# What are the differences between different types of flux density in radio astronomy?

I am new to radio astronomy and have started to analyze some radio observational data of pulsars recently. I am wondering about the differences between "peak flux density", "integrated flux density", " mean flux density", and "pulse flux density" of pulsars in radio.

• We then define the peak flux density $$S_{\mathrm{peak}}$$ as the maximum flux density of the profile. If the profile is roughly Gaussian, then this corresponds to the height of the Gaussian's peak.
• We get the mean flux density $$S_{\mathrm{mean}}$$ by averaging the flux density over one rotation period. If you want, you think of it using the equivalent width of the profile $$W$$, leading to the relation $$S_{\mathrm{mean}}=\frac{W}{P}S_{\mathrm{peak}}$$ with $$P$$ the rotation period, although this is just reorganizing the equation for the definition of equivalent width.
• Integrated flux density is a sometimes ambiguous term. I've seen it used to refer to integrating the profile in time over one rotation period and averaging the result -- in other words, $$S_{\mathrm{mean}}$$ -- and to refer to simply integrating the profile over one rotation period without averaging, using the resulting quantity as a proxy for energy or fluence. This is sometimes used in single pulse studies, where you could compute this "integrated flux density" for both the average profile, if one is available, and for single pulses. This provides one way -- albeit roundabout -- to define things like giant pulses, by saying that a giant pulse is any single pulse with an integrated flux density at least some chosen factor larger than the integrated flux density of the integrated profile.