EAZY: A Fast, Public Photometric Redshift Code

Gabriel B. Brammer; Pieter G. van Dokkum; Paolo Coppi

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EAZY: A Fast, Public Photometric Redshift Code

Gabriel B. Brammer, Pieter G. van Dokkum, Paolo Coppi

arXiv:0807.1533v1Jul 10, 2008astro-ph

TL;DR

EAZY targets photometric-redshift estimation when spectroscopy is unavailable or biased, a common challenge for faint galaxy surveys. It combines flexible template fitting, priors, and model-derived defaults, and performs well on public datasets while providing reliability information and explicit limitations.

Problem
Photometric-redshift calibration is difficult when spectroscopic redshifts are unavailable or represent a biased subset, especially for faint K-selected galaxies.
Method
EAZY fits nonnegative linear combinations of templates and uses model-derived templates and priors plus a wavelength-dependent template-error function instead of spectroscopic-sample training.
Results
A 1-sigma scatter of 0.034 in dz/(1+z) is reported for K-selected samples in CDF-South and other deep fields.
Takeaways & Limitations
EAZY provides photometric redshifts and formal uncertainties for deep surveys lacking representative spectroscopic calibration samples.
Takeaways & Limitations
Catastrophic outliers can arise from template mismatch, color-redshift degeneracies, anomalous photometry, or incorrect spectroscopic matches or identifications.

Abstract

from arXiv · show

We describe a new program for determining photometric redshifts, dubbed EAZY. The program is optimized for cases where spectroscopic redshifts are not available, or only available for a biased subset of the galaxies. The code combines features from various existing codes: it can fit linear combinations of templates, it includes optional flux- and redshift-based priors, and its user interface is modeled on the popular HYPERZ code. A novel feature is that the default template set, as well as the default functional forms of the priors, are not based on (usually highly biased) spectroscopic samples, but on semi-analytical models. Furthermore, template mismatch is addressed by a novel rest-frame template error function. This function gives different wavelength regions different weights, and ensures that the formal redshift uncertainties are realistic. We introduce a redshift quality parameter, Q_z, that provides a robust estimate of the reliability of the photometric redshift estimate. Despite the fact that EAZY is not "trained" on spectroscopic samples, the code (with default parameters) performs very well on existing public datasets. For K-selected samples in CDF-South and other deep fields we find a 1-sigma scatter in dz/(1+z) of 0.034, and we provide updated photometric redshift catalogs for the FIRES, MUSYC, and FIREWORKS surveys.

1. INTRODUCTION

Photometric redshifts are essential for faint galaxies beyond spectroscopic reach, but their reliability depends strongly on template selection and representative calibration data. EAZY addresses biased or incomplete spectroscopy with model-derived templates, priors, and template-error weighting.

Motivation: Photometric redshifts are used almost exclusively for galaxies fainter than R ∼25, because spectroscopic samples are generally limited to relatively bright optical galaxies.Template fitting derives redshifts by comparing observed broad- or medium-band photometry with synthetic photometry across templates and redshifts.
Prior approaches: Existing photometric-redshift codes differ in how they generate synthetic photometry and interpret residuals, including χ2 minimization, linear template combinations, and Monte Carlo methods.Examples include HYPERZ, ImpZ, Le PHARE, and GREGZ.
Sources of reliability: Reliable photometric redshifts require high-quality, multi-band photometry that samples strong continuum features such as Lyman or Balmer breaks.The passage identifies template-set selection as especially important when photometry is otherwise good.
Calibration challenge: Iteratively adapting templates can improve photometric-redshift results, but evaluating that optimization requires a large, random spectroscopic subset of the full photometric sample.That assumption is often violated for samples substantially fainter than the spectroscopic limit.
EAZY approach: EAZY is designed for incomplete or biased spectroscopy by using a wavelength-dependent template-error function, linear template combinations, priors, and semi-analytical-model defaults.The default template set and redshift-magnitude priors are derived from semi-analytical models rather than spectroscopic training samples.

2. IMPLEMENTATION

EAZY estimates photometric redshifts by fitting templates across a redshift grid, using nonnegative template combinations, model-derived template sets and priors, and wavelength-dependent template errors.

Basic algorithm: EAZY minimizes flux residuals over a user-defined redshift grid, fitting synthetic filter fluxes to observed fluxes with their uncertainties.Fits are performed in linear flux space, allowing proper treatment of flux errors and negative measurements.
Basic algorithm: Nonnegative linear combinations of templates address galaxies that are poorly represented by any single template.The code supports one-, two-, or all-template fits, trading accuracy against computational cost.
Optimized template set: The optimized template set uses nonnegative matrix factorization of stellar-population models and semi-analytic-model photometry rather than spectroscopic calibration samples.Five PÉGASE-based templates are supplemented by a young, dusty template because the semi-analytic models lack extremely dusty galaxies.
Optimized template set: The model-derived templates span a broader range of optical-NIR colors than the empirical CK set and contain more realistic rest-UV information.The additional UV coverage is important when optical filters sample rest-frame ultraviolet wavelengths.
Template error function: The rest-frame template error function weights wavelength regions according to residual mismatch, with lowest errors in the optical and larger errors in the UV and NIR.Its shape reflects variable dust extinction in the UV and uncertain stellar populations, thermal dust emission, and PAH features in the NIR.
Bayesian prior and outputs: Magnitude-based Bayesian priors constrain redshift probabilities, while posterior outputs include the maximum-probability redshift zp and marginalized estimate zmp.The priors are derived from model redshift distributions in magnitude bins; zmp smooths small-scale systematics and permits a coarse redshift grid.

