Unknown Redshift Research Articles

A Lens Finder Map to Check Claimed High-z Galaxies behind SMACS J0723.3-7327

The first science image released by the James Webb Space Telescope (JWST) reveals numerous galaxies in the distant background of the galaxy cluster SMACS J0723.3-7327. Some have claimed redshifts of up to z ≃ 20, challenging standard cosmological models for structure formation. Here, we present a lens model for SMACS J0723.3-7327 anchored on five spectroscopically confirmed systems at 1.38 ≤ z ≤ 2.21 that are multiply lensed, along with 12 other systems with proposed image counterparts sharing common colors, spectral energy distributions, and morphological features, but having unknown redshifts. Constrained only by their image positions, and where available, redshifts, our lens model correctly reproduces the positions and correctly predicts the morphologies and relative brightnesses of all these image counterparts, as well as providing geometrically determined redshifts spanning 1.4 ≲ z ≲ 6.7 for the 12 candidate multiply lensed galaxies lacking spectroscopic measurements. From this lens model, we create a lens finder map that defines regions over which galaxies beyond a certain redshift are predicted to be multiply lensed. Applying this map to three galaxies claimed to be at 10 ≲ z ≲ 20, we find no image counterparts at locations (with an uncertainty of ∼0.″5) where they ought to be sufficiently magnified to be detectable—suggesting instead that these galaxies lie at z ≲ 1.7–3.2. In lieu of spectroscopy, the creation of reliable lens finder maps for cluster fields is urgently needed to test and constrain redshifts inferred from photometry for a rapidly increasing number of candidate high-z galaxies found with JWST.

Estimation of redshift and associated uncertainty of Fermi/LAT extragalactic sources with Deep Learning

ABSTRACT With the advancement of technology, machine learning-based analytical methods have pervaded nearly every discipline in modern studies. Particularly, a number of methods have been employed to estimate the redshift of gamma-ray loud active galactic nuclei (AGN), which are a class of supermassive black hole systems known for their intense multi-wavelength emissions and violent variability. Determining the redshifts of AGNs is essential for understanding their distances, which, in turn, sheds light on our current understanding of the structure of the nearby universe. However, the task involves a number of challenges, such as the need for meticulous follow-up observations across multiple wavelengths and astronomical facilities. In this study, we employ a simple yet effective deep learning model with a single hidden layer having 64 neurons and a dropout of 0.25 in the hidden layer on a sample of AGNs with known redshifts from the latest AGN catalogue, 4LAC-DR3, obtained from Fermi-LAT. We utilized their spectral, spatial, and temporal properties to robustly predict the redshifts of AGNs as well quantify their associated uncertainties by modifying the model using two different variational inference methods. We achieve a correlation coefficient of 0.784 on the test set from the frequentist model and 0.777 and 0.778 from both the variants of variational inference, and, when used to make predictions on the samples with unknown redshifts, we achieve mean predictions of 0.421, 0.415, and 0.393, with standard deviations of 0.258, 0.246, and 0.207 from the models, respectively.

TDCOSMO

We have measured the redshifts and single-aperture velocity dispersions of eight lens galaxies using the data collected by the Echellette Spectrograph and Imager (ESI) and Low Resolution Imaging Spectrometer (LRIS) at W.M. Keck observatory on different observing nights spread over three years (2018–2020). These results, combined with other ancillary data, such as high-resolution images of the lens systems, and time delays, are necessary to increase the sample size of the quasar-galaxy lens systems for which the Hubble constant can be measured, using the time-delay strong lensing method, hence increasing the precision of its inference. Typically, the 2D spectra of the quasar-galaxy lens systems get spatially blended due to seeing by ground-based observations. As a result, the extracted lensing galaxy (deflector) spectra become significantly contaminated by quasar light, which affects the ability to extract meaningful information about the deflector. To account for spatial blending and extract less contaminated and higher signal-to-noise ratio (S/N) 1D spectra of the deflectors, a forward modeling method has been implemented. From the extracted spectra, we have measured redshifts using prominent absorption lines and single aperture velocity dispersions using the penalized pixel fitting code pPXF. In this paper, we report the redshifts and single aperture velocity dispersions of eight lens galaxies – J0147+4630, B0445+123, B0631+519, J0659+1629, J0818−2613, J0924+0219, J1433+6007, and J1817+2729. Among these systems, six do not have previously measured velocity dispersions; for the other two, our measurements are consistent with previously reported values. Additionally, we have measured the previously unknown redshifts of the deflectors in J0818−2613 and J1817+2729 to be 0.866 ± 0.002 and 0.408 ± 0.002, respectively.

