During Kepler's main mission, nearly 20 pulsating subdwarf B (sdB: extreme horizontal branch stars) were discovered. Many of these stars were observed for three years, accumulating over 1.5 million observations. Only through these extended observations have we been able to identify pulsation modes, applying constraints for structure models. Discoveries include nearly-evenly-spaced asymptotic period overtones which represent the interior structure and rotationally-induced frequency multiplets from which we have learned that rotation periods are long, even when in short-period binaries. This paper reviews progress on observational constraints and highlights some of our discoveries including radially differential rotation, conflicting stratification indicators and mode lifetimes.

We challenge the assumptions present in previous efforts to model the ensemble of detected Kepler systems, which require a dichotomous stellar population of ‘fertile’ and ‘sterile’ planet producing stars. We remove the assumption of Rayleigh distributed mutual inclinations between planets and show that the need for two distinct stellar populations disappears when the inner part of planetary disks are assumed to be flat, rather than flared.

The joint variability of chromospheric emission with the integrated flux in the Kepler visible band for the Sun as a star is examined. No correlation between our Ca II K line parameter and the Kepler passband is seen, suggesting that visible-band variability in solar-like stars is mostly independent of solar-like chromospheric activity. However, the K-line parameter time series and the total solar flux in the infrared K band appear weakly correlated, reflecting the wavelength dependence of the relationship between magnetic activity and broadband variability. We then apply a schematic, three-component model as a framework for the discussion of stellar photometric variability as observed by Kepler. The model confirms that spots tend to dominate stellar photometric variability in the visible though interesting cases do emerge where the facular disk coverage may become important in determining the amplitude of broadband variability.

The goal of this paper is to take steps towards estimating the frequency of terrestrial planets in the habitable zones of their host stars, using planet counts from the Kepler mission. The method is to assume that an analytical form for the underlying distribution function, numerically simulate the observing procedure, compare the simulated and real observations, and iterate the model parameters to achieve convergence in the sense of least-squares. The underlying distribution can then be extrapolated to a region of interest, here the terrestrial habitable-zone range. In this regime (small radii, long periods), the instrument noise makes such detections essentially impossible below a fairly sharply defined threshold signal level. This threshold can be estimated from the existing data. By taking this cutoff into account, the distribution of planets, as a function of radius and period, can be estimated with minimal bias. Extending this distribution to terrestrial planets in habitable-zone orbits can yield an estimate of eta-sub-Earth.

K2 is the mission concept for a repurposed Kepler mission that uses two reaction wheels to maintain the satellite attitude and provide ~81 days of coverage for ten 105 deg2 fields along the ecliptic in the first 2.5 years of operation. We examine stellar populations based on the updated Besançon model of the Galaxy, comment on the general properties for the entire ecliptic plane, and provide stellar occurrence rates in the first six tentative K2 campaigns grouped by spectral type and luminosity class. For each campaign we distinguish between main the sequence stars and giants, and provide their density profile as a function of galactic latitude. We introduce the crowding metric that serves for optimized target selection across the campaigns. For all main sequence stars we compute the expected planetary occurrence rates for three planet sizes: 2–4, 4–8 and 8–32 R⊕ with orbital periods up to 50 days. In conjunction with Gaia and the upcoming Transiting Exoplanet Survey Satellite and Plato missions, K2 will become a gold mine for stellar and planetary astrophysics.

We examined the complete short cadence sample of fundamental-mode Kepler RR Lyrae stars to further investigate the recently discovered dynamical effects such as period doubling and additional modes. Here we present the findings on four stars. V450 Lyr may be a non-classical double-mode RR Lyrae star pulsating in the fundamental mode and the second overtone. For the three remaining stars we observe the interaction of three different modes. Since the period ratios are close to resonant values, we observe quasi-repetitive patterns in the pulsation cycles in the stars. These findings support the mode-resonance explanations of the Blazhko effect.

