Constraint on the time variation of the fine-structure constant with the
  SDSS-III/BOSS DR12 quasar sample
  From the Sloan Digital Sky Survey (SDSS) Data Release 12, which covers the
full Baryonic Oscillation Spectroscopic Survey (BOSS) footprint, we investigate
the possible variation of the fine-structure constant over cosmological
time-scales. We analyse the largest quasar sample considered so far in the
literature, which contains 13175 spectra (10363 from SDSS-III/BOSS DR12 + 2812
from SDSS-II DR7) with redshift $z<\,$1. We apply the emission-line method on
the [O III] doublet (4960, 5008 A) and obtain $\Delta\alpha/\alpha= \left(0.9
\pm 1.8\right)\times10^{-5}$ for the relative variation of the fine-structure
constant. We also investigate the possible sources of systematics:
misidentification of the lines, sky OH lines, H$\,\beta$ and broad line
contamination, Gaussian and Voigt fitting profiles, optimal wavelength range
for the Gaussian fits, chosen polynomial order for the continuum spectrum,
signal-to-noise ratio and good quality of the fits. The uncertainty of the
measurement is dominated by the sky subtraction. The results presented in this
work, being systematics limited, have sufficient statistics to constrain
robustly the variation of the fine-structure constant in redshift bins ($\Delta
z\approx$ 0.06) over the last 7.9 Gyr. In addition, we study the [Ne III]
doublet (3870, 3969 A) present in 462 quasar spectra and discuss the systematic
effects on using these emission lines to constrain the fine-structure constant
variation. Better constraints on $\Delta\alpha/\alpha\ $ ($<$10$^{-6}$) using
the emission-line method would be possible with high-resolution spectroscopy
and large galaxy/qso surveys.
