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unit of sigma in nonadiabatic calculation

Posted: Sun Feb 19, 2023 12:56 am
by anwesha
Hi,
I am a bit confused with the units of the non-adiabatic exp(-i*sigma*t) term

mode period = 2*pi/sigma (from documentation) --> so here sigma is the angular frequency having unit (1/rad)
now the output omega by gyre is dimensionless.
sigma = omega*sqrt(GM/R^3) --> sqrt(GM/R^3) has unit of (1/s) --> so sigma here is the normal frequency having unit of (1/s)

what am I missing here in my understanding?

Re: unit of sigma in nonadiabatic calculation

Posted: Sun Feb 19, 2023 3:30 pm
by rhtownsend
Hi Anwesha --

Thanks for your questions!
anwesha wrote:
Sun Feb 19, 2023 12:56 am
mode period = 2*pi/sigma (from documentation) --> so here sigma is the angular frequency having unit (1/rad)
In fact, the unit of sigma is rad/second (since sigma = 2*pi/period). That's sometimes also written as 1/second, since radians are unitless.
anwesha wrote:
Sun Feb 19, 2023 12:56 am
now the output omega by gyre is dimensionless.
sigma = omega*sqrt(GM/R^3) --> sqrt(GM/R^3) has unit of (1/s) --> so sigma here is the normal frequency having unit of (1/s)
The 1/second you mention here is the same as the 1/second I give above.

Hope this answers your question!

cheers,

Rich

Re: unit of sigma in nonadiabatic calculation

Posted: Mon Feb 20, 2023 9:28 am
by anwesha
Hi Rich,

thank you so much for the clarification. So, if I want the eigen frequencies in 'rad/s' to compare with lamb and Brunt Vaisala (both of which I have found in rad/s) that would simply mean I will be using sigma (without having any additional factor of 2pi)?

Re: unit of sigma in nonadiabatic calculation

Posted: Mon Feb 20, 2023 9:31 am
by rhtownsend
Yes, that's right -- assuming the Brunt is also in rad/s.