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Photo-z's with Bayesian priors on physical properties of galaxies
Masayuki Tanaka
0 – Photoz primer
1 – A new photoz code
2 – Some results
0 – photo-z primer
Info from an astronomical observation is fundamentally 2D.
Photon energy
Our physical understandingSpectral stretch (= redshift)
Cosmology
distance
Spectral energy distribution of galaxies
A sample BOSS/SDSS-III spectrum from Thomas+ 2013
Why don't you get spec-z's for all the galaxies?
That's impossible! Spec-z's are VERY expensive for two reasons.
1 – Depth:To get unbiased redshfits for i~22.5 objects on 8m telescopes, you need
~1 hour
Probably not a fair comparison, but if you just want to detect an i=22.5 object with imaging, you just need
10 seconds!
Why don't you get spec-z's for all the galaxies?
2 – Multiplexity:e.g., VLT/VIMOS: ~150 galaxies in one go
Again as a non-fair comparison, a single pointing with HSC (1.5sqdeg) detects >10^4 objects.
Spectroscopy vs. imaging
Technique spectral resolution depth Ngal (~redshift accuracy) (1h on 8m)
Low-res spectroscopy R~1000 i<~23 ~100
Broad-band imaging R~5 i~26 ~10^5
Spectroscopy is a technique to precisely measure redshifts for relatively bright galaxies.
Photometric redshift based on imaging data is a technique to infer redshifts of a large number of objects with a limited accuracy.
Three categories for photo-z estimators
1 – template fitting : old-fashioned but powerful technique
2 – numerical fitting (polynomial, random forest, ANN) : relatively new technique
3 – spatial clustering : very new technique
Template fitting technique
Use SEDs of galaxies as a priori knowledge and infer redshifts.
SEDs can be either observed ones, theoretical ones, PCA templates. But, it is often a problem whether you cover all the diversity of spectral types of galaxies at all redshifts.
Advantage is that you can go deeper than spec-z.
Template fitting technique
Numerical technique
Polynomial fitting by Connolly+ 1996.
There are many numerical techniques: artificial neural network, random forest, etc.
An unbiased training spec-z sample that uniformly covers the multi-color space is essential. Obviously, you cannot go beyond the spectroscopic limit. A good thing is that there is no physics involved here.
Numerical technique (machine learning)
There are many numerical techniques: artificial neural network, random forest, etc.
An unbiased training spec-z sample that uniformly covers the multi-color space is essential. Obviously, you cannot go beyond the spectroscopic limit. A good thing is that there is no physics involved here.
Collister and Lahav 2004
Numerical technique (machine learning)
Kind et al. 2013
There are many numerical techniques: artificial neural network, random forest, etc.
An unbiased training spec-z sample that uniformly covers the multi-color space is essential. Obviously, you cannot go beyond the spectroscopic limit. A good thing is that there is no physics involved here.
Cross-correlation with spec-z sample
Cross-correlation between photometric and spectroscopic sample:
If the spectroscopic objects are located within a narrow redshift slice,
Integrated angular cross-correlation:
measure this from data measurable UNmeasurable
Integrated dark matter correlation functiondN/dz of photometric sample
Refer to Menard+ 2013 for details
Cross-correlation with spec-z sample - continued
z
dN/dz
z
spectroscopic sample
If photometric sample has a narrow, single peak in dN/dz, then bias can be considered as a constant and its evolution can be ignored.
Cross-correlation with spec-z sample - continued
z
dN/dz
z
spectroscopic sample photometric sample
If photometric sample has a narrow, single peak in dN/dz, then bias can be considered as a constant and its evolution can be ignored.
dN/dz
Cross-correlation with spec-z sample - continued
z
dN/dz
z
spectroscopic sample
..but, if the photometric sample has multiple redshift peaks, then the bias evolution of the photometric sample is an issue.
Cross-correlation with spec-z sample - continued
z
dN/dz
z
spectroscopic sample
..but, if the photometric sample has multiple redshift peaks, then the bias evolution of the photometric sample is an issue.
dN/dz
photometric sample
Need bp(z) at these peaks to translate the clustering signal into dn/dz
Three categories for photo-z estimators
Template fitting: Pros: Can be applied to beyond spectroscopic flux limit. Generally works slow. Cons: Need to be calibrated against a 'reasonably' representative spec-z sample
Numerical fitting: Pros: No need to worry about physics. Works fast Cons: Need to be calibrated against 100% representative spec-z sample. Cannot be applied beyong spectroscopic limit.
Spatial clustering: Pros: Works for very faint galaxies. Cons: Need a large number of spec-z sample over a wide redshift range. But it does not have to be a representative sample. Cannot get redshift for individual galaxies. Bias evolution is an issue.
Three categories for photo-z estimators
Template fitting: Pros: Can be applied to beyond spectroscopic flux limit. Generally works slow. Cons: Need to be calibrated against a 'reasonably' representative spec-z sample
Numerical fitting: Pros: No need to worry about physics. Works fast Cons: Need to be calibrated against a representative spec-z sample. Cannot be applied beyond spectroscopic limit.
