Photometric Noise Research Articles

Pop-cosmos: A Comprehensive Picture of the Galaxy Population from COSMOS Data

We present pop-cosmos: a comprehensive model characterizing the galaxy population, calibrated to 140,938 (r < 25 selected) galaxies from the Cosmic Evolution Survey (COSMOS) with photometry in 26 bands from the ultraviolet to the infrared. We construct a detailed forward model for the COSMOS data, comprising: a population model describing the joint distribution of galaxy characteristics and its evolution (parameterized by a flexible score-based diffusion model); a state-of-the-art stellar population synthesis model connecting galaxies’ intrinsic properties to their photometry; and a data model for the observation, calibration, and selection processes. By minimizing the optimal transport distance between synthetic and real data, we are able to jointly fit the population and data models, leading to robustly calibrated population-level inferences that account for parameter degeneracies, photometric noise and calibration, and selection. We present a number of key predictions from our model of interest for cosmology and galaxy evolution, including the mass function and redshift distribution; the mass–metallicity-redshift and fundamental metallicity relations; the star-forming sequence; the relation between dust attenuation and stellar mass, star formation rate, and attenuation-law index; and the relation between gas-ionization and star formation. Our model encodes a comprehensive picture of galaxy evolution that faithfully predicts galaxy colors across a broad redshift (z < 4) and wavelength range.

The β Pictoris b Hill sphere transit campaign

The β Pictoris system is the closest known stellar system with directly detected gas giant planets, an edge-on circumstellar disc, and evidence of falling sublimating bodies and transiting exocomets. The inner planet, β Pictoris c, has also been indirectly detected with radial velocity (RV) measurements. The star is a known δ Scuti pulsator, and the long-term stability of these pulsations opens up the possibility of indirectly detecting the gas giant planets through time delays of the pulsations due to a varying light travel time. We search for phase shifts in the δ Scuti pulsations consistent with the known planets β Pictoris b and c and carry out an analysis of the stellar pulsations of β Pictoris over a multi-year timescale. We used photometric data collected by the BRITE-Constellation, bRing, ASTEP, and TESS to derive a list of the strongest and most significant δ Scuti pulsations. We carried out an analysis with the open-source python package maelstrom to study the stability of the pulsation modes of β Pictoris in order to determine the long-term trends in the observed pulsations. We did not detect the expected signal for β Pictoris b or β Pictoris c. The expected time delay is 6 s for β Pictoris c and 24 s for β Pictoris b. With simulations, we determined that the photometric noise in all the combined data sets cannot reach the sensitivity needed to detect the expected timing drifts. An analysis of the pulsational modes of β Pictoris using maelstrom showed that the modes themselves drift on the timescale of a year, fundamentally limiting our ability to detect exoplanets around β Pictoris via pulsation timing.

Reconstructing Intrinsic Stellar Noise with Stellar Atmospheric Parameters and Chromospheric Activity

Accurately characterizing the intrinsic stellar photometric noise induced by stellar astrophysics, such as stellar activity, granulation, and oscillations, is of crucial importance for detecting transiting exoplanets. In this study, we investigate the relation between the intrinsic stellar photometric noise, quantified by the Kepler combined differential photometric precision (CDPP) metric, and the level of stellar chromospheric activity, indicated by the S-index of Ca ii H K lines derived from LAMOST spectra. Our results reveal a clear positive correlation between the S-index and robust rms values of CDPP, with the correlation becoming more significant at higher activity levels and on longer timescales. We have therefore built an empirical relation between the robust rms values of CDPP and the S-index as well as T eff, log g, [Fe/H], and the apparent magnitude, with the XGBoost regression algorithm, using the LAMOST–Kepler common star sample as the training set. This method achieves a precision of ∼20 ppm for inferring the intrinsic noise from the S-index and other stellar labels on a 6 hr integration duration. We have applied this empirical relation to the full LAMOST DR7 spectra database and obtained the intrinsic noise predictions for 1,358,275 stars. The resultant catalog is publicly available and expected to be valuable for optimizing target selection for future exoplanet-hunting space missions, such as the Earth 2.0 mission.

