A K ‐band central disc surface brightness correlation with scalelength for early‐type disc galaxies, and the inclination correction

The K ‐band light profiles from two statistically complete, diameter‐limited samples of disc galaxies have been simultaneously modelled with a seeing‐convolved Sérsic r 1/ n bulge and a seeing‐convolved exponential disc. This has enabled an accurate separation of the bulge and disc light, and hence an estimate of the central disc surface brightness μ 0, K and the disc scalelength h . There exists a bright envelope of galaxy discs in the μ 0,K –log h diagram; for the early‐type (≤Sbc–Sc) disc galaxies μ 0, K is shown to increase with log  h , with a slope of ∼2 and a correlation coefficient equal to 0.75. This relation exists over a range of disc scalelengths from 0.5 to 10 kpc (H 0 =75 km s −1  Mpc −1 ) . In general, galaxy types Scd or later are observed to deviate from this relation; they have fainter surface brightnesses for a given scalelength. With a subsample of 59 low‐inclination (i≤50°) and 29 high‐inclination (i≥50°) galaxies having morphological types ranging from S0 to Sc, the need for an inclination correction to the K ‐band disc surface brightness is demonstrated. Certain selection criteria biases which have troubled previous surface brightness inclination tests (for example, whether the galaxies are selected from a magnitude‐ or diameter‐limited sample) do not operate in the μ 0,K –log h diagram. Measured central disc surface brightnesses are found to be significantly (>5 σ ) brighter for the high‐inclination disc galaxies than for the low‐inclination disc galaxies. With no surface brightness inclination correction or allowance for the trend between μ 0, K and log  h , the standard deviation to the distribution of μ 0, K values is ∼1 mag arcsec −2 , while the standard deviation about the mean μ 0,K –log h relation decreases from 0.69 mag arcsec −2 , when no inclination correction is applied, to 0.47 mag arcsec −2 when the inclination correction is applied. Possible changes to the disc scalelength with inclination, as a result of radial gradients in the disc opacity, have been explored. The maximum possible sizes for such corrections are too small to provide a valid explanation for the difference between the low‐ and high‐inclination disc galaxies in the μ 0,K –log h diagram.