scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Kepler-432: a red giant interacting with one of its two long-period giant planets

TL;DR: In this paper, the authors reported the discovery of Kepler-432b, a giant planet (M_b = 5.41^(+0.12)_(-0.036)_−0.039)R_Jup) transiting an evolved star with an eccentricity of e=0.
Abstract: We report the discovery of Kepler-432b, a giant planet (M_b = 5.41^(+0.32)_(-0.18)M_Jup, R_b = 1.145^(+0.036)_(-0.039)R_Jup) transiting an evolved star (M_* = 1.32^(+0.10)_(-0.07)M_⊙, R_* = 4.06^(+0.12)_(-0.08)R_⊙) with an orbital period of P_b = 52.501129^(+0.000067)_(-0.000053) days. Radial velocities (RVs) reveal that Kepler-432b orbits its parent star with an eccentricity of e=0.5134^(+0.0098)_(-0.0089), which we also measure independently with asterodensity profiling (AP; e=0.507^(+0.039)_(-0.114)), thereby confirming the validity of AP on this particular evolved star. The well-determined planetary properties and unusually large mass also make this planet an important benchmark for theoretical models of super-Jupiter formation. Long-term RV monitoring detected the presence of a non-transiting outer planet (Kepler-432c; M_c sin i_c = 2.43^(+0.22)_(-0.24) M_Jup, P_c = 406.2^(+3.9)_(-2.5) days), and adaptive optics imaging revealed a nearby (0".87), faint companion (Kepler-432B) that is a physically bound M dwarf. The host star exhibits high signal-to-noise ratio asteroseismic oscillations, which enable precise measurements of the stellar mass, radius, and age. Analysis of the rotational splitting of the oscillation modes additionally reveals the stellar spin axis to be nearly edge-on, which suggests that the stellar spin is likely well aligned with the orbit of the transiting planet. Despite its long period, the obliquity of the 52.5 day orbit may have been shaped by star–planet interaction in a manner similar to hot Jupiter systems, and we present observational and theoretical evidence to support this scenario. Finally, as a short-period outlier among giant planets orbiting giant stars, study of Kepler-432b may help explain the distribution of massive planets orbiting giant stars interior to 1 AU.

Summary (7 min read)

2.1. Kepler Observations

  • The Kepler mission and its photometric performance are described in Borucki et al. (2010), and the characteristics of the detector on board the spacecraft are described in Koch et al. (2010) and van Cleve (2008).
  • Kepler432b was published by the Kepler team as a Kepler Object of Interest (KOI) and planetary candidate (designated KOI-1299; see Batalha et al. 2013), and after also being identified as a promising asteroseismic target, it was observed in shortcadence (SC) mode for 8 quarters.
  • The authors note that a pair of recent papers have now confirmed the planetary nature of this transiting companion via radial velocity measurements (Ciceri et al. 2015; Ortiz et al. 2015).
  • The full photometric time series, normalized in each quarter, is shown in Figure 1. 19 Among the other 95 such planets listed in The Exoplanet Orbit Database (exoplanets.org), none transit.

2.2. Light-curve Analysis

  • A transit light-curve analysis of Kepler-432b was performed previously by Sliski & Kipping (2014).
  • In that work, the authors first detrended the Simple Aperture Photometry (SAP) Kepler data20 for quarters 1–17 using the CoFiAM (Cosine Filtering with Autocorrelation Minimization) algorithm and then regressed the cleaned data with the multimodal nested sampling algorithm MultiNest (Feroz et al. 2009) coupled to a Mandel & Agol (2002) planetary transit model.
  • The authors light-curve model employs the quadratic limb darkening Mandel & Agol (2002) routine with the Kipping (2010) “resampling” prescription for accounting for the smearing of the long-cadence data.
  • In cases where the parent star’s mean density is independently constrained, a transit light-curve can be used to constrain the orbital eccentricity and argument of periastron (Dawson & Johnson 2012; Kipping 2014a).

3.1. Speckle Imaging

  • Speckle imaging observations of Kepler-432 were performed on UT 2011 June 16 at the 3.5 m WIYN telescope on Kitt Peak, AZ, using the Differential Speckle Survey Instrument (DSSI; Horch et al. 2010).
  • DSSI provides simultaneous images in two filters using a dichroic beam splitter and two identical EMCCDs.