Long-term Swift and multiwavelength observations of two TeV-detected blazars with unknown redshifts

Long-term Swift and multiwavelength observations of two TeV-detected blazars with unknown redshifts

Multiple-component spectral analysis of 24 Fermi LAT GRBs and the Eiso-Ei,peak relation

The use of correlations between various observable quantities for Gamma-ray bursts (GRBs) has been the subject of much interest and discussion. In particular, many studies have explored the Eiso-Ei,peak relation, its origin and its potential use as a means to discriminate between GRBs from various progenitors. Observations of GRBs through the Fermi Gamma-Ray Space Telescope have also opened up the possibility of studying this correlation over a wide range of energies from keVs to GeVs. While the correlation has been studied through Fermi Large Area Telescope (LAT) GRBs with measured redshifts, its compatibility with LAT GRBs without measured redshifts is yet to be tested. In this paper, we study this correlation with a sample of 24 Fermi LAT GRBs with unknown redshift. We analyze their data between 8 keV and 100 GeV through single and multiple-component spectral models. We use the results of this analysis to study the compatibility of these GRBs with the Eiso-Ei,peak relation by varying the redshift continuously between 0.3 and 10.5. We find that all 24 GRBs are compatible with the Eiso-Ei,peak relation within a 1-sigma uncertainty for a certain redshift range. The range of compatible redshifts found for each GRB remains consistent with observed redshifts for long GRBs.

Plug-in cross-dispersing module for the Large Binocular Telescope’s infrared spectrograph LUCI

The large binocular telescope (LBT) can spectrally characterize faint objects from the ultraviolet (UV) to the near infrared (NIR) using two instruments, such as multiobjects double spectrograph (MODS) and LBT utility camera in the infrared (LUCI), which are pairs of imagers and spectrographs. Although LUCI can cover the NIR bands (0.9 to 2.4 μm), we currently need to use both LUCIs at the same time with existing gratings and filters. We report on the design and initial construction of a modular system called mask-oriented breadboard implementation for unscrambling spectra (MOBIUS) that enables a single LUCI to produce a full NIR spectrum (0.9 to 2.4 μm) in a single exposure. MOBIUS is a Littrow type spectrograph that is installed within the limited space of exchangeable mask frame space of LUCI. This plug-in concept requires no modification to the current instrument while dispersing the input slit perpendicular to the dispersion direction of the gratings in LUCI. With MOBIUS, we can utilize a slit length up to 2.3 arcsecond to acquire zJHK spectra without mixing orders at the LUCI image plane. In binocular observations with the LBT, a MODS spectrograph will be used with a LUCI + MOBIUS to acquire spectra across the full optical NIR wavelength range from 0.3 to 2.4 μm simultaneously. This will benefit studies of transient sources from rotating asteroids in our solar system to gamma-ray bursts, as well as anything with broad spectral features or unknown redshifts. The design process, tolerances, and initial table-top testing results to verify the operation of MOBIUS are presented in this work.

Bayesian Methods for Inferring Missing Data in the BATSE Catalog of Short Gamma-Ray Bursts

The knowledge of the redshifts of Short-duration Gamma-Ray Bursts (SGRBs) is essential for constraining their cosmic rates and thereby the rates of related astrophysical phenomena, particularly Gravitational Wave Radiation (GWR) events. Many of the events detected by gamma-ray observatories (e.g., BATSE, Fermi, and Swift) lack experimentally measured redshifts. To remedy this, we present and discuss a generic data-driven probabilistic modeling framework to infer the unknown redshifts of SGRBs in the BATSE catalog. We further explain how the proposed probabilistic modeling technique can be applied to newer catalogs of SGRBs and other astronomical surveys to infer the missing data in the catalogs.

