Is dark matter present in NGC4736? An iterative spectral method for finding mass distribution in spiral galaxies

An iterative method for reconstructing mass distribution in spiral galaxies using a thin disk approximation is developed. As an example, the method is applied to galaxy NGC 4736; its rotation curve does not allow one to employ a model with a massive spherical halo. We find a global mass distribution in this galaxy (without non-baryonic dark matter) that agrees perfectly with the high resolution rotation curve of the galaxy. This mass distribution is consistent with the $I$-band luminosity profile with the mean mass-to-light ratio $M/L_I=1.2$, and also agrees with the amount of hydrogen observed in the outermost regions of the galaxy. We predict the total mass of the galaxy to be only $3.43\times10^{10}M_{\sun}$. It is very close to the value predicted by the modified gravity models and much less than the currently accepted value of $5.0\times10^{10}M_{\sun}$ (with $\approx70%$ of the mass in a dark matter halo).