<p>For starters, let's say we observe a pulsar for a certain amount of time. We're interested in getting its <em>integrated profile</em>, which means we fold the data at the spin period of the pulsar and average it out, which removes noise. The integrated profile is essentially a plot of flux density as a function of rotational phase. I'm going to call it simply the <em>profile</em> for now, to avoid confusion.</p>
<ul>
<li><p>We then define the <strong>peak flux density</strong> <span class="math-container">$S_{\mathrm{peak}}$</span> 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.</p>
</li>
<li><p>We get the <strong>mean flux density</strong> <span class="math-container">$S_{\mathrm{mean}}$</span> by averaging the flux density over one rotation period. If you want, you think of it using the <em>equivalent width</em> of the profile <span class="math-container">$W$</span>, leading to the relation
<span class="math-container">$$S_{\mathrm{mean}}=\frac{W}{P}S_{\mathrm{peak}}$$</span>
with <span class="math-container">$P$</span> the rotation period, although this is just reorganizing the equation for the definition of equivalent width.</p>
</li>
<li><p><strong>Integrated flux density</strong> 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, <span class="math-container">$S_{\mathrm{mean}}$</span> -- 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 &quot;integrated flux density&quot; 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.</p>
</li>
<li><p><strong>Pulse flux density</strong> could also mean a variety of things. I'd guess it's referring to the single pulse equivalent of integrated flux density, but it depends on context.</p>
</li>
</ul>
<p>If you can get your hands on a copy, the <em>Handbook of Pulsar Astronomy</em> briefly talks about some of these terms.</p>

CC BY-SA 4.0
2023-08-29T15:29:55.917Z
2023-08-29T15:29:55.917Z
HDE 226868
<p>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 &quot;peak flux density&quot;, &quot;integrated flux density&quot;, &quot; mean flux density&quot;, and &quot;pulse flux density&quot; of pulsars in radio.</p>

<observational-astronomy><radio-astronomy><terminology><pulsar>
What are the differences between different types of flux density in radio astronomy?
tzu18
# What are the differences between different types of flux density in radio astronomy?

(Asked by: username_0 on 2023-08-29)

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.

**Tags:** observational-astronomy, radio-astronomy, terminology, pulsar

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## 1 answers

### Answer by username_1 on 2023-08-29. Score: 2 | Accepted answer

For starters, let's say we observe a pulsar for a certain amount of time. We're interested in getting its *integrated profile*, which means we fold the data at the spin period of the pulsar and average it out, which removes noise. The integrated profile is essentially a plot of flux density as a function of rotational phase. I'm going to call it simply the *profile* for now, to avoid confusion.

* 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.
* **Pulse flux density** could also mean a variety of things. I'd guess it's referring to the single pulse equivalent of integrated flux density, but it depends on context.

If you can get your hands on a copy, the *Handbook of Pulsar Astronomy* briefly talks about some of these terms.


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