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Binary and multiple stellar systems have importance in three main areas of astronomy and astrophysics. First, because of the relatively simple gravitational interaction at work in the case of binary stars, these systems provide a basic check on stellar structure and evolution theory since the masses may be determined through observation. When these masses can be linked to other properties of the two stars, such as luminosity, color, and radius, they can provide very stringent constraints on stellar models. Second, the statistics of binary and multiple star systems provide clues to star formation mechanisms and environmental effects in the galactic gravitational potential and in clusters. Although a number of good results have been obtained in nearby star clusters and associations, knowledge of the field population has been somewhat limited until recently by a lack of large, complete samples of binaries. However, there appears to be a great deal of promise in this area for the coming decade in part due to astrometric satellites such as Hipparcos and Gaia. Third, the binary scenario is invoked to explain several important types of astrophysical phenomena such as Type Ia supernovae, cataclysmic variables, and stellar x-ray sources. Since the first of these mentioned is a standard candle for the extragalactic distance scale, it may even be said binary stars play a minor role in field of cosmology. However, in this chapter, the focus will mainly be on normal stars in binary and multiple-stellar systems. The basic physics of binaries will be reviewed, and the observational methods in use today will be discussed together with their limitations and prospects for the future. Finally, an overview of the current science in the three main areas mentioned where binaries have a significant impact will be given. © Springer Science+Business Media Dordrecht 2013.

Introduction Two or more stars that are located close together in space interact gravitationally, causing deviations from linear motion as each star is accelerated. If we consider the case of two stars with a physical separation of many times the radius of either star (but still close enough to generate significant accelerations), it is sufficient to consider the stars as point masses. The equations of motion for such a system can be solved by assuming the inverse-square law of gravity and applying Newton's laws of motion. Newton's solution elegantly explained Kepler's laws of planetary motion, since one of the general solutions of motion is an ellipse with the more massive body (the Sun, in the case of the Solar System) at one focus. Kepler's third law of planetary motion (i.e. the harmonic law) as applied to the binary-star situation can be written where m1 and m2 are the masses of the two stars in solar units, a is the semi-major axis of the relative orbital ellipse in astronomical units, and P is the orbital period of the system in years. If you can only apply this formula, then it is not possible to obtain individual masses from the observables on the right-hand side, nor is the mass sum possible without an estimate of the parallax of the system (which allows for the conversion of a from an angular measure to astronomical units). Furthermore, while it is usually possible to measure the orbital period to high precision, the application of the formula is complicated by the fact that the semi-major axis, and implicitly the parallax, is raised to the third power. © Cambridge University Press 2013.

The Differential Speckle Survey Instrument (DSSI) is a dual-channel speckle imaging system that takes speckle patterns in two colors simultaneously using two electron-multiplying CCD cameras. The system has been shown to deliver excellent photometry of binary stars under good observing conditions, which raises the question of whether results of similar quality can be obtained on extended objects such as minor planets, and if so, to what limiting magnitude. In this study, we present speckle image reconstructions of images of 2 Pallas, 216 Kleopatra, and 283 Emma made from data taken at the WIYN 3.5-m Telescope at Kitt Peak. We compare two different phase reconstruction algorithms: (1) an iterative technique, and (2) a relaxation technique. Since Pallas is a flattened disk, Kleopatra has a dumbbell shape, and Emma is a binary asteroid with known orbital parameters, these three targets represent three distinct image morphologies that allow for a robust comparison of the two phase reconstruction programs. Prospects for future work in this area with DSSI are discussed. This work is funded by NSF grant AST-0908125.

After the success of Hanbury Brown, Davis, and their collaborators in measuring all stellar diameters resolvable by the 166-m interferometer at Narrabri nearly four decades ago, research into optical intensity interferometry was largely discontinued. Signal-to-noise ratios and timing resolutions limited the technique to relatively bright stars over a narrow bandwidth. Modern photon-correlation electronics, however, may help to revive the technique, allowing for increased temporal resolution and longer baselines. In this paper, the PicoHarp 300 Time-Correlated Single Photon Counting System is characterized in order to demonstrate its ability to perform interferometric measurements. Time correlations of coherent and incoherent source apertures are measured and their autocorrelations compared with theory. The speed of light is also directly measured using the shift in temporal correlation between offset detectors. Finally, the possibility of two independent systems, linked between two large-aperture telescopes, is discussed with the goal of determining whether longer baselines can be achieved.

