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 Sersic 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 mu (0,K) and the disc scalelength h. There exists a bright envelope of galaxy discs in the mu (0,K)-log h diagram; for the early-type (less than or equal to Sbc-Sc) disc galaxies mu (0,K) is shown to increase with log h, with a slope of similar to2 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 less than or equal to 50 degrees) and 29 high-inclination (i greater than or equal to 50 degrees) galaxies having morphological types ranging from SO 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 mu (0,K)-log h diagram. Measured central disc surface brightnesses are found to be significantly (>5 sigma) 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 mu (0,K) and log h, the standard deviation to the distribution of mu (0,K) values is similar to1 mag arcsec(-2), while the standard deviation about the mean mu (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 mu (0,K)-log h diagram.