Pulsating stars with Kepler

Variable stars with the Kepler space telescope

László Molnár11affiliation: molnar.laszlo@csfk.mta.hu , Róbert Szabó11affiliation: molnar.laszlo@csfk.mta.hu , Emese Plachy11affiliation: molnar.laszlo@csfk.mta.hu Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary

Abstract here.

AAVSO keywords = photometry — asteroseismology — Variable Stars — surveys; ADS keywords = stars: variables: general; surveys; techniques: photometric



The Kepler space telescope, as a Discovery-class space mission, was built to carry out a specific set of tasks to meet well-defined goals. It was conceived to do exoplanet statistics, and determine \(\eta_{Earth}\), the frequency of small, rocky planets within the habitable zone of their stars (Borucki, 2016). However, it turned out to be, as many astronomers had hoped, much more than just an exoplanet-statistics mission. It is fair to say that during the last few years, Kepler has not only transformed our understanding of exoplanets but also revolutionized the field of stellar astrophysics.

But all good things come to an end, and the primary mission of Kepler ended in 2013, after collecting data from more than 160 thousand stars in the same patch of sky for four years, quasi-continuously. This was not the end of the telescope itself though. With only two functioning reaction wheels remaining to point the spacecraft, an ingenious new mission called K2 was initiated (Howell et al., 2014). The telescope that was once built for a singular purpose, was transformed into a community resource, open to any targets available within its new observing fields. It observes in 80-day campaigns along the Ecliptic, and at the time of writing finishes its 10th observing run with only minor technical problems.

The discoveries of the primary and extended missions of Kepler can already fill books. Kepler, along with the other space photometric missions, opened up a new window for us to explore what was considered utterly unreachable a century ago: the insides of stars. In this review we focus on the most important or interesting results about variable stars: stars that show light variations due to excited pulsation modes, turbulent convection, binarity, cataclysmic or eruptive events. Some of these are out of reach of an amateur astronomer, but most of them are interesting to all variable star enthusiasts.

Kepler data

The success of Kepler mission resulted from the combination of its unprecedented photometric accuracy (\(10^{-5}-10^{-6}\) relative precision), the length and the continuity of the observations, as well as the fast data sampling (1 and 30 minute cadence), that led to discoveries of light variation well below millimagnitude level and insight into the details of long-term behavior of a large number of stellar targets.

However, like all instruments, Kepler too has unwanted artificial effects that contaminate the beautiful light curves. The most puzzling issue for which no perfect solution exists, is stitching the individual data quarters to each other. In order to keep the solar panels pointed towards the Sun, the telescope had to roll 90 degrees after every three month, and as a consequence the targets ended up on different detectors for every quarter of a year, often causing significant differences in the measured flux. The correction of these differences requires scaling, shifting, and detrending of the observed flux, and are especially challenging for stars that show slow and irregular variability. Kepler light curves are also affected by a sinusoidal variability with the Kepler-year (372.5 d, the orbital period of spacecraft around the Sun) due to the change of the thermal properties of the telescope elements. The amplitude and the phase of this effect is dependent on the position of the star within the field of view (Bányai et al., 2013).

Astronomers do not have to bother with these problems in the K2 mission any more—but other issues appeared instead. Due to the inherent instability of the positioning with only two functioning reaction wheels, the attitude of the telescope drifts (it rolls back and forth about the optical axis) and corrective manoeuvres are required at every 6 hours. The roll and correction causes stars to move across slightly differently sensitive pixels, causing distinctive 6-hour jumps to be present in the light curves. These effects are the strongest for stars that fall close to the edges of the field of view. Another source of noise is the zodiacal light, light scattered from the fine dust in the inner Solar System, that increases the background noise towards the end of each campaign.

Nevertheless, thanks to the Earth-trailing, i.e., heliocentric orbit of Kepler the data are devoid of other problems typical of space telescopes operating in low-Earth orbit. Instruments like CoRoT and the BRITE satellites are prone to scattered light from the Earth and the Moon, temperature changes when crossing the shadow of the Earth, and degradation or gaps in the data when they cross the swarm of charged particles, called South-Atlantic Anomaly. The patches of sky observed or targeted by Kepler are shown in Figure XXX.

The core exoplanet science of the original mission was led by the Kepler Science Team. But in order to exploit the wealth of stellar oscillation data provided by Kepler optimally, a large collaboration (Kepler Asteroseismic Science Consortium) was also formed, which consists of some 600 scientists around the globe, and produced most of the results presented in this paper.

