Asteroseismology of luminous red giants with Kepler I: Long Period Variables with radial and non-radial modes

While long period variables (LPVs) have been extensively investigated, especially with MACHO and OGLE data for the Magellanic Clouds, there still exist open questions in their pulsations regarding the excitation mechanisms, radial order and angular degree assignment. Here, we perform asteroseismic analyses on LPVs observed by the 4-year Kepler mission. Using a cross-correlation method, we detect unambiguous pulsation ridges associated with radial fundamental modes ($n=1$) and overtones ($n\geqslant2$), where the radial order assignment is made by using theoretical frequencies and observed frequencies. Our results confirm that the amplitude variability seen in semiregulars is consistent with oscillations being solar-like. We identify that the dipole modes, $l=1$, are dominant in the radial orders of $3\leq n \leq6$, and that quadrupole modes, $l=2$, are dominant in the first overtone $n=2$. A test of seismic scaling relations using Gaia DR2 parallaxes reveals the possibility that the relations break down when $\nu_{\rm max}$ $\lesssim$ 3 $\mu$Hz (R $\gtrsim$ 40 R$_{\odot}$, or log $\rm L/L_{\odot}$ $\gtrsim$ 2.6). Our homogeneous measurements of pulsation amplitude and period for 3213 LPVs will be very valuable for probing effects of pulsation on mass loss, in particular in those stars with periods around 60 days, which has been argued as a threshold of substantial pulsation-triggered mass loss.