Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Kepler”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,009 records · Page 56

MODEL-INDEPENDENT STELLAR AND PLANETARY MASSES FROM MULTI-TRANSITING EXOPLANETARY SYSTEMS

Precise exoplanet characterization requires precise classification of exoplanet host stars. The masses of host stars are commonly estimated by comparing their spectra to those predicted by stellar evolution models. However, spectroscopically determined properties are difficult to measure accurately for stars that are substantially different from the Sun, such as M-dwarfs and evolved stars. Here, we propose a new method to dynamically measure the masses of transiting planets near mean-motion resonances and their host stars by combining observations of transit timing variations with radial velocity (RV) measurements. We derive expressions to analytically determine the mass of each member of the system and demonstrate the technique on the Kepler-18 system. We compare these analytic results to numerical simulations and find that the two are consistent. We identify eight systems for which our technique could be applied if follow-up RV measurements are collected. We conclude that this analysis would be optimal for systems discovered by next-generation missions similar to TESS or PLATO, which will target bright stars that are amenable to efficient RV follow-up.

79 ASTRONOMY AND ASTROPHYSICS↗

ASGARD: A LARGE SURVEY FOR SLOW GALACTIC RADIO TRANSIENTS. I. OVERVIEW AND FIRST RESULTS

Searches for slow radio transients and variables have generally focused on extragalactic populations, and the basic parameters of Galactic populations remain poorly characterized. We present a large 3 GHz survey performed with the Allen Telescope Array (ATA) that aims to improve this situation: ASGARD, the ATA Survey of Galactic Radio Dynamism. ASGARD observations spanned two years with weekly visits to 23 deg{sup 2} in two fields in the Galactic plane, totaling 900 hr of integration time on science fields and making it significantly larger than previous efforts. The typical blind unresolved source detection limit was 10 mJy. We describe the observations and data analysis techniques in detail, demonstrating our ability to create accurate wide-field images while effectively modeling and subtracting large-scale radio emission, allowing standard transient-and-variability analysis techniques to be used. We present early results from the analysis of two pointings: one centered on the microquasar Cygnus X-3 and one overlapping the Kepler field of view (l = 76 Degree-Sign , b = +13. Degree-Sign 5). Our results include images, catalog statistics, completeness functions, variability measurements, and a transient search. Out of 134 sources detected in these pointings, the only compellingly variable one is Cygnus X-3, and no transients are detected. We estimate number counts for potential Galactic radio transients and compare our current limits to previous work and our projection for the fully analyzed ASGARD data set.

79 ASTRONOMY AND ASTROPHYSICS↗

ASSEMBLY OF PROTOPLANETARY DISKS AND INCLINATIONS OF CIRCUMBINARY PLANETS

The Kepler satellite has discovered a number of transiting planets around close binary stars. These circumbinary systems have highly aligned planetary and binary orbits. In this paper, we explore how the mutual inclination between the planetary and binary orbits may reflect the physical conditions of the assembly of protoplanetary disks and the interaction between protostellar binaries and circumbinary disks. Given the turbulent nature of star-forming molecular clouds, it is possible that the gas falling onto the outer region of a circumbinary disk and the central protostellar binary have different axes of rotation. Thus, the newly assembled circumbinary disk can be misaligned with respect to the binary. However, the gravitational torque from the binary produces a warp and twist in the disk, and the back-reaction torque tends to align the disk and the binary orbital plane. We present a new, analytic calculation of this alignment torque and show that the binary-disk inclination angle can be reduced appreciably after the binary accretes a few percent of its mass from the disk. Our calculation suggests that in the absence of other disturbances, circumbinary disks and planets around close (sub-AU) stellar binaries, for which mass accretion onto the proto-binary is very likely to have occurred, are expected to be highly aligned with the binary orbits, while disks and planets around wide binaries can be misaligned. Measurements of the mutual inclinations of circumbinary planetary systems can provide a clue to the birth environments of such systems.

79 ASTRONOMY AND ASTROPHYSICS↗

IS QUASAR OPTICAL VARIABILITY A DAMPED RANDOM WALK?

