diff_scheme, Growth Rate and Amplitudes

[KrawalloQualle]

Hello dear GYRE users,

I'm more or less new to GYRE and stellar oscillation physics in general so please excuse if my questions are a bit dumb.
I have read as much about GYRE as the time frame of my master thesis allows me but there are still a few questions unanswered.
I don't know if it would be better to make multiple posts and if this is wished, I will do so but for the moment, everything will be put into this one.

If it helps with answering any of my questions, the overall task is to calculate eigenmodes, their frequencies, including damping factors and luminosity amplitudes for a 5 mass star on the main sequence. p- and g-modes are both important (I need to simulate the luminosity time series later, so everything that goes in there, needs to be taken into account). However focus should lie on l=2 g-modes.
Clear is that I need non-adiabatic calculations for that. Now to the unclear parts:

1. Since I am new to the topic of numerical solving of stellar oscillation equations, I don't know when to use which diff_scheme. In the 2018 paper it is stated that Runge-Kutta is more stable than Magnus for non-adiabatic calculations. Does that mean, I should always prefer Runge-Kutta when considering non-adiabaticity? Or is there more to it?

2. In general: is there a difference to what diff-scheme is best for p- and g-modes respectively?

3. The imaginary part of the frequency characterizes the damping of the mode. And the eta output parameter is the growth rate. So eta should be something like e^{imaginary part of omega}. But I'm a bit confused of how the sign in front of eta comes to be? Does it just take the sign of Im(omega) and puts it in front of eta? (Maybe I'm just missing something)

4. I'm not sure on how to get luminosity amplitudes from the output GYRE provides. There is a formula in the [Dup2003] paper which is linked for the effective temperature perturbation amplitude f_T and the effective gravity perturbation amplitude f_g but there seem to be coefficients included which GYRE does not calculate. And I am not even sure if this is what I need. I don't completely understand the paper and I have yet to find suitable literature to do so.

This is quite a bit of unclear stuff and I'm sure some of it is easily answered by looking into the right literature I haven't found yet so again: Sorry if some of these are stupid questions but the time I have to spend on research is getting short.

I'm very grateful for every little bit of knowledge and advice you can give me.

Cheers and have a nice day
Jess

[rhtownsend]

Hello dear GYRE users,

I'm more or less new to GYRE and stellar oscillation physics in general so please excuse if my questions are a bit dumb.
I have read as much about GYRE as the time frame of my master thesis allows me but there are still a few questions unanswered.
I don't know if it would be better to make multiple posts and if this is wished, I will do so but for the moment, everything will be put into this one.

If it helps with answering any of my questions, the overall task is to calculate eigenmodes, their frequencies, including damping factors and luminosity amplitudes for a 5 mass star on the main sequence. p- and g-modes are both important (I need to simulate the luminosity time series later, so everything that goes in there, needs to be taken into account). However focus should lie on l=2 g-modes.
Clear is that I need non-adiabatic calculations for that. Now to the unclear parts:

1. Since I am new to the topic of numerical solving of stellar oscillation equations, I don't know when to use which diff_scheme. In the 2018 paper it is stated that Runge-Kutta is more stable than Magnus for non-adiabatic calculations. Does that mean, I should always prefer Runge-Kutta when considering non-adiabaticity? Or is there more to it?

2. In general: is there a difference to what diff-scheme is best for p- and g-modes respectively?

3. The imaginary part of the frequency characterizes the damping of the mode. And the eta output parameter is the growth rate. So eta should be something like e^{imaginary part of omega}. But I'm a bit confused of how the sign in front of eta comes to be? Does it just take the sign of Im(omega) and puts it in front of eta? (Maybe I'm just missing something)

4. I'm not sure on how to get luminosity amplitudes from the output GYRE provides. There is a formula in the [Dup2003] paper which is linked for the effective temperature perturbation amplitude f_T and the effective gravity perturbation amplitude f_g but there seem to be coefficients included which GYRE does not calculate. And I am not even sure if this is what I need. I don't completely understand the paper and I have yet to find suitable literature to do so.

This is quite a bit of unclear stuff and I'm sure some of it is easily answered by looking into the right literature I haven't found yet so again: Sorry if some of these are stupid questions but the time I have to spend on research is getting short.

I'm very grateful for every little bit of knowledge and advice you can give me.

Cheers and have a nice day
Jess

Hi Jess --

Thanks for your questions, and welcome to the GYRE community!

1. Regarding Runge-Kutta and Magnus: my long-term home is that we can modify the Magnus scheme to work well with non-adiabatic calculations. But for now, I would recommend you always use COLLOC_GL2 the scheme (which is equivalent to a second-order implicit Runge-Kutta scheme).

2. Not really.

3. The eta output parameter is actually the normalized growth rate defined by Stellingwerf (1978; http://adsabs.harvard.edu/abs/1978AJ.....83.1184S). It is positive for unstable modes, and negative for damped (stable) modes; and it's magnitude is |eta| <= 1. It gives an indication of the balance between driving and damping throughout the star; but to find the actual growth or decay rate of a mode, you need to look art the imaginary part of the angular frequency. If sigma is the angular frequency in Hz, then the time-evolution of the mode amplitude is exp(-Im[sigma] t), so the growth rate is -Im[sigma].

