What is Specific Intensity in Astrophysics?

[shanepitts]

I am currently autodidacting the basics of astrophysics, and I of course came across the term specific intensity. The book explicates that it is defined as the differential of intensity per frequency element. But is there a better explanation so that I could lean closer towards a visualization of this particular type of intensity?

 

[Matterwave]

The specific intensity is just as you stated. It is the intensity per unit frequency element. In fact, in astrophysics, we sometimes call the specific intensity just the intensity.

It is kind of a weird concept, and I'm not entirely sure how I can explain it to you in an intuitive fashion. Are you comfortable with the definition of intensity itself, and it is only the specific intensity that bothers you?

If that is the case, then the problem becomes a lot easier to explain. The specific intensity is simply used to separate out the spectrum of light that you receive. When you look at a astronomical light source, it is usually emitting in many different frequencies of light. As such, the specific intensity tells you, in addition to the intensity information, how much light there is at each specific frequency. Integrating the specific intensity over all frequencies will give you the total intensity.

 

[litup]

So couldn't you relate specific intensity to the bands you see in audio in a graphics equalizer? Like a specific intensity of say 1 Khz to 1.5 khz bandwidth then the specific intensity would be what you would measure between those two frequencies. So for light, it would be say the band from say 400 nm to 450 nm color band, something like the violet portion of the visible spectrum or say 700 to 750 nm in the IR area.

Does that sound reasonable?

 

[Matterwave]

Yes, it's pretty similar in the sense of splitting up a continuous or semi-continuous frequency band of a wave into it's spectrum. But I don't think the "intensity" part of it is very analogous.

 

[litup]

I was just thinking of the adjustability of each band in a graphics equalizer, where you have plus or minus 10 or 15 db in each band, but the intensity part could be related to a spectrum analyzer, in this case light instead of audio.

I work with light spectrum analyzers and they can split up a spectrum and measure wavebands a few nm wide.

So the specific intensity I think would be related to putting the total spectrum through filters to read out some wavelength, like 700 to 705 nm or something like that.

In astronomy there is the hydrogen alpha line filter, a very fine bandwidth filter where you can see things on the sun in much more detail at a very exact wavelength of 656.28 nm to see emission nebulae and solar prominences and the like. That is a good example of using a specific intensity filter, that is a very narrow bandwidth for sure!

 

[Matterwave]

You can make whatever analogy you want, as long as it makes some sense. But I wouldn't push the analogy too far is what I was saying.

 

[litup]

One thing I don't know about 'specific intensity': if it is the intensity of certain wavelengths, is there some criteria for deciding on just what the bandwidth is? 1 nanometer? 10? Any idea there? I have to picture it in terms of spectrum analysis, like having a spectrum analyzer tuned to a certain center frequency with a certain band plus and minus but have no idea what that would be. If you were thinking of UV at 250 nm wavelength then what frequency plus and minus would be considered the correct bandwidth to call it 'specific intensity'?

In a spectrum analyzer, the 'intensity' part is just the normal response on the Y axis as far as what level of brightness is indicated. I assume 'intensity' is = brightness?

 

[Matterwave]

In the theory of specific intensity, the wavelengths form a continuous set. Therefore the "bandwidth" as you say would be infinitesimal. Like a function f(x), there is a value f(x) for every value x, which form a continuum. Practically speaking of course, to calculate a specific intensity from observation, the bandwidth (effectively your binning) will depend on your detector (spectroscope) and its ability to separate out wavelengths. As I am only a lowly theorist, I can not tell you what the state of the art is in spectroscopic technology.

 

[litup]

In the theory of specific intensity, the wavelengths form a continuous set. Therefore the "bandwidth" as you say would be infinitesimal. Like a function f(x), there is a value f(x) for every value x, which form a continuum. Practically speaking of course, to calculate a specific intensity from observation, the bandwidth (effectively your binning) will depend on your detector (spectroscope) and its ability to separate out wavelengths. As I am only a lowly theorist, I can not tell you what the state of the art is in spectroscopic technology.

So specific intensity is the intensity of a single wave? I can assure you spectroscopy is not up to THAT level!

At optical wavelengths anyway. RF would be another thing.

 

[Matterwave]

Science is filled with distributions which are continuous, but in practice we must make them discrete. This is not restricted to specific intensity.

Continuous functions are a lot easier to work with, and then the specific scientist who is working on it can bin the data in his own way as convenient.

 

[litup]

Science is filled with distributions which are continuous, but in practice we must make them discrete. This is not restricted to specific intensity.

Continuous functions are a lot easier to work with, and then the specific scientist who is working on it can bin the data in his own way as convenient.

Are you saying then, that the specificity of the specific intensity is a variable? It might be one wavelength for one scientist but 10 wavelengths for another and 100 for a third?

 

[Matterwave]

Are you saying then, that the specificity of the specific intensity is a variable? It might be one wavelength for one scientist but 10 wavelengths for another and 100 for a third?

In a practical setting, your binning will indeed depend on your applications, and therefore which scientist is doing what. This is not uncommon, in fact, it is very very common, because no computer can ever store an uncountably infinite number of data points, so everything we do in practice must be discrete, whereas almost everything in theory is continuous (much easier to work with)!

You will see this when taking integrals for example, and the computer approximates them by the Riemann sum, or when doing differential equations, and the computer takes time steps and uses the Euler method or the Runge Kutta method.

 

[litup]

In a practical setting, your binning will indeed depend on your applications, and therefore which scientist is doing what. This is not uncommon, in fact, it is very very common, because no computer can ever store an uncountably infinite number of data points, so everything we do in practice must be discrete, whereas almost everything in theory is continuous (much easier to work with)!

You will see this when taking integrals for example, and the computer approximates them by the Riemann sum, or when doing differential equations, and the computer takes time steps and uses the Euler method or the Runge Kutta method.

So the bottom line is 'specific' isn't so specific.