Asteroseismogyrometry of low-mass red giants I The SOLA inversion method

During the past 10 years the unprecedented quality and frequencyresolution of asteroseismic data provided by space photometry hasrevolutionized the study of red-giant stars providing us with thepossibility to probe the interior of thousands of these targets. Our aimis to present an asteroseismic tool which allows to determine the totalangular momentum of stars, without a priori inference of their internalrotational profile. We adopt and adapt to red giants the asteroseismicinversion technique developed by Pijpers (2003} for the case of the Sun.The method has been tested assuming different artificial sets of data,including also modes with harmonic degree l> 1. We estimate with anaccuracy of 14.5% the total angular momentum of the red-giant star KIC4448777 observed by Kepler during the first four consecutive years ofoperation.} Our results indicate that the measurement of the totalangular momentum of red-giant stars can be determined with a fairly highprecision by means of asteroseismology by using a small set ofrotational splittings of only dipolar modes and that our method, basedon observations of stellar pulsations, provides a powerful mean fortesting and modeling transport of angular momentum in stars.