The damped random walk (DRW) model is increasingly used to model the variability in quasar optical light curves, but it is still uncertain whether the DRW model provides an adequate description of quasar optical variability across all timescales. Using a sample of OGLE quasar light curves, we consider four modifications to the DRW model by introducing additional parameters into the covariance function to search for deviations from the DRW model on both short and long timescales. We find good agreement with the DRW model on timescales that are well sampled by the data (from a month to a few years), possibly with some intrinsic scatter in the additional parameters, but this conclusion depends on the statistical test employed and is sensitive to whether the estimates of the photometric errors are correct to within {approx}10%. On very short timescales (below a few months), we see some evidence of the existence of a cutoff below which the correlation is stronger than the DRW model, echoing the recent finding of Mushotzky et al. using quasar light curves from Kepler. On very long timescales (>a few years), the light curves do not constrain models well, but are consistent with the DRW model.

79 ASTRONOMY AND ASTROPHYSICS↗

HABITABLE ZONES AROUND MAIN-SEQUENCE STARS: NEW ESTIMATES

Identifying terrestrial planets in the habitable zones (HZs) of other stars is one of the primary goals of ongoing radial velocity (RV) and transit exoplanet surveys and proposed future space missions. Most current estimates of the boundaries of the HZ are based on one-dimensional (1D), cloud-free, climate model calculations by Kasting et al. However, this model used band models that were based on older HITRAN and HITEMP line-by-line databases. The inner edge of the HZ in the Kasting et al. model was determined by loss of water, and the outer edge was determined by the maximum greenhouse provided by a CO{sub 2} atmosphere. A conservative estimate for the width of the HZ from this model in our solar system is 0.95-1.67 AU. Here an updated 1D radiative-convective, cloud-free climate model is used to obtain new estimates for HZ widths around F, G, K, and M stars. New H{sub 2}O and CO{sub 2} absorption coefficients, derived from the HITRAN 2008 and HITEMP 2010 line-by-line databases, are important improvements to the climate model. According to the new model, the water-loss (inner HZ) and maximum greenhouse (outer HZ) limits for our solar system are at 0.99 and 1.70 AU, respectively, suggesting that the present Earth lies near the inner edge. Additional calculations are performed for stars with effective temperatures between 2600 and 7200 K, and the results are presented in parametric form, making them easy to apply to actual stars. The new model indicates that, near the inner edge of the HZ, there is no clear distinction between runaway greenhouse and water-loss limits for stars with T{sub eff} {approx}< 5000 K, which has implications for ongoing planet searches around K and M stars. To assess the potential habitability of extrasolar terrestrial planets, we propose using stellar flux incident on a planet rather than equilibrium temperature. This removes the dependence on planetary (Bond) albedo, which varies depending on the host star's spectral type. We suggest that conservative estimates of the HZ (water-loss and maximum greenhouse limits) should be used for current RV surveys and Kepler mission to obtain a lower limit on {eta}{sub Circled-Plus }, so that future flagship missions like TPF-C and Darwin are not undersized. Our model does not include the radiative effects of clouds; thus, the actual HZ boundaries may extend further in both directions than the estimates just given.

79 ASTRONOMY AND ASTROPHYSICS↗

THE QUASIPERIODIC AUTOMATED TRANSIT SEARCH ALGORITHM

We present a new algorithm for detecting transiting extrasolar planets in time-series photometry. The Quasiperiodic Automated Transit Search (QATS) algorithm relaxes the usual assumption of strictly periodic transits by permitting a variable, but bounded, interval between successive transits. We show that this method is capable of detecting transiting planets with significant transit timing variations without any loss of significance-{sup s}mearing{sup -}as would be incurred with traditional algorithms; however, this is at the cost of a slightly increased stochastic background. The approximate times of transit are standard products of the QATS search. Despite the increased flexibility, we show that QATS has a run-time complexity that is comparable to traditional search codes and is comparably easy to implement. QATS is applicable to data having a nearly uninterrupted, uniform cadence and is therefore well suited to the modern class of space-based transit searches (e.g., Kepler, CoRoT). Applications of QATS include transiting planets in dynamically active multi-planet systems and transiting planets in stellar binary systems.

