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Luminosity Functions



 
 
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  #1  
Old August 13th 07, 07:49 PM posted to sci.astro.research
PoorRichard
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Posts: 6
Default Luminosity Functions

A few details and a question.

I have a sample of n objects (all of the same type).

The n objects constitute all of the known ones (from literature/databases)
in a certain region of the sky, R.

I then consulted a survey catalog, a survey that covered R. Luminosities
were computed for each (detected) object using the catalog flux data. Upper
limits were assumed for censored objects.

-


My question is, what approach for computing a (meaningful) LF is best in
this situation? I have been reading many of the major papers on LFs (Schmidt
1968; Lynden-Bell 1971; Schechter 1976; etc.)...but it has not all fully
digested yet .

TIA for any words of wisdom.


PR
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  #2  
Old August 13th 07, 10:28 PM posted to sci.astro.research
Phillip Helbig---remove CLOTHES to reply
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Posts: 198
Default Luminosity Functions

In article , "PoorRichard"
writes:

My question is, what approach for computing a (meaningful) LF is best in
this situation? I have been reading many of the major papers on LFs (Schmidt
1968; Lynden-Bell 1971; Schechter 1976; etc.)...but it has not all fully
digested yet .


We need one additional piece of information. Are these objects and
cosmologically significant distances? If so, then there is the whole
issue of calculating absolute magnitudes (which is what luminosity
functions are usually concerned with) from apparent magnitudes, and
volumes (which is what luminosity functions are usually concerned with)
from redshift intervals (and angles)---both of which depend on the
cosmological model. If these are objects at cosmological distances,
then the question arises as to whether you really need the LF or just
some parameterisation of the m-z plane. Depending on what you need it
for, you might not even need to parameterise it at all.

Also, don't assume too quickly that the LF is a power law. There are
cases when other functions---with the same number of free
parameters---give better fits than power laws.

What are the objects and what are your plans?
  #3  
Old August 14th 07, 07:38 AM posted to sci.astro.research
PoorRichard
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Posts: 6
Default Luminosity Functions

"Phillip Helbig---remove CLOTHES to reply"
wrote in message ...
In article , "PoorRichard"
writes:

My question is, what approach for computing a (meaningful) LF is best in
this situation? I have been reading many of the major papers on LFs

(Schmidt
1968; Lynden-Bell 1971; Schechter 1976; etc.)...but it has not all fully
digested yet .


We need one additional piece of information. Are these objects and
cosmologically significant distances?



Ah yes, that is important! The objects (type 2 AGN) are fairly local; z
0.03. I am dealing with cm wavelength.

Thanks
  #4  
Old August 15th 07, 07:49 AM posted to sci.astro.research
Phillip Helbig---remove CLOTHES to reply
external usenet poster
 
Posts: 198
Default Luminosity Functions

In article , "PoorRichard"
writes:

We need one additional piece of information. Are these objects and
cosmologically significant distances?


Ah yes, that is important! The objects (type 2 AGN) are fairly local; z
0.03. I am dealing with cm wavelength.


OK, the cosmological redshift is negligible; that makes things a lot
simpler.

Next question.

Are you interested in the number of objects of a given absolute
luminosity per volume, or the number of objects of a given apparent
magnitude per redshift interval? This doesn't really matter since the
conversion is trivial at these redshifts, but it might simplify the
discussion.

Important questions: what is the actual problem you are workin on? How
large is the data set? What are the selection criteria and how complete
is the sample?
  #5  
Old August 24th 07, 09:06 AM posted to sci.astro.research
PoorRichard
external usenet poster
 
Posts: 6
Default Luminosity Functions

"Phillip Helbig---remove CLOTHES to reply"
wrote in message ...

Are you interested in the number of objects of a given absolute
luminosity per volume, or the number of objects of a given apparent
magnitude per redshift interval? This doesn't really matter since the
conversion is trivial at these redshifts, but it might simplify the
discussion.


Hello. Good question. The former is what I am after. I have been playing
around with logarithmic bins of width delta_L = 10^.4 (one so-called "radio
magnitude").

Important questions: what is the actual problem you are workin on? How
large is the data set? What are the selection criteria and how complete
is the sample?


As described above, I compiled from the literature a list of all known
objects, of the type, in a region of the sky that was covered by a
particular survey. n ~ 100. I am interested in the various radio statistics
of a sample of the objects, at the wavelength of the survey. As for the
completeness of the sample, that is a good question. For one thing, I
restricted z 0.03. How might I further test such a sample for
completeness?

tia
  #6  
Old August 30th 07, 08:43 AM posted to sci.astro.research
Phillip Helbig---remove CLOTHES to reply
external usenet poster
 
Posts: 198
Default Luminosity Functions

In article , "PoorRichard"
writes:

"Phillip Helbig---remove CLOTHES to reply"
wrote in message ...

Are you interested in the number of objects of a given absolute
luminosity per volume, or the number of objects of a given apparent
magnitude per redshift interval? This doesn't really matter since the
conversion is trivial at these redshifts, but it might simplify the
discussion.


Hello. Good question. The former is what I am after.


OK, then presumably you are more interested in the physical properties
of the objects rather than what is actually observed. Fortunately,
converting between observed z and apparent brightness to physical volume
and absolute brightness can be done independently of the cosmological
model at your low redshifts.

I have been playing
around with logarithmic bins of width delta_L = 10^.4 (one so-called "radio
magnitude").


In general, I would recommend not using bins. You automatically
introduce several free parameters: number of bins, boundaries of bins
etc. Even if one decides for some "objective scheme", there are
several: same number of objects per bin, bins of equal width etc and the
number of bins is still a free parameter.

I would recommend constructing the cumulative luminosity function (i.e.
number of objects brighter than a certain radio flux) and fit the
parameters of the function to that. Of course, there is still the
question of what function to fit. Traditionally, a power law is
assumed. However, it is in some cases possible to get a better fit
using another function with the same number of free parameters. (Check
out Lutz Wisotzki's article on QSO LFs in ASTRONOMISCHE NACHRICHTEN from
a few years ago.) You can quantify your goodness of fit via standard
statistical techniques. As long as it is not too bad but also not to
good, you're probably OK. When you are done, you can compare the sample
to the fitted function with a K-S test.

As described above, I compiled from the literature a list of all known
objects, of the type, in a region of the sky that was covered by a
particular survey. n ~ 100. I am interested in the various radio statistics
of a sample of the objects, at the wavelength of the survey. As for the
completeness of the sample, that is a good question. For one thing, I
restricted z 0.03. How might I further test such a sample for
completeness?


OK, but maybe it is complete to z = 0.03. How were they selected? The
survey (it seems there was only 1) must have certain detection
thresholds based on surface brightness, brightness, proximity to another
object etc. If the physical objects cover a range of surface
brightnesses, this might be an issue. A certain number of objects might
be missed if they are too close to other objects. The brightness and
surface brightness criteria might also depend on the distance between
the objects (i.e. there might be a general lower limit of brightness for
the survey, but I might miss an object at the lower limit if it is very
near a bright object).
 




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