A Relationship between Stellar Age and Spot Coverage

Morris, Brett M.

doi:10.3847/1538-4357/ab79a0

Cited by 51 publications

(26 citation statements)

References 74 publications

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“…ABC, LFI and SBI 2 are all heterogeneous terms for approaches to problems where the likelihood is analytically intractable, but data can be simulated. Problems of this type are common in astronomy, and have led to a recent rise in work implementing SBI models, in a wide range of areas including cosmology (Jennings et al 2016; 2020), solar physics (Weiss et al 2021), supermassive black holes (Witzel et al 2020), exoplanets (Sandford et al 2019;Hsu et al 2020;Bryson et al 2020;Kunimoto & Bryson 2021), stellar astronomy (Cisewski-Kehe et al 2019;Kunimoto & Matthews 2020;Morris 2020), galactic astronomy (Mor et al 2019;Cheng et al 2020), dark matter studies (Hermans et al 2020), and extragalactic astronomy (Aufort et al 2020;Tortorelli et al 2020;He et al 2020;Enzi et al 2020).…”

Section: Simulation-based Inferencementioning

confidence: 99%

Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference

Huppenkothen,

Bachetti

2021

Preprint

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Because many of our X-ray telescopes are optimized towards observing faint sources, observations of bright sources like X-ray binaries in outburst are often affected by instrumental biases. These effects include dead time and photon pile-up, which can dramatically change the statistical inference of physical parameters from these observations. While dead time is difficult to take into account in a statistically consistent manner, simulating dead time-affected data is often straightforward. This structure makes the issue of inferring physical properties from dead time-affected observations fall into a class of problems common across many scientific disciplines. There is a growing number of methods to address them under the names of Approximate Bayesian Computation (ABC) or Simulation-Based Inference (SBI), aided by new developments in density estimation and statistical machine learning. In this paper, we introduce SBI as a principled way to infer variability properties from dead time-affected light curves. We use Sequential Neural Posterior Estimation to estimate the posterior probability for variability properties. We show that this method can recover variability parameters on simulated data even when dead time is variable, and present results of an application of this approach to NuSTAR observations of the galactic black hole X-ray binary GRS 1915+105.

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Section: Simulation-based Inferencementioning

confidence: 99%

Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference

Huppenkothen,

Bachetti

2021

Preprint

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“…It is likely that several simplifications must be made in order to make this approach tractable. This was done to some extent in Morris (2020b), who derived a closed form expression for the flux by ignoring certain projection effects, such as the self-occultation of large spots by the limb of the star, and neglected variations in limb darkening within spots. Such a model could admit a closed-form solution to the GP covariance and may be better at capturing the effects of small spots, at the expense of the ability to model larger spots.…”

Section: Small Spotsmentioning

confidence: 99%

“…While we believe the spot coverage results of that paper are predominantly driven by the prior (due to the strong degeneracy between the spot contrast and the number of spots; see §4.2 in Luger et al 2021b), the ensemble analysis employed in that paper is nevertheless a powerful technique to infer spot properties. Our work builds on that of Morris (2020b) by deriving a closed form solution to the likelihood function (as opposed to a sample-based likelihood-free inference algorithm) and by harnessing the covariance structure of the data when doing inference (as opposed to relying solely on the amplitude of the data).…”

Section: Starspots and Stellar Variabilitymentioning

confidence: 99%

Mapping stellar surfaces II: An interpretable Gaussian process model for light curves

Luger,

Foreman-Mackey,

Hedges

2021

Preprint

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The use of Gaussian processes (GPs) as models for astronomical time series datasets has recently become almost ubiquitous, given their ease of use and flexibility. GPs excel in particular at marginalization over the stellar signal in cases where the variability due to starspots rotating in and out of view is treated as a nuisance, such as in exoplanet transit modeling. However, these effective models are less useful in cases where the starspot signal is of primary interest since it is not obvious how the parameters of the GP model are related to the physical properties of interest, such as the size, contrast, and latitudinal distribution of the spots. Instead, it is common practice to explicitly model the effect of individual starspots on the light curve and attempt to infer their properties via optimization or posterior inference. Unfortunately, this process is degenerate, ill-posed, and often computationally intractable when applied to stars with more than a few spots and/or to ensembles of many light curves. In this paper, we derive a closed-form expression for the mean and covariance of a Gaussian process model that describes the light curve of a rotating, evolving stellar surface conditioned on a given distribution of starspot sizes, contrasts, and latitudes. We demonstrate that this model is correctly calibrated, allowing one to robustly infer physical parameters of interest from one or more stellar light curves, including the typical radii and the mean and variance of the latitude distribution of starspots. Our GP has far-ranging implications for understanding the variability and magnetic activity of stars from both light curves and radial velocity (RV) measurements, as well as for robustly modeling correlated noise in both transiting and RV exoplanet searches. Our implementation is efficient, user-friendly, and open source, available as the Python package starry_process.

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“…We will show that even though individual light curves are not very constraining, light curves of many stars observed at different inclinations can uniquely constrain certain properties of the surfaces of those stars. This idea was recently explored to some extent in Morris (2020b), who used ensemble analyses to derive constraints on spot coverage areas as a function of stellar age. However, one of the main conclusions of the present paper is that quantities like the total spot coverage and the total number of spots are not direct observables in single-band photometry.…”

Section: Introductionmentioning

confidence: 99%

Mapping stellar surfaces I: Degeneracies in the rotational light curve problem

Luger,

Foreman-Mackey,

Hedges

et al. 2021

Preprint

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Thanks to missions like Kepler and TESS, we now have access to tens of thousands of high precision, fast cadence, and long baseline stellar photometric observations. In principle, these light curves encode a vast amount of information about stellar variability and, in particular, about the distribution of starspots and other features on their surfaces. Unfortunately, the problem of inferring stellar surface properties from a rotational light curve is famously ill-posed, as it often does not admit a unique solution. Inference about the number, size, contrast, and location of spots can therefore depend very strongly on the assumptions of the model, the regularization scheme, or the prior. The goal of this paper is twofold: (1) to explore the various degeneracies affecting the stellar light curve "inversion" problem and their effect on what can and cannot be learned from a stellar surface given unresolved photometric measurements; and (2) to motivate ensemble analyses of the light curves of many stars at once as a powerful data-driven alternative to common priors adopted in the literature. We further derive novel results on the dependence of the null space on stellar inclination and limb darkening and show that single-band photometric measurements cannot uniquely constrain quantities like the total spot coverage without the use of strong priors. This is the first in a series of papers devoted to the development of novel algorithms and tools for the analysis of stellar light curves and spectral time series, with the explicit goal of enabling statistically robust inference about their surface properties.

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A Relationship between Stellar Age and Spot Coverage

Cited by 51 publications

References 74 publications

Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference

Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference

Mapping stellar surfaces II: An interpretable Gaussian process model for light curves

Mapping stellar surfaces I: Degeneracies in the rotational light curve problem

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