Closure relations during the plateau emission of Swift GRBs and the fundamental plane

Abstract The Neil Gehrels Swift observatory observes gamma-ray burst (GRB) plateaus in X-rays. We test the reliability of the closure relations through the fireball model when dealing with GRB plateau emissions. We analyze 455 X-ray light curves collected by Swift from 2005 January until 2019 August for which the redshifts are either known or unknown using the phenomenological Willingale 2007 model. Using these fits, we analyze the emission mechanisms and astrophysical environments of these GRBs through the closure relations within the time interval of the plateau emission. Finally, we test the three-dimensional fundamental plane relation (Dainotti relation) which connects the prompt peak luminosity, the time at the end of the plateau (rest frame), and the luminosity at that time, for the GRBs with redshift, concerning groups determined by the closure relations. This allows us to check if the intrinsic scatter σint of any of these groups is reduced compared to previous literature. The most fulfilled environments for the electron spectral distribution, p > 2, are wind slow cooling (SC) and interstellar material (ISM) slow cooling for cases in which the parameter q, which indicates the flatness of the plateau emission and accounts for the energy injection, is 0 and 0.5, respectively, in cases with both known and unknown redshifts. We also find that for short GRBs all ISM environments with q = 0 have the smallest σint = 0.04 ± 0.15 in terms of the fundamental plane relation holding a probability of occurring by chance of p = 0.005. We have shown that the majority of GRBs presenting plateau emission fulfill the closure relations, including the energy injection, with a particular preference for the wind SC environment. The subsample of GRBs that fulfill the given relations can be used as possible standard candles and can suggest a way to reduce the intrinsic scatter of these studied relationships.

The spectra of IceCube neutrino candidate sources – I. Optical spectroscopy of blazars

ABSTRACT There is mounting evidence that ultra-energetic neutrinos of astrophysical origin may be associated with blazars. Here, we investigate a unique sample of 47 blazars, ∼20 of which could be new neutrino sources. In particular, we focus on 17 objects of yet unknown redshift, for which we present optical spectroscopy secured at the Gran Telescopio Canarias and the ESO Very Large Telescope. We find all sources but one (a quasar) to be BL Lac objects. For nine targets we are able to determine the redshift (0.09 < z < 1.6), while for the others we set a lower limit on it, based on either the robust detection of intervening absorption systems or on an estimation derived from the absence of spectral signatures of the host galaxy. In some spectra, we detect forbidden and semiforbidden emission lines with luminosities in the range 1040–1041 erg s−1. We also report on the spectroscopy of seven blazars possibly associated with energetic neutrinos that partially meet the criteria of our sample and are discussed in the Appendix. These results represent the starting point of our investigation into the real nature of these objects and their likelihood of being neutrino emitters.

Accurate precision cosmology with redshift unknown gravitational wave sources

Gravitational waves can provide an accurate measurement of the luminosity distance to the source but cannot provide the source redshift unless the degeneracy between mass and redshift can be broken. This makes it essential to infer the redshift of the source independently to measure the expansion history of the Universe. We show that by exploiting the clustering scale of the gravitational wave sources with galaxies of a known redshift, we can infer the expansion history from redshift unknown gravitational wave sources. By using gravitational wave sources of unknown redshift that are detectable from the network of gravitational wave detectors with Advanced LIGO design sensitivity, we will be able to obtain accurate and precise measurements of the local Hubble constant, the expansion history of the Universe, and the gravitational wave bias parameter, which captures the distribution of gravitational wave sources with respect to the redshift tracer distribution. While we showcase its application to low redshift gravitational waves, this technique will be applicable also to the high redshift gravitational wave sources detectable from Laser Interferometer Space Antenna (LISA), Cosmic Explorer (CE), and Einstein Telescope (ET). Moreover, this method will also be applicable to samples of supernovae and fast radio bursts with unknown or photometric redshifts.

Search for Radio Remnants of Nearby Off-axis Gamma-Ray Bursts in a Sample of Swift/BAT Events

Abstract The multi-messenger discovery of gravitational waves (GWs) and light from the binary neutron star (NS) merger GW170817, associated with gamma-ray burst (GRB) 170817A and kilonova AT2017gfo, has marked the start of a new era in astrophysics. GW170817 has confirmed that binary NS mergers are progenitors of at least some short GRBs. The peculiar properties of the GRB 170817A radio afterglow, characterized by a delayed onset related to the off-axis geometry, have also demonstrated how some nearby short GRBs may not be identified as such with standard short-timescale electromagnetic follow-up observations. Building upon this new information, we performed late-time radio observations of a sample of four short GRBs with unknown redshift and no previously detected afterglow in the Swift/BAT sample in order to identify nearby ( Mpc) off-axis GRB candidates via their potential late-time radio signatures. We find a previously uncatalogued radio source within the error region of GRB 130626 with a flux density consistent with an NS radio flare at a distance of ∼100 Mpc. An origin related to a persistent radio source unrelated to the GRB cannot be excluded nor confirmed given the high chance of false positives in error regions as large as those considered here, and the limited time baseline of our observations. Further radio (and X-ray) follow-up observations are needed to better understand the origin of this source.

