arXiv subjects

Alexander Shapiro

Publications and source records attributed to Alexander Shapiro.

At least 19 recordsLinked to original sources

arXiv2026

Towards understanding stellar variability at the sub m/s level: granulation-induced variability across the optical spectrum

Detecting the radial velocity signal of Earth-mass exoplanets requires the characterisation and removal of granulation-induced radial velocity variability from spectroscopic observations. By coupling three-dimensional (3D) hydrodynamic (HD) simulations to a radiative transfer code, we can isolate and study the effect of granulation on stellar lines. In this study we isolated the impact of granulation on spectral line shapes and shifts for the largest and most diverse synthetic spectral line sample to date. Our aims were twofold. First, we quantified how granulation affects the temporal evolution of shapes and shifts of 72 unblended spectral lines in two wavelength regions: 5500-5600 {\AA} and 6100-6200 {\AA}, from disc centre to the stellar limb. Second, we investigated if spectral lines behave coherently in their line shape variability. We find that weak lines show the largest radial-velocity variability due to granulation, up to 40 m/s at disc centre and 50 m/s at the stellar limb. On the other hand, strong lines exhibit larger variability in equivalent width than weak lines across the stellar disc. In addition, the equivalent width and line depth of a spectral line are strongly linearly correlated with its radial velocity. While granulation affects all three of these quantities, planetary Doppler shifts only affect radial velocities, opening the door to new granulation-mitigation methods. Lastly, we find that the radial velocity and equivalent width of most spectral lines in our sample evolve coherently in time, with the Fe I and Ca I lines behaving the most similarly. Due to the coherency, line blends will not significantly affect the temporal behaviour of RV and line shape, as induced by granulation. Besides, the coherency between spectral lines offer the opportunity to create disc-integrated spectra of many lines simultaneously, which will be explored in future work.

astro-ph.SR↗

arXiv2026

A Scalable Path to Astrometric Exomoon Discoveries with the Nautilus Space Observatory

Moons orbiting exoplanets (exomoons) can be detected through the reflex motion they impart to their host planet, which is recoverable in relative star-planet astrometric time series. The signal grows with moon mass and orbital separation and decreases with distance, so the nearest and least massive imaged planets are the most favorable targets. Recovering small (<Earth-mass) moons requires continuous, long-baseline, high-precision monitoring that is only practical with a dedicated or nearly dedicated facility. Building on recent simulations of astrometric exomoon detection and of the resulting population yields, we argue that the scalable, replicable architecture of the Nautilus Space Observatory is uniquely suited to this problem, and we outline a staged campaign. In an initial phase, one or a few small apertures target the nearest imaged giant planets--a high-reward but low-probability search focused on the closest stars. As the array is built out, the astrometric noise floor decreases and the same technique extends the search to the nearest such systems among nearby stars of spectral type K and earlier. This would be performed in parallel with high-contrast imaging and spectral characterization of the host planets and in synergy with a companion starshade concept for imaging Earth-like planets around the same nearby stars. Nautilus thus provides a scalable path from the first detection of a nearby exomoon toward a systematic search for exomoons around the closest stars.

astro-ph.IM↗

arXiv2026

Nautilus: Fast Time-Resolved Spectroscopy of GKM Stellar Flares and Their Implications for Planetary Habitability

Low-mass GKM dwarfs are prime targets for finding habitable-zone Earth-sized planets, but their frequent flares, especially on M~dwarfs, can strongly affect planetary atmospheres through enhanced UV/XUV radiation and stellar proton events, which can drive complex photochemistry and accelerate atmospheric escape. Current atmospheric and habitability models of planets around low-mass stars often rely on simplified flare inputs, such as fixed-temperature blackbodies or approximate optical-to-UV/XUV conversions. However, recent observations show that M~dwarfs' flare temperatures and spectral shapes can vary significantly with flare energy, phase, and stellar type, and that optical-based flare observations may underestimate the flare energy in the UV. Time-resolved spectroscopic flare observations of G- and K-dwarfs also remain rare compared to those of M dwarfs. Here, we propose that the Nautilus Space Observatory concept can provide a unique opportunity to obtain fast-cadence, precisely flux-calibrated, moderate-resolution NUV-to-NIR spectroscopy of flares across a large sample of GKM dwarfs. These observations will measure the time-dependent flare energy budget from the near-UV/blue continuum to the optical and near-infrared continuum, while resolving key chromospheric lines that trace the underlying flare physics. We aim to construct a statistical library of empirical flare spectral templates organized by flare and stellar properties, including flare energy, flare phase, and host-star spectral type. This library will provide a practical bridge between observed stellar flare properties and the radiation inputs required for planetary atmospheric evolution and habitability simulations.