3.2. Adaptive Optics Imaging

  • The object was not detected in the speckle images because they were taken with less aperture and the expected contrast ratios are larger in R and I—using the properties of the companion as derived in the following section, the authors estimate D ~R 6.7 and D ~I 6.6.
  • These magnitudes are consistent with non-detections in the speckle images, as plotted in Figure 3.

3.3. Properties of the Visual Companion

  • The faint visual companion to Kepler-432 could be a background star or a physically bound main-sequence companion.
  • The authors first estimate the background stellar density in the direction of Kepler-432 using the TRILEGAL stellar population synthesis tool (Girardi et al. 2005): they expect 49,000 sources per deg2 that are brighter than ~K 19s (the detection limit of their observation).
  • This translates to 0.06 sources (of any brightness and color) expected in their 16 arcsec2 image, and thus the a priori probability of a chance alignment is low.
  • The authors then use the observed magnitude differences between the stars to search for an appropriate match to the companion in the isochrone.
  • In reality, the semi-major axis may be smaller (if the authors observed it near apastron of an eccentric orbit with the major axis in the plane of the sky), or significantly larger (due to projections into the plane of the sky and the unknown orbital phase).

4.1. Spectroscopic Observations

  • The authors used the Tillinghast Reflector Echelle Spectrograph (TRES; Fűrész 2008) mounted on the 1.5 m Tillinghast Reflector at the Fred L. Whipple Observatory (FLWO) on Mt. Hopkins, AZ, to obtain 84 high-resolution spectra of Kepler-432 between UT 2011 March 23 and 2014 June 18.
  • Typical exposure times were 15–30 minutes and resulted in extracted signal-tonoise ratios (S/Ns) between about 20 and 45 per resolution element.
  • This allows us to report the absolute systemic velocity, gabs.
  • The authors are aware of specific TRES hardware malfunctions (and upgrades) that occurred during the time span of their data that, in addition to small zero-point shifts (typically < -10 m s 1), caused degradation (or improvement) of RV precision for particular observing runs.
  • Like TRES, FIES is a temperature-controlled, fiber-fed instrument and has a resolving power through the medium fiber of ~R 46,000, a wavelength coverage of ~3600–7400 Å, and wavelength calibration determined from ThAr emissionline spectra.

4.2. Spectroscopic Reduction and Radial Velocity Determination

  • The authors will discuss the reduction of spectra from both instruments collectively but only briefly (more details can be found in Buchhave et al. 2010) while detailing the challenges presented by their particular data set.
  • The authors used 21 orders (spanning 4290–6280 Å), rejecting those plagued by telluric lines, fringing in the red, and low S/N in the blue.
  • The median RV of HD 182488 was calculated for each run, which the authors applied as shifts to the Kepler432 velocities, keeping in mind that each shift introduces additional uncertainty.
  • This indicates that the additional uncertainty introduced by run-to-run correction already adequately accounts for the instrumental uncertainty, and the authors do not need to explicitly include an additional error term to account for it.
  • The authors used the CfA library of synthetic spectra, which are based on Kurucz model atmospheres (Kurucz 1992).

5.1. Background

  • Cool stars exhibit brightness variations due to oscillations driven by near-surface convection (Houdek et al. 1999; Aerts et al. 2010), which are a powerful tool to study their density profiles and evolutionary states.
  • A simple asteroseismic analysis is based on the average separation of modes of equal spherical degree ( nD ) and the frequency of maximum oscillation power (nmax), using scaling relations to estimate the mean stellar density, surface gravity, radius, and mass (Kjeldsen & Bedding 1995; Stello et al.

5.2. Frequency Analysis

  • The time series was prepared for asteroseismic analysis from the raw Kepler target pixel data using the Kepler, Asteroseismic Science Operations, Center filter (Handberg & Lund 2014).
  • Fortunately, the ℓ = 1 mixed modes follow a frequency pattern that arises from coupling of the p-modes in the envelope, which have approximately equal spacing in frequency ( nD ), to gmodes in the core, which are approximately equally spaced in period (DP).
  • The mode frequencies from each fit were compared to the mean values, and the fitter that differed least overall was selected to provide the frequency solution.
  • The authors discuss the rotation of the star further in Section 5.3.
  • Revised values of nD and nmax can be obtained from the measured mode frequencies and amplitudes.

