How do you compute the integrated magnitude of various objects

I understand how to compute the integrated, or combined magnitude, of
a binary star system and a multiple star system. But how do you
compute the integrated magnitude of extended objects - like galaxies,
a comet nucleous or open clusters, assuming that you have some idea of
their average brightness and size? Can someone point me to a book or
article on the same? - Kurt

PrisNo6 wrote:

I understand how to compute the integrated, or combined magnitude, of
a binary star system and a multiple star system. But how do you
compute the integrated magnitude of extended objects - like galaxies,
a comet nucleous or open clusters, assuming that you have some idea of
their average brightness and size? Can someone point me to a book or
article on the same? - Kurt

Galaxy photometry table
http://casa.colorado.edu/~rachford/a...phot_data.html

http://www.google.com/search?q=calcu...de%22+gala xy

PrisNo6 wrote:

I understand how to compute the integrated, or combined magnitude, of
a binary star system and a multiple star system. But how do you
compute the integrated magnitude of extended objects - like galaxies,
a comet nucleous or open clusters, assuming that you have some idea of
their average brightness and size? Can someone point me to a book or
article on the same? - Kurt

Galaxy photometry table
http://casa.colorado.edu/~rachford/a...phot_data.html

http://www.google.com/search?q=calcu...de%22+gala xy

Sam Wormley wrote in message ...
PrisNo6 wrote: . . . [H]ow do you compute the integrated magnitude of
extended objects - like galaxies, . . .
Sam replied: snip - with website references

Sam, thanks for the reference regarding determining the integrated
magnitude of a galaxy from surface brightness:

http://casa.colorado.edu/~rachford/a...phot_data.html

From the references you provided and searching my library some more, I
ended up with:

SB_mpas = m_vi + 2.5 * (log_10 ( pi * ab ) ) (Eq. 1.0)

where

m_vi is the integrated magnitude
a is the major axis (not diameter) of the extended object in arcsecs
b is the major axis (not diameter) of the extended object in arcsecs
SB_mpas is the surface brightness in magnitudes per arcsec
pi * ab is the general equation for the area of an ellipsis; pi * r^2
being the special case for a circle.

Covington's Astrophotography in Appendix A gives an analogous formula
to that in the referenced web page for circular objects:

SB_mpas = m_vi + 2.5 * (log_10 ( ( pi * d^2) / 4 ) (Eq. 2.0)

whe d = diameter of the extended object in arcsecs

These appear to be variations on a more general rule that surface
brightness in MPAS equals the integrated magnitude plus the magnitude
of the surface area of the extended object - like a galaxy:

SB_mpas = m_vi + 2.5 * (log (surface area of object / arcsecs ) )
(Eq. 1.1)

So the converse equation (surface brightness to integrated magnitude)
is:

m_vi = SB_mpas - 2.5 * (log_10 (pi*ab)) (Eq. 3.0 )

m_vi = SB_mpas - 2.5 * (log_10 (pi) - 2.5 * (log_10 (ab) ) (Eq. 3.1)
m_vi = SB_mpas - 1.242875 - 2.5 * (log_10 (ab) ) (Eq. 3.2)

I have read about, but not applied, a DSO galaxy hunters a rule of
thumb that:

m_vi = SB_mpas - 9.0 (Eq. 4.0 ) or

SB_mpas = m_vi + 9.0 (Eq. 4.1)

which in sentence form means that the integrated magnitude of the
faintest galaxy (as listed in galaxy catalogues) detectable on a given
night is the surface brightness of the night sky (in mpas) on that
particular observing night minus 9.0.

If an "average" sized DSO galaxy is assumed to be 1/2 by 1 arcmin (or
30 arcsecs x 60 arcsecs), then the last two terms of equation 3.2
evaluate to:

1.242875 + 2.5 * (log_10 ( 1200 )) = 9.0

and Eq. 3.2 becomes the rule of thumb:

m_vi = SB_mpas - 9.0 (Eq. 4.0 )

I assume that this is where the galaxy observing rule of thumb comes
from.