Optical sparse telescope arrays and scintillation noise

ABSTRACT Fresnel propagation of starlight after it passes through high altitude turbulence in the Earth’s atmosphere results in random fluctuations of the intensity at ground level, known as scintillation. This effect adds random noise to photometric measurements with ground-based optical telescopes. Spatial correlation of the intensity fluctuations means that the fractional photometric noise due to scintillation may be substantially smaller for a sparse array of small aperture telescopes than for a single large aperture of the same total area. Assuming that the photometric noise for each telescope is independent, averaging the light curves measured by N telescopes reduces the noise by a factor of $\sqrt{N}$. For example, for bright stars, the signal-to-noise ratio of a 2.54 m telescope can be achieved for an array of thirty 20 cm telescopes if the scintillation noise measured for each telescope is uncorrelated. In this paper, we present results from simulation and from observations at the Isaac Newton Telescope. These explore the impact that several parameters have on the measured correlation of the scintillation noise between neighbouring telescopes. We show that there is significant correlation between neighbouring telescopes with separations parallel to the wind direction of the dominant high altitude turbulent layer. We find that the telescopes in an array should be separated by at least twice their aperture diameter so that there is negligible correlation of the photometric noise. We discuss additional benefits of using sparse telescope arrays, including reduced cost and increased field of view.

TESS search for substellar companions through pulsation timing of δ Scuti stars

Early-type main-sequence pulsating stars such as δ Scuti variables are one of the least explored class of targets in the search for exoplanets. Pulsation timing (PT) is an alternative technique to the most effective search methods. It exploits the light-travel-time effect (LTTE) to infer the presence of additional massive bodies around a pulsating star by measuring a periodic phase modulation of its signal. PT has been extremely successful in discovering and characterizing stellar binaries when it was applied to high-precision light curves over long temporal baselines, such as those delivered by the Kepler mission. In favorable conditions, the sensitivity of PT can reach the planetary-mass regime; one such candidate has already been claimed. The advent of TESS, with its nearly full-sky coverage and the availability of full-frame images, opens a great opportunity to expand this field of research. In this work, we present a pilot study aimed to understand the potential of PT as applied to TESS data, which are considerably different from Kepler data in terms of photometric noise, sampling cadence, and temporal baseline. We focused on the most favorable class of δ Scuti, that is, those showing strong pulsations and very simple frequency spectra. After the development of a customized pipeline, we were able to detect candidate companions for two targets in the (sub-)stellar mass regime: Chang 134 (43 ± 5 Mjup, P ≃ 82 days) and V393 Car (≳100 Mjup, P ≳ 700 days). Our results also highlight the limiting factors of this technique and the importance of an accurate absolute time calibration for future missions such as PLATO.

The Role of Binarity and Stellar Rotation in the Split Main Sequence of NGC 2422

In addition to the extended main-sequence turnoffs widely found in young and intermediate-age (∼600 Myr to 2 Gyr old) star clusters, some younger clusters even exhibit split main sequences (MSs). Different stellar rotation rates are proposed to account for the bifurcated MS pattern, with red and blue MSs (rMS and bMS) populated by fast and slowly rotating stars, respectively. Using photometry from Gaia Early Data Release 3, we report a Galactic open cluster with a bifurcated MS, NGC 2422 (∼90 Myr). We exclude the possibilities that the bifurcated MS pattern is caused by photometric noise or differential reddening. We aim to examine if stellar rotation can account for the split MS. We use spectra observed with the Canada–France–Hawaii Telescope and the Southern African Large Telescope and directly measured , the projected rotational velocities, for stars populating the bMS and rMS. We find that their values are weakly correlated with their loci in the color–magnitude diagram because of contamination caused by a large fraction of rMS stars with low projected rotational velocities. Based on the spectral energy distribution fitting method, we suggest that these slowly rotating stars at the rMS may hide a binary companion, which breaks the expected –color correlation. Future time-domain studies focusing on whether these slowly rotating stars are radial velocity variables are crucial to test the roles of stellar rotation and binarity in generating the split MSs.

On the Evolution of Rotational Modulation Amplitude in Solar-mass Main-sequence Stars

We investigate the relation between rotation periods P rot and photometric modulation amplitudes R per for ≈4000 Sun-like main-sequence stars observed by Kepler, using P rot and R per from McQuillan et al., effective temperature T eff from LAMOST DR6, and parallax data from Gaia EDR3. As has been suggested in previous works, we find that P rot scaled by the convective turnover time τ c, or the Rossby number Ro, serves as a good predictor of R per: R per plateaus at around 1% in relative flux for 0.2 ≲ Ro/Ro⊙ ≲ 0.4, and decays steeply with increasing Ro for 0.4 ≲ Ro/Ro⊙ ≲ 0.8, where Ro⊙ denotes Ro of the Sun. In the latter regime we find ∼ −4.5 to −2.5, although the value is sensitive to detection bias against weak modulation and may depend on other parameters including T eff and surface metallicity. The existing X-ray and Ca ii H and K flux data also show transitions at Ro/Ro⊙ ∼ 0.4, suggesting that all these transitions share the same physical origin. We also find that the rapid decrease of R per with increasing Ro causes rotational modulation of fainter Kepler stars with Ro/Ro⊙ ≳ 0.6 to be buried under the photometric noise. This effect sets the longest P rot detected in the McQuillan et al. sample as a function of T eff and obscures the signature of stalled spin down that has been proposed to set in around Ro/Ro⊙ ∼ 1.

