Introduction
Introduction to the Exoplanet Zoo
This figure only includes planets discovered via one of the three main methods discussed in this thesis: transit, radial velocity, and imaging. The next section discusses the open questions in exoplanet astrophysics that I focus on in this paper.
Open Questions in Planet Formation
For cold Jupiters, however, in-situ gravitational collapse is a possibility, albeit complicated by the very fast inward migration timescales expected for any formed clumps (Nayakshin, 2017), as well as the uncertainty about how smaller giant planets ( closer to Jupiter mass) stopped accreting gas after collapsing early in the lifetime of the disc (Drazkowska et al., 2022). Giant planets “forget” their initial entropy over time, and within a few Myr progress along the Kelvin-Hemholtz cooling path (Marley et al., 2007).
Observational Techniques
Measuring accurate stellar radii is a topic in itself (Fulton et al., 2017), but this is beyond the scope of this thesis. Transit-derived planet radii already give us insight into the planet as a 'world' (e.g. the radii of small, presumably rocky planets are inconsistent with the presence of an extended H/He envelope, Zeng et al., 2019), but a Understanding the bulk composition, size and metallicity of the atmosphere, and the bulk metallicity of a planet (among other interesting inferable quantities) depends on independent measurements of its mass.
The Importance of Software
In addition to precise relative astrometry, VLTI/GRAVITY is equipped with a Wollaston prism for polarization measurements and two spectrometers for simultaneous acquisition of spectra of the science target and the edge-tracking object. A remarkable set of examples of the value of reproducible open source software is the Early Release Science (ERS) output from JWST.
Thesis Outline
The results of the two fits that allow for correlated noise in the SPHERE data are shown in Figure 3.11. A new formulation of the Starspot model and the consequences of the Starspot structure.” In: The Astrophysical Journal320, p.
Overfitting Affects the Reliability of Radial Velocity Mass Esti-
Abstract
2021, hereafter SM21) published radial velocity masses for two of the V1298 Tau planets using an advanced Gaussian process regression framework. In an attempt to further constrain the masses of the V1298 Tau planets, we obtained 36 RVs using Keck/HIRES and analyzed them according to published RVs and photometry.
Data
The CARMENES and HARPS-N RVs have been published in SM21 and the HIRES RVs are new to this study. However, a "rule of thumb" of the CPS HIRES observer is to use the shorter B5 deck (3.5" x 0.861") in poor viewing conditions, as the Doppler pipeline sky subtraction algorithm is unreliable when the PSF The star fills the gap.
Cross Validation Tests
In both figures, the residuals from the HIRES and CARMENES data have a much larger spread around 0 than the HARPS-N points. This is a hallmark of overfitting and indicates that the preferred SM21 model is not representative of the process generating the data.
Potential Causes of Overfitting
In other words, we expect the CARMENES activity signal to be a scalar multiple of the HIRES. This effect suggests that the Kepler signals in the SM21 preference fit are not a viable description of the RV variability on timescales larger than the rotation period.
Summary & Discussion
Both the K2 and TESS data cover less than one complete beat period of the two largest-amplitude periodic signals, but the LCO photometry (which is simultaneous with the RVs of SM21) covers a longer time baseline. However, we found that fitting all the data together with only a single rotation period forces all the instrumental GP amplitudes to 0. Many of the effects we have discussed are subtle, and we encourage others to study them further.
Appendix: Gaussian Processes and Occam’s Razor
A perfectly covariant matrix, in which all data points are perfectly correlated, will consist of all 1s12, and the covariance vectors will all exist. This exercise shows that the determinant of the covariance matrix quantifies how “clustered” the covariance vectors corresponding to each data point are in hyperspace. More clustered covariance vectors receive a large probability increase, while less clustered/more independent covariance vectors receive a smaller increase.
Acknowledgements
The Astropy Project: Building an Open Science Project and Status of the v2.0 Core Package.” In: The Astronomical Journal p. Diving beneath the sea of stellar activity: chromatic radial velocities of the young AU Mic planetary system. In: The Astronomical Journal p. TESS analysis of the directly imaged exoplanet host star HIP 65426.” In: American Astronomical Society Meeting Abstracts.
First VLTI/GRAVITY Observations of HIP 65426 b: Evidence
Abstract
In this paper, we present new astrometric data from VLTI/GRAVITY HIP 65426 b, a cool, giant exoplanet at a predicted distance of 92 au from its parent planet. The posterior eccentricity still depends on the prior, so we extensively interpret and discuss the limits of the posterior constraints presented here.
Introduction
Some of the residues published in van Leeuwen (2007) were damaged (Brandt et al., 2021), which Nielsen et al. Stellar Activity and Star-Planet Interaction." In: Monthly Notices of the Royal Astronomical Society 512.4, pp HIRES: The Echelle High Resolution Spectrometer on the Keck 10m Telescope." In: Proceedings of the SPIE.
Data
Orbit Analysis
Blunt et al., 2020) for all fits, taking advantage of the ability to fit companion RVs introduced in version 2.0.0. AIC calculates the first term as the probability of the existing data given the maximum likelihood model. Astrometric data is visible as a pink dot in the lower left corner of the panel.