79 ASTRONOMY AND ASTROPHYSICS↗

THE INTERIOR STRUCTURE CONSTANTS AS AN AGE DIAGNOSTIC FOR LOW-MASS, PRE-MAIN-SEQUENCE DETACHED ECLIPSING BINARY STARS

We propose a novel method for determining the ages of low-mass, pre-main-sequence stellar systems using the apsidal motion of low-mass detached eclipsing binaries. The apsidal motion of a binary system with an eccentric orbit provides information regarding the interior structure constants of the individual stars. These constants are related to the normalized stellar interior density distribution and can be extracted from the predictions of stellar evolution models. We demonstrate that low-mass, pre-main-sequence stars undergoing radiative core contraction display rapidly changing interior structure constants (greater than 5% per 10 Myr) that, when combined with observational determinations of the interior structure constants (with 5%-10% precision), allow for a robust age estimate. This age estimate, unlike those based on surface quantities, is largely insensitive to the surface layer where effects of magnetic activity are likely to be most pronounced. On the main sequence, where age sensitivity is minimal, the interior structure constants provide a valuable test of the physics used in stellar structure models of low-mass stars. There are currently no known systems where this technique is applicable. Nevertheless, the emphasis on time domain astronomy with current missions, such as Kepler, and future missions, such as LSST, has the potential to discover systems where the proposed method will be observationally feasible.

79 ASTRONOMY AND ASTROPHYSICS↗

Cr-K EMISSION LINE AS A CONSTRAINT ON THE PROGENITOR PROPERTIES OF SUPERNOVA REMNANTS

We perform a survey of the Cr, Mn, and Fe-K emission lines in young supernova remnants (SNRs) with the Japanese X-ray astronomy satellite Suzaku. The Cr and/or Mn emission lines are detected in 3C 397 and 0519-69.0 for the first time. We also confirm the detection of these lines in Kepler, W49B, N103B, and Cas A. We derive the line parameters (i.e., the line centroid energy, flux, and equivalent width (EW)) for these six sources and perform a correlation analysis for the line center energies of Cr, Mn, and Fe. Also included in the correlation analysis are Tycho and G344.7-0.1 for which the Cr, Mn, and Fe-K line parameters were available in the literature through Suzaku observations. We find that the line center energies of Cr correlate very well with that of Fe and that of Mn. This confirms our previous findings that Cr, Mn, and Fe are spatially co-located, share a similar ionization state, and have a common origin in the supernova nucleosynthesis. We find that the ratio of the EW of the Cr emission line to that of Fe ({gamma}{sub Cr/Fe}{identical_to}EW(Cr)/EW(Fe)) provides useful constraints on the SNR progenitors and on the SN explosion mechanisms: for SNRs with {gamma}{sub Cr/Fe} > 2%, a Type Ia origin is favored (e.g., N103B, G344.7-0.1, 3C 397, and 0519-69.0); for SNRs with {gamma}{sub Cr/Fe} < 2%, they could be of either core-collapse origin or carbon-deflagration Ia origin.

79 ASTRONOMY AND ASTROPHYSICS↗

TESTING CONVECTIVE-CORE OVERSHOOTING USING PERIOD SPACINGS OF DIPOLE MODES IN RED GIANTS

Uncertainties on central mixing in main-sequence (MS) and core He-burning (He-B) phases affect key predictions of stellar evolution such as late evolutionary phases, chemical enrichment, ages, etc. We propose a test of the extension of extra-mixing in two relevant evolutionary phases based on period spacing ({Delta}P) of solar-like oscillating giants. From stellar models and their corresponding adiabatic frequencies (respectively, computed with ATON and LOSC codes), we provide the first predictions of the observable {Delta}P for stars in the red giant branch and in the red clump (RC). We find (1) a clear correlation between {Delta}P and the mass of the helium core (M{sub He}); the latter in intermediate-mass stars depends on the MS overshooting, and hence it can be used to set constraints on extra-mixing during MS when coupled with chemical composition; and (2) a linear dependence of the average value of the asymptotic period spacing (({Delta}P){sub a}) on the size of the convective core during the He-B phase. A first comparison with the inferred asymptotic period spacing for Kepler RC stars also suggests the need for extra-mixing during this phase, as evinced from other observational facts.

