Quantifying the Potential Redshift Information in Photometric Data from Stage IV Galaxy Surveys
Core Concepts
The potentially recoverable redshift information content of photometric data from Stage IV galaxy surveys, including LSST, Euclid, Roman, and CASTOR, can be quantified using an informationtheoretic metric without assuming a specific redshift estimation method or prior information.
Abstract
The paper presents a holistic exploration of the potentially recoverable redshift information in photometric data from Stage IV galaxy surveys, including LSST, Euclid, Roman, and CASTOR. The authors use an informationtheoretic metric called TheLastMetric to quantify the redshift information content without assuming a specific redshift estimation method or prior information.
The key findings are:

LSST photometry contains the most redshift information across all redshifts, peaking around z ≈ 0.6. The addition of infrared photometry from Euclid and Roman significantly improves the redshift information content at higher redshifts due to the detection of the Balmer break.

While earlier work suggested that UV photometry would be uninformative for redshifts z ≥ 1.7, the authors find that the impact of breaking the LymanBalmer degeneracy is suppressed in populationlevel metrics due to the smaller number of sources that satisfy the combined UV, optical, and infrared magnitude limits.

The authors analyze the colorcolor distributions and spectral energy distributions (SEDs) of galaxies with the largest and smallest gains in redshift information when additional photometry is included. They find that galaxies with the largest information gains tend to have SEDs with strong spectral features, while those with information loss have flatter SEDs.

The informationtheoretic approach developed in this work can be applied more broadly to quantify the impact of combining photometric datasets, changing experimental design choices, and evaluating systematics mitigation procedures.
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A holistic exploration of the potentially recoverable redshift information of Stage IV galaxy surveys
Stats
The potentially recoverable redshift information content, as measured by the TheLastMetric, peaks around z ≈ 0.6 for LSST photometry alone.
The addition of infrared photometry from Euclid and Roman significantly improves the redshift information content at higher redshifts.
Quotes
"The potentially recoverable redshift information content of photometric data from Stage IV galaxy surveys, including LSST, Euclid, Roman, and CASTOR, can be quantified using an informationtheoretic metric without assuming a specific redshift estimation method or prior information."
"While earlier work suggested that UV photometry would be uninformative for redshifts z ≥ 1.7, the authors find that the impact of breaking the LymanBalmer degeneracy is suppressed in populationlevel metrics due to the smaller number of sources that satisfy the combined UV, optical, and infrared magnitude limits."
Deeper Inquiries
How can the informationtheoretic approach developed in this work be applied to optimize other aspects of survey design, such as the choice of wavelength and filter coverage, depth of overlapping survey footprints, and cadence?
The informationtheoretic approach introduced in this work, particularly through the use of TheLastMetric, provides a robust framework for optimizing various aspects of survey design. By quantifying the potentially recoverable redshift information from photometric data, this method allows researchers to make informed decisions regarding the choice of wavelength and filter coverage. For instance, by analyzing the mutual information between redshift and photometry across different filter combinations, survey designers can identify which filters contribute the most to redshift estimation. This can lead to the selection of optimal filter sets that maximize the information gain, thereby enhancing the overall effectiveness of the survey.
Moreover, the depth of overlapping survey footprints can be optimized by assessing how additional photometric data from overlapping regions contributes to the information content. By evaluating the information gain from different combinations of surveys, planners can determine the ideal depth and area coverage that would yield the highest redshift recovery efficiency. This is particularly relevant in multisurvey scenarios where the integration of data from different telescopes can either enhance or dilute the information available.
Finally, the cadence of observations can also be optimized using this informationtheoretic approach. By analyzing how the timing and frequency of observations affect the information content, survey designers can establish a cadence that maximizes the potential for redshift recovery. This could involve prioritizing certain filters or wavelengths during specific observational windows to capture critical spectral features that are essential for accurate redshift estimation.
What other astrophysical or cosmological properties beyond redshift could be assessed using an informationtheoretic metric for parameter recovery?
Beyond redshift, the informationtheoretic metric developed in this work can be applied to assess a variety of astrophysical and cosmological properties. For instance, galaxy mass and star formation rate (SFR) are two critical parameters that could benefit from an informationtheoretic approach. By quantifying the mutual information between photometric data and these properties, researchers can evaluate how well different photometric bands constrain estimates of galaxy mass and SFR.
Additionally, the informationtheoretic framework can be extended to study the properties of galaxy clusters, such as their mass distribution and dynamical state. By analyzing the information content related to cluster photometry, researchers can derive insights into the underlying physical processes governing cluster formation and evolution.
Furthermore, the approach can be utilized to investigate the properties of dark matter and dark energy by examining the relationships between galaxy distributions and cosmological parameters. By assessing the information content in photometric data related to galaxy clustering statistics, researchers can gain insights into the nature of dark energy and its influence on the expansion of the universe.
How could an informationtheoretic metric be developed for components of cosmological probes, such as the redshift distribution n(z) derived from galaxy clustering statistics, or for endtoend cosmological parameter constraints from photometry and imaging?
To develop an informationtheoretic metric for components of cosmological probes, such as the redshift distribution n(z) derived from galaxy clustering statistics, one could start by establishing a joint probability distribution that encompasses both the galaxy clustering data and the redshift information. By applying TheLastMetric framework, researchers can quantify the mutual information between the clustering statistics and the redshift distribution, allowing for a deeper understanding of how well the clustering data informs the redshift estimates.
This approach could also be extended to endtoend cosmological parameter constraints derived from photometry and imaging. By integrating the information content from various photometric datasets, researchers can create a comprehensive model that captures the relationships between different cosmological parameters and their corresponding observational data. The informationtheoretic metric would enable the assessment of how well different combinations of photometric data contribute to the overall constraints on cosmological parameters, such as the Hubble constant, matter density, and dark energy equation of state.
In summary, the development of an informationtheoretic metric for these components would involve constructing joint probability distributions, quantifying mutual information, and analyzing the contributions of various datasets to the overall cosmological understanding, thereby enhancing the precision and accuracy of cosmological parameter recovery.