[gnuastro-commits] master 4c78d1c 2/2: Book: added discussion on converting pixels to microJanskys

[Mohammad Akhlaghi]

branch: master
commit 4c78d1c78e12e2907106e762e57a169cf4d7af01
Author: Mohammad Akhlaghi <mohammad@akhlaghi.org>
Commit: Mohammad Akhlaghi <mohammad@akhlaghi.org>

    Book: added discussion on converting pixels to microJanskys
    
    In many cases, it is useful to convert an image's pixel values to
    microJanskies (to compare pixel values between various instruments or
    filters).
    
    With this commit, a discussion has been added in the "Brightness, Flux,
    Magnitude and Surface brightness" section of the book.
    
    This was done after a discussion with Ignacio Trujillo, Raul Infante-Sainz
    and Samane Raji.
---
 doc/announce-acknowledge.txt |  2 ++
 doc/gnuastro.texi            | 25 ++++++++++++++++++++++++-
 2 files changed, 26 insertions(+), 1 deletion(-)

diff --git a/doc/announce-acknowledge.txt b/doc/announce-acknowledge.txt
index 2457afd..8ff3cba 100644
--- a/doc/announce-acknowledge.txt
+++ b/doc/announce-acknowledge.txt
@@ -5,7 +5,9 @@ Raul Infante-Sainz
 Alberto Madrigal
 Sylvain Mottet
 Francois Ochsenbein
+Samane Raji
 Zahra Sharbaf
+Ignacio Trujillo
 
 
 
diff --git a/doc/gnuastro.texi b/doc/gnuastro.texi
index b3d2c71..f4f0539 100644
--- a/doc/gnuastro.texi
+++ b/doc/gnuastro.texi
@@ -18668,12 +18668,35 @@ Using the zero point magnitude (@mymath{Z}), we can 
write the magnitude relation
 
 @dispmath{m = -2.5\log_{10}(B) + Z}
 
+@cindex Janskys (Jy)
+@cindex AB magnitude
+@cindex Magnitude, AB
+Having the zero point of an image, you can convert its pixel values to 
physical units of microJanskys (or @mymath{\mu{}Jy}) to enable direct 
pixel-based comparisons with images from other instruments (just note that this 
assumes instrument and observation signatures are corrected, things like the 
flat-field or the Sky).
+This conversion can be done with the fact that in the AB magnitude 
standard@footnote{@url{https://en.wikipedia.org/wiki/AB_magnitude}}, 
@mymath{3631Jy} corresponds to the zero-th magnitude, therefore 
@mymath{B\equiv3631\times10^{6}\mu{Jy}} and @mymath{m\equiv0}.
+We can therefore estimate the brightness (@mymath{B_z}, in @mymath{\mu{Jy}}) 
corresponding to the image zero point (@mymath{Z}) using this equation:
+
+@dispmath{m - Z = -2.5\log_{10}(B/B_z)}
+@dispmath{0 - Z = -2.5\log_{10}({3631\times10^{6}\over B_z})}
+@dispmath{B_z = 3631\times10^{\left(6 - {Z \over 2.5} \right)} \mu{Jy}}
+
+@cindex SDSS
+Because the image zero point corresponds to a pixel value of @mymath{1}, the 
@mymath{B_z} value calculated above also corresponds to a pixel value of 
@mymath{1}.
+Therefore you simply have to multiply your image by @mymath{B_z} to convert it 
to @mymath{\mu{Jy}}.
+Don't forget that this only applies when your zero point was also estimated in 
the AB magnitude system.
+On the command-line, you can easily estimate this value for a certain zero 
point with AWK, then multiply it to all the pixels in the image with 
@ref{Arithmetic}.
+For example let's assume you are using an SDSS image with a zero point of 22.5:
+
+@example
+bz=$(echo 22.5 | awk '@{print 3631 * 10^(6-$1/2.5)@}')
+astarithmetic sdss.fits $bz x --output=sdss-in-muJy.fits
+@end example
+
 @cindex Steradian
 @cindex Angular coverage
 @cindex Celestial sphere
 @cindex Surface brightness
 @cindex SI (International System of Units)
-Another important concept is the distribution of brightness over its area.
+Another important concept is the distribution of an object's brightness over 
its area.
 For this, we define the @emph{surface brightness} to be the magnitude of an 
object's brightness divided by its solid angle over the celestial sphere (or 
coverage in the sky, commonly in units of arcsec@mymath{^2}).
 The solid angle is expressed in units of arcsec@mymath{^2} because 
astronomical targets are usually much smaller than one steradian.
 Recall that the steradian is the dimension-less SI unit of a solid angle and 1 
steradian covers @mymath{1/4\pi} (almost @mymath{8\%}) of the full celestial 
sphere.