Spatial clustering: Pros: Works for very faint galaxies. Cons: Need a large number of spec-z sample over a wide redshift range. But it does not have to be a representative sample. Cannot get redshift for individual galaxies. Bias evolution is an issue.
Three categories for photo-z estimators
Template fitting: Pros: Can be applied to beyond spectroscopic flux limit. Generally works slow. Cons: Need to be calibrated against a 'reasonably' representative spec-z sample
Numerical fitting: Pros: No need to worry about physics. Works fast Cons: Need to be calibrated against 100% representative spec-z sample. Cannot be applied beyong spectroscopic limit.
Spatial clustering: Pros: Works for very faint galaxies. Cons: Need a large number of spec-z sample over a wide redshift range. But it does not have to be a representative sample. Cannot get redshift for individual galaxies. Bias evolution is an issue.
1 – A new photo-z code: overview
Motivation
You are probably not interested in muddy details of the photo-z business, but in short:
1 – as a galaxy person, I would like to know individual redshifts and physical properties. → clustering redshift is not an option
2 – I would like to go below the spectroscopic flux limit → template fitting is the only option
3 – Most templates used in the literature are observed ones at z=0, but we know galaxies evolve → generate SPS templates and apply Bayesian priors to let those templates evolve
The code outputs: -- P(galaxy), P(AGN), P(star) with corresponding redshifts -- stellar mass, SFR, and dust extinction fully marginalized over all the other parameters including redshift
The code finally got a name!
The code did not have a name for a long time. It has been called TANAKA just to distinguish it from other codes, but it is not a unique name – there are 1.3million Tanaka's in Japan! It is now tentatively called MIZUKI: MasayukI's photo-Z compUting KIt
a-1) Sample SED
a-2) Priors: N(z), SFR vs M*, extinctin vs SFR
Assume that we can reconstruct N(z) reasonably well with the 30-band photo-z in COSMOS and also assume this functional form:
data
functional fit
18<i<19 24<i<25
A 'floor' suggested by Hildebrandt+2012
a-2) Priors: N(z), SFR vs M*, extinctin vs SFR
SFR and stellar mass are correlated in star forming galaxies. That relation is known to evolve with redshift.
Wuyts et al. 2011
a-2) Priors: N(z), SFR vs M*, extinctin vs SFR
Sobral et al. 2012
SFR and extinction are known to correlate. It seems that correlation evolves with redshift.
d) Template error function
3 – Results
Assumed data set
The observed COSMOS grizY photometry as an input.
Assume the 30-band photo-z's as the truth table.
Consider objects down to i=25 for now.
It is REALLY BAD that we do not have the u-band photometry.
DO NOT EXPECT TO SEE GOOD PHOTO-Z'S IN THE FOLLOWING SLIDES!!!
'Raw' photo-z
dispersion f_outlier
0.100 33.5 %
Photo-z with template errfn
dispersion f_outlier
0.100 33.5 %
0.083 29.5 %
Photo-z with errfn + M*-SFR prior
dispersion f_outlier
0.100 33.5 %
0.083 29.5 %
0.073 26.9 %
Photo-z with errfn + M*-SFR + tau_V-SFR
dispersion f_outlier
0.100 33.5 %
0.083 29.5 %
0.073 26.9 %
0.065 22.3 %
Photo-z with errfn + M*-SFR + tau_V-SFR + N(z)
dispersion f_outlier
0.100 33.5 %
0.083 29.5 %
0.073 26.9 %
0.065 22.3 %
0.059 19.3 %
Is this code any better than the existing codes?
In this particular case, we got
i=24.0: f_outliers ~20% (Mizuki), ~30% (LePhare) i=25.0: f_outleirs ~35% (Mizuki), ~50% (LePhare)
So, it seems Mizuki is slightly better than LePhare.
HSC survey
Miyazaki-san made all of my points. I would encourage you to use data from HSC!
Systematic biasDahlen et al. 2013
Mizuki uncalibrated Mizuki calibrated
Systematic bias
Hildebrandt et al. 2013
(CFHTLS)
Mizuki calibrated
Is P(z) reliable?
Dahlen et al. 2013
dN/dz reconstruction
black: input
red: sum z_phot
green: sum P(z)
Use point estimates and discard z_phot>1.4...?
dN/dz reconstruction
black: input
red: sum z_phot
green: sum P(z)
<0.02
Observing condition dependent...
Nishizawa+ 2010:
4 – Summary
Summary
Evolving priors on physical properties of galaxies are useful!
A template error function is useful, too.
We now can get physical properties measured in a self-consistent manner.
Systematic photo-z offset. Why?
P(z) is not very precise at this point, but I will wait for real HSC photometry off the pipeline.
Need further work on dn/dz reconstruction and outlier clipping.
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