<p>In essence read of the peak flux value and if a point source this will be the same as your integrated flux.</p>

<p>to elaborate on this:</p>

<p>In this question your source appears to be comparable to your beam. so I would treat as a point source. - note you might also want to consider that many people apply a "match filter" to their data if dealing with faint point source emission - this smooths the map - increasing the effective beam size within the map and also there may be some flux loss (see for example: <a href="http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1707.00990" rel="nofollow noreferrer">http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1707.00990</a>)</p>

<p>You will see this (mJy/beam to mJy) is also discussed here: <a href="http://www.eaobservatory.org/jcmt/help/" rel="nofollow noreferrer">http://www.eaobservatory.org/jcmt/help/</a> </p>

<p>For a real point source, a peak brightness value reported in units of mJy is the same as a peak brightness value reported in mJy/beam.</p>

<p>But what happens if we have a map in mJy/beam and we want to obtain an integrated intensity value, a total flux value? We first sum up a number of pixels and now we want to get our units correct from mJy/beam to mJy…</p>

<p>Total Flux = flux summed over a number of pixels/(number of pixels in a beam)</p>

<p>Then your units are:</p>

<p>[mJy*pixels/beam] / [pixels/beam] = [mJy].</p>

<p>Now we know that For a Gaussian:</p>

<p>Beam Area =  2 × π × σ² [arcsec]</p>

<p>where the σ of the Gaussian beam can be calculated from the JCMT FWHM values at 850 and 450 microns (reminder the beam components are provided in Dempsey’s 2013 paper).</p>

<p>FWHM = 2 σ √(2 ln 2)   [arcsec]</p>

<p>So we can use the FWHM to obtain σ to calculate the Beam Area and report the beam area in terms of pixels:</p>

<p>number of pixels in a beam = Beam Area [arcsec] / (pixel length)²</p>

<p>Finally I should add you will also want to do an aperture correction - see Dempsey et al 2013's calibration paper if you are using an aperture of a different size than 60".</p>

CC BY-SA 3.0
2017-10-13T00:14:54.513Z
2017-10-13T00:14:54.513Z
Bubbles
<p>I have a fits file of the galaxy m87 produced by SCUBA 2 and I am wondering how I obtain the fluxes at 450 and 850 microns. the output image gives pixel magnitudes in mJy/beam where I want to find eh flux for a certain part of the galaxy. I am as far as summit the values of all pixels within an aperture but I am not sure where to go from there to obtain the flux as there are more than one pixel within the FWHM. say I have a an aperture of radius 1.5 pixels that gives a sum of 6985.04885203 mJy/beam with a pixel size of 3.99999999 arc seconds and a beam size of 13 arc seconds how do I obtain the flux for that aperture at that wavelength?</p>

CC BY-SA 3.0
2016-12-07T13:17:11.370Z
Are you looking for flux in  $\frac{photons}{m^2-Hz}$ ? Also, it's not clear what "beam" is here. Do you have the flux per spectral bandwidth in each pixel?  The point is: we could all go look up exactdly how SCUBA2 works, but it's friendlier if you provide the information so we know exactly what database you are working with.
Carl Witthoft
<galaxy><photometry>
How do I get flux density when I have mJy/beam , beam size and pixel size in an astronomical image
Luke
# How do I get flux density when I have mJy/beam , beam size and pixel size in an astronomical image

(Asked by: username_0 on 2016-12-06)

I have a fits file of the galaxy m87 produced by SCUBA 2 and I am wondering how I obtain the fluxes at 450 and 850 microns. the output image gives pixel magnitudes in mJy/beam where I want to find eh flux for a certain part of the galaxy. I am as far as summit the values of all pixels within an aperture but I am not sure where to go from there to obtain the flux as there are more than one pixel within the FWHM. say I have a an aperture of radius 1.5 pixels that gives a sum of 6985.04885203 mJy/beam with a pixel size of 3.99999999 arc seconds and a beam size of 13 arc seconds how do I obtain the flux for that aperture at that wavelength?

**Tags:** galaxy, photometry
> **Comments:**
> **username_1**: Are you looking for flux in  $\frac{photons}{m^2-Hz}$ ? Also, it's not clear what "beam" is here. Do you have the flux per spectral bandwidth in each pixel?  The point is: we could all go look up exactdly how SCUBA2 works, but it's friendlier if you provide the information so we know exactly what database you are working with.  

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## 1 answers

### Answer by username_2 on 2017-10-13. Score: 1

In essence read of the peak flux value and if a point source this will be the same as your integrated flux.

to elaborate on this:

In this question your source appears to be comparable to your beam. so I would treat as a point source. - note you might also want to consider that many people apply a "match filter" to their data if dealing with faint point source emission - this smooths the map - increasing the effective beam size within the map and also there may be some flux loss (see for example: <http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1707.00990>)

You will see this (mJy/beam to mJy) is also discussed here: <http://www.eaobservatory.org/jcmt/help/>

For a real point source, a peak brightness value reported in units of mJy is the same as a peak brightness value reported in mJy/beam.

But what happens if we have a map in mJy/beam and we want to obtain an integrated intensity value, a total flux value? We first sum up a number of pixels and now we want to get our units correct from mJy/beam to mJy…

Total Flux = flux summed over a number of pixels/(number of pixels in a beam)

Then your units are:

[mJy\*pixels/beam] / [pixels/beam] = [mJy].

Now we know that For a Gaussian:

Beam Area = 2 × π × σ² [arcsec]

where the σ of the Gaussian beam can be calculated from the JCMT FWHM values at 850 and 450 microns (reminder the beam components are provided in Dempsey’s 2013 paper).

FWHM = 2 σ √(2 ln 2) [arcsec]

So we can use the FWHM to obtain σ to calculate the Beam Area and report the beam area in terms of pixels:

number of pixels in a beam = Beam Area [arcsec] / (pixel length)²

Finally I should add you will also want to do an aperture correction - see Dempsey et al 2013's calibration paper if you are using an aperture of a different size than 60".


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