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The detection of mixed modes in red giants with space missions CoRoT and Kepler has revealed their deep internal structure. These modes allow us to characterize the pattern of pressure modes (through the measurement of their asymptotic frequency separation $Delta u$) and the pattern of gravity modes (through the determination of their asymptotic period spacing $DeltaPi_1$). It has been shown that red giant branch (RGB) stars regroup on a well-defined sequence in the $Delta u$-$DeltaPi_1$ plane. Our first goal is to theoretically explain the features of this sequence and understand how it can be used to probe the interiors of red giants. Using a grid of red giant models computed with MESA, we demonstrate that red giants join the $Delta u$-$DeltaPi_1$ sequence whenever electron degeneracy becomes strong in the core. We argue that this can be used to estimate the central densities of these stars, and potentially to measure the amount of core overshooting during the main sequence part of the evolution. We also investigate a puzzling subsample of red giants that are located below the RGB sequence, in contradiction with stellar evolution models. After checking the measurements of the asymptotic period spacing for these stars, we show that they are mainly intermediate-mass red giants. This is doubly peculiar because these stars should have non-degenerate cores and are expected to be located well above the RGB sequence. We show that these peculiarities are well accounted for if these stars result from the interaction between two low-mass ($Mlesssim2,M_odot$) close companions during the red giant branch phase. If the secondary component has already developed a degenerate core before mass transfer begins, it becomes an intermediate-mass giant with a degenerate core. The secondary star is then located below the degenerate sequence, in agreement with the observations.
First-ascent red giants with masses below about $2,M_odot$ ignite helium in their degenerate core as a flash. Stellar evolution codes predict that the He flash consists of a series of consecutive subflashes. The detection of mixed modes in red giants
(Abridged). We introduce the Aarhus Red Giants Challenge, a series of detailed comparisons between widely used stellar evolution and oscillation codes aiming at establishing the minimum level of uncertainties in properties of red giants arising solel
Context. The large quantity of high-quality asteroseismic data that obtained from space-based photometric missions and the accuracy of the resulting frequencies motivate a careful consideration of the accuracy of computed oscillation frequencies of s
Binaries in double-lined spectroscopic systems provide a homogeneous set of stars. Differences of parameters, such as age or initial conditions, which otherwise would have strong impact on the stellar evolution, can be neglected. The observed differe
Asteroseismology allows us to probe stellar interiors. Mixed modes can be used to probe the physical conditions in red giant cores. However, we still need to identify the physical mechanisms that transport angular momentum inside red giants, leading