Testing the general theory of relativity using gravitational wave propagation from dark standard sirens

ABSTRACT Alternative theories of gravity predict modifications in the propagation of gravitational waves (GW) through space–time. One of the smoking-gun predictions of such theories is the change in the GW luminosity distance to GW sources as a function of redshift relative to the electromagnetic (EM) luminosity distance expected from EM probes. We propose a multimessenger test of the theory of general relativity from the propagation of GWs by combining EM and GW observations to resolve these issues from GW sources without EM counterparts (which are also referred to as dark standard sirens). By using the relation between the geometric distances accessible from baryon acoustic oscillation measurements, and luminosity distance measurements from the GW sources, we can measure any deviation from the general theory of relativity via the GW sources of unknown redshift that will be detectable by networks of GW detectors such as LIGO, Virgo, and KAGRA. Using this technique, the fiducial value of the frictional term can be measured to a precision $\Xi _0=0.98^{+0.04}_{-0.23}$ after marginalizing over redshift dependence, cosmological parameters, and GW bias parameters with ∼3500 dark standard sirens of masses $30\, \rm M_\odot$ each distributed up to redshift z = 0.5. For a fixed redshift dependence, a value of $\Xi _0=0.99^{+0.02}_{-0.02}$ can be measured with a similar number of dark sirens. Application of our methodology to the far more numerous dark standard sirens detectable with next-generation GW detectors, such as LISA, Einstein Telescope and Cosmic Explorer, will allow achievement of higher accuracy than possible from use of bright standard sirens.

On the Investigation of the Closure Relations for Gamma-Ray Bursts Observed by Swift in the Post-plateau Phase and the GRB Fundamental Plane

Abstract Gamma-ray Bursts (GRBs) are the most explosive phenomena in the universe after the big bang. A large fraction of GRB lightcurves (LCs) shows X-ray plateaus. We perform the most comprehensive analysis of all GRBs (with known and unknown redshifts) with plateau emission observed by The Neil Gehrels Swift Observatory from its launch until 2019 August. We fit 455 LCs showing a plateau and explore whether these LCs follow closure relations, relations between the temporal and spectral indices of the afterglow, corresponding to two distinct astrophysical environments and cooling regimes within the external forward shock (ES) model, and find that the ES model works for the majority of cases. The most favored environments are a constant-density interstellar or wind medium with slow cooling. We also confirm the existence of the fundamental plane relation between the rest-frame time and luminosity at the end of the plateau emission and the peak prompt luminosity for this enlarged sample, and test this relation on groups corresponding to the astrophysical environments of our known redshift sample. The plane becomes a crucial discriminant corresponding to these environments in terms of the best-fitting parameters and dispersions. Most GRBs for which the closure relations are fulfilled with respect to astrophysical environments have an intrinsic scatter σ compatible within 1σ of that of the “Gold” GRBs, a subset of long GRBs with relatively flat plateaus. We also find that GRBs satisfying closure relations indicating a fast cooling regime have a lower σ than ever previously found in literature.

Testing KiDS cross-correlation redshifts with simulations

Measuring cosmic shear in wide-field imaging surveys requires accurate knowledge of the redshift distribution of all sources. The clustering-redshift technique exploits the angular cross-correlation of a target galaxy sample with unknown redshifts and a reference sample with known redshifts. It represents an attractive alternative to colour-based methods of redshift calibration. Here we test the performance of such clustering redshift measurements using mock catalogues that resemble the Kilo-Degree Survey (KiDS). These mocks are created from the MICE simulation and closely mimic the properties of the KiDS source sample and the overlapping spectroscopic reference samples. We quantify the performance of the clustering redshifts by comparing the cross-correlation results with the true redshift distributions in each of the five KiDS photometric redshift bins. Such a comparison to an informative model is necessary due to the incompleteness of the reference samples at high redshifts. Clustering mean redshifts are unbiased at |Δz|< 0.006 under these conditions. The redshift evolution of the galaxy bias of the reference and target samples represents one of the most important systematic errors when estimating clustering redshifts. It can be reliably mitigated at this level of precision using auto-correlation measurements and self-consistency relations, and will not become a dominant source of systematic error until the arrival of Stage-IV cosmic shear surveys. Using redshift distributions from a direct colour-based estimate instead of the true redshift distributions as a model for comparison with the clustering redshifts increases the biases in the mean to up to |Δz|∼0.04. This indicates that the interpretation of clustering redshifts in real-world applications will require more sophisticated (parameterised) models of the redshift distribution in the future. If such better models are available, the clustering-redshift technique promises to be a highly complementary alternative to other methods of redshift calibration.