4. To get a better understanding of how to calculate luminosity perturbations from temperature perturbations, have a look at Stamford & Watson (1981; http://adsabs.harvard.edu/abs/1981Ap%26SS..77..131S). Also, realize that GYRE will never be able to predict the *absolute* amplitude of luminosity perturbations, as it is a linear code and therefore does not predict mode amplitudes. Rather, it can tell us about the *relative* amplitude (and phase) of luminosity perturbations across multiple passbands, and/or compared to radial velocity variations.

I hope this helps!

cheers,

Rich

[KrawalloQualle]

Hi Rich,

thank you very much! This already helped me a great deal and I hope the paper will enlighten me concerning amplitudes.

I have one further question though:
Why is the COLLOC_GL2 more advisable than the GL4 or GL6 scheme? Is is just because of run time advantages? Or is there a completely different reason?

Cheers
Jess

[rhtownsend]

Hi Rich,

thank you very much! This already helped me a great deal and I hope the paper will enlighten me concerning amplitudes.

I have one further question though:
Why is the COLLOC_GL2 more advisable than the GL4 or GL6 scheme? Is is just because of run time advantages? Or is there a completely different reason?

Cheers
Jess

Good question. It's because the GL4 and GL6 schemes seem to have difficulty in finding non-adiabatic oscillation frequencies -- quite often, they fail to converge to a nearby mode in the complex-frequency plane. I'm still working on improving their convergence properties, but for now GL2 is the way to go.

cheers,

Rich

[KrawalloQualle]

Alright, thank you very much, Rich!
For now everything is more or less clear.

Cheerio
Jess

[benfernando]

Hi all,

Sorry to post again on an old topic but I've managed to get myself a bit confused about point 3 - the signs of eta and Im(sigma).

I note that eta is defined in Stellingwerf 1978, such that eta > 0 is unstable and eta <0 is stable.

I've also seen the definition above used, where eta = - Im(sigma). This suggests that eta and Im(sigma) should always have opposite signs, but in the model I've attached (based off Paparo 2018), it looks like for a given mode, both eta and Im(omega) have the same sign. I don't quite see how this works? The normalisation (eta' to eta) and dimensionalisation (omega to sigma) presumably does not change the sign.

I'm sure this is a pretty simple issue, so sorry to bother you all. I can't seem to attach the nad output so I've pasted a couple lines below.

Best
Ben


1 2
M_star R_star
0.3978400000000000E+034 0.2604318534030796E+012
1 2 3 4 5 6 7 8 9 10 11 12
l n_pg n_p n_g Re(omega) Im(omega) E_norm Re(freq) Im(freq) Delta_p Delta_g eta
2 -121 0 121 0.2003309489750999E+001 -0.6549285414897081E-006 0.7554878503341776E+001 0.2003309489750999E+001 -0.6549285414897081E-006 0.2167034725446049E+000 0.3973594779380975E+002 -0.5455698505542567E+000

[rhtownsend]

Hi all,

Sorry to post again on an old topic but I've managed to get myself a bit confused about point 3 - the signs of eta and Im(sigma).

I note that eta is defined in Stellingwerf 1978, such that eta > 0 is unstable and eta <0 is stable.

I've also seen the definition above used, where eta = - Im(sigma). This suggests that eta and Im(sigma) should always have opposite signs, but in the model I've attached (based off Paparo 2018), it looks like for a given mode, both eta and Im(omega) have the same sign. I don't quite see how this works? The normalisation (eta' to eta) and dimensionalisation (omega to sigma) presumably does not change the sign.

I'm sure this is a pretty simple issue, so sorry to bother you all. I can't seem to attach the nad output so I've pasted a couple lines below.

Best
Ben


1 2
M_star R_star
0.3978400000000000E+034 0.2604318534030796E+012
1 2 3 4 5 6 7 8 9 10 11 12
l n_pg n_p n_g Re(omega) Im(omega) E_norm Re(freq) Im(freq) Delta_p Delta_g eta
2 -121 0 121 0.2003309489750999E+001 -0.6549285414897081E-006 0.7554878503341776E+001 0.2003309489750999E+001 -0.6549285414897081E-006 0.2167034725446049E+000 0.3973594779380975E+002 -0.5455698505542567E+000

Hi Ben --

Thanks for your question. The relationship between the sign of Im(sigma) and the sign of eta really depends on what time dependence is implicitly assumed for the oscillations. In the older literature, perturbations are assumed to have a time dependence f(t) ~ exp(i sigma t). Therefore, negative Im(sigma) corresponds to exponential growth (instability) and positive eta.

However, GYRE assumes perturbations have a time dependence f(t) ~ exp(-i sigma t) (see, e.g., equation 7 of Townsend, Goldstein & Zweibel 2018, MNRAS 475, 879). This means that *positive* sigma corresponds to exponential growth and positive eta.

Hope that explains things!

cheers,

Rich