I understand that for outstanding skies, the MPAS of a night sky is
around 21 MPAS (ZLM 6.2-6.3); for a more typical suburban light
polluted sky of ZLM 5.6, MPAS is around 20.0.

So, armed with a suitable cross-referencing table or equation
translating ZLM or NELM (naked eye limiting magnitude) in
sky-brightness in MPAS, I could then use online or planetarium
catalogues like your suggestion of:

http://casa.colorado.edu/~rachford/a...phot_data.html

to decide whether to try observing an undetected galaxy in better
skies on another night or, for large mpas differences, to filter
galaxies out of my observing list altogether?

From other (other than Sam - who provides so many other valuable
posts) DSO lurkers, do I have the right picture of how this works?

Thanks - Kurt

Sam Wormley wrote in message ...
PrisNo6 wrote: . . . [H]ow do you compute the integrated magnitude of
extended objects - like galaxies, . . .
Sam replied: snip - with website references

Sam, thanks for the reference regarding determining the integrated
magnitude of a galaxy from surface brightness:

http://casa.colorado.edu/~rachford/a...phot_data.html

From the references you provided and searching my library some more, I
ended up with:

SB_mpas = m_vi + 2.5 * (log_10 ( pi * ab ) ) (Eq. 1.0)

where

m_vi is the integrated magnitude
a is the major axis (not diameter) of the extended object in arcsecs
b is the major axis (not diameter) of the extended object in arcsecs
SB_mpas is the surface brightness in magnitudes per arcsec
pi * ab is the general equation for the area of an ellipsis; pi * r^2
being the special case for a circle.

Covington's Astrophotography in Appendix A gives an analogous formula
to that in the referenced web page for circular objects:

SB_mpas = m_vi + 2.5 * (log_10 ( ( pi * d^2) / 4 ) (Eq. 2.0)

whe d = diameter of the extended object in arcsecs

These appear to be variations on a more general rule that surface
brightness in MPAS equals the integrated magnitude plus the magnitude
of the surface area of the extended object - like a galaxy:

SB_mpas = m_vi + 2.5 * (log (surface area of object / arcsecs ) )
(Eq. 1.1)

So the converse equation (surface brightness to integrated magnitude)
is:

m_vi = SB_mpas - 2.5 * (log_10 (pi*ab)) (Eq. 3.0 )

m_vi = SB_mpas - 2.5 * (log_10 (pi) - 2.5 * (log_10 (ab) ) (Eq. 3.1)
m_vi = SB_mpas - 1.242875 - 2.5 * (log_10 (ab) ) (Eq. 3.2)

I have read about, but not applied, a DSO galaxy hunters a rule of
thumb that:

m_vi = SB_mpas - 9.0 (Eq. 4.0 ) or

SB_mpas = m_vi + 9.0 (Eq. 4.1)

which in sentence form means that the integrated magnitude of the
faintest galaxy (as listed in galaxy catalogues) detectable on a given
night is the surface brightness of the night sky (in mpas) on that
particular observing night minus 9.0.

If an "average" sized DSO galaxy is assumed to be 1/2 by 1 arcmin (or
30 arcsecs x 60 arcsecs), then the last two terms of equation 3.2
evaluate to:

1.242875 + 2.5 * (log_10 ( 1200 )) = 9.0

and Eq. 3.2 becomes the rule of thumb:

m_vi = SB_mpas - 9.0 (Eq. 4.0 )

I assume that this is where the galaxy observing rule of thumb comes
from.

I understand that for outstanding skies, the MPAS of a night sky is
around 21 MPAS (ZLM 6.2-6.3); for a more typical suburban light
polluted sky of ZLM 5.6, MPAS is around 20.0.

