Asteroseismic measurement of core and envelope rotation rates for 2006 red giant branch stars

Tens of thousands of red giant stars in the Kepler data exhibit solar-like oscillations. Their oscillations enable us to study the internal physics from core to surface, such as differential rotation. However, envelope rotation rates have been measured for only a dozen RGB stars so far. The limited sample hinders the theoretical interpretation of angular momentum transport in post-main-sequence phases. We apply a new approach to calculate the asymptotic frequencies of mixed modes, which accounts for the so-called near-degeneracy effects and leads to more proper measurements of envelope rotation rates. By fitting these asymptotic expressions to the observations, we obtain measurements of the properties of g modes and mean core and envelope rotation rates. Among 2495 stars with clear mixed-mode patterns, we found that 800 show doublets and 1206 show triplets, doubling the size of pre-existing catalogues. This led us to discover an over-density of stars that narrowly distribute around a well-defined ridge in the plane showing core rotation rate versus evolution along the RGB. With this work, we also increase the sample of stars with measured envelope rotation rates by two orders of magnitude. We find a decreasing trend between envelope rotation rates and evolution, implying that the envelopes slow down with expansion, as expected. We find 243 stars whose envelope rotation rates are significantly larger than zero. For these stars, the core-to-envelope rotation ratios are around 20 and show a large spread with evolution. Several stars show extremely mild differential rotations, with core-to-surface ratios between 1 and 2. These stars also have very slow core rotation rates, suggesting that they go through a peculiar rotational evolution. We also discovered more stars located below the degeneracy sequence, which will provide the opportunity to study the history of possible stellar mergers.