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.