Spectral Analysis
The results of the following fits are shown and compared: (1) literature astrometry only (i.e. no GRAVITY data; gray), (2) literature astrometry and the first era of GRAVITY data (dark pink outline), (3) literature astrometry and the second era of GRAVITY data (light pink outline), (4) GRAVITY astrometry only (i.e. no literature data), and (5) all astrometric data (i.e. the accepted fit; purple outline). This allows us to understand the shape of the posterior eccentricity (Figure 3.8); the probability is slightly higher at lower eccentricities, but the prior volume is lower here. We therefore chose to set the RV of the SINFONI data to 0 for the fits presented here.
Discussion & Conclusion
Also shown are the GP hyperparameters (defined as in equation 4 of Wang et al., 2020) for the SPHERE IFS spectral data (length scale and amplitude). According to the results of Marleau et al., 2019, this is a preliminary suggestion that HIP 65426 b did not reach its current position by scattering after disc scattering. Considering this limitation, in this work we repeated the analysis presented in Petrus et al. 2021), who compared the available spectral and photometric data of HIP 65426 b with the self-consistent BT-Settl and Exo-REM grids.
Acknowledgements
Extracting Stellar Activity Signals from Radial Velocity Measurements Using Neural Networks.” In: The Astronomical Journal 164.2, 49, p. On the radii of single, rapidly rotating fully convective M-dwarf stars.” In: The Astronomical Journal p. Exoplanet mimics: testing the behavior of stellar activity in radial velocity signals.” In: The Astronomical Journal 159.1, 23, p.
Origin Story & Scope of this Chapter
As an undergraduate researcher, I led a paper describing the Orbits for the Impatient algorithm (Blunt et al., 2017), a method for fitting the orbits of directly imaged planets. The resulting software package wasorbitize!, version 1, which we officially released in late 2018 and released in PASP the following year (Blunt et al., 2020). This chapter describes a subset of the new additions to the code in version 2, released in 2021 and beyond.
How orbitize! Works
That said, if the mass of the planet can be safely assumed to be negligible compared to the mass of the star, then the total mass obtained from Kepler analysis can be considered a constraint on the dynamical mass of the primary . In practice, the reverse logic is often used: an independent constraint on the mass of the primary (from e.g. spectroscopic analysis) is used as a prior on the total mass when the planet mass is small and can be ignored. Because the shapes of the posteriors of directly imaged planets' orbits are often multimodal, highly covariant and non-Gaussian, many standard posterior calculation tools, such as the widely used Affine-invariant MCMC sampler (Foreman-Mackey et al., 2013) struggle to converge.
Jointly Fitting Radial Velocities
In particular, planetary RV measurements have been shown to break the inclination/eccentricity degeneracy ( Schwarz et al., 2016 ). In the first fit, we included a GP noise model to account for the impact of rotationally modulated magnetic activity on the RVs ( Rajpaul et al., 2015 ). We computed a Markov chain representation of the posterior using emcee (Foreman-Mackey et al., 2013). We visually inspected the chains to ensure appropriate burn-in and production periods.
Jointly Fitting Absolute Astrometric Data
Discovery of the radial velocity of an eccentric Jupiterian world orbiting at 18 a.e. In: The Astronomical Journal p. Analysis of Radial Velocity Data Using Compressed Sensing Techniques.” In: Monthly Notices of the Royal Astronomical Society 464.1, p. A Gaussian Process Framework for Modeling Stellar Activity Signals in Radial Velocity Data.” In: Monthly Notices of the Royal Astronomical Society 452.3, p.
A New-and-improved Gaussian Process Regression Module for
Motivation & Gaussian Process Model Description
On the time scales of the stellar rotation period (~1 day, for faster rotators, to hundreds of days for slower ones), active regions dominate the activity signal. 1 is the amplitude of the Gaussian process, analogous to the amplitude of the correlated deviation from RV=0. The black curve shows the best-fit prediction of the GPR model, given a fixed value of the shape parameter𝜂.
How to Use it
Perturbations in Orbital Alignment of Directly Imaged Low Orbital Cover Exoplanets." In: The Astronomical Journal p. Interpreting the Atmospheric Composition of Exoplanets: Sensitivity to Planet Formation Assumptions." In: The Astrophysical Journal p.
Validating the Model
Applications
Future Directions
Radial Velocity Frontiers
These datasets will be invaluable probes of stellar activity, especially as more IR EPRV instruments come online. It will also be necessary to intensively monitor older stars with activity signals dominated by faculae more similar to the Sun, in order not to start adjusting the solar activity signal to "noise" to the detriment of our more general understanding of stellar activity. In the somewhat longer term, I think it will be important to study the wavelength dependence of stellar activity time series in order to evaluate the model I presented in Chapter 5.
Frontiers in Exoplanet Imaging
This idea has the potential to separate the convective and rotational components of RV activity (Siegel et al., in preparation), which could lead to deep insights into young stars, and V1298 Tau in particular. For the population of cold Jupiters as a whole, more regenerative studies that seek to specifically assess the reliability of parameters derived from these models (such as C/O; Xuan et al., 2022) will increase our confidence in the interpretation physical values in the spectral assembly of corner plots. Absolute astrometry from Gaia can be combined with relative astrometry and radial velocity measurements to refine the orbits and dynamical masses of cool Jupiters, as well as detect (or not) previously undetected inner planets in cool Jupiters, which will be important for continued progress on the question of whether highly fragmented cold Jupiters like HIP 65426 form via scattering (Bryan et al., 2016).
The Next 50 Years