5.3. Host Star Inclination

  • The line-of-sight inclination of a rotating star can be determined by measuring the relative heights of rotationally split modes (Gizon & Solanki 2003).
  • Figure 6 shows that all dipole modes observed for Kepler-432 are split into doublets, which the authors interpret as triplets with the central peak missing, indicating a rotation axis nearly perpendicular to the line of sight (inclination i = 90°).
  • Huber et al. (2013b) similarly found no difference between the inclination angle of p-dominated and gdominated mixed modes in Kepler-56.
  • Unless mode lifetimes are much shorter than the observing baseline, the Lorentzian profiles of the modes will not be well resolved, and the mode heights will vary.

5.4. Modeling

  • Two approaches may be used when performing asteroseismic modeling.
  • The first is the so-called grid-based method, which uses evolutionary tracks that cover a wide range of metallicities and masses and searches for the best-fitting model using nD , nmax, Teff , and [Fe H] as constraints (e.g., Stello et al.
  • The theoretical frequencies were calculated using GYRE (Townsend & Teitler 2013) and were corrected for near-surface effects using the power-law correction of Kjeldsen et al. (2008) for radial modes.
  • The second analysis was performed with the Aarhus Stellar Evolution Code (ASTEC; Christensen-Dalsgaard 2008a), with theoretical frequencies calculated using the Aarhus adiabatic oscillation package (Christensen-Dalsgaard 2008b).
  • The bestfitting model was found in a similar manner as the first analysis, although the mixing length parameter was kept fixed at a value of α = 1.8.

6. ORBITAL SOLUTION

  • Instead, the authors adopt best-fit parameters from the mode of each distribution, which they identify from the peak of the probability density function (PDF).
  • The resulting orbital solution using these parameters has velocity residuals larger than expected from the nominal RV uncertainties.
  • To account for the observed velocity residuals, the authors re-run their MCMC with the inclusion of an additional RV jitter term.
  • The authors report the best-fit orbital and physical planetary parameters in Table 5, which also includes the set of parameters additionally constrained by dynamical stability simulations, as described in the N-body analysis of Section 8.

7. FALSE POSITIVE SCENARIOS

  • An apparent planetary signal (transit or RV) can sometimes be caused by astrophysical false positives.
  • To test against the scenarios described, the authors computed the line bisector spans for the TRES spectra.
  • In the following paragraphs, the authors explain why other interpretations are unlikely.
  • Not only is this inconsistent with the observed outer orbital period (407 days), but the authors detect no significant photometric signal near either of these periods.
  • As the authors have shown in Section 5, Kepler-432 exhibits strong oscillations, so one may wonder whether these could induce the observed RV signal for the outer planet.

8.1. Methodology

  • Following the Keplerian MCMC fitting procedure described in Section 6, the authors wish to understand whether these posterior solutions are dynamically stable—i.e., whether they describe realistic systems that could survive to the 3.5 Gyr age of the system.
  • The authors perform integrations of both coplanar and inclined systems.
  • The authors first explore the less computationally expensive coplanar case to understand the behavior of the system, and then extend the simulations to include inclination in the outer orbit, which has the additional potential to constrain the mutual inclination of the planets.
  • To understand this stability, the authors utilize the integration algorithm described in Payne et al. (2013).
  • The longitude of ascending node for the outer planet is drawn randomly from a uniform distribution between 0 and π2 .

8.2. Coplanar Stability

  • While this is not a particularly long integration period compared with the period of the planets (~50 and ~400 days), the authors demonstrate that even during this relatively short integration, approximately half of the systems become unstable.
  • As described above, separations greater than ~10 AU indicate that the system has suffered an instability.
  • The authors illustrate in Figure 11 the successive restriction of the parameter space in the mass–eccentricity plane for the outer planet (m e,c c) as the integration timescales increase.
  • The authors find that the long-term stable systems occupy a significantly smaller region of parameter space in the m e,c c plane.
  • That is, the authors use a Gaussian kernel density estimator to smooth the posterior distribution and select the mode (i.e., the value with the largest probability density).

8.3. Inclined-system Stability

  • In these inclined system integrations, the outer planet has an inclination that is not edge-on, and hence a mass for the outer planet that is inflated compared to its minimum edge-on value, as described in Section 8.1.
  • Integrating these stable systems while keeping the pre-assigned inclinations for the outer planet (i.e., the authors do not rerandomize the inclinations), they integrate this subset on to 105 yr and find that the number of stable systems subsequently reduces to ~N 104.
  • There is a small population with significantly higher eccentricities and relative inclinations that remains stable at =t 105 yr, and it is possible that these systems exhibit strong Kozai oscillations, but their long-term (>105 yr) behavior has not been investigated.
  • The authors emphasize that the inclinations and longitudes of the ascending node were assigned randomly, and hence it is possible that specifically chosen orbital alignments could allow for enhanced stability in certain cases.
  • Simulating the effect of poorly characterized or hypothetical orbits, or the interactions between expanding stars and their planets, is beyond the scope of the current paper, and instead the authors simply remind the reader of these complications.