Assessing the Transiting Exoplanet Survey Satellite’s Yield of Rocky Planets Around Nearby M Dwarfs

Terrestrial planets are easier to detect around M dwarfs than other types of stars, making them promising for next-generation atmospheric characterization studies. The Transiting Exoplanet Survey Satellite (TESS) mission has greatly increased the number of known M-dwarf planets that we can use to perform population studies, allowing us to explore how the rocky planet occurrence rate varies with host radius, following in the footsteps of past work with Kepler data. In this paper, we use simulations to assess TESS’s yield of small (0.5 R ⊕ < R p < 2 R ⊕) planet candidates around nearby (d < 30 pc) M dwarfs. We highlight the underappreciated fact that, while TESS was indeed expected to find a large number of planets around M dwarfs overall, it was not expected to have a high planetary yield for the latest M dwarfs. Furthermore, we find that TESS has detected fewer planets around stars with R ⋆ < 0.3 R ⊙ than even was expected (11 observed versus 24 ± 5 expected). We find evidence that the photometric noise of stars in the TESS bandpass increases with decreasing radius for M dwarfs. However, this trend cannot explain the observed distribution of planets. Our main conclusions are (1) the planet occurrence rate likely does not increase, and may decrease for the latest M dwarfs; and (2) there are at least 17, and potentially three times that number, transiting planets around nearby late-M dwarfs that still will not be detected by the end of TESS’s fourth year.

Model for Multi-View Residual Covariances Based on Perspective Deformation

In this work, we derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. The core of our approach is the formulation of the residual covariances as a combination of geometric and photometric noise sources. And our key novel contribution is the derivation of a term modelling how local 2D patches suffer from perspective deformation when imaging 3D surfaces around a point. Together, these add up to an efficient and general formulation which not only improves the accuracy of both feature-based and direct methods, but can also be used to estimate more accurate measures of the state entropy and hence better founded point visibility thresholds. We validate our model with synthetic and real data and integrate it into photometric and feature-based Bundle Adjustment, improving their accuracy with a negligible overhead.

The relation between X-ray and ultraviolet variability of quasars

ABSTRACT The relation between X-ray and UV/optical variability in AGNs has been explored in many individual sources, however a large sample study is yet absent. Through matching the XMM-Newton serendipitous X-ray and UV source catalogs with SDSS quasars, we build a sample of 802 epoch-pairs of 525 quasars showing clear variability in logFX − logFUV space. After correcting for the effect of photometric noise, we find 35.6 ± 2.1 per cent of the epoch-pairs show asynchronous variability between X-ray and UV (brightening in one band but dimming in the other). This indicates only in 28.8 ± 4.2 per cent of the epoch-pairs the X-ray and UV variability are intrinsically coordinated. The variability synchronicity exhibits no dependence on physical parameters of quasars or the time lag of the epoch-pairs, except for stronger variability tends to have stronger synchronicity. Switches between synchronous and asynchronous variability are also seen in individual sources. The poor coordination clearly contradicts both the X-ray reprocessing model and the accretion rate variation model for AGN variability. The ratios of the observed X-ray variability amplitude to that in UV span a broad range and peak at ∼2. The dominant fraction of the ratios appear too small to be attributed to X-ray reprocessing, and too large for accretion rate variation. The inhomogeneous disc model which incorporates both X-ray and UV/optical variability in AGNs is favoured by the observed stochastic relation between X-ray and UV variations.

