A test of broad band typing using HSC synthetic colors of parameter-interpolated AMBRE spectra. The typing is done by chi square probabilities.

This confidence contours are a result of a test spectrum (colors of S/N = 200, Teff = 7350K, Logg = 4.0, Z = 0.25, [alpha/Fe] = 0.1). From this confidence contours, we can find that Teff and Log g are well determined. The metallicity is sometime converged. We cannot determine the [alpha/Fe].

I tried the broad band stellar typing of observed SDSS/SEGUE spectra using PS1 photometries.
This is not a final result because I have not yet corrected the galactic extinction of model spectra.
 
I used 32 F-stars of SDSS/SEGUE in Lee et al. (2011), AJ, 141, 90. The stars have PS1 photometries and g-r color < 0.4 (a color selection for F stars). Using the observed PS1 grizy fluxes and the synthetic PS1 fluxes of interpolated AMBRE models, I found the best fit model spectra.
 
An example of a SDSS spectrum (black), the best fit model (blue), and the best fit model which was convolved by a Gaussian kernel of FWHM=0.3nm (a substitute for LSF) (red).

Residuals of all the stars. (Please ignore the colors.) The residuals are distributed around zero. The large residuals at some line features are due to a miss-match of the LSF. 

 
 

The Galactic extinction both for input fluxes and output model spectra was corrected. I used the SFD98 dust map in the `extinctions` Python package and the extinction curve of Fitzpatrick (1999) in the `dust_extinction` Python package. 
 
This is an example of a reproduced model spectrum and the same star as above. There are no big changes. 

 
A confidence contours of estimated parameters. 

 
Residuals of all the spectra. Residual = SDSS - Model 
Black — 0.2 < g-r < 0.4, red — g-r < 0.2.

 
 
R.M.S of the relative residuals on the gri color-color diagram.
Relative residual = (SDSS - Model) / SDSS * 100.
 
The green box is the F star selection window. I plot stars outside of the window for comparison. In the window, the RMS is about 10%.

 
 
 
 

I checked the best model spectra when the flux uncertainties of PS1 become worse, in particularly, when they are comparable to the HSC level (magerr = 0.01), because the PS1 photometries of the stars we use have small magnitude errors, on average, ~0.003. 
 
This is the RMS of the relative residuals as a function of g - r colors. Three cases of the magnitude errors, 0.005, 0.01, 0.1 mag, are shown, as well as the original uncertainties. The means of RMS are 11.0 for the original and 12.8 for '0.01 mag’ (HSC level). Stars in the figure are the mean RMS.
 

Mean RMS: 
Original – 11.0
MagErr=0.005 – 11.9
MagErr=0.01 – 12.8
MagErr=0.1 – 18.5
 
 
Minimum reduced chi squares are distributed around 1, but the worst case (0.1 mag) shows the lowest value.

Mean min red. chisq: 
Original – 6.8
MagErr=0.005 – 6.1
MagErr=0.01 – 1.4
MagErr=0.1 – 0.6
 

Robust RMS of fractional residuals. 
I use sigma clipping (3 sigma, 10 iterations) for the fractional residuals. This is roughly RMS of continuum. 
 
Mean robust RMSs:
Original: 4.0%
MagErr=0.005: 3.9%
MagErr=0.01: 4.2%
MagErr=0.1: 6.8%
 
Robust RMS and g-r color for the original and three cases of mag errors. 

 
This figure is only for the original PS1 data.