Using our state-of-the-art 2-channel speckle imaging instrument, we have recently obtained diffraction-limited optical images at the 8-m Gemini-N telescope. The primary science goal was to search for faint (delta_mag = 4-6 mag) and nearby (<0.05") stellar companions around potential planet hosting stars as part of the small small exoplanet validation for the NASA Kepler and ESA CoRoT missions. As a demonstration of the instrument capabilities on Gemini, we achieved an angular resolution of ~20 mas which yielded the highest resolution ground-based optical image of the Pluto-Charon system ever obtained. Our instrument is likely to return to Gemini-N in mid-2013 for observations by general community programs

Electron-multiplying CCD cameras are now being widely used in speckle imaging, and have been shown to deliver excellent photometric precision under good observing conditions. Successful image reconstructions have been made on binary stars fainter than 14th magnitude. However, improving the speckle signal-to-noise ratio and the fidelity of image reconstructions for faint sources would be extremely helpful in several areas of research where diffraction-limited images are required, including our own ongoing speckle observations of Kepler exoplanet candidate stars using the WIYN Telescope at Kitt Peak. In this paper, we investigate (1) robust cosmic ray rejection and (2) removal of low signal-to-noise frames as two ways to maximize data quality for faint source observations. Cosmic ray rejection is not normally a major concern in speckle imaging due to the brightness of the targets traditionally observed and the short frame times. Nonetheless, when imaging faint targets, more frames are needed to achieve a given signal-to-noise ratio, increasing the chance of cosmic ray events on the detector, and even a single cosmic ray hit in the frame sequence can significantly affect the source detection ability and photometry obtained in the observation. Similarly, faint sources often exhibit some frames with a well-defined image core while in other frames it is difficult to tell if the source is even present, primarily due to seeing variation during the observation. A new speckle reduction algorithm has been created that removes cosmic rays without throwing out frames and rejects frames with bad seeing, and its performance is investigated to determine to what extent this can improve source detection and photometric reliability in the final reconstructed image. Funding for this work was provided by the Kepler Science Center and by NSF Grant AST-0908125.

M dwarfs dominate the solar neighborhood population, accounting for three of every four stars. Their broad mass range — from 62% down to 8% that of the Sun — creates a rich dynamical laboratory that can be used to challenge stellar and binary formation models. Our Orbital Architectures project is constructing a large sample of orbits for nearby M dwarf systems to establish their distributions in period, mass ratio, semimajor axis, and eccentricity, with the goal of building crucial empirical evidence that will constrain models of multi-star formation and evolution. These orbits have been observed during the 20+ year RECONS astrometry program at the CTIO/SMARTS 0.9m, enhanced by a new speckle interferometry campaign at SOAR with HRCam+SAM to map the shorter-period orbits. Together, these observing efforts will map ~120 orbits of nearby M dwarfs with orbital periods spanning 0 to 30 years, providing the richest set of data ever collected for these ubiquitous stars. The speckle observations at SOAR resolve systems and provide magnitude differences between components, many of which already have orbits mapped by the RECONS astrometry program. The synergy of 0.9m and SOAR observations allows us to determine individual component masses, and to compare those masses to their fluxes in the Kron-Cousins I band. Here we present a new mass-luminosity relation for M dwarfs in the I band, populated with 40 masses focused on the low-mass end of the M dwarf sequence. This work has been supported by NSF grants AST-0507711, AST-0908402, AST-1109445, AST-141206, and AST-1715551.