astro-ph.SR↗

arXiv2026

Decoding the Radial Velocity Signatures of Solar Faculae with 3D MHD Simulations

We model the solar radial velocity (RV) signal induced by faculae, the dominant contributor to RV variability in Sun-like stars. We use a representative case of a facular patch transiting the visible solar disk as the Sun rotates to disentangle various physical effects contributing to the RV signal. Our approach is based on 3D radiative magnetohydrodynamic (MHD) simulations of the solar photosphere and upper convection zone with the MURaM code and spectral synthesis with the MPS-ATLAS code. We show that the faculae-induced RV strongly depends on the facular position on the solar disk. Near disk centre, facular magnetic fields inhibit the convective blueshift and thus produce a relative redshift of the solar spectrum. Surprisingly, when located closer to the limb, namely at heliocentric angles greater than about $60^\circ$, faculae produce a relative blueshift. This transition from redshift to blueshift is caused by the effect of magnetic fields on horizontal flows, which dominate the signal near the limb, and on the visibility of these flows. In combination with solar rotation, this centre-to-limb dependence of the facular effect leads to a complex RV profile during the facular transit and, in particular, to a phase lag between the maximum of the RV signal and the facular crossing of the central meridian. We further show that, in contrast to stellar reflex motion, the facular signal strongly depends on the spectral line in which it is measured.

astro-ph.SR↗

arXiv2026

Synthetic disk-integrated absorption lines isolating stellar granulation for high-precision RV studies

We present a novel method for constructing high-accuracy, time-varying disk-integrated stellar absorption line profiles that isolate the effects of granulation alone. This framework provides an effectively unlimited supply of physically consistent training data, offering a unique opportunity to study granulation-driven velocity variability with no contamination from other stellar processes or instrumental systematics. Our interpolation scheme enables accurate profile generation at arbitrary limb angles and successfully reproduces observed disk integrated solar bisector shapes from IAG spectra. Using four Fe I lines (525.0, 615.2, 617.3, and 627.1 nm), we produce 1000 model star disk-integrated realisations per line and find an isolated granulation-induced RV scatter of 0.16-0.21 m s^-1. Using our synthetic profiles and assuming infinite signal-to-noise, we find strong correlations between various line-shape metrics and convective blueshift, demonstrating that line-shape diagnostics can, in principle, trace granulation effects. Equivalent width proves the strongest diagnostic, achieving up to 60% scatter reduction. However, the strength of all simple line shape diagnostics rapidly diminishes once photon noise is injected. Even when artificially boosting the signal to represent a spectrum containing ~1000 spectral lines, the achievable improvement with these metrics remains below 10% at typical signal-to-noise ratios. Our results highlight the need for more robust, noise-resilient diagnostics and position our synthetic dataset as a valuable testbed for developing and benchmarking such methods.

astro-ph.SR↗

arXiv2026

Stochastic Optimal Control with Side Information and Bayesian Learning

We study infinite-horizon stochastic optimal control problems with observable side information: a Markov chain that modulates an unknown context-conditional randomness distribution. Since this distribution is unknown, we propose a Bayesian reformulation based on a parametric density model and posterior predictive dynamics, which yields a Bayesian Bellman equation. We prove posterior consistency under Markov samples and, under correct specification and identifiability, uniform convergence of the Bayesian value function. Finally, we establish Bernstein--von Mises-type asymptotic normality for the data-driven contextual optimal value.

math.OC↗

arXiv2025

Simulations of facular magnetic fields on cool stars I: Main sequence stars with solar metallicity

Stellar convection in the presence of magnetic field affects the emergent intensity, as well as the structure and evolution of cool main-sequence dwarfs. We aim to understand the effect of faculae-like field strengths on near-surface stellar convection using 3D radiative MHD simulations of near-surface magneto-convection. We compare simulations of F, G, K and M main-sequence stars with a small-scale dynamo (SSD) to faculae-like spatially averaged field strengths (from 100 to 500 G). We focus on the effect of imposed magnetic field on the thermodynamic stratification and velocities, along with the bolometric intensity and surface field strength. Imposed magnetic fields result in reduced average density and gas pressure near the surface compared to the SSD simulations. The temperature stratification also shows a dip at and just below the stellar surface. The changes in average bolometric intensity are within a percent, with different trends with field strength for different stellar types. In addition, the convective velocities are reduced. The magnitude of changes in thermodynamic quantities are related to field strength as well as the stellar $T_{\rm eff}$. Faculae-strength magnetic fields modify the near surface convection by reducing gas pressure and density as well as suppressing convection in regions with strong field concentrations. The strength of these effects depends on the stellar type.

