The idea behind this line of research is simple: due to the cosmological expansion, the spectrum of a galaxy is stretched toward the red end of the spectrum and, therefore, in a given photometric system, the spectrum of identical galaxies at different distances is weighted differently. The field of photometric redshift (photo-z) estimation benefited from this new wealth of data. et al., 2020), and Roman Space Telescope ( Green et al., 2012), all driven by a new reliance on the possibility to pursue precision cosmology by combining high precision and deep photometry for very large samples of galaxies with a largely incomplete spectroscopic knowledge. Rubin Observatory Legacy Survey of Space and Time (LSST, LSST Science Collaboration et al., 2009), Euclid ( Laureijs et al., 2011), Cosmic Evolution Survey (COSMOS, Scoville et al., 2007), James Webb Space Telescope (JWST, Kauffmann, O. With its enormous success, SDSS also paved the way to present and future survey projects, such as the Dark Energy Survey (DES, The Dark Energy Survey Collaboration, 2005), the Kilo-Degree Survey (KiDS, de Jong et al., 2013), Hyper Suprime-Cam Survey (HSC, Aihara et al., 2018), Vera C. Among many other applications, this survey made the widest astrophysical community able to explore different approaches to the evaluation of galaxy distances. The true turning point, however, came with the era of Sloan Digital Sky Survey (SDSS, York et al., 2000), the first extensive multi-band and spectroscopic native digital survey of the sky. This led to the development of alternative techniques, collectively called photometric redshift estimation methods, first proposed by Baum (1962) and better formalized by Butchins (1981) and in the seminal paper of Connolly et al. In the past, such distances could be obtained only for small samples of objects via the displacement (redshift) of spectral features caused by the cosmological expansion, but the time-consuming and expensive spectroscopy could not be effectively used, either on very faint sources or on large samples of galaxies. Most open questions in cosmology, such as galaxy formation and evolution, the distribution of dark matter, or the understanding of large-scale structure, rely on an accurate estimate of galaxy distances.
In such a context, we summarize what was learned and proposed in more than a decade of research. They also provided a new impetus in the investigation of hybrid and deep learning techniques, aimed at conjugating the positive peculiarities of different methodologies, thus optimizing the estimation accuracy and maximizing the photometric range coverage, which are particularly important in the high-z regime, where the spectroscopic ground truth is poorly available.
The recent photometric redshift data challenges, organized within several survey projects, like LSST and Euclid, pushed the exploitation of the observed multi-wavelength and multi-dimensional data or ad hoc simulated data to improve and optimize the photometric redshifts prediction and statistical characterization based on both Spectral Energy Distribution (SED) template fitting and machine learning methodologies. Furthermore, to accomplish main and legacy science objectives of future or incoming large and deep survey projects, such as James Webb Space Telescope (JWST), James Webb Space Telescope (LSST), and Euclid, a crucial role is played by an accurate estimation of photometric redshifts, whose knowledge would permit the detection and analysis of extended and peculiar sources by disentangling low-z from high-z sources and would contribute to solve the modern cosmological discrepancies. The importance of the current role of data-driven science is constantly increasing within Astrophysics, due to the huge amount of multi-wavelength data collected every day, characterized by complex and high-volume information requiring efficient and, as much as possible, automated exploration tools. 2Department of Physics Ettore Pancini, University Federico II, Naples, Italy.1INAF Astronomical Observatory of Capodimonte, Naples, Italy.Massimo Brescia 1 * Stefano Cavuoti 1,2 * Oleksandra Razim 2 Valeria Amaro 2 Giuseppe Riccio 1 Giuseppe Longo 2
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