Very high energy γ-ray emission from two blazars of unknown redshift and upper limits on their distance

ABSTRACT We report on the detection of very high energy (VHE; E > 100 GeV) γ-ray emission from the BL Lac objects KUV 00311−1938 and PKS 1440−389 with the High Energy Stereoscopic System (H.E.S.S.). H.E.S.S. observations were accompanied or preceded by multiwavelength observations with Fermi/LAT, XRT and UVOT onboard the Swift satellite, and ATOM. Based on an extrapolation of the Fermi/LAT spectrum towards the VHE γ-ray regime, we deduce a 95 per cent confidence level upper limit on the unknown redshift of KUV 00311−1938 of $z$ < 0.98 and of PKS 1440−389 of $z$ < 0.53. When combined with previous spectroscopy results, the redshift of KUV 00311−1938 is constrained to 0.51 ≤ $z$ < 0.98 and of PKS 1440−389 to 0.14 ⪅ $z$ < 0.53.

Physical Characterization of an Unlensed, Dusty Star-forming Galaxy at z = 5.85

Abstract We present a physical characterization of MM J100026.36+021527.9 (a.k.a. “Mambo-9”), a dusty star-forming galaxy (DSFG) at z = 5.850 ± 0.001. This is the highest-redshift unlensed DSFG (and fourth most distant overall) found to date and is the first source identified in a new 2 mm blank-field map in the COSMOS field. Though identified in prior samples of DSFGs at 850 μm to 1.2 mm with unknown redshift, the detection at 2 mm prompted further follow-up as it indicated a much higher probability that the source was likely to sit at z > 4. Deep observations from the Atacama Large Millimeter and submillimeter Array (ALMA) presented here confirm the redshift through the secure detection of 12CO(J = 6→5) and p-H2O (21,1 → 20,2). Mambo-9 is composed of a pair of galaxies separated by 6 kpc with corresponding star formation rates of 590 M ⊙ yr−1 and 220 M ⊙ yr−1, total molecular hydrogen gas mass of (1.7 ± 0.4) × 1011 M ⊙, dust mass of (1.3 ± 0.3) × 109 M ⊙, and stellar mass of ( ) × 109 M ⊙. The total halo mass, (3.3 ± 0.8) × 1012 M ⊙, is predicted to exceed 1015 M ⊙ by z = 0. The system is undergoing a merger-driven starburst that will increase the stellar mass of the system tenfold in τ depl = 40−80 Myr, converting its large molecular gas reservoir (gas fraction of ) into stars. Mambo-9 evaded firm spectroscopic identification for a decade, following a pattern that has emerged for some of the highest-redshift DSFGs found. And yet, the systematic identification of unlensed DSFGs like Mambo-9 is key to measuring the global contribution of obscured star formation to the star formation rate density at z ≳ 4, the formation of the first massive galaxies, and the formation of interstellar dust at early times (≲1 Gyr).

Multi-TeV Flaring from High-energy Blazars: An Evidence of the Photohadronic Process

Abstract High-energy peaked blazars are known to undergo episodes of flaring in GeV–TeV gamma-rays involving different timescales. This flaring mechanism is not well understood, despite long-term simultaneous multiwavelength observations. These gamma-rays en route to Earth undergo attenuation by the extragalactic background light. Using the photohadronic model, where the seed photons follow a power-law spectrum and a template extragalactic background light model, we derive a simple relation between the observed multi-TeV gamma-ray flux and the intrinsic flux with a single parameter. We study 42 flaring epochs of 23 blazars and excellent fits to most of the observed spectra are obtained, strengthening the photohadronic origin of multi-TeV gamma-rays. We can also constrain the power spectrum of the seed photons during the flaring period. Stringent bounds on the blazars of unknown redshifts, whose multi-TeV flaring spectra are known, can be placed using the photohadronic model.