3. APPLICATION

EAZY is evaluated on diverse deep-field photometric catalogs without explicit spectroscopic calibration, using nearly 2000 spectroscopic redshifts as an assessment sample. Its default configuration performs well overall, while template choices, simultaneous fitting, priors, and neural-network comparisons reveal important differences and limitations.

Evaluation sample: 1989 spectroscopic redshifts spanning 0 < zspec ≲ 4 were collected to evaluate EAZY on combined deep multi-wavelength survey catalogs.The spectroscopic sample was used to assess, rather than explicitly calibrate, the photometric redshifts.
Default performance: σ = 0.034 for the entire spectroscopic sample, increasing to σ = 0.075 above zspec > 1.5.Systematic deviations are generally small, but zphot underestimates zspec by approximately 5% at z = 1.0−1.4.
Default performance: 5% of the spectroscopic sample are catastrophic outliers, defined by ∆z/(1 + z) > 5σ.The sample was not cut based on signal-to-noise or possible AGN indicators, which could contribute to poor estimates.
Parameter tests: The best template and parameter set significantly lowers the number of sources with ∆z/(1+z) > 0.2, although the number of 5σ outliers is nearly constant across configurations.Without the template error function, most outliers have zphot >> zspec, potentially scattering bright low-redshift galaxies into high-redshift samples.
Template tests: The synthetic PÉGASE templates reduce systematic effects relative to empirical templates without requiring spectroscopic calibration corrections.Empirical templates produce higher scatter and systematic underestimation over 0.5 < zspec < 1.5, while BR07 templates show zphot systematically low by ∆z ∼0.2 above zspec > 1.5.
Template tests: Simultaneously fitting multiple PÉGASE templates produces a striking reduction in σ compared with single-template fits.The trade-off is that single-template spectral classification is unavailable, while improved precision may support more physical sample separations using rest-frame colors.
Prior tests: The redshift prior generally improves zphot but does not reliably discriminate between multiple probability peaks.It can resolve some Balmer-break/Lyman-break degeneracies, but fails for other galaxies near zspec ∼3 with zphot ∼0.2.
Neural-network comparison: EAZY has lower scatter than ANNz in the full MUSYC-HDFS sample and among 18 galaxies at zspec > 2.The reported values are σ = (0.046, 0.100) for EAZY and ANNz in the full sample, and σ = (0.075, 0.105) for the high-redshift subset.

4. RELIABILITY OF PHOTOMETRIC REDSHIFTS

EAZY’s confidence intervals generally provide reasonable uncertainty estimates, while Q_z helps identify less reliable redshifts. Tests also show that modest photometric changes and limited filters can produce systematic effects that representative spectroscopic samples may miss.

4.1. Confidence intervals: 41% of sources fall outside the nominal 68% confidence interval, compared with 32% expected, but a 0.01 × (1 + zspec) expansion reduces discrepancies to 29%.Monte Carlo simulations support the consistency of the probability distributions and confidence intervals with the zphot distributions produced from perturbed fluxes.
4.2. Reliability parameter: A small number of sources lie well outside even the 99% confidence intervals because of template mismatch, color-redshift degeneracies, anomalous photometry, or spectroscopic errors.Broad or multimodal probability distributions can help identify some catastrophic outliers, but sharply peaked distributions may remain problematic.
4.2. Reliability parameter: Q_z-based quality cuts eliminate many outliers at the expense of a small number of satisfactory estimates, without preferentially removing high-redshift sources.The zphot scatter increases sharply above Q_z = 2−3 in synthetic and observed samples, and the reported scatter is 0.3 (0.4).
4.3. The false security of zphot – zspec plots: 5% zeropoint offsets produce visible systematic effects between 0 < zphot < 1, while high-redshift spectroscopic comparisons can appear nearly unchanged.Thus, agreement between two photometric catalogs or algorithms can conceal systematic uncertainties beyond the spectroscopic sample’s flux limits.
4.3. The false security of zphot – zspec plots: At 1 < z < 2, spectroscopic comparisons suggest σ = 0.037 for the full CDFS filters and σ = 0.048 for the partial POWIR filters, despite discrepancies above z > 1.25.The resulting surface densities in the 1.5 < z < 2 and 2 < z < 2.5 bins differ by more than a factor of 2 depending on filter coverage.

5. SUMMARY

EAZY is designed for deep photometric surveys whose spectroscopic calibration samples are incomplete or biased. It avoids spectroscopic-sample scatter minimization through model-based templates and a template error function, while providing practical reliability diagnostics and supporting improved redshift estimation for faint galaxy samples.

5. SUMMARY: EAZY uses a semi-analytical-model template set and a template error function instead of minimizing zphot–zspec scatter on a potentially biased spectroscopic sample.The error function accounts for random and systematic differences between observed photometry and templates without spectroscopic calibration optimization.
5. SUMMARY: The code’s uncertainty estimates behave well for galaxies with spectroscopic redshifts, although this behavior cannot be tested identically for most objects without spectroscopy.The paper emphasizes that nonrepresentative spectroscopic samples can make photometric-redshift reliability assessments misleading.
5. SUMMARY: Q_z is expected to provide a reasonable indication of photometric-redshift robustness in practice.This diagnostic is particularly relevant when limited filter coverage permits systematic effects that the spectroscopic comparison sample does not trace.
5. SUMMARY: Reliable photometric redshifts remain necessary for progress on faint galaxy samples, motivating complete faint K-selected samples and deeper photometric tests.The paper notes ongoing medium-band observations of ∼10^5 galaxies with K ≤21.5 as a test of broad-band results.