We present the first results of a multiyear program to map the orbits of M-dwarf multiples within 25 pc. The observations were conducted primarily during 2019-2020 using speckle interferometry at the Southern Astrophysical Research Telescope in Chile, using the High-Resolution Camera mounted on the adaptive optics module (HRCam+SAM). The sample of nearby M dwarfs is drawn from three sources: multiples from the RECONS long-term astrometric monitoring program at the SMARTS 0.9 m; known multiples, for which these new observations will enable or improve orbit fits; and candidate multiples flagged by their astrometric fits in Gaia Data Release 2 (DR2). We surveyed 333 of our 338 M dwarfs via 830 speckle observations, detecting companions for 63% of the stars. Most notably, this includes new companions for 76% of the subset selected from Gaia DR2. In all, we report the first direct detections of 97 new stellar companions to the observed M dwarfs. Here we present the properties of those detections, the limits of each nondetection, and five orbits with periods 0.67-29 yr already observed as part of this program. Companions detected have projected separations of 0.″024-2.″0 (0.25-66 au) from their primaries and have ΔI ≲ 5.0 mag. This multiyear campaign will ultimately map complete orbits for nearby M dwarfs with periods up to 3 yr, and provide key epochs to stretch orbital determinations for binaries to 30 yr. © 2022. The Author(s). Published by the American Astronomical Society.

A program of speckle observations at Lowell Observatory's Discovery Channel Telescope (DCT) and the Gemini North and South Telescopes will be described. It has featured the Differential Speckle Survey Instrument (DSSI), built at Southern Connecticut State University in 2008. DSSI is a dual-port system that records speckle images in two colors simultaneously and produces diffraction limited images to V∼ 16.5 mag at Gemini and V∼ 14.5 mag at the DCT. Of the several science projects that are being pursued at these telescopes, three will be highlighted here. The first is high-resolution follow-up observations for Kepler and K2 exoplanet missions, the second is a study of metal-poor spectroscopic binaries in an attempt to resolve these systems and determine their visual orbits en route to making mass determinations, and the third is a systematic survey of nearby late-type dwarfs, where the multiplicity fraction will be directly measured and compared to that of G dwarfs. The current status of these projects is discussed and some representative results are given.

We present the validation and characterization of Kepler-61b: a 2.5 R_Earth planet orbiting near the inner edge of the habitable zone of a low-mass star. Our characterization of the host star Kepler-61 is based upon our identification of a spectroscopically similar star located 4.9 pc from Earth. This proxy star to Kepler-61 has a published direct interferometric radius and effective temperature measurement, which we apply in tandem with the Kepler photometry to characterize the planet Kepler-61b. The technique of identifying a nearby proxy star with directly measured properties allows for an independent check on stellar characterization via the traditional measurements with stellar spectra and evolutionary models. In this case, such a check had profound implications for the putative habitability of Kepler-61b. This work was performed in part under contract with the California Institute of Technology (Caltech) funded by NASA through the Sagan Fellowship Program

We measure the mass of a modestly irradiated giant or "warm Jupiter," KOI-94d, in order to calculate its density. We wish to determine whether this planet, which is in a 22 day orbit and receives 107 times as much incident flux as the Earth, is bloated like "hot Jupiters" or as dense as our own Jupiter. In addition to its warm Jupiter, KOI-94 hosts at least 3 smaller planets, all of which were detected through transits by the Kepler Mission. This presents the opportunity to characterize a multi-planet system and to test dynamic stability and formation theory through observations of the masses and orbital elements of these planets. With 26 radial velocity measurements of KOI-94 from the W. M. Keck Observatory/HIRES, we measure the mass of the giant planet and upper limits to the masses of the three smaller planets. Transit timing variations will allow us to hone the mass measurements of the three smaller planets. Using the KOI-94 system and all other planets with published values for both mass and radius, we establish two fundamental planes for exoplanets that relate their mass, incident flux, and radius from a few Earth masses up to ten Jupiter masses: log(Rp/RE) = 0.007 + 0.53 log(M/ME) - 0.001 log(F/[erg/s/cm^2]) for Mp < 150ME; log(Rp/RE) = 0.67 - 0.036 log(M/ME) + 0.06 log(F/[erg/s/cm^2]) for Mp > 150ME. We also solve these planes in density-mass-flux space: log(ρp/[g/cm^3]) = 0.69 - 0.57 log(M/ME) + 0.02 log(F/[erg/s/cm^2]) for Mp < 150ME; log(ρp/[g/cm^3]) = -1.23 + 1.10 log(M/ME) - 0.18 log(F/[erg/s/cm^2]) for Mp > 150ME.