9. DISCUSSION

  • The properties of the star and planets of Kepler-432 are unusual in several ways among the known exoplanets, which makes it a valuable system to study in detail.
  • Close examination of the system may provide insight into the processes of planet formation and orbital evolution in such regimes.
  • Kepler-432 is also the first planet orbiting a giant star to have its eccentricity independently determined by RVs and photometry, which helps address a concern that granulation noise in giants can inhibit such photometric measurements.

9.1. Comparing the Eccentricity from AP versus RVs

  • AP provides an independent technique for measuring orbital eccentricities with photometry alone, via the so-called photoeccentric effect (Dawson & Johnson 2012), and can be used as a tool to evaluate the quality of planet candidates (Tingley et al. 2011).
  • It was originally envisioned as a technique for measuring eccentricities (Kipping et al. 2012), but other effects, such as a background blend, can also produce AP effects (Kipping 2014a).
  • The results may be visually compared in Figure 13.
  • The analysis presented here demonstrates that AP can produce accurate results for giant stars.
  • Timecorrelated noise may still be an important factor in giant host stars that are more evolved than Kepler-432 (such as Kepler91), for which granulation becomes more pronounced (Mathur et al. 2011).

9.2. A Benchmark for Compositions of Super-Jupiters

  • Kepler-432b has a measured mass, radius, and age, which allows us to investigate its bulk composition.
  • Moreover, most of the super-Jupiters are highly irradiated, which further complicates modeling and interpretation of planetary structure.
  • Kepler-432b receives only about 20% of the insolation of a 3 day hot Jupiter orbiting a Sun-like star.
  • In Figure 14, the authors compare the mass and radius of Kepler-432b to age- and insolation-appropriate planetary models (Fortney et al. 2007) of varying core mass.
  • The radius is apparently slightly inflated but is somewhat consistent (1σ) with that of a planet lacking a core of heavy elements.

9.3. Jupiters Do (Briefly) Orbit Giants within 0.5 AU

  • As discussed previously, the authors do not know of many transiting giant planets orbiting giant stars.
  • That is, perhaps massive main-sequence stars simply harbor very few planets with separations less than 1 AU.
  • In the second scenario, the authors consider that Kepler-432b may be a member of a more numerous group of planets interior to ~0.5 AU that exist around main-sequence F- and A-type stars but do not survive through the red giant phase when the star expands to a significant fraction of an AU.
  • While typically tidal interaction leading to circularization and orbital decay has been modeled to depend only on tides in the planet, Jackson et al. (2008) show that tides in the star (which are strongly dependent on the stellar radius) can also influence orbital evolution.
  • For similar arguments and additional discussion, see Jones et al. (2014).

9.4. Implications for Giant Planet Formation and Migration

  • Assuming that giant planets form beyond the ice line (located at ~4.9 AU for a star with ~ M M1.4 , using the approximation of Ida & Lin 2005), both Kepler-432b and c have experienced significant inward migration.
  • The apparent alignment between the stellar spin axis and the orbit of the inner planet presents a puzzle; if the (initially circular, coplanar) planets migrated via multi-body interactions, the authors would expect both the eccentricities and the inclinations to grow.
  • Unfortunately, because the authors are unable to constrain the mutual inclination of the planets, they cannot say whether they are mutually well aligned (which would argue against planet–planet scattering) or not.
  • Ideally, the authors would also measure the sky-projected spin–orbit angle, λ, in order to detect any such conspiring misalignment and calculate the true obliquity.
  • In their investigation of hot Jupiter obliquities, Winn et al. (2010) suggested that well-aligned hot Jupiters may have been misaligned previously, and that subsequent tidal interaction may have realigned the stellar rotation with the planetary orbit, perhaps influencing the convective envelope independently of the interior.