Solar-like oscillations

Probably the single greatest breakthrough that Kepler delivered for stellar astrophysics is the huge number of stars where solar-like oscillations have been detected. Detailed asteroseismic analysis is now routinely used to determine the physical parameters of stars, and, by extension, exoplanets. Asteroseismic modeling, e.g., fitting the spectrum of observed oscillation modes with values calculated from theoretical models, is extremely powerful, for multiple reasons. First, it requires photometric measurements instead of spectroscopic ones, so it can be done for a large number of stars simultaneously, with a relatively small telescope. (Although with the need of very high precision: oscillation signals are closer to the \(\mu\)mag level than the mmag level usually accessible with ground-based instruments.) Secondly, although resolved observations are not possible for distant stars, detailed seismic (i.e. intensity) observations allow for the determination of global parameters, like mass, radius, and age much more precisely, than with any other methods. The typical precision is 3-5% in mass and radius and 10% in age for main-sequence stars. The latter can be appreciated if we mention that the age of a typical (not so young) main sequence star can be determined with rather large (30-50%) uncertainties based on spectroscopic information alone. And any age or radius information about exoplanets is only as good as our knowledge on their host stars.

Before CoRoT and Kepler, seismic information was available only for a handful of stars, mainly through spectroscopic observations or small space telescopes, like WIRE. In contrast, Kepler delivered seismic information for hundreds of main-sequence stars (brightest ones), and over 15 thousand red giants in the original Kepler field. Many more is expected from the ongoing K2 Mission. This amount of stars with accurate asteroseismic information already makes galactic archaeology and population studies possible. Thus, we can learn more about the history of our Galaxy, the stellar formation rate, initial mass function, etc., especially in conjunction of Gaia, the flagship mission of the European Space Agency, which provides accurate distances and proper motions for roughly one billion stars.

Kepler-16 A&B, the two solar-like components of a visual binary allowed the execution of an exquisite proof–of–concept seismological study (Metcalfe et al., 2012). The masses of these stars are 1.10 \(\pm\) 0.01 and 1.06 \(\pm\) 0.01 solar masses and were resolvable even with Kepler’s not-so-good resolving power (it was optimized to gather as much photons, as possible, hence the large pixels and relatively low spatial resolution). Thus, the oscillation spectra were derived for both stars, and their parameters could be determined independently and without any prior assumptions. Reassuringly, the age of the two objects (6.8 \(\pm\) 0.4 billion years) and their bulk chemical compositions were found to be identical. That is what one would expect if the two objects were formed from the same blob of interstellar material at the same time. What’s more, 16 Cyg A and B are close enough to us that their radii can be measured directly, and as such, they can help us validate the asteroseismic relations that are based on our knowledge of the Sun. Data from the CHARA (Center for High Angular Resolution Astronomy) Array revealed that the seismic and interferometric radii of solar-like stars agree within a few percent (White et al., 2013).

Not only individual stars can be scrutinized by applying asteroseismological methods. Models can be constrained even more if our object belongs to a stellar cluster, since in this case the cluster members were presumably formed from the same molecular cloud roughly at the same time (although recently evidence is accumulating for multi-epoch star formation in globular clusters). In the original Kepler field there were four open clusters (NGC 6811, NGC 6819, the very old NGC 6791, and NGC 6866, the youngest of the four). Their red giant population was investigated in great detail in a large number of studies based on the Kepler data. For example, a new methodology was developed to determine cluster membership probability based on seismic constraints (Stello et al., 2011) and the very uncertain mass loss was studied along the red giant branch evolution (Miglio et al., 2012), again, based on Kepler’s seismic information.

The detection of seismic signals from the main sequence of an open cluster is a much harder task, since main-sequence stars are usually much fainter then their evolved fellow cluster members. Therefore this breakthrough was only recently reached: Lund et al. (2016) succeeded in detecting seismic signals from main-sequence stars in the Hyades cluster for the first time. Many more, already well studied, fiducial clusters will be observed during the K2 extension including the Pleiades, M44, M67, M35, etc., that will allow a stringent test for our knowledge of stellar evolution. Miglio et al. (2016) detected solar-like oscillation in the K giants belonging to the globular cluster M4 in the K2 Mission. This is also remarkable given the difficulty presented by the crowded nature of the target.

To close this section we briefly mention the synergies of stellar oscillatons with exoplanetary science. The first one is the measurement of the radius of the previously discovered hot Jupiter, HAT-P-7b in the Kepler field. With the help of asteroseismology the radius of the host star was measured by more than an order of magnitude more precisely compared to traditional methods (Christensen-Dalsgaard et al., 2010). Similar improvement was a