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To explore the hypothesis of a common source of variability in two time series, observers may estimate the magnitude‐squared coherence (MSC), which is a frequency‐domain view of the cross correlation. For time series that do not have uniform observing cadence, MSC can be estimated using Welch's overlapping segment averaging. However, multitaper has superior statistical properties to Welch's method in terms of the tradeoff between bias, variance, and bandwidth. The classical multitaper technique has recently been extended to accommodate time series with underlying uniform observing cadence from which some observations are missing. This situation is common for solar and geomagnetic data sets, which may have gaps due to breaks in satellite coverage, instrument downtime, or poor observing conditions. We demonstrate the scientific use of missing‐data multitaper magnitude‐squared coherence by detecting known solar mid‐term oscillations in simultaneous, missing‐data time series of solar Lyman α$\\alpha $flux and geomagnetic Disturbance Storm Time index. Due to their superior statistical properties, we recommend that multitaper methods be used for all heliospheric time series with underlying uniform observing cadence. Plain Language Summary The magnitude‐squared coherence (MSC) statistic detects oscillations with the same origin that show up in different types of measurements. For example, daily measurements of the air temperature at noon and the number of visitors to an outdoor swimming pool would likely have high MSC at a period of 1 year. This paper demonstrates how to apply a recently developed multitaper technique for estimating MSC between series of measurements that have some missing values. Our demonstration series are (a) the sun's brightness at a particular wavelength of ultraviolet light and (b) the disturbance of an equatorial ring of current in Earth's magnetosphere. MSC estimates show that both series trace solar oscillations with periods between 50 days and 5 years. Because of its superior statistical properties, we recommend that the multitaper method demonstrated here be widely adopted for analysis of heliospheric measurement series. Key Points Haley (2021, https://doi.org/10.1109/LSP.2021.3105926) extended the multitaper method for estimating magnitude‐squared coherence (MSC) to accommodate time series with missing data We demonstrate missing‐data multitaper MSC by showing that solar Lyman α flux and Dst index jointly trace known solar midterm oscillations We suggest that multitaper should be the preferred frequency domain method for heliospheric applications due to its superior performance

The properties of planet-forming midplanes of protostellar disks remain largely unprobed by observations due to the high optical depths of common molecular lines. However, rotational emission lines from rare isotopologues may have optical depth near unity in the vertical direction, so that the lines are strong enough to be detected, yet remain transparent enough to trace the disk midplane. We have computed chemical models of protostellar disks including different C and O isotopes and detailed photochemical reactions. The CO condensation front is in the giant planet-forming region, within 20 AU of the star. We show that the optical depths of low-order rotational lines of C17O are around unity, which suggests that it may be possible to see into the disk midplane using C17O. In lower-mass disks, the slightly more abundant C18O is a possible midplane probe. ALMA observations would provide estimates of the disk midplane temperature if CO ice line were spatially resolved. With our computed C17O/H2 abundance ratio, we would also be able to measure disk surface densities from the fluxes of low-order C17O transitions.

While the Lomb-Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60-year history of developing variance-suppressing power spectrum estimators, but most are not used in astronomy because they are formulated for time series with uniform observing cadence and without seasonal or daily gaps. Here we demonstrate how to apply the missing-data multitaper power spectrum estimator to spacecraft data with uniform time intervals between observations but missing data during thruster fires or momentum dumps. The F-test for harmonic components may be applied to multitaper power spectrum estimates to identify statistically significant oscillations that would not rise above a white noise-based false alarm probability. Multitapering improves the dynamic range of the power spectrum estimate and suppresses spectral window artifacts. We show that the multitaper - F-test combination applied to Kepler observations of KIC 6102338 detects differential rotation without requiring iterative sinusoid fitting and subtraction. Significant signals reside at harmonics of both fundamental rotation frequencies and suggest an antisolar rotation profile. Next we use the missing-data multitaper power spectrum estimator to identify the oscillation modes responsible for the complex \"scallop shell\" shape of the K2 light curve of EPIC 203354381. We argue that multitaper power spectrum estimators should be used for all time series with regular observing cadence.

Based on radial velocities, EXORAP photometry, and activity indicators, the HADES team reported a 16.3-day rotation period for the M dwarf GJ 3942. However, an RV--H\\(\\alpha\\) magnitude-squared coherence estimate has significant peaks at frequencies 1/16 cycles/day and 1/32 cycles/day. We re-analyze HADES data plus Hipparcos, SuperWASP, and TESS photometry to see whether the rotation period could be 32 days with 16-day harmonic. SuperWASP shows no significant periodicities, while the Hipparcos observing cadence is suboptimal for detecting 16- and 32-day periodicities. Although the average TESS periodogram has peaks at harmonics of 1/16 cycles/day, the harmonic sequence is not fully resolved according to the Rayleigh criterion. The TESS observations suggest a 1/16 cycles/day rotation frequency and a 1/32 cycles/day subharmonic, though resolution makes the TESS rotation detection ambiguous.

