Relative Flux Calibration of the LAMOST Spectroscopic Survey of the Galactic Anti-center

We have developed and implemented an iterative algorithm of flux calibration for the LAMOST Spectroscopic Survey of the Galactic anti-center (LSS-GAC). For a given LSS-GAC plate, the spectra are first processed with a set of nominal spectral response curves (SRCs) and used to derive initial stellar atmospheric parameters (effective temperature $T_{\rm eff}$, surface gravity log\,$g$ and metallicity [Fe/H]) as well as dust reddening $E(B-V)$ of all targeted stars. For each of the sixteen spectrographs, several F-type stars of good signal-to-noise ratios (SNRs) are then selected as flux standard stars for further, iterative spectral flux calibration. Comparison of spectrophotometric colours, deduced from the flux-calibrated spectra, with the photometric measurements yields average differences of 0.02$\pm$0.07 and $-$0.04$\pm$0.09\,mag for the $(g-r)$ and $(g-i)$, respectively. The relatively large negative offset in $(g-i)$ is due to the fact that we have opted not to correct for the telluric bands, most notably the atmospheric A-band in the wavelength range of $i$-band. Comparison of LSS-GAC multi-epoch observations of duplicate targets indicates that the algorithm has achieved an accuracy of about 10 per cent in relative flux calibration for the wavelength range 4000 -- 9000\,Å. The shapes of SRC deduced for the individual LAMOST spectrographs are found to vary by up to 30 per cent for a given night, and larger for different nights, indicating that the derivation of SRCs for the individual plates is essential in order to achieve accurate flux calibration for the LAMOST spectra.