Duplicated Modes

Sometimes two modes with the same \(\npg\) are found during a calculation. This violates the expectation that \(\npg\) be monotonic-increasing, and can happen for a few reasons.

Bad Stellar Model

If the input stellar doesn’t conserve mass properly, then one or more bogus (unphysical) modes can appear with the same \(\npg\) as an existing mode, but a significantly different frequency. Such modes can also be spotted because their radial order is very different from the adjacent-in-frequency modes.

Bogus modes arise because the input stellar model doesn’t conserve mass. GYRE assumes that the density \(\rho\) and interior mass \(M_{r}\) are related by equation (5). Given that there are many different ways to discretize this equation, there is a certain amount of numerical ‘slop’ that arises when going from discrete form assumed in the stellar evolution code that generated the model (e.g., MESA) through to the discrete form implicitly assumed by GYRE. This slop can sometimes produce bogus modes, and the fix is to re-create the model with a higher spatial resolution.

Another possibility arises if the input stellar model contains density discontinuities that aren’t properly marked using double points. Often, these discontinuities can be diagnosed by plotting the \(I_0\) or \(I_1\) first integrals (for radial and dipole modes, respectively) as a function of radius. These first integrals should vanish everywhere (as shown by Takata 2006a), but will typically show abrupt jumps to non-zero values at the location of unmarked discontinuities. The fix is to re-create the model with double points inserted as necessary; in the case of MESA models, this can be achieved using the add_double_points_to_pulse_data parameter of the &controls namelist group.

Non-adiabatic Effects

When non-adiabatic effects cause a mode to be mis-classified (as discussed in the Missing Modes section), often the incorrect \(\npg\) value duplicates that of another mode. As before, a mis-classification must be fixed manually by determining which adiabatic mode the problematic non-adiabatic mode corresponds to.