9.5. Evidence for Spin–Orbit Evolution

  • During the main-sequence lifetime of Kepler-432, the current position of the planets would be too far from the star to raise any significant tides, but the star is now several times its original size, such that at periastron, the inner planet passes within 7.7 stellar radii of the star.
  • Their analysis of individual ℓ = 1 modes in Section 5.3 showed they were consistent with~ 90 inclination for both core and envelope.
  • While the evidence presented thus far for realignment of the Kepler-432 system is circumstantial, there may be additional evidence to support the scenario.
  • The authors find this to be an unlikely scenario given the periodogram of the Kepler data .
  • If, however, a spot excited during periastron lasted only slightly more than one rotation period, the authors would expect to see a second peak in the folded light-curve, with an amplitude dependent on the spot lifetime and phase dependent on the rotation period.

10. SUMMARY

  • The authors have presented herein the discovery of the Kepler-432 planetary system, consisting of two giant planets orbiting a red giant star, and a faint visual companion that is probably a physically bound M dwarf with an orbital separation of at least 750 AU.
  • The inner planet (P = 52.5 days) transits the star, allowing a more detailed study of its properties.
  • This evidence for ongoing SPI further supports the obliquity realignment scenario.
  • Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant DNRF106).
  • This research has also made use of the APASS database, located at the AAVSO Web site.

Did you find this useful? Give us your feedback

Figures (24)

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI
TL;DR: Modules for Experiments in Stellar Astrophysics (MESA) as discussed by the authors can now simultaneously evolve an interacting pair of differentially rotating stars undergoing transfer and loss of mass and angular momentum, greatly enhancing the prior ability to model binary evolution.
Abstract: We substantially update the capabilities of the open-source software instrument Modules for Experiments in Stellar Astrophysics (MESA). MESA can now simultaneously evolve an interacting pair of differentially rotating stars undergoing transfer and loss of mass and angular momentum, greatly enhancing the prior ability to model binary evolution. New MESA capabilities in fully coupled calculation of nuclear networks with hundreds of isotopes now allow MESA to accurately simulate advanced burning stages needed to construct supernova progenitor models. Implicit hydrodynamics with shocks can now be treated with MESA, enabling modeling of the entire massive star lifecycle, from pre-main sequence evolution to the onset of core collapse and nucleosynthesis from the resulting explosion. Coupling of the GYRE non-adiabatic pulsation instrument with MESA allows for new explorations of the instability strips for massive stars while also accelerating the astrophysical use of asteroseismology data. We improve treatment of mass accretion, giving more accurate and robust near-surface profiles. A new MESA capability to calculate weak reaction rates "on-the-fly" from input nuclear data allows better simulation of accretion induced collapse of massive white dwarfs and the fate of some massive stars. We discuss the ongoing challenge of chemical diffusion in the strongly coupled plasma regime, and exhibit improvements in MESA that now allow for the simulation of radiative levitation of heavy elements in hot stars. We close by noting that the MESA software infrastructure provides bit-for-bit consistency for all results across all the supported platforms, a profound enabling capability for accelerating MESA's development.

2,166 citations

Journal ArticleDOI
TL;DR: Modules for Experiments in Stellar Astrophysics (MESA) as discussed by the authors can now simultaneously evolve an interacting pair of differentially rotating stars undergoing transfer and loss of mass and angular momentum, greatly enhancing the prior ability to model binary evolution.
Abstract: We substantially update the capabilities of the open-source software instrument Modules for Experiments in Stellar Astrophysics (MESA). MESA can now simultaneously evolve an interacting pair of differentially rotating stars undergoing transfer and loss of mass and angular momentum, greatly enhancing the prior ability to model binary evolution. New MESA capabilities in fully coupled calculation of nuclear networks with hundreds of isotopes now allow MESA to accurately simulate advanced burning stages needed to construct supernova progenitor models. Implicit hydrodynamics with shocks can now be treated with MESA, enabling modeling of the entire massive star lifecycle, from pre-main sequence evolution to the onset of core collapse and nucleosynthesis from the resulting explosion. Coupling of the GYRE non-adiabatic pulsation instrument with MESA allows for new explorations of the instability strips for massive stars while also accelerating the astrophysical use of asteroseismology data. We improve treatment of mass accretion, giving more accurate and robust near-surface profiles. A new MESA capability to calculate weak reaction rates "on-the-fly" from input nuclear data allows better simulation of accretion induced collapse of massive white dwarfs and the fate of some massive stars. We discuss the ongoing challenge of chemical diffusion in the strongly coupled plasma regime, and exhibit improvements in MESA that now allow for the simulation of radiative levitation of heavy elements in hot stars. We close by noting that the MESA software infrastructure provides bit-for-bit consistency for all results across all the supported platforms, a profound enabling capability for accelerating MESA's development.

