SIMBAD references

We developed a numerical method to compute the gravitational field of an infinitely thin axisymmetric disc with an arbitrary surface mass density profile. We evaluate the gravitational potential by a split quadrature using the double exponential rule and obtain the acceleration vector by numerically differentiating the potential by Ridder's algorithm. The new method is of around 12 digit accuracy and sufficiently fast because requiring only one-dimensional integration. By using the new method, we show the rotation curves of some non-trivial discs: (i) truncated power-law discs, (ii) discs with a non-negligible centre hole, (iii) truncated Mestel discs with edge softening, (iv) double power-law discs, (v) exponentially damped power-law discs, and (vi) an exponential disc with a sinusoidal modulation of the density profile. Also, we present a couple of model fittings to the observed rotation curve of M33: (i) the standard deconvolution by assuming a spherical distribution of the dark matter and (ii) a direct fit of infinitely thin disc mass with a double power-law distribution of the surface mass density. Although the number of free parameters is a little larger, the latter model provides a significantly better fit. The fortran 90 programs of the new method are electronically available.