Baum (1962)
Colors of early type galaxies measured from 9 bands with a photometer were turned into a low resolution SED to determine distances of galaxy clusters relative to other clusters of galaxies.
--better cost efficiency if only approximate redshift is needed
PPT you may interested:
Talked about the influerence of bands to the redshift results
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&ved=0CHAQFjAI&url=http%3A%2F%2Fwww.astro.caltech.edu%2Ftwiki_phat%2Fpub%2FMain%2FPHATMeetingJPL%2FCoe.ppt&ei=hdPlUvniOs7hsATsu4L4DQ&usg=AFQjCNGXO4AQf9UqcLPXmLCeRI2GOORo3A&sig2=SqgvOU7wVamxblQKW3Qq1Q&bvm=bv.59930103,d.cWc&cad=rjt
Colors of early type galaxies measured from 9 bands with a photometer were turned into a low resolution SED to determine distances of galaxy clusters relative to other clusters of galaxies.
Koo (1985)
Colors (from photographic plate material) were compared to colors expected for
synthetic Bruzual-Charlot SEDs. Redshifts were estimated from iso-z lines in color- color diagrams.
Loh & Spillar (1986) used χ2-minimization for redshift estimates
Pello and others developed a method of `permitted’ redshifts; the intersection of the permitted redshift intervalls for all galaxy colors measured defines `the’ redshift of a galaxy.
Photometric redshifts have become very popular since the middle of the 1990s
--well calibrated, deep multi-waveband data (HDF, other deep fields, SDSS)
--representative spectroscopic data sets available to test method (Keck, VLT,SDSS...)
Colors (from photographic plate material) were compared to colors expected for
synthetic Bruzual-Charlot SEDs. Redshifts were estimated from iso-z lines in color- color diagrams.
Loh & Spillar (1986) used χ2-minimization for redshift estimates
Pello and others developed a method of `permitted’ redshifts; the intersection of the permitted redshift intervalls for all galaxy colors measured defines `the’ redshift of a galaxy.
Photometric redshifts have become very popular since the middle of the 1990s
--well calibrated, deep multi-waveband data (HDF, other deep fields, SDSS)
--representative spectroscopic data sets available to test method (Keck, VLT,SDSS...)
Photometric Redshifts: Methods
Template based:
color-space tessellation, χ2-minimization, maximum likelihood, Baysian ... uses physical information: SED’s (sizes, compactness...),
... and therefore biased extrapolates reasonably ok into unknown territory
Learning based:
Nearest Neighbour, Kd-tree, Direct fitting, Neural Networks, Support Vector Machines, Kernel Regression, Regression Trees & Random Forests...
ignores physical information: and therefore unbiased,
can uncover unknown dependencies requires large training set, bad in extrapolation
ABOVE IS FROM: http://www.mpe.mpg.de/opinas/talks/photoz_rb.pdf
Template based:
color-space tessellation, χ2-minimization, maximum likelihood, Baysian ... uses physical information: SED’s (sizes, compactness...),
... and therefore biased extrapolates reasonably ok into unknown territory
Learning based:
Nearest Neighbour, Kd-tree, Direct fitting, Neural Networks, Support Vector Machines, Kernel Regression, Regression Trees & Random Forests...
ignores physical information: and therefore unbiased,
can uncover unknown dependencies requires large training set, bad in extrapolation
Direct Fitting
developed by Connolly et al 1995, applied to z=0-0.6 galaxies with limiting magnitudes in U-, B-, R- and I-photographic plate-bands of 23, 22, 21, 20.
The redshift is described as a linear or quadratic function of the magnitudes of the galaxies in several bands. Coefficients are determined with a spectroscopic training set by linear regression.
developed by Connolly et al 1995, applied to z=0-0.6 galaxies with limiting magnitudes in U-, B-, R- and I-photographic plate-bands of 23, 22, 21, 20.
The redshift is described as a linear or quadratic function of the magnitudes of the galaxies in several bands. Coefficients are determined with a spectroscopic training set by linear regression.
`advantage’: no physical assumptions to be made beyond the fact that the training set and
data set are statistically very similar.
`disadvantage’: coefficients do not apply to data sets obtained to fainter or higher redshift or modestly different type of galaxies.
Method has been applied in three-dimensional color-space to HDF data by Wang et al. 1998
--> other option: fit combination of SSPs or CSP + dust (old+medium+young+dust)
`disadvantage’: coefficients do not apply to data sets obtained to fainter or higher redshift or modestly different type of galaxies.
