale height and the density of the brightest magnitude bin, while other magnitude bins are fixed to the mean LLF of Cruz et al.. We find an equally good fit with the two free parameters and the best-fit scale height is again 380 pc, but the 90% confidence interval is between 340 and 420 pc.