Stellar rotation is a well-known quantity for tens of thousands of stars. In contrast, differential rotation (DR) is only known for a handful of stars because DR cannot be measured directly. We present rotation periods for more than 24,000 active stars in the Kepler field. Thereof, more than 18,000 stars show a second period, which we attribute to surface differential rotation. Our rotation periods are consistent with previous measurements and the theory of magnetic braking. Our results on DR paint a rather different picture: The temperature dependence of the absolute shear δΩ is split into two groups separated around 6000 K. For the cooler stars δΩ only slightly increases with temperature, whereas stars hotter than 6000 K show large scatter. This is the first time that DR has been measured for such a large number of stars.

Fundamental mode classical Cepheids have light curves which repeat accurately enough that we can watch them evolve (change period). The new level of accuracy and quantity of data with the Kepler and MOST satellites probes this further. An intriguing result was found in the long time-series of Kepler data for V1154 Cyg the one classical Cepheid (fundamental mode, P = 4.9 d) in the field, which has short term changes in period (≃20 minutes), correlated for ≃10 cycles (period jitter). To follow this up, we obtained a month long series of observations of the fundamental mode Cepheid RT Aur and the first overtone pulsator SZ Tau. RT Aur shows the traditional strict repetition of the light curve, with the Fourier amplitude ratio R1/R2 remaining nearly constant. The light curve of SZ Tau, on the other hand, fluctuates in amplitude ratio at the level of approximately 50%. Furthermore prewhitening the RT Aur data with 10 frequencies reduces the Fourier spectrum to noise. For SZ Tau, considerable power is left after this prewhitening in a complicated variety of frequencies.

The Blazhko effect is the conspicuous amplitude and phase modulation of the pulsation of RR Lyrae stars that was discovered in the early 20th century. The field of study of this mysterious modulation has recently been invigorated thanks to the space photometric missions providing long, uninterrupted, ultra-precise time-series data. In this paper I give a brief overview of the new observational findings related to the Blazhko effect, such as extreme modulations, irregular modulation cycles and additional periodicities. I argue that these findings together with dedicated ground-based efforts provide us now with a fairly complete picture and a good starting point to theoretical investigations. Indeed, new, unpredicted dynamical phenomena have been discovered in Blazhko RR Lyrae stars, such as period doubling, high-order resonances, three-mode pulsation and low-dimensional chaos. These led to the proposal of a new explanation to this century-old enigma, namely a high-order resonance between radial modes. Along these lines I present the latest efforts and advances from the theoretical point of view. Lastly, amplitude variations in Cepheids are discussed.

Ranked near the top of the long list of exciting discoveries made with NASA's Kepler photometer is the detection of transiting circumbinary planets. In just over a year the number of such planets went from zero to seven, including a multi-planet system with one of the planets in the habitable zone (Kepler-47). We are quickly learning to better detect and characterize these planets, including the recognition of their transit timing and duration variation “smoking gun” signature. Even with only a handful of such planets, some exciting trends are emerging.

The International Year of Astronomy marks the 400th anniversary of Kepler's Astronomia nova and the first use of the telescope for astronomy, most notably leading to Galileo's Sidereus nuncius (1610). Kepler's book for the first time argued strongly for a physical basis to astronomical explanations. Galileo's work showed that a coherent understanding was more important for scientific progress than specific proofs. The efforts of both astronomers undermined the traditional geocentric cosmology and essentially brought about the birth of modern astronomy.

The question ‘Are supernovae important sources of dust?’ is a contentious one. Observations with the Infrared Astronomical Satellite (IRAS) and the Infrared Space Observatory (ISO) only detected very small amounts of hot dust in supernova remnants. Here, we review observations of two young Galactic remnants with the Submillimetre Common User Bolometer Array (SCUBA), which imply that large quantities of dust are produced by supernovae. The association of dust with the Cassiopeia A remnant is in question owing to the contamination of foreground material. In this paper, we compare the emission from cold dust with CO emission towards Kepler’s supernova remnant. We detect very little CO at the location of the submillimetre peaks. A comparison of masses from the CO and the dust clouds are made, and we estimate the 3σ upper limit on the gas-to-dust ratios to be in the range 20–60. These results suggest that we cannot yet rule out freshly-formed or swept-up circumstellar dust in Kepler’s supernova remnant.