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#1




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; LyndenBell 1971; Schechter 1976; etc.)...but it has not all fully digested yet . TIA for any words of wisdom. PR 
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#2




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; LyndenBell 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 mz 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 functionswith the same number of free parametersgive better fits than power laws. What are the objects and what are your plans? 
#3




Luminosity Functions
"Phillip Helbigremove 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; LyndenBell 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




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




Luminosity Functions
"Phillip Helbigremove 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 socalled "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




Luminosity Functions
In article , "PoorRichard"
writes: "Phillip Helbigremove 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 socalled "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 KS 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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