1,401 citations

Journal ArticleDOI
TL;DR: In this article, the authors systematically characterize solar-like oscillations and granulation for 16,094 oscillating red giants, using end-of-mission long-cadence data.
Abstract: The Kepler mission has provided exquisite data to perform an ensemble asteroseismic analysis on evolved stars. In this work we systematically characterize solar-like oscillations and granulation for 16,094 oscillating red giants, using end-of-mission long-cadence data. We produced a homogeneous catalog of the frequency of maximum power (typical uncertainty $\\sigma_{\ u_{\\rm max}}$=1.6\\%), the mean large frequency separation ($\\sigma_{\\Delta\ u}$=0.6\\%), oscillation amplitude ($\\sigma_{\\rm A}$=4.7\\%), granulation power ($\\sigma_{\\rm gran}$=8.6\\%), power excess width ($\\sigma_{\\rm width}$=8.8\\%), seismically-derived stellar mass ($\\sigma_{\\rm M}$=7.8\\%), radius ($\\sigma_{\\rm R}$=2.9\\%), and thus surface gravity ($\\sigma_{\\log g}$=0.01 dex). Thanks to the large red giant sample, we confirm that red-giant-branch (RGB) and helium-core-burning (HeB) stars collectively differ in the distribution of oscillation amplitude, granulation power, and width of power excess, which is mainly due to the mass difference. The distribution of oscillation amplitudes shows an extremely sharp upper edge at fixed $\ u_{\\rm max}$, which might hold clues to understand the excitation and damping mechanisms of the oscillation modes. We find both oscillation amplitude and granulation power depend on metallicity, causing a spread of 15\\% in oscillation amplitudes and a spread of 25\\% in granulation power from [Fe/H]=-0.7 to 0.5 dex. Our asteroseismic stellar properties can be used as reliable distance indicators and age proxies for mapping and dating galactic stellar populations observed by Kepler. They will also provide an excellent opportunity to test asteroseismology using Gaia parallaxes, and lift degeneracies in deriving atmospheric parameters in large spectroscopic surveys such as APOGEE and LAMOST.

168 citations


Cites background from "Kepler-432: a red giant interacting..."

  • ...It has also provided an excellent opportunity to implement Galactic archaeology (Miglio et al. 2013; Stello et al. 2015; Casagrande et al. 2016; Sharma et al. 2016) and to characterize exoplanet properties (Huber et al. 2013a; Quinn et al. 2015)....

    [...]

  • ...…(Hekker et al. 2011a), grid-based modeling (Stello & Gilliland 2009; Kallinger et al. 2010b; Huber et al. 2013b; Chaplin et al. 2014b), and individual frequency modeling (Kallinger et al. 2008; di Mauro et al. 2011; Deheuvels et al. 2012; Quinn et al. 2015; Di Mauro et al. 2016; Li et al. 2018)....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a comprehensive assessment of the uncertainties associated with the lensing models and the size distribution of galaxies is presented, and an end-to-end simulation from the source plane to the final ultraviolet luminosity function (LF) that accounts for all lensing effects and systematic uncertainties by comparing several mass models is presented.
Abstract: With the Hubble Frontier Fields program, gravitational lensing has provided a powerful way to extend the study of the ultraviolet luminosity function (LF) of galaxies at $z \sim 6$ down to unprecedented magnitude limits. At the same time, significant discrepancies between different studies were found at the very faint end of the LF. In an attempt to understand such disagreements, we present a comprehensive assessment of the uncertainties associated with the lensing models and the size distribution of galaxies. We use end-to-end simulations from the source plane to the final LF that account for all lensing effects and systematic uncertainties by comparing several mass models. In addition to the size distribution, the choice of lens model leads to large differences at magnitudes fainter than $M_{UV} = -15~$ AB mag, where the magnification factor becomes highly uncertain. We perform MCMC simulations that include all these uncertainties at the individual galaxy level to compute the final LF, allowing, in particular, a crossover between magnitude bins. The best LF fit, using a modified Schechter function that allows for a turnover at faint magnitudes, gives a faint-end slope of $\alpha = -2.01_{-0.14}^{+0.12}$, a curvature parameter of $\beta = 0.48_{-0.25}^{+0.49}$, and a turnover magnitude of $M_{T} = -14.93_{-0.52}^{+0.61}$. Most importantly our procedure shows that robust constraints on the LF at magnitudes fainter than $M_{UV} = -15~$ AB remain unrealistic. More accurate lens modeling and future observations of lensing clusters with the James Webb Space Telescope can reliably extend the UV LF to fainter magnitudes.

