Flux Density (Jy) to Luminosity when wavelength is involved

[Aiveenoka]

Hi,
I think my problem may be a little trivial however I have been stuck on it for quite some time. I have plots of flux density (Jy) versus wavelength in order to look at a particular forbidden line. I want to find the luminosity of the line, however as I am dealing with Jy [W/(m^2 Hz)] I do not know how to deal with the frequency unit.

I am using the luminosity formula 4*pi*R^2*integral_flux_density. I am only looking at the main bit of the spectrum which I circle in the attached image.

I attempted to handle the Hz by multiplying my integral_flux_density by a correction value (s*λ^2)/c where s is the sampling value (the wavelength difference divided by the number of values) and c the speed of light. However the units do not work out.
I came up with my correction value based on:
Janksy unit = W m^-2 Hz^-1 (ignoring the 10^-26)
This is the same as dF/dv where v is nu the frequency symbol

I need dF/dv to go to dF/dλ

v=c/λ -> dv = - (c/λ^2) *dL

dF/dλ = dF/dv * dv/dλ

dF/dλ = - dF/dv * c/λ^2

dF/d\nu = -dF/dλ * (λ^2)/c

Any assistance would be greatly appreciated.
Thanks,
A :)

 

[mfb]

That looks fine.

For each sampling between λ and Δλ, you have a frequency range between c/λ and c/(λ+Δλ) ≈ c/λ (1-Δλ/λ) which corresponds to a spectral width of cΔλ/λ^2. This has a unit of Hz, you can multipliy it with Jy to get W/m^2 for that sampling point, and sum over all points.

 

[Aiveenoka]

Thank you for your response, mfb. Your reply makes sense to me.
I realized I'd been implementing the correction factor wrongly. However I still cannot achieve reasonable answers. For this source (T Tau) I know that M-dot must be (or at least close to) 1E-6 and I am presently obtaining many values, but the one with the most accurate calculation is 10^20...

I attach the spreadsheet of this work to see if anything can be spotted. The green flux densities correspond to the circled area in my previous attachment of the image of my spectra.

A :)

 

[mfb]

I don't see an attachment.

Janksy unit = W m^-2 Hz^-1 (ignoring the 10^-26)

Maybe there is your factor of 10^26?

 

[Aiveenoka]

I think you are right! I had tried that before but in vain, however like I said I had been implementing the correction factor wrong. I shall try again right now and let you know and if needs be I'll actually attach the document this time, sorry about that.
Thank you,
A

 

[Aiveenoka]

It works! You're brilliant :) Thank you!