Multifrequency study of the gamma-ray flaring BL Lacertae object PKS 2233–148 in 2009–2012

We study the jet physics of the BL Lac object PKS 2233-148 making use of synergy of observational data sets in the radio and gamma-ray energy domains. The four-epoch multi-frequency (4-43 GHz) VLBA observations focused on the parsec-scale jet were triggered by a flare in gamma-rays registered by the Fermi-LAT on April 23, 2010. We also used 15 GHz data from the OVRO 40-m telescope and MOJAVE VLBA monitoring programs. Jet shape of the source is found to be conical on scales probed by the VLBA observations setting a lower limit of about 0.1 on its unknown redshift. Nuclear opacity is dominated by synchrotron self-absorption, with a wavelength-dependent core shift $r_{\text{core[mas]}}\approx0.1\lambda_{[\text{cm}]}$ co-aligned with the innermost jet direction. The turnover frequency of the synchrotron spectrum of the VLBI core shifts towards lower frequencies as the flare propagates down the jet, and the speed of this propagation is significantly higher, about 1.2 mas/yr, comparing to results from traditional kinematics based on tracking bright jet features. We have found indications that the gamma-ray production zone in the source is located at large distances, 10-20 pc, from a central engine, and could be associated with the stationary jet features. These findings favour synchrotron self-Compton, possibly in a combination with external Compton scattering by infrared seed photons from a slow sheath of the jet, as a dominant high-energy emission mechanism of the source.

Modelling the luminosity function of long gamma-ray bursts using Swift and Fermi

I have used a sample of long Gamma Ray Bursts (GRBs) common to both \emph{Swift} and \emph{Fermi} to re-derive the parameters of the Yonetoku correlation. This allowed me to self-consistently estimate pseudo redshifts of all the bursts with unknown redshifts. This is the first time such a large sample of GRBs from these two instruments are used, both individually and in conjunction, to model the long GRB luminosity function. The GRB formation rate is modelled as the product of the cosmic star formation rate and a GRB formation efficiency for a given stellar mass. An exponential cut-off powerlaw luminosity function fits the data reasonably well, with $\nu = 0.6$ and $ L_b = 5.4 \times10^{52} \, \rm{erg.s^{-1}},$ and does not require a cosmological evolution. In the case of a broken powerlaw, it is required to incorporate a sharp evolution of the break given by $L_{b}\sim0.3\times10^{52}\left(1+z\right)^{2.90} \, \rm{erg.s^{-1}},$ and the GRB formation efficiency (degenerate up to a beaming factor of GRBs) decreases with redshift as $\propto\left(1+z\right)^{-0.80}.$ However it is not possible to distinguish between the two models. The derived models are then used as templates to predict the distribution of GRBs detectable by CZTI on board \emph{AstroSat}, as a function of redshift and luminosity. This demonstrates that via a quick localization and redshift measurement of even a few CZTI GRBs, \emph{AstroSat} will help in improving the statistics of GRBs both typical and peculiar.

Photo-$z$ estimation: An example of nonparametric conditional density estimation under selection bias

Redshift is a key quantity for inferring cosmological model parameters. In photometric redshift estimation, cosmologists use the coarse data collected from the vast majority of galaxies to predict the redshift of individual galaxies. To properly quantify the uncertainty in the predictions, however, one needs to go beyond standard regression and instead estimate the full conditional density $f(z|\mathbf{x})$ of a galaxy’s redshift $z$ given its photometric covariates $\mathbf{x}$. The problem is further complicated by selection bias: usually only the rarest and brightest galaxies have known redshifts, and these galaxies have characteristics and measured covariates that do not necessarily match those of more numerous and dimmer galaxies of unknown redshift. Unfortunately, there is not much research on how to best estimate complex multivariate densities in such settings. Here we describe a general framework for properly constructing and assessing nonparametric conditional density estimators under selection bias, and for combining two or more estimators for optimal performance. We propose new improved photo-$z$ estimators and illustrate our methods on data from the Sloan Data Sky Survey and an application to galaxy–galaxy lensing. Although our main application is photo-$z$ estimation, our methods are relevant to any high-dimensional regression setting with complicated asymmetric and multimodal distributions in the response variable.