HELIOS-Retrieval: An Open-source, Nested Sampling Atmospheric Retrieval Code, Application to the HR 8799 Exoplanets and Inferred Constraints for Planet Formation

We present an open-source retrieval code named HELIOS-Retrieval (hereafter HELIOS-R), designed to obtain chemical abundances and temperature-pressure profiles from inverting the measured spectra of exoplanetary atmospheres. In the current implementation, we use an exact solution of the radiative transfer equation, in the pure absorption limit, in our forward model, which allows us to analytically integrate over all of the outgoing rays (instead of performing Gaussian quadrature). Two chemistry models are considered: unconstrained chemistry (where the mixing ratios are treated as free parameters) and equilibrium chemistry (enforced via analytical formulae, where only the elemental abundances are free parameters). The nested sampling algorithm allows us to formally implement Occam's Razor based on a comparison of the Bayesian evidence between models. We perform a retrieval analysis on the measured spectra of the HR 8799b, c, d and e directly imaged exoplanets. Chemical equilibrium is disfavored by the Bayesian evidence for HR 8799b, c and d. We find supersolar C/O, C/H and O/H values for the outer HR 8799b and c exoplanets, while the inner HR 8799d and e exoplanets have substellar C/O, substellar C/H and superstellar O/H values. If these retrieved properties are representative of the bulk compositions of the exoplanets, then they are inconsistent with formation via gravitational instability (without late-time accretion) and consistent with a core accretion scenario in which late-time accretion of ices occurred differently for the inner and outer exoplanets. For HR 8799e, we find that spectroscopy in the K band is crucial for constraining C/O and C/H. HELIOS-R is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).Comment: 27 pages, 21 figures, 3 tables, published in A

Exoplanet phase curves: observations and theory

Phase curves are the best technique to probe the three dimensional structure of exoplanets' atmospheres. In this chapter we first review current exoplanets phase curve observations and the particular challenges they face. We then describe the different physical mechanisms shaping the atmospheric phase curves of highly irradiated tidally locked exoplanets. Finally, we discuss the potential for future missions to further advance our understanding of these new worlds.Comment: Fig.5 has been updated. Table 1 and corresponding figures have been updated with new values for WASP-103b and WASP-18b. Contains a table sumarizing phase curve observation

Exoplanet Atmosphere Measurements from Transmission Spectroscopy and other Planet-Star Combined Light Observations

It is possible to learn a great deal about exoplanet atmospheres even when we cannot spatially resolve the planets from their host stars. In this chapter, we overview the basic techniques used to characterize transiting exoplanets - transmission spectroscopy, emission and reflection spectroscopy, and full-orbit phase curve observations. We discuss practical considerations, including current and future observing facilities and best practices for measuring precise spectra. We also highlight major observational results on the chemistry, climate, and cloud properties of exoplanets.Comment: Accepted review chapter; Handbook of Exoplanets, eds. Hans J. Deeg and Juan Antonio Belmonte (Springer-Verlag). 22 pages, 6 figure

Atmospheric retrieval of exoplanets

Exoplanetary atmospheric retrieval refers to the inference of atmospheric properties of an exoplanet given an observed spectrum. The atmospheric properties include the chemical compositions, temperature profiles, clouds/hazes, and energy circulation. These properties, in turn, can provide key insights into the atmospheric physicochemical processes of exoplanets as well as their formation mechanisms. Major advancements in atmospheric retrieval have been made in the last decade, thanks to a combination of state-of-the-art spectroscopic observations and advanced atmospheric modeling and statistical inference methods. These developments have already resulted in key constraints on the atmospheric H2O abundances, temperature profiles, and other properties for several exoplanets. Upcoming facilities such as the JWST will further advance this area. The present chapter is a pedagogical review of this exciting frontier of exoplanetary science. The principles of atmospheric retrievals of exoplanets are discussed in detail, including parametric models and statistical inference methods, along with a review of key results in the field. Some of the main challenges in retrievals with current observations are discussed along with new directions and the future landscape

Verification of frequency characteristics of load devices declared by the manufacturer

The aim of the work was to clarify the possibility of determining the frequency characteristics of load devices according to the parameters of transients, the rate of rise of the leading edge, its duration, the presence or absence of overshoot, the form of the transient process. The main objective of the study was to determine the load parameters required to perform the calculation. To confirm this hypothesis about the influence of the selected parameters, the method of physical experiment was used. The specification of indicators for operational parameters may be relevant when organizing the input control of incoming purchased products for various applied tasks. The improvement of input control algorithms, the implementation of time characteristics checks instead of frequency ones will confirm the compliance of the characteristics declared by the manufacturer or supplier of this equipment and provide the possibility of identifying the internal structure of devices to ensure their compatibility with other equipment used in production, as well as expand the technological capabilities of enterprises. The indicated problem seems promising for a number of organizations operating complex electronic equipment, as well as for domestic manufacturers of electronic devices. The relevance of the study also lies in reducing the amount required for the verification process of equipment by increasing the computational load. In addition, dynamic identification by transient parameters increases the speed of verification

Titanium oxide and chemical inhomogeneity in the atmosphere of the exoplanet WASP-189 b

The temperature of an atmosphere decreases with increasing altitude, unless a shortwave absorber that causes a temperature inversion exists1. Ozone plays this role in the Earth’s atmosphere. In the atmospheres of highly irradiated exoplanets, the shortwave absorbers are predicted to be titanium oxide (TiO) and vanadium oxide (VO)2. Detections of TiO and VO have been claimed using both low-3,4,5,6 and high-7 spectral-resolution observations, but subsequent observations have failed to confirm these claims8,9,10 or overturned them11,12,13. Here we report the unambiguous detection of TiO in the ultra-hot Jupiter WASP-189 b14 using high-resolution transmission spectroscopy. This detection is based on applying the cross-correlation technique15 to many spectral lines of TiO from 460 to 690 nm. Moreover, we report detections of metals, including neutral and singly ionized iron and titanium, as well as chromium, magnesium, vanadium and manganese (Fe, Fe+, Ti, Ti+, Cr, Mg, V, Mn). The line positions of the detected species differ, which we interpret as a consequence of spatial gradients in their chemical abundances, such that they exist in different regions or dynamical regimes. This is direct observational evidence for the three-dimensional thermochemical stratification of an exoplanet atmosphere derived from high-resolution ground-based spectroscopy

Atomic iron and titanium in the atmosphere of the exoplanet KELT-9b

To constrain the formation history of an exoplanet, we need to know its chemical composition. With an equilibrium temperature of about 4,050 kelvin, the exoplanet KELT-9b (also known as HD 195689b) is an archetype of the class of ultrahot Jupiters that straddle the transition between stars and gas-giant exoplanets and are therefore useful for studying atmospheric chemistry. At these high temperatures, iron and several other transition metals are not sequestered in molecules or cloud particles and exist solely in their atomic forms5. However, despite being the most abundant transition metal in nature, iron has not hitherto been detected directly in an exoplanet because it is highly refractory. The high temperatures of KELT-9b imply that its atmosphere is a tightly constrained chemical system that is expected to be nearly in chemical equilibrium and cloud-free, and it has been predicted that spectral lines of iron should be detectable in the visible range of wavelengths. Here we report observations of neutral and singly ionized atomic iron (Fe and Fe⁺) and singly ionized atomic titanium (Ti⁺) in the atmosphere of KELT-9b. We identify these species using cross-correlation analysis of high-resolution spectra obtained as the exoplanet passed in front of its host star. Similar detections of metals in other ultrahot Jupiters will provide constraints for planetary formation theories