Avoided crossings between non-radial modes in low mass RGB stars

Non-radial p modes and g modes appear simultaneously in red giant stars. Their frequencies have different variation rates, causing their frequencies to become close during stellar evolution so that avoided crossings appear. The separation between regions where acoustic waves and gravity waves propagate for l = 1, 2 and 3 is different, which results in the coupling efficiency also being different. We present the results of numerical computations of the models we study. We find that the two kinds of modes for l = 2 and 3 need to be closer in frequency in order for a complete exchange to occur, compared to the case for modes with l = 1. Their scaled oscillation frequencies also present better regularity with evolution than modes with l = 1. In order to study the effect of the avoided crossings in detail, we set the mode which has the smallest mode inertia to be the p mode. We plot the two kinds of modes for l = 1, 2 and 3 in frequency and period échelle diagrams and find modes of l = 2 and 3 fit the two relations better; they are more equally spaced in frequency and period than modes with l = 1. Under careful observation of the two kinds of échelle diagrams for l = 2 and 3, we still find that some p modes shift a little from being equally spaced in frequency and some g modes, which are close to those p modes in period, shift a little from being equally spaced in period. Then, we study the relation between the deviation from period being equally spaced and the mode inertia of g modes for different l. The g modes of l = 1 with a period closer to the p mode have less inertia and the deviation is bigger in the period échelle diagram. Their deviation is also obvious. However g modes of l = 2 and 3 shift a little or have almost no deviation from being equally spaced in period, even though some of them may have strong coupling and close mode inertia like in the p modes. So, we suggest a possible method for measuring period spacing of g modes precisely using mixed g modes with l = 2 and 3 that have fewer observed mixed g modes than for l = 1. (research papers)