79 ASTRONOMY AND ASTROPHYSICS↗

A HOT URANUS ORBITING THE SUPER METAL-RICH STAR HD 77338 AND THE METALLICITY-MASS CONNECTION

We announce the discovery of a low-mass planet orbiting the super metal-rich K0V star HD 77338 as part of our ongoing Calan-Hertfordshire Extrasolar Planet Search. The best-fit planet solution has an orbital period of 5.7361 {+-} 0.0015 days and with a radial velocity semi-amplitude of only 5.96 {+-} 1.74 ms{sup -1}, we find a minimum mass of 15.9{sup +4.7}{sub -5.3} M{sub Circled-Plus }. The best-fit eccentricity from this solution is 0.09{sup +0.25}{sub -0.09}, and we find agreement for this data set using a Bayesian analysis and a periodogram analysis. We measure a metallicity for the star of +0.35 {+-} 0.06 dex, whereas another recent work finds +0.47 {+-} 0.05 dex. Thus HD 77338b is one of the most metal-rich planet-host stars known and the most metal-rich star hosting a sub-Neptune-mass planet. We searched for a transit signature of HD 77338b but none was detected. We also highlight an emerging trend where metallicity and mass seem to correlate at very low masses, a discovery that would be in agreement with the core accretion model of planet formation. The trend appears to show that for Neptune-mass planets and below, higher masses are preferred when the host star is more metal-rich. Also a lower boundary is apparent in the super metal-rich regime where there are no very low mass planets yet discovered in comparison to the sub-solar metallicity regime. A Monte Carlo analysis shows that this low-mass planet desert is statistically significant with the current sample of 36 planets at the {approx}4.5{sigma} level. In addition, results from Kepler strengthen the claim for this paucity of the lowest-mass planets in super metal-rich systems. Finally, this discovery adds to the growing population of low-mass planets around low-mass and metal-rich stars and shows that very low mass planets can now be discovered with a relatively small number of data points using stable instrumentation.

79 ASTRONOMY AND ASTROPHYSICS↗

CHEMICAL TRANSPORT AND SPONTANEOUS LAYER FORMATION IN FINGERING CONVECTION IN ASTROPHYSICS

A region of a star that is stable to convection according to the Ledoux criterion may nevertheless undergo additional mixing if the mean molecular weight increases with radius. This process is called fingering (thermohaline) convection and may account for some of the unexplained mixing in stars such as those that have been polluted by planetary infall and those burning {sup 3}He. We propose a new model for mixing by fingering convection in the parameter regime relevant for stellar (and planetary) interiors. Our theory is based on physical principles and supported by three-dimensional direct numerical simulations. We also discuss the possibility of formation of thermocompositional staircases in fingering regions, and their role in enhancing mixing. Finally, we provide a simple algorithm to implement this theory in one-dimensional stellar codes, such as KEPLER and MESA.

79 ASTRONOMY AND ASTROPHYSICS↗

PHOTOPHORETIC SEPARATION OF METALS AND SILICATES: THE FORMATION OF MERCURY-LIKE PLANETS AND METAL DEPLETION IN CHONDRITES

Mercury's high uncompressed mass density suggests that the planet is largely composed of iron, either bound within metal (mainly Fe-Ni) or iron sulfide. Recent results from the MESSENGER mission to Mercury imply a low temperature history of the planet which questions the standard formation models of impact mantle stripping or evaporation to explain the high metal content. Like Mercury, the two smallest extrasolar rocky planets with mass and size determination, CoRoT-7b and Kepler-10b, were found to be of high density. As they orbit close to their host stars, this indicates that iron-rich inner planets might not be a nuisance of the solar system but be part of a general scheme of planet formation. From undifferentiated chondrites, it is also known that the metal to silicate ratio is highly variable, which must be ascribed to preplanetary fractionation processes. Due to this fractionation, most chondritic parent bodies-most of them originated in the asteroid belt-are depleted in iron relative to average solar system abundances. The astrophysical processes leading to metal silicate fractionation in the solar nebula are essentially unknown. Here, we consider photophoretic forces. As these forces particularly act on irradiated solids, they might play a significant role in the composition of planetesimals forming at the inner edge of protoplanetary disks. Photophoresis can separate high thermal conductivity materials (iron) from lower thermal conductivity solids (silicate). We suggest that the silicates are preferentially pushed into the optically thick disk. Subsequent planetesimal formation at the edge moving outward leads to metal-rich planetesimals close to the star and metal depleted planetesimals farther out in the nebula.