Method has been applied in three-dimensional color-space to HDF data by Wang et al. 1998
Template methods
Measured colors (or fluxes) are compared to colors (or fluxes) predicted for various
template SEDs and redshifts; best fitting redshift, SED-type and object type (star,
galaxy QSO) are derived. Methods: BPZ (Benitez), Hyperz (Bolzanella/Pello),
LePhare (Arnouts), COSMOS (Mobasher), ZEBRA (Feldmann et al.), PHOTO-z
(Bender), ...
Which templates ?
-- Coleman, Wu & Weedman (1990), empirical spectro-photometric SEDs from low-z gals. -- templates derived from stellar population models, eg. BC-templates
Which templates ?
-- Coleman, Wu & Weedman (1990), empirical spectro-photometric SEDs from low-z gals. -- templates derived from stellar population models, eg. BC-templates
-- self-calibrated, optimized or semi-empirical templates preferred
-- difficulties: --- restframe UV-extension of the SEDs galaxies (use
synthetic spectra or broad band photometry)
--- finding a sufficiently representative SED set
How many templates?
--depends on science question ..., too many may hurt!
--eigenspectra can provide continuous set (method: Connolly et al 1995, applied by Yip et al 2004 to 170000 SDSS-spectra with r<18 and median redshift of 0.1),
--> 3 eigenspectra are sufficient to describe the variances of the SEDs up to 2% --> 5 more appropriate for large redshift range
--> ideally, make eigenspectra dependent on redshift
synthetic spectra or broad band photometry)
--- finding a sufficiently representative SED set
How many templates?
--depends on science question ..., too many may hurt!
--eigenspectra can provide continuous set (method: Connolly et al 1995, applied by Yip et al 2004 to 170000 SDSS-spectra with r<18 and median redshift of 0.1),
--> 3 eigenspectra are sufficient to describe the variances of the SEDs up to 2% --> 5 more appropriate for large redshift range
--> ideally, make eigenspectra dependent on redshift
Baysian photometric redshift estimates:
prob(B and A) = prob(A and B) = prob(A|B)*prob(B) = prob(B|A)*prob(A)
=> Bayes’ theorem:
prob(B|A) * prob(A) /prob(A|B) = prob(B)
now, translate: A=Model, B=Data:
prob(data|model) * prob(model)/ prob(model|data) =prob(data)
prob(model) is called the prior probability for the model (parameters), prob(data) is a number and thus simply a normalization parameter.
prob(model) is usually ignored in χ2-minimization and maximum likelihood, it can be used to include our prior knowledge/prejudice: e.g. no red ellipticals at z>1, no low metallicity objects at low z, no galaxies with MB < -26, low Sersic n indicates late type SED, large apparent size means low z and thus helps to improve photometric redshifts.
prob(B and A) = prob(A and B) = prob(A|B)*prob(B) = prob(B|A)*prob(A)
=> Bayes’ theorem:
prob(B|A) * prob(A) /prob(A|B) = prob(B)
now, translate: A=Model, B=Data:
prob(data|model) * prob(model)/ prob(model|data) =prob(data)
prob(model) is called the prior probability for the model (parameters), prob(data) is a number and thus simply a normalization parameter.
prob(model) is usually ignored in χ2-minimization and maximum likelihood, it can be used to include our prior knowledge/prejudice: e.g. no red ellipticals at z>1, no low metallicity objects at low z, no galaxies with MB < -26, low Sersic n indicates late type SED, large apparent size means low z and thus helps to improve photometric redshifts.
PPT you may interested:
Talked about the influerence of bands to the redshift results
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&ved=0CHAQFjAI&url=http%3A%2F%2Fwww.astro.caltech.edu%2Ftwiki_phat%2Fpub%2FMain%2FPHATMeetingJPL%2FCoe.ppt&ei=hdPlUvniOs7hsATsu4L4DQ&usg=AFQjCNGXO4AQf9UqcLPXmLCeRI2GOORo3A&sig2=SqgvOU7wVamxblQKW3Qq1Q&bvm=bv.59930103,d.cWc&cad=rjt
收集程序的网站：
photo Z的程序
eazy
Brammer 2008
Brammer 2008
BPZ
Also see Narciso Benitez's BPZ page, including BPZ v1.98b.
ZEBRA
can get age, max et al.
hyperz Bolzonella 2000
lephase 2006
光谱拟合程序FAST
The main difference with HYPERZ is that (1) FAST fits fluxes instead of magnitudes, (2) you can completely define your own grid of input stellar population parameters, (3) you can easily input photometric redshifts and their confidence intervals, and (4) FAST calculates calibrated confidence intervals for all parameters. However, note that, although it can be used as one, FAST is not a photometric redshift code
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