What Is the Schechter Function?

[jl294]

Schechter Function...

I''m very confused with what the difference is between the Schechter Function and 'Maximum likelihood method' or 1/Vmax method? Are the later two methods to be applied to the Schechter or are they completely different functions to calculate LF altogether?

Cheers

 

[zhermes]

These are completely different things. The Schechter function describes the luminosity function of galaxies [see: http://en.wikipedia.org/wiki/Luminosity_function_(astronomy ) ]; while the maximum likelihood and 1/vmax methods are statistical methods of fitting a function (e.g. the Schechter function) to a set of data [see: http://en.wikipedia.org/wiki/Maximum_likelihood ]

 

[jl294]

OK. What do you think is the best method for fitting Schechter function for Galaxy Groups? The distance is roughly similar for these galaxies, so 1/Vmax method wouldn't be applicable right?

Cheers

 

[zhermes]

I'm not sure, I've never done it myself. I'm sure it depends on the situation---and I'm sure you're right, if the distances are comparable, 1/Vmax isn't doing much.
I think there is also a lot of variety on how to implement a maximum likelihood method---I don't think its a specific algorithm.

 

[pmacias]

The Schechter Function is a mathematical function used in astronomy to describe the distribution of galaxies in a given volume of space. It is often used to model the luminosity function (LF) of galaxies, which is a measure of the number of galaxies with a given luminosity. The Schechter Function was first proposed by astronomer Paul Schechter in 1976 and has since been widely used in studies of galaxy populations.

The Schechter Function is a power law function that has three parameters: α, M*, and φ*. α represents the slope of the function at the faint end, M* is the characteristic magnitude at which the function turns over, and φ* is the normalization factor. These parameters can be determined by fitting the Schechter Function to observational data.

The Maximum Likelihood Method and 1/Vmax Method are two different statistical techniques used to estimate the parameters of the Schechter Function. These methods take into account the completeness of the data and allow for a more accurate determination of the parameters. They are not separate functions, but rather methods to calculate the parameters of the Schechter Function.

In summary, the Schechter Function is a mathematical function used to describe the distribution of galaxies, while the Maximum Likelihood Method and 1/Vmax Method are statistical techniques used to estimate the parameters of this function. They are not separate functions, but rather tools used to analyze and understand galaxy populations.