So, armed with a suitable cross-referencing table or equation
translating ZLM or NELM (naked eye limiting magnitude) in
sky-brightness in MPAS, I could then use online or planetarium
catalogues like your suggestion of:

http://casa.colorado.edu/~rachford/a...phot_data.html

to decide whether to try observing an undetected galaxy in better
skies on another night or, for large mpas differences, to filter
galaxies out of my observing list altogether?

From other (other than Sam - who provides so many other valuable
posts) DSO lurkers, do I have the right picture of how this works?

Thanks - Kurt

fisherka wrote:
[snip]
From the references you provided and searching my library some more, I
ended up with:

SB_mpas = m_vi + 2.5 * (log_10 ( pi * ab ) ) (Eq. 1.0)

where

m_vi is the integrated magnitude
a is the major axis (not diameter) of the extended object in arcsecs
b is the major axis (not diameter) of the extended object in arcsecs
SB_mpas is the surface brightness in magnitudes per arcsec

Surface brightness is brightness per unit area. So, rather than "mpas"
(magnitude per arc second), it should be MPSAS or magnitude per *square*
arcsecond.

pi * ab is the general equation for the area of an ellipsis; pi * r^2
being the special case for a circle.
[snip]

The above formula will produce a good approximation for galaxies. The pros add
fudge factors depending on galaxy type. But for this forum, the above formula
is plenty accurate.

I have read about, but not applied, a DSO galaxy hunters a rule of
thumb that:

m_vi = SB_mpas - 9.0 (Eq. 4.0 ) or

SB_mpas = m_vi + 9.0 (Eq. 4.1)

That will not convert from surface brightness (MPSAS) to integrated visual
magnitude. It is a rough conversion from brightness per square arcsecond to
brightness per square arcminute. The more accurate conversion is to subract or
add 8.9. But at 1:00 am, it's easier to work with whole numbers )

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
=============
Email: Remove "ic" from .comic above to respond

fisherka wrote:
[snip]
From the references you provided and searching my library some more, I
ended up with:

SB_mpas = m_vi + 2.5 * (log_10 ( pi * ab ) ) (Eq. 1.0)

where

m_vi is the integrated magnitude
a is the major axis (not diameter) of the extended object in arcsecs
b is the major axis (not diameter) of the extended object in arcsecs
SB_mpas is the surface brightness in magnitudes per arcsec

Surface brightness is brightness per unit area. So, rather than "mpas"
(magnitude per arc second), it should be MPSAS or magnitude per *square*
arcsecond.

pi * ab is the general equation for the area of an ellipsis; pi * r^2
being the special case for a circle.
[snip]

The above formula will produce a good approximation for galaxies. The pros add
fudge factors depending on galaxy type. But for this forum, the above formula
is plenty accurate.

I have read about, but not applied, a DSO galaxy hunters a rule of
thumb that:

m_vi = SB_mpas - 9.0 (Eq. 4.0 ) or

SB_mpas = m_vi + 9.0 (Eq. 4.1)

That will not convert from surface brightness (MPSAS) to integrated visual
magnitude. It is a rough conversion from brightness per square arcsecond to
brightness per square arcminute. The more accurate conversion is to subract or
add 8.9. But at 1:00 am, it's easier to work with whole numbers )

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
=============
Email: Remove "ic" from .comic above to respond

c (Bill Ferris) wrote in message ...
Surface brightness is brightness per unit area. So, rather than "mpas"
(magnitude per arc second), it should be MPSAS or magnitude per *square*
arcsecond.

Bill, thanks for pointing out the obvious blunder - square not circle
incidence. So, the above equations are wrong. Looks I'm going back
to the drawing board! - Thanks - Kurt

c (Bill Ferris) wrote in message ...
Surface brightness is brightness per unit area. So, rather than "mpas"
(magnitude per arc second), it should be MPSAS or magnitude per *square*
arcsecond.

Bill, thanks for pointing out the obvious blunder - square not circle
incidence. So, the above equations are wrong. Looks I'm going back
to the drawing board! - Thanks - Kurt