A new non-linear limb-darkening law for LTE stellar atmosphere models - Calculations for-5.0 <= log[M/H] <=+1,2000 K <= T-eff <= 50000 K at several surface gravities

A new non-linear limb-darkening law, based on the Least-Squares Method (LSM ), is presented. This law is able to describe the intensity distribution mu ch more accurately than any of the old ones given that the differences I(mo del)-I(fitting) are of some order of magnitude smaller than those derived f rom other approximations. This new law shows several advantages: it represe nts well the intensity distribution, the flux is conserved with high accura cy and it permits the use of a single law for the whole HR Diagram since th e bi-parametric laws are only marginally valid in certain ranges of effecti ve temperatures. The limb-darkening coefficients are computed for the 12 co mmonly used photometric bands uvbyUBV RIJHK. Bolometric and monochromatic c alculations are also available. The computations are presented for 19 metal licities ranging from 10(-5) up to 10(+1) solar abundances, with log g vary ing between 0 and 5.0 and effective temperatures between 2000 K-50000 K. Re sults for microturbulent velocities of 0, 1, 2, 4, 8 km/s are also availabl e. With this set of data it was possible to investigate, for the first time , the influence of such parameters in the limb-darkening. Limb-brightening, instead of limb-darkening, was detected for some models. It is shown that the limb-darkening coefficients derived using the Flux Con servation Method (FCM) do not describe very well the intensity distribution , mainly near the border of the disk. On the contrary, the present coeffici ents, based on the LSM, represent very well the function I(mu) at any part of the disk for any filter or wavelength, log g, effective temperature, met allicity and microturbulent velocity. The results are presented in 46 tables for the 12 filters (bolometric) and can be retrieved from the CDS. Due to the size of the remaining tables, mai nly the monochromatic, these are available only on request (CD ROMs).