Comparison of Observed Galaxy Properties with Semianalytic Model Predictions Using Machine Learning

Abstract With current and upcoming experiments such as the Wide Field Infrared Survey Telescope, Euclid, and Large Synoptic Survey Telescope, we can observe up to billions of galaxies. While such surveys cannot obtain spectra for all observed galaxies, they produce galaxy magnitudes in color filters. This data set behaves like a high-dimensional nonlinear surface, an excellent target for machine learning. In this work, we use a lightcone of semianalytic galaxies tuned to match Cosmic Assembly Near-infrared Deep Legacy Survey (CANDELS) observations from Lu et al. to train a set of neural networks on a set of galaxy physical properties. We add realistic photometric noise and use trained neural networks to predict stellar masses and average star formation rates (SFRs) on real CANDELS galaxies, comparing our predictions to SED-fitting results. On semianalytic galaxies, we are nearly competitive with template-fitting methods, with biases of 0.01 dex for stellar mass, 0.09 dex for SFR, and 0.04 dex for metallicity. For the observed CANDELS data, our results are consistent with template fits on the same data at 0.15 dex bias in and 0.61 dex bias in the SFR. Some of the bias is driven by SED-fitting limitations, rather than limitations on the training set, and some is intrinsic to the neural network method. Further errors are likely caused by differences in noise properties between the semianalytic catalogs and data. Our results show that galaxy physical properties can in principle be measured with neural networks at a competitive degree of accuracy and precision to template-fitting methods.

Where Have All the Solar-like Stars Gone? Rotation Period Detectability at Various Inclinations and Metallicities

Abstract The plethora of photometric data collected by the Kepler space telescope has promoted the detection of tens of thousands of stellar rotation periods. However, these periods are not found to an equal extent among different spectral types. Interestingly, early G-type stars with near-solar rotation periods are strongly underrepresented among those stars with known rotation periods. In this study we investigate whether the small number of such stars can be explained by difficulties in the period determination from photometric time series. For that purpose, we generate model light curves of early G-type stars with solar rotation periods for different inclination angles, metallicities, and (magnitude-dependent) noise levels. We find that the detectability is determined by the predominant type of activity (i.e., spot or faculae domination) on the surface, which defines the degree of irregularity of the light curve, and further depends on the level of photometric noise. These two effects significantly complicate the period detection and explain the lack of solar-like stars with known near-solar rotation periods. We conclude that the rotation periods of the majority of solar-like stars with near-solar rotation periods remain undetected to date. Finally, we promote the use of new techniques to recover more periods of near-solar rotators.

The effect of emission lines on the performance of photometric redshift estimation algorithms

ABSTRACT We investigate the effect of strong emission line galaxies on the performance of empirical photometric redshift estimation methods. In order to artificially control the contribution of photometric error and emission lines to total flux, we develop a PCA-based stochastic mock catalogue generation technique that allows for generating infinite signal-to-noise ratio model spectra with realistic emission lines on top of theoretical stellar continua. Instead of running the computationally expensive stellar population synthesis and nebular emission codes, our algorithm generates realistic spectra with a statistical approach, and – as an alternative to attempting to constrain the priors on input model parameters – works by matching output observational parameters. Hence, it can be used to match the luminosity, colour, emission line and photometric error distribution of any photometric sample with sufficient flux-calibrated spectroscopic follow-up. We test three simple empirical photometric estimation methods and compare the results with and without photometric noise and strong emission lines. While photometric noise clearly dominates the uncertainty of photometric redshift estimates, the key findings are that emission lines play a significant role in resolving colour space degeneracies and good spectroscopic coverage of the entire colour space is necessary to achieve good results with empirical photo-z methods. Template-fitting methods, on the other hand, must use a template set with sufficient variation in emission line strengths and ratios, or even better, first estimate the redshift empirically and fit the colours with templates at the best-fit redshift to calculate the K-correction and various physical parameters.

Photometric redshift calibration with self-organising maps

Accurate photometric redshift calibration is central to the robustness of all cosmology constraints from cosmic shear surveys. Analyses of the Kilo-Degree Survey (KiDS) re-weighted training samples from all overlapping spectroscopic surveys to provide a direct redshift calibration. Using self-organising maps we demonstrate that this spectroscopic compilation is sufficiently complete for KiDS, representing 99% of the effective 2D cosmic shear sample. We used the SOM to define a 100% represented “gold” cosmic shear sample, per tomographic bin. Using mock simulations of KiDS and the spectroscopic training set, we estimated the uncertainty on the SOM redshift calibration, and we find that photometric noise, sample variance, and spectroscopic selection effects (including redshift and magnitude incompleteness) induce a combined maximal scatter on the bias of the redshift distribution reconstruction (Δ⟨z⟩ = ⟨z⟩est − ⟨z⟩true) of σΔ⟨z⟩ ≤ 0.006 in all tomographic bins. Photometric noise and spectroscopic selection effects contribute equally to the observed scatter. We show that the SOM calibration is unbiased in the cases of noiseless photometry and perfectly representative spectroscopic datasets, as expected from theory. The inclusion of both photometric noise and spectroscopic selection effects in our mock data introduces a maximal bias of Δ⟨z⟩ = 0.013 ± 0.006, or Δ⟨z⟩ ≤ 0.025 at 97.% confidence, once quality flags have been applied to the SOM. The method presented here represents a significant improvement over the previously adopted direct redshift calibration implementation for KiDS, owing to its diagnostic and quality assurance capabilities. The implementation of this method in future cosmic shear studies will allow better diagnosis, examination, and mitigation of systematic biases in photometric redshift calibration.

