Missing Modes

For adiabatic oscillation calculations using gyre, the radial order \(\numpg\) of modes found should be monotonic-increasing[1]. Departures from this behavior can occur for a number of reasons.

Insufficient Frequency Resolution

If the frequency grid has insufficient resolution, then gyre can skip modes during the bracketing phase, as discussed in the Limitations of the Numerical Method section. The signature of insufficient frequency resolution is that an even number of consecutive modes is missed — most often, an adjacent pair of modes.

To fix this problem, first check that the distribution of points in the frequency grids matches (approximately) the expected distribution of mode eigenfrequencies:

• In the asymptotic limit of large radial order, p modes are uniformly distributed in frequency (see, e.g., Aerts et al., 2010). Hence, to search for these modes set grid_type='LINEAR' in the &scan namelist group(s).

• Likewise, in the asymptotic limit of large radial order, g modes are uniformly distributed in period. Hence, to search for these modes set grid_type='INVERSE' in the &scan namelist group(s).

• For rotating stars, the asymptotic behaviors mentioned apply in the co-rotating reference frame, not in the inertial reference frame. So, be sure to also set grid_frame ='COROT_I'|'COROT_O' in the &scan namelist group.

Next, try increasing the number of points in the frequency grids, simply by increasing the n_freq parameter in the &scan namelist group(s).

Tip

A good rule of thumb is that n_freq should be around 5 times larger than the number of modes expected to be found.

Insufficient Spatial Resolution

If the spatial grid has insufficient resolution, then certain modes can simply be absent from the (finite) set of distinct numerical solutions, as discussed in the Limitations of the Numerical Method section. The signature of insufficient spatial resolution is that modes that are found have radial orders comparable to the number of grid points \(N\) in the grid; and that the eigenfunctions of these modes are barely resolved (cf. Fig. 5).

To fix this problem, first check that the w_osc, w_exp and w_ctr weighting parameters in the &grid namelist group are set to reasonable values (see the Recommended Values section). If that doesn’t improve things, try gradually increasing both w_osc and w_ctr.

Non-adiabatic Effects

When undertaking non-adiabatic calculations, modes can be mis-classified or completely missed. The former situation arises because the expectation of monotonic-increasing \(\numpg\) formally applies only to adiabatic oscillations; while it can also work reasonably well for weakly non-adiabatic cases, there are no guarantees. If mis-classification does occur, then it must be fixed manually by determining which adiabatic mode the problematic non-adiabatic mode corresponds to.

Missing modes occur for a different reason: if a mode has a large growth rate, then the usual adiabatic method for establishing initial trial roots can fail to find it. In such cases, the alternative contour method performs very well.

Footnotes

[1]

The sole exception is \(\ell=1\) modes, where \(\numpg=0\) is skipped due to the way the Takata 2006b classification scheme is set up.