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Why in Astrophysics it is used νL_{ν} (where ν is the frequency and L_{ν} is the luminosity at that frequency) in the emission spectrum of an accretion disk?
Here's why I think it is so: to reduce the graph size!but why often in the plot of luminosity (where there are ν in abscissa and ν*Lν in ordinate) there is the product between ν and Lν and not only Lν?
Could you pls provide a reference source? I suspect that ##L_{\nu}## would be a spectral luminosity, i.e. luminosity per an unit frequency interval, measured in units ##(W/Hz)##. By multiplying this value and a specific frequency interval ##\nu##, you should get the total luminosity in Watts over this specific interval.Why in Astrophysics it is used νL_{ν} (where ν is the frequency and L_{ν} is the luminosity at that frequency) in the emission spectrum of an accretion disk?
I'm studying the AGNs for my undergraduate thesis, so i have many reference sources, but for example you can find this type of writing on: Dan Maoz "Astrophysics in a Nutshell".Could you pls provide a reference source? I suspect that ##L_{\nu}## would be a spectral luminosity, i.e. luminosity per an unit frequency interval, measured in units ##(W/Hz)##. By multiplying this value and a specific frequency interval ##\nu##, you should get the total luminosity in Watts over this specific interval.
Accretion disk are of different scales, depending on the mass of the blackhole. But guessing from your profile pic and the similarity of the field I assume you are talking about the supermassive blackhole accreting galactic matter; more precisely Active Galactic Nuclei(AGNs).
Here's why I think it is so: to reduce the graph size!
There's something you missed, sometimes the graph is plotted logarithmically, otherwise in powers of 10. This is because the Spectrum is expected to account for the variations across the whole electromagnetic range, and hence the graph would be too big if plotted in normal units.
View attachment 230147
A similar reasoning goes for plotting the product νL_{ν}. In log units this is easier to see. Notice that log(νL_{ν})=logν+logL_{ν}. Now look at the above graph, a simple subtraction will tell you that the y axis of the graph scales from -24 to -35 if only logL_{ν} is plotted.
Another reason might be by convention. Usually AGNs have a typical double hump(the shapes vary for different sources) structure when plotted as a product. In field they usually fit the different emission mechanics to this double hump structure; not that you can't do this for just luminosity, it's just what they do.
PS: Why I think this can't be from concrete theoretical calculation? Well, it doesn't matter if you plot luminosity or the product of luminosity and frequency, since the only quantity with nontrivial variations is the luminosity. Besides there are options in plotting program to plot ν^{2}L_{ν}.
Ah good, I think I found quite a nice explanation in Carroll&Ostlies: "An Introduction to Modern Astrophysics", two snapshots below. If I got it right, when you construct graph like this, the area under the curve of an interval will be proportional to the amount of energy received in that interval (i.e. "equal areas under the graph correspond to equal amounts of energy").I'm studying the AGNs for my undergraduate thesis, so i have many reference sources, but for example you can find this type of writing on: Dan Maoz "Astrophysics in a Nutshell".
Yes, ##L_{\nu}## is measured in units ##(W/Hz)##.