Phenotypic redshifts with self-organizing maps: A novel method to characterize redshift distributions of source galaxies for weak lensing

ABSTRACT Wide-field imaging surveys such as the Dark Energy Survey (DES) rely on coarse measurements of spectral energy distributions in a few filters to estimate the redshift distribution of source galaxies. In this regime, sample variance, shot noise, and selection effects limit the attainable accuracy of redshift calibration and thus of cosmological constraints. We present a new method to combine wide-field, few-filter measurements with catalogues from deep fields with additional filters and sufficiently low photometric noise to break degeneracies in photometric redshifts. The multiband deep field is used as an intermediary between wide-field observations and accurate redshifts, greatly reducing sample variance, shot noise, and selection effects. Our implementation of the method uses self-organizing maps to group galaxies into phenotypes based on their observed fluxes, and is tested using a mock DES catalogue created from N-body simulations. It yields a typical uncertainty on the mean redshift in each of five tomographic bins for an idealized simulation of the DES Year 3 weak-lensing tomographic analysis of σΔz = 0.007, which is a 60 per cent improvement compared to the Year 1 analysis. Although the implementation of the method is tailored to DES, its formalism can be applied to other large photometric surveys with a similar observing strategy.

How to Measure Galaxy Star Formation Histories. II. Nonparametric Models

Abstract Nonparametric star formation histories (SFHs) have long promised to be the “gold standard” for galaxy spectral energy distribution (SED) modeling as they are flexible enough to describe the full diversity of SFH shapes, whereas parametric models rule out a significant fraction of these shapes a priori. However, this flexibility is not fully constrained even with high-quality observations, making it critical to choose a well-motivated prior. Here, we use the SED-fitting code Prospector to explore the effect of different nonparametric priors by fitting SFHs to mock UV–IR photometry generated from a diverse set of input SFHs. First, we confirm that nonparametric SFHs recover input SFHs with less bias and return more accurate errors than do parametric SFHs. We further find that, while nonparametric SFHs robustly recover the overall shape of the input SFH, the primary determinant of the size and shape of the posterior star formation rate as a function of time (SFR(t)) is the choice of prior, rather than the photometric noise. As a practical demonstration, we fit the UV–IR photometry of ∼6000 galaxies from the Galaxy and Mass Assembly survey and measure scatters between priors to be 0.1 dex in mass, 0.8 dex in SFR100 Myr, and 0.2 dex in mass-weighted ages, with the bluest star-forming galaxies showing the most sensitivity. An important distinguishing characteristic for nonparametric models is the characteristic timescale for changes in SFR(t). This difference controls whether galaxies are assembled in bursts or in steady-state star formation, corresponding respectively to (feedback-dominated/accretion-dominated) models of galaxy formation and to (larger/smaller) confidence intervals derived from SED fitting. High-quality spectroscopy has the potential to further distinguish between these proposed models of SFR(t).

TFAW: Wavelet-based signal reconstruction to reduce photometric noise in time-domain surveys

Context. There have been many efforts to correct systematic effects in astronomical light curves to improve the detection and characterization of planetary transits and astrophysical variability. Algorithms such as the trend filtering algorithm (TFA) use simultaneously-observed stars to measure and remove systematic effects, and binning is used to reduce high-frequency random noise. Aims. We present TFAW, a wavelet-based modified version of TFA. First, TFAW aims to increase the periodic signal detection and second, to return a detrended and denoised signal without modifying its intrinsic characteristics. Methods. We modified TFA’s frequency analysis step adding a stationary wavelet transform filter to perform an initial noise and outlier removal and increase the detection of variable signals. A wavelet-based filter was added to TFA’s signal reconstruction to perform an adaptive characterization of the noise- and trend-free signal and the underlying noise contribution at each iteration while preserving astrophysical signals. We carried out tests over simulated sinusoidal and transit-like signals to assess the effectiveness of the method and applied TFAW to real light curves from TFRM. We also studied TFAW’s application to simulated multiperiodic signals. Results. TFAW improves the signal detection rate by increasing the signal detection efficiency (SDE) up to a factor ∼2.5× for low S/R light curves. For simulated transits, the transit detection rate improves by a factor ∼2 − 5× in the low-S/R regime compared to TFA. TFAW signal approximation performs up to a factor ∼2× better than bin averaging for planetary transits. The standard deviations of simulated and real TFAW light curves are ∼40% better compared to TFA. TFAW yields better MCMC posterior distributions and returns lower uncertainties, less biased transit parameters and narrower (by approximately ten times) credibility intervals for simulated transits. TFAW is also able to improve the characterization of multiperiodic signals. We present a newly-discovered variable star from TFRM.

