diff_scheme, Growth Rate and Amplitudes

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KrawalloQualle
Posts: 4
Joined: Mon Feb 11, 2019 6:07 am

diff_scheme, Growth Rate and Amplitudes

Post by KrawalloQualle » Mon Feb 11, 2019 9:39 am

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

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rhtownsend
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Posts: 305
Joined: Sun Mar 31, 2013 4:22 pm

Re: diff_scheme, Growth Rate and Amplitudes

Post by rhtownsend » Wed Feb 13, 2019 11:14 am

KrawalloQualle wrote:
Mon Feb 11, 2019 9:39 am
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
Posts: 4
Joined: Mon Feb 11, 2019 6:07 am

Re: diff_scheme, Growth Rate and Amplitudes

Post by KrawalloQualle » Mon Feb 18, 2019 2:09 am

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

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rhtownsend
Site Admin
Posts: 305
Joined: Sun Mar 31, 2013 4:22 pm

Re: diff_scheme, Growth Rate and Amplitudes

Post by rhtownsend » Mon Feb 18, 2019 9:37 am

KrawalloQualle wrote:
Mon Feb 18, 2019 2:09 am
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
Posts: 4
Joined: Mon Feb 11, 2019 6:07 am

Re: diff_scheme, Growth Rate and Amplitudes

Post by KrawalloQualle » Mon Feb 25, 2019 2:20 am

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

Cheerio
Jess

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