We present results from high-resolution, optical to near-IR imaging of host stars of Kepler Objects of Interest (KOIs), identified in the original Kepler field. Part of the data were obtained under the Kepler imaging follow-up observation program over six years (2009-2015). Almost 90% of stars that are hosts to planet candidates or confirmed planets were observed. We combine measurements of companions to KOI host stars from different bands to create a comprehensive catalog of projected separations, position angles, and magnitude differences for all detected companion stars (some of which may not be bound). Our compilation includes 2297 companions around 1903 primary stars. From high-resolution imaging, we find that ∼10% (∼30%) of the observed stars have at least one companion detected within 1″ (4″). The true fraction of systems with close (≲4″) companions is larger than the observed one due to the limited sensitivities of the imaging data. We derive correction factors for planet radii caused by the dilution of the transit depth: assuming that planets orbit the primary stars or the brightest companion stars, the average correction factors are 1.06 and 3.09, respectively. The true effect of transit dilution lies in between these two cases and varies with each system. Applying these factors to planet radii decreases the number of KOI planets with radii smaller than 2 R⊕ by ∼2%-23% and thus affects planet occurrence rates. This effect will also be important for the yield of small planets from future transit missions such as TESS. © 2017. The American Astronomical Society. All rights reserved.

We have added references to Tables 3 and 8 (last column in each table). Below is a sample of both tables; the full tables are available in machine-readable form.

We report the discovery of HAT-P-67b, which is a hot-Saturn transiting a rapidly rotating F-subgiant. HAT-P-67b has a radius of Rp=2.085 -0.071 +0.096 RJ, and orbites a M∗ = 1.642-0.072 +0.155 M, R∗ = 2.546-0.099 +0.0084 R host star in a ∼4.81 day period orbit. We place an upper limit on the mass of the planet via radial velocity measurements to be Mp &lt; 0.59 MJ, and a lower limit of &gt;0.056 MJ by limitations on Roche lobe overflow. Despite being a subgiant, the host star still exhibits relatively rapid rotation, with a projected rotational velocity of v sin I∗ = 35.8 ±1.1 km s-1, which makes it difficult to precisely determine the mass of the planet using radial velocities. We validated HAT-P-67b via two Doppler tomographic detections of the planetary transit, which eliminate potential eclipsing binary blend scenarios. The Doppler tomographic observations also confirm that HAT-P-67b has an orbit that is aligned to within 12, in projection, with the spin of its host star. HAT-P-67b receives strong UV irradiation and is among one of the lowest density planets known, which makes it a good candidate for future UV transit observations in the search for an extended hydrogen exosphere. © 2017. The American Astronomical Society. All rights reserved.

We report the detection of a transiting super-Earth-sized planet (R = 1.39 ± 0.09 R⊕ ) in a 1.4-day orbit around L 168-9 (TOI-134), a bright M1V dwarf (V = 11, K = 7.1) located at 25.15 ± 0.02 pc. The host star was observed in the first sector of the Transiting Exoplanet Survey Satellite (TESS) mission. For confirmation and planet mass measurement purposes, this was followed up with ground-based photometry, seeing-limited and high-resolution imaging, and precise radial velocity (PRV) observations using the HARPS and Magellan/PFS spectrographs. By combining the TESS data and PRV observations, we find the mass of L 168-9 b to be 4.60 ± 0.56 M⊕ and thus the bulk density to be 1.74-0.33+0.44 times higher than that of the Earth. The orbital eccentricity is smaller than 0.21 (95% confidence). This planet is a level one candidate for the TESS mission's scientific objective of measuring the masses of 50 small planets, and it is one of the most observationally accessible terrestrial planets for future atmospheric characterization. © ESO 2020.