GPU-accelerated hierarchical Bayesian estimation of luminosity functions using flux-limited observations with photometric noise

We describe a computational framework for hierarchical Bayesian inference with simple (typically single-plate) parametric graphical models that uses graphics processing units (GPUs) to accelerate computations, enabling deployment on very large datasets. Its C++ implementation, CUDAHM (CUDA for Hierarchical Models) exploits conditional independence between instances of a plate, facilitating massively parallel exploration of the replication parameter space using the single instruction, multiple data architecture of GPUs. It provides support for constructing Metropolis-within-Gibbs samplers that iterate between GPU-accelerated robust adaptive Metropolis sampling of plate-level parameters conditional on upper-level parameters, and Metropolis-Hastings sampling of upper-level parameters on the host processor conditional on the GPU results. CUDAHM is motivated by demographic problems in astronomy, where density estimation and linear and nonlinear regression problems must be addressed for populations of thousands to millions of objects whose features are measured with possibly complex uncertainties. We describe a thinned latent point process framework for modeling such demographic data. We demonstrate accurate GPU-accelerated parametric conditional density deconvolution for simulated populations of up to 300,000 objects in ~1 hour using a single NVIDIA Tesla K40c GPU. Supplementary material provides details about the CUDAHM API and the demonstration problem.

Implementation of a 1-2 keV point-projection x-ray spectrometer on the National Ignition Facility.

A point-projection soft X-ray Opacity Spectrometer (OpSpec) has been implemented to measure X-ray spectra from ∼1 to 2 keV on the National Ignition Facility (NIF). Measurement of such soft X-rays with open-aperture point-projection detectors is challenging because only very thin filters may be used to shield the detector from the hostile environment. OpSpec diffracts X-rays from 540 to 2100 eV off a potassium (or rubidium) acid phthalate (KAP or RbAP) crystal onto either image plates or, most recently, X-ray films. A "sacrificial front filter" strategy is used to prevent crystal damage, while 2 or 3 rear filters protect the data. Since May 2017, OpSpec has been recording X-ray transmission data for iron-magnesium plasmas on the NIF, at "Anchor 1" plasma conditions (temperature ∼150 eV, density ∼7 × 1021 e -/cm3). Upgrades improved OpSpec's performance on 6 NIF shots in August and December 2017, with reduced backgrounds and 100% data return using filter stacks as thin as 2.9 μm (total). Photometric noise is beginning to meet requirements, and further work will reduce systematic errors.

Hierarchical Probabilistic Inference of the Color–Magnitude Diagram and Shrinkage of Stellar Distance Uncertainties

Abstract We present a hierarchical probabilistic model for improving geometric stellar distance estimates using color–magnitude information. This is achieved with a data-driven model of the color–magnitude diagram, not relying on stellar models but instead on the relative abundances of stars in color–magnitude cells, which are inferred from very noisy magnitudes and parallaxes. While the resulting noise-deconvolved color–magnitude diagram can be useful for a range of applications, we focus on deriving improved stellar distance estimates relying on both parallax and photometric information. We demonstrate the efficiency of this approach on the 1.4 million stars of the Gaia TGAS sample that also have AAVSO Photometric All Sky Survey magnitudes. Our hierarchical model has 4 million parameters in total, most of which are marginalized out numerically or analytically. We find that distance estimates are significantly improved for the noisiest parallaxes and densest regions of the color–magnitude diagram. In particular, the average distance signal-to-noise ratio (S/N) and uncertainty improve by 19% and 36%, respectively, with 8% of the objects improving in S/N by a factor greater than 2. This computationally efficient approach fully accounts for both parallax and photometric noise and is a first step toward a full hierarchical probabilistic model of the Gaia data.