astro-ph.SR↗

arXiv2025

The algebraic modular functor conjecture in type $A_n$ quantum Teichm\"uller theory

Fock and Goncharov introduced a quantization of higher Teichm\"uller theory using cluster Poisson varieties and their noncommutative deformations, associating to a complex semisimple Lie group $G$ and a marked surface $S$ a quantum algebra $\mathbb{L}_{G,S}$ equipped with an action of the surface mapping class group. They conjectured that these quantizations form an algebraic analog of a modular functor: cutting a surface along a simple closed curve should correspond to a canonical gluing isomorphism for the associated algebras. In this paper we prove this conjecture for $G = \mathrm{PGL}_{n+1}$. Our approach requires two extensions of the Fock-Goncharov framework: (1) enhanced moduli spaces incorporating additional boundary data, providing algebro-geometric analogs of Fenchel-Nielsen twist coordinates; and (2) the residue universal Laurent ring, a refinement of the quantum universal Laurent ring obtained by localizing and imposing residue conditions. Using these tools, we construct canonical cutting isomorphisms that are equivariant under mapping class group actions and suffice to reconstruct the entire algebra $\mathbb{L}_{G,S}$ from data associated to the cut surface.

math.QA↗

arXiv2025

Central Limit Theorems for Sample Average Approximations in Stochastic Optimal Control

We establish central limit theorems for the Sample Average Approximation (SAA) method in discrete-time, finite-horizon stochastic optimal control. Our analysis is based on an abstract limit theorem for stochastic backward recursions, which yields a recursive characterization of the limiting laws. Applied to the dynamic programming principle, this framework gives Gaussian limits for SAA value functions under unique optimal policies. The asymptotic variance at each stage decomposes into a current-stage variance and a propagated future variance, demonstrating how statistical uncertainty accumulates backward through time. We also apply the framework to the linear quadratic regulator, derive explicit limiting laws and variance formulas, and provide numerical illustrations of the resulting variance decomposition. Finally, we discuss the form of the limit laws under nonunique optimal policies.

math.OC↗

arXiv2025

Risk-averse formulations of Stochastic Optimal Control and Markov Decision Processes

The aim of this paper is to investigate risk-averse and distributionally robust modeling of Stochastic Optimal Control (SOC) and Markov Decision Process (MDP). We discuss construction of conditional nested risk functionals, a particular attention is given to the Value-at-Risk measure. Necessary and sufficient conditions for existence of non-randomized optimal policies in the framework of robust SOC and MDP are derived. We also investigate sample complexity of optimization problems involving the Value-at-Risk measure.

math.OC↗

arXiv2025

Towards understanding stellar variability at the sub m/s level: Isolating granulation signals in synthetic spectral lines

Granulation in the photospheres of FGK-type stars induces variability in absorption lines, complicating exoplanet detection via radial velocities and characterisation via transmission spectroscopy. We aim to quantify the impact of granulation on the radial velocity and bisector asymmetry of stellar absorption lines of varying strengths and at different limb angles. We use 3D radiation-hydrodynamic simulations from MURaM paired with MPS-ATLAS radiative transfer calculations to synthesise time series' for four Fe I lines at different limb angles for a solar-type star. Our line profiles are synthesised at an extremely high resolution (R = 2,000,000), exceeding what is possible observationally and allowing us to capture intricate line shape variations. We introduce a new method of classifying the stellar surface into three components and use this to parameterise the line profiles. Our parameterisation method allows us to disentangle the contributions from p-modes and granulation, providing the unique opportunity to study the effects of granulation without contamination from p-mode effects. We validate our method by comparing radial velocity power spectra of our granulation time series to observations from the LARS spectrograph. We find that we are able to replicate the granulation component extracted from observations of the Fe I 617 nm line at the solar disk centre. We use our granulation-isolated results to show variations in convective blueshift and bisector asymmetry at different limb angles, finding good agreement with empirical results. We show that weaker lines have higher velocity contrast between granules and lanes, resulting in higher granulation-induced velocity fluctuations. Our parameterisation provides a computationally efficient strategy to construct new line profiles, laying the groundwork for future improvements in mitigating stellar noise in exoplanet studies.

