The recent detection of gravitational waves (GWs) by pulsar timing array (PTA) collaborations spurred a variety of questions regarding the origin of the signal and the properties of its sources. The amplitude of a GW background produced by inspiralling supermassive black holes (SMBHs) can be predicted in a relatively robust manner from the present-day merged remnants, observed as single SMBHs at the centers of galaxies, but falls short of the signal measured by PTAs by a significant amount, requiring equal mass mergers, extremely short delay times, and no accretion in order to achieve a modest consistency. In this work, we revisit NANOGrav's 15-yr data set and reassess the aforementioned discrepancy using the full spectral information captured by PTA data. As previously noted in the literature, the discrete number of point sources contributing to the background may lead to deviations in the observed spectrum relative to the average ($h^2_c \propto f^{-4/3}$) due to Poisson fluctuations, providing additional information about the source population beyond the background amplitude. We derive a simple expression for the characteristic strain distribution given a SMBH model, which is generally applicable regardless of the method used to model the black hole population. We then refit the NANOGrav free spectrum using a minimal model based on the local mass function, showing that the current GW measurement requires roughly $\sim 10$ times more black holes than suggested by local observations and disfavors mass functions dominated by few very heavy sources, with the typical mass that contributes to the background $\lesssim 10^{10}M_{\odot}$. Given the range of SMBH models found to be consistent with the isotropic background, we address what is the typical number sources that would be individually detectable, given the current sensitivity.
We present optical spectroscopy of 710 solar neighborhood stars collected over twenty years to catalog chromospheric activity and search for stellar activity cycles. The California Legacy Survey stars are amenable to exoplanet detection using precise radial velocities, and we present their Ca II H and K time series as a proxy for stellar and chromospheric activity. Using the HIRES spectrometer at Keck Observatory, we measured stellar flux in the cores of the Ca II H and K lines to determine S-values on the Mt. Wilson scale and the log(R'HK) metric, which is comparable across a wide range of spectral types. From the 710 stars, with 52,372 observations, 285 stars are sufficiently sampled to search for stellar activity cycles with periods of 2-25 years, and 138 stars show stellar cycles of varying length and amplitude. S-values can be used to mitigate stellar activity in the detection and characterization of exoplanets. We use them to probe stellar dynamos and to place the Sun's magnetic activity into context among solar neighborhood stars. Using precise stellar parameters and time-averaged activity measurements, we find tightly constrained cycle periods as a function of stellar temperature between log(R'HK) of -4.7 and -4.9, a range of activity in which nearly every star has a periodic cycle. These observations present the largest sample of spectroscopically determined stellar activity cycles to date.
Small planets ($R_{p} \leq 4 R_{\oplus}$) are divided into rocky super-Earths and gaseous sub-Neptunes separated by a radius gap, but the mechanisms that produce these distinct planet populations remain unclear. Binary stars are the only main-sequence systems with an observable record of the protoplanetary disk lifetime and mass reservoir, and the demographics of planets in binaries may provide insights into planet formation and evolution. To investigate the radius distribution of planets in binary star systems, we observed 207 binary systems hosting 283 confirmed and candidate transiting planets detected by the Kepler mission, then recharacterized the planets while accounting for the observational biases introduced by the secondary star. We found that the population of planets in close binaries ($\rho \leq 100$ au) is significantly different from the planet population in wider binaries ($\rho > 300$ au) or single stars. In contrast to planets around single stars, planets in close binaries appear to have a unimodal radius distribution with a peak near the expected super-Earth peak of $R_{p} \sim 1.3 R_{\oplus}$ and a suppressed population of sub-Neptunes. We conclude that we are observing the direct impact of a reduced disk lifetime, smaller mass reservoir, and possible altered distribution of solids reducing the sub-Neptune formation efficiency. Our results demonstrate the power of binary stars as a laboratory for exploring planet formation and as a controlled experiment of the impact of varied initial conditions on mature planet populations.