Astronomers who search for periodic signals using Lomb-Scargle periodograms rely on false alarm level (FAL) estimates to identify statistically significant peaks. Although FALs are often calculated from white noise models, many astronomical time series suffer from red noise. Prewhitening is a statistical technique in which a continuum model is subtracted from log power spectrum estimate, after which the observer can proceed with a white-noise treatment. Here we present a prewhitening-based method of calculating frequency-dependent FALs. We fit power laws and autoregressive models of order 1 to each Lomb-Scargle periodogram by minimizing the Whittle approximation to the negative log-likelihood (NLL), then calculate FALs based on the best-fit model power spectrum. Our technique is a novel extension of the Whittle NLL to datasets with uneven time sampling. We demonstrate FAL calculations using observations of \\(\\alpha\\)~Cen~B, GJ~581, HD 192310, synthetic data from the radial velocity (RV) Fitting Challenge, and {\\it Kepler} observations of a differential rotator. The {\\it Kepler} data analysis shows that only true rotation signals are detected by red-noise FALs, while white-noise FALs suggest all spurious peaks in the low-frequency range are significant. A high-frequency sinusoid injected into \\(\\alpha\\)~Cen~B \\(\\log R^{\\prime}_{HK}\\) observations exceeds the 1\\% red-noise FAL despite having only 8.9\\% of the power of the dominant rotation signal. In a periodogram of HD 192310 RVs, peaks associated with differential rotation and planets are detected against the 5\\% red-noise FAL without iterative model fitting or subtraction. Software for calculating red noise-based FALs is available on GitHub.

Doppler planet searches are complicated by stellar activity, through which cyclical changes in the host star's photosphere and chromosphere can mask or mimic planetary signals. A popular technique for modeling stellar activity is to apply a quasiperiodic Gaussian process (GP) kernel, which provides a flexible model with rigorous error propagation. However, observers must guard against overfitting, as a GP may be flexible enough to subsume other signals besides the one it is intended to model. To counteract overfitting, we introduce a curvature-penalizing objective function for fitting GP models to long-term magnetic activity cycles. We also demonstrate that a Gaussian filter can be an effective method of detrending radial velocities (RVs) so that shorter-period signals can be extracted even in the absence of a mathematical model of the long-term trend. We apply our methods to the heavily studied 55 Cancri system, fitting Keplerian orbits plus the GP activity-cycle model. We show that a 4-Keplerian model that includes planets b, c, e, and f combined with a GP for the activity cycle performs at least as well as the widely agreed-upon 5-planet system with its own GP activity model. Our results suggest that the existence of planet d cannot be established from the RVs alone; additional data are required for confirmation.

To explore the hypothesis of a common source of variability in two time series, observers may estimate the magnitude-squared coherence (MSC), which is a frequency-domain view of the cross correlation. For time series that do not have uniform observing cadence, MSC can be estimated using Welch's overlapping segment averaging. However, multitaper has superior statistical properties to Welch's method in terms of the tradeoff between bias, variance, and bandwidth. The classical multitaper technique has recently been extended to accommodate time series with underlying uniform observing cadence from which some observations are missing. This situation is common for solar and geomagnetic datasets, which may have gaps due to breaks in satellite coverage, instrument downtime, or poor observing conditions. We demonstrate the scientific use of missing-data multitaper magnitude-squared coherence by detecting known solar mid-term oscillations in simultaneous, missing-data time series of solar Lyman \\(\\alpha\\) flux and geomagnetic Disturbance Storm Time index. Due to their superior statistical properties, we recommend that multitaper methods be used for all heliospheric time series with underlying uniform observing cadence.

Voyager 2 observations revealed that the internal luminosity of Neptune is an order of magnitude higher than that of Uranus. If the two planets have similar interior structures and cooling histories, the luminosity of Neptune can only be explained by invoking some energy source beyond gravitational contraction. This paper investigates whether Centaur impacts could provide the energy necessary to produce the luminosity of Neptune. The major findings are (1) that impacts on both Uranus and Neptune are too infrequent to provide luminosities of order the observed value for Neptune, even for optimistic impact-rate estimates, and (2) that Uranus and Neptune rarely have significantly different impact-generated luminosities at any given time. Uranus and Neptune most likely have structural differences that force them to cool and contract at different rates.

A pileup near 1~AU in the semimajor axis distribution of giant exoplanets has been visually identified using log-spaced distribution plots. Here we propose that looking for features in a log-spaced semimajor axis distribution of giant planets is problematic. We use the Bayesian Blocks algorithm to analyze the linear-spaced semimajor axis distribution, and find that the apparent pileup is not significant.

The semimajor axis distribution of giant exoplanets appears to have a pileup near 1 AU. Photoevaporation opens a gap in the inner few AU of gaseous disks before dissipating them. Here we investigate whether photoevaporation can significantly affect the final distribution of giant planets by modifying gas surface density and hence Type II migration rates near the photoevaporation gap. We first use an analytic disk model to demonstrate that newly-formed giant planets have a long migration epoch before photoevaporation can significantly alter their migration rates. Next we present new 2-D hydrodynamic simulations of planets migrating in photoevaporating disks, each paired with a control simulation of migration in an otherwise identical disk without photoevaporation. We show that in disks with surface densities near the minimum threshold for forming giant planets, photoevaporation alters the final semimajor axis of a migrating gas giant by at most 5% over the course of 0.1 Myr of migration. Once the disk mass is low enough for photoevaporation to carve a sharp gap, migration has almost completely stalled due to the low surface density of gas at the Lindblad resonances. We find that photoevaporation modifies migration rates so little that it is unlikely to leave a significant signature on the distribution of giant exoplanets.