79 ASTRONOMY AND ASTROPHYSICS↗

SOLAR CYCLE VARIABILITY AND SURFACE DIFFERENTIAL ROTATION FROM Ca II K-LINE TIME SERIES DATA

Analysis of over 36 yr of time series data from the NSO/AFRL/Sac Peak K-line monitoring program elucidates 5 components of the variation of the 7 measured chromospheric parameters: (a) the solar cycle (period {approx} 11 yr), (b) quasi-periodic variations (periods {approx} 100 days), (c) a broadband stochastic process (wide range of periods), (d) rotational modulation, and (e) random observational errors, independent of (a)-(d). Correlation and power spectrum analyses elucidate periodic and aperiodic variation of these parameters. Time-frequency analysis illuminates periodic and quasi-periodic signals, details of frequency modulation due to differential rotation, and in particular elucidates the rather complex harmonic structure (a) and (b) at timescales in the range {approx}0.1-10 yr. These results using only full-disk data suggest that similar analyses will be useful for detecting and characterizing differential rotation in stars from stellar light curves such as those being produced by NASA's Kepler observatory. Component (c) consists of variations over a range of timescales, in the manner of a 1/f random process with a power-law slope index that varies in a systematic way. A time-dependent Wilson-Bappu effect appears to be present in the solar cycle variations (a), but not in the more rapid variations of the stochastic process (c). Component (d) characterizes differential rotation of the active regions. Component (e) is of course not characteristic of solar variability, but the fact that the observational errors are quite small greatly facilitates the analysis of the other components. The data analyzed in this paper can be found at the National Solar Observatory Web site http://nsosp.nso.edu/cak{sub m}on/, or by file transfer protocol at ftp://ftp.nso.edu/idl/cak.parameters.

79 ASTRONOMY AND ASTROPHYSICS↗

INTRODUCING CAFein, A NEW COMPUTATIONAL TOOL FOR STELLAR PULSATIONS AND DYNAMIC TIDES

Here we present CAFein, a new computational tool for investigating radiative dissipation of dynamic tides in close binaries and of non-adiabatic, non-radial stellar oscillations in isolated stars in the linear regime. For the latter, CAFein computes the non-adiabatic eigenfrequencies and eigenfunctions of detailed stellar models. The code is based on the so-called Riccati method, a numerical algorithm that has been successfully applied to a variety of stellar pulsators, and which does not suffer from the major drawbacks of commonly used shooting and relaxation schemes. Here we present an extension of the Riccati method to investigate dynamic tides in close binaries. We demonstrate CAFein's capabilities as a stellar pulsation code both in the adiabatic and non-adiabatic regimes, by reproducing previously published eigenfrequencies of a polytrope, and by successfully identifying the unstable modes of a stellar model in the {beta} Cephei/SPB region of the Hertzsprung-Russell diagram. Finally, we verify CAFein's behavior in the dynamic tides regime by investigating the effects of dynamic tides on the eigenfunctions and orbital and spin evolution of massive main sequence stars in eccentric binaries, and of hot Jupiter host stars. The plethora of asteroseismic data provided by NASA's Kepler satellite, some of which include the direct detection of tidally excited stellar oscillations, make CAFein quite timely. Furthermore, the increasing number of observed short-period detached double white dwarfs (WDs) and the observed orbital decay in the tightest of such binaries open up a new possibility of investigating WD interiors through the effects of tides on their orbital evolution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DETECTION OF HIGH-DEGREE PROGRADE SECTORAL MODE SEQUENCES IN THE A-STAR KIC 8054146?

This paper examines the 46 frequencies found in the {delta} Sct star KIC 8054146 involving a frequency spacing of exactly 2.814 cycles day{sup -1} (32.57 {mu}Hz), which is also a dominant low-frequency peak near or equal to the rotational frequency. These 46 frequencies range up to 146 cycles day{sup -1}. Three years of Kepler data reveal distinct sequences of these equidistantly spaced frequencies, including the basic sequence and side lobes associated with other dominant modes (i.e., small amplitude modulations). The amplitudes of the basic sequence show a high-low pattern. The basic sequence follows the equation f{sub m} = 2.8519 + m*2.81421 cycles day{sup -1} with m ranging from 25 to 35. The zero-point offset and the lack of low-order harmonics eliminate an interpretation in terms of a Fourier series of a non-sinusoidal light curve. The exactness of the spacing eliminates high-order asymptotic pulsation. The frequency pattern is not compatible with simple hypotheses involving single or multiple spots, even with differential rotation. The basic high-frequency sequence is interpreted in terms of prograde sectoral modes. These can be marginally unstable, while their corresponding low-degree counterparts are stable due to stronger damping. The measured projected rotation velocity (300 km s{sup -1}) indicates that the star rotates with {approx}>70% of the Keplerian break-up velocity. This suggests a near equator-on view. We qualitatively examine the visibility of prograde sectoral high-degree g-modes in integrated photometric light in such a geometrical configuration and find that prograde sectoral modes can reproduce the frequencies and the odd-even amplitude pattern of the high-frequency sequence.