astro-ph.SR↗

arXiv2025

Minimax asymptotics

In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem that approximates the true population problem and study the limiting distributions of these estimators as the sample size tends to infinity. The main technical tool we employ in our analysis is the theory of sensitivity analysis of parameterized mathematical optimization problems. Our results go well beyond the existing literature and show that these limiting distributions are highly non-Gaussian in general and normal in simple specific cases. These results open up the way for the development of statistical inference methods in parametric minimax problems.

math.ST↗

arXiv2024

Distributionally robust stochastic optimal control

The main goal of this paper is to discuss the construction of distributionally robust counterparts of stochastic optimal control problems. Randomized and non-randomized policies are considered. In particular, necessary and sufficient conditions for the existence of non-randomized policies are given.

math.OC↗

arXiv2024

Cluster structure on genus 2 spherical DAHA: seven-colored flower

We construct an embedding of the Arthamonov-Shakirov algebra of genus 2 knot operators into the quantized coordinate ring of the cluster Poisson variety of exceptional finite mutation type $X_7$. The embedding is equivariant with respect to the action of the mapping class group of the closed surface of genus 2. The cluster realization of the mapping class group action leads to a formula for the coefficient of each monomial in the genus 2 Macdonald polynomial of type $A_1$ as sum over lattice points in a convex polyhedron in 7-dimensional space.

math.RT↗

arXiv2024

Ruijsenaars wavefunctions as modular group matrix coefficients

We give a description of the Halln\"as--Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element $S\in SL(2,\mathbb{Z})$ acting on the Hilbert space of $GL(2)$ quantum Teichm\"uller theory on the punctured torus. The $GL(2)$ Macdonald polynomials are then obtained as special values of the analytic continuation of these matrix coefficients. The main tool used in the proof is the cluster structure on the moduli space of framed $GL(2)$-local systems on the punctured torus, and an $SL(2,\mathbb{Z})$-equivariant embedding of the $GL(2)$ spherical DAHA into the quantized coordinate ring of the corresponding cluster Poisson variety.

math-ph↗

arXiv2023

A roadmap for the atmospheric characterization of terrestrial exoplanets with JWST

Ultra-cool dwarf stars are abundant, long-lived, and uniquely suited to enable the atmospheric study of transiting terrestrial companions with JWST. Amongst them, the most prominent is the M8.5V star TRAPPIST-1 and its seven planets. While JWST Cycle 1 observations have started to yield preliminary insights into the planets, they have also revealed that their atmospheric exploration requires a better understanding of their host star. Here, we propose a roadmap to characterize the TRAPPIST-1 system -- and others like it -- in an efficient and robust manner. We notably recommend that -- although more challenging to schedule -- multi-transit windows be prioritized to mitigate the effects of stellar activity and gather up to twice more transits per JWST hour spent. We conclude that, for such systems, planets cannot be studied in isolation by small programs, but rather need large-scale, jointly space- and ground-based initiatives to fully exploit the capabilities of JWST for the exploration of terrestrial planets.

astro-ph.EP↗

arXiv2023

Rectangularity and duality of distributionally robust Markov Decision Processes

The main goal of this paper is to discuss several approaches to formulation of distributionally robust counterparts of Markov Decision Processes, where the transition kernels are not specified exactly but rather are assumed to be elements of the corresponding ambiguity sets. The intent is to clarify some connections between the game and static formulations of distributionally robust MDPs, and delineate the role of rectangularity associated with ambiguity sets in determining these connections.

math.OC↗

arXiv2023

Episodic Bayesian Optimal Control with Unknown Randomness Distributions

Stochastic optimal control with unknown randomness distributions has been studied for a long time, encompassing robust control, distributionally robust control, and adaptive control. We propose a new episodic Bayesian approach that incorporates Bayesian learning with optimal control. In each episode, the approach learns the randomness distribution with a Bayesian posterior and subsequently solves the corresponding Bayesian average estimate of the true problem. The resulting policy is exercised during the episode, while additional data/observations of the randomness are collected to update the Bayesian posterior for the next episode. We show that the resulting episodic value functions and policies converge almost surely to their optimal counterparts of the true problem if the parametrized model of the randomness distribution is correctly specified. We further show that the asymptotic convergence rate of the episodic value functions is of the order $O(N^{-1/2})$, where $N$ is the number of episodes given that only one data point is collected in each episode. We develop an efficient computational method based on stochastic dual dynamic programming (SDDP) for a class of problems that have convex cost functions and linear state dynamics. Our numerical results on a classical inventory control problem verify the theoretical convergence results, and numerical comparison with two other methods demonstrate the effectiveness of the proposed Bayesian approach.

math.OC↗