79 ASTRONOMY AND ASTROPHYSICS↗

FAST STAR, SLOW STAR; OLD STAR, YOUNG STAR: SUBGIANT ROTATION AS A POPULATION AND STELLAR PHYSICS DIAGNOSTIC

Stellar rotation is a strong function of both mass and evolutionary state. Missions such as Kepler and CoRoT provide tens of thousands of rotation periods, drawn from stellar populations that contain objects at a range of masses, ages, and evolutionary states. Given a set of reasonable starting conditions and a prescription for angular momentum loss, we address the expected range of rotation periods for cool field stellar populations (∼0.4-2.0 M{sub ☉}). We find that cool stars fall into three distinct regimes in rotation. Rapid rotators with surface periods less than 10 days are either young low-mass main sequence (MS) stars, or higher mass subgiants which leave the MS with high rotation rates. Intermediate rotators (10-40 days) can be either cool MS dwarfs, suitable for gyrochronology, or crossing subgiants at a range of masses. Gyrochronology relations must therefore be applied cautiously, since there is an abundant population of subgiant contaminants. The slowest rotators, at periods greater than 40 days, are lower mass subgiants undergoing envelope expansion. We identify additional diagnostic uses of rotation periods. There exists a period-age relation for subgiants distinct from the MS period-age relations. There is also a period-radius relation that can be used as a constraint on the stellar radius, particularly in the interesting case of planet host stars. The high-mass/low-mass break in the rotation distribution on the MS persists onto the subgiant branch, and has potential as a diagnostic of stellar mass. Finally, this set of theoretical predictions can be compared to extensive datasets to motivate improved modeling.

79 ASTRONOMY AND ASTROPHYSICS↗

KOI-142, THE KING OF TRANSIT VARIATIONS, IS A PAIR OF PLANETS NEAR THE 2:1 RESONANCE

The transit timing variations (TTVs) can be used as a diagnostic of gravitational interactions between planets in a multi-planet system. Many Kepler Objects of Interest (KOIs) exhibit significant TTVs, but KOI-142.01 stands out among them with an unrivaled ≅12 hr TTV amplitude. Here we report a thorough analysis of KOI-142.01's transits. We discover periodic transit duration variations (TDVs) of KOI-142.01 that are nearly in phase with the observed TTVs. We show that KOI-142.01's TTVs and TDVs uniquely detect a non-transiting companion with a mass ≅0.63 that of Jupiter (KOI-142c). KOI-142.01's mass inferred from the transit variations is consistent with the measured transit depth, suggesting a Neptune-class planet (KOI-142b). The orbital period ratio P{sub c} /P{sub b} = 2.03 indicates that the two planets are just wide of the 2:1 resonance. The present dynamics of this system, characterized here in detail, can be used to test various formation theories that have been proposed to explain the near-resonant pairs of exoplanets.

79 ASTRONOMY AND ASTROPHYSICS↗

CALCULATING THE HABITABLE ZONE OF BINARY STAR SYSTEMS. II. P-TYPE BINARIES

We have developed a comprehensive methodology for calculating the circumbinary habitable zone (HZ) in planet-hosting P-type binary star systems. We present a general formalism for determining the contribution of each star of the binary to the total flux received at the top of the atmosphere of an Earth-like planet and use the Sun's HZ to calculate the inner and outer boundaries of the HZ around a binary star system. We apply our calculations to the Kepler's currently known circumbinary planetary systems and show the combined stellar flux that determines the boundaries of their HZs. We also show that the HZ in P-type systems is dynamic and, depending on the luminosity of the binary stars, their spectral types, and the binary eccentricity, its boundaries vary as the stars of the binary undergo their orbital motion. We present the details of our calculations and discuss the implications of the results.

79 ASTRONOMY AND ASTROPHYSICS↗