160 citations

Journal ArticleDOI
TL;DR: In this paper, a simple test is developed to estimate the detectability of solar-like oscillations in TESS photometry of any given star, based on an all-sky stellar and planetary synthetic population.
Abstract: New insights on stellar evolution and stellar interiors physics are being made possible by asteroseismology. Throughout the course of the Kepler mission, asteroseismology has also played an important role in the characterization of exoplanet-host stars and their planetary systems. The upcoming NASA Transiting Exoplanet Survey Satellite (TESS) will be performing a near all-sky survey for planets that transit bright nearby stars. In addition, its excellent photometric precision, combined with its fine time sampling and long intervals of uninterrupted observations, will enable asteroseismology of solar-type and red-giant stars. Here we develop a simple test to estimate the detectability of solar-like oscillations in TESS photometry of any given star. Based on an all-sky stellar and planetary synthetic population, we go on to predict the asteroseismic yield of the TESS mission, placing emphasis on the yield of exoplanet-host stars for which we expect to detect solar-like oscillations. This is done for both the target stars (observed at a 2-min cadence) and the full-frame-image stars (observed at a 30-min cadence). A similar exercise is also conducted based on a compilation of known host stars. We predict that TESS will detect solar-like oscillations in a few dozen target hosts (mainly subgiant stars but also in a smaller number of F dwarfs), in up to 200 low-luminosity red-giant hosts, and in over 100 solar-type and red-giant known hosts, thereby leading to a threefold improvement in the asteroseismic yield of exoplanet-host stars when compared to Kepler's.

131 citations


Cites background from "Kepler-432: a red giant interacting..."

  • ...…Johnson et al. 2007), data from Kepler have led to the discovery of several giant planets with short orbital periods (Porb.50 d) orbiting asteroseismic red-giant branch stars (4 planets in 3 systems, to be precise; Huber et al. 2013b; Lillo-Box et al. 2014; Ciceri et al. 2015; Quinn et al. 2015)....

    [...]

References
More filters
Journal ArticleDOI
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.

35,161 citations


"Kepler-432: a red giant interacting..." refers methods in this paper

  • ...…identified both visually and via periodogram analysis), they were fit with two Keplerian orbits using a Markov Chain Monte Carlo (MCMC) algorithm with the Metropolis-Hastings rule (Metropolis et al. 1953; Hastings 1970) and a Gibbs sampler (a review of which can be found in Casella & George 1992)....

    [...]

Journal ArticleDOI
TL;DR: In this article, a reprocessed composite of the COBE/DIRBE and IRAS/ISSA maps, with the zodiacal foreground and confirmed point sources removed, is presented.
Abstract: We present a full-sky 100 μm map that is a reprocessed composite of the COBE/DIRBE and IRAS/ISSA maps, with the zodiacal foreground and confirmed point sources removed. Before using the ISSA maps, we remove the remaining artifacts from the IRAS scan pattern. Using the DIRBE 100 and 240 μm data, we have constructed a map of the dust temperature so that the 100 μm map may be converted to a map proportional to dust column density. The dust temperature varies from 17 to 21 K, which is modest but does modify the estimate of the dust column by a factor of 5. The result of these manipulations is a map with DIRBE quality calibration and IRAS resolution. A wealth of filamentary detail is apparent on many different scales at all Galactic latitudes. In high-latitude regions, the dust map correlates well with maps of H I emission, but deviations are coherent in the sky and are especially conspicuous in regions of saturation of H I emission toward denser clouds and of formation of H2 in molecular clouds. In contrast, high-velocity H I clouds are deficient in dust emission, as expected. To generate the full-sky dust maps, we must first remove zodiacal light contamination, as well as a possible cosmic infrared background (CIB). This is done via a regression analysis of the 100 μm DIRBE map against the Leiden-Dwingeloo map of H I emission, with corrections for the zodiacal light via a suitable expansion of the DIRBE 25 μm flux. This procedure removes virtually all traces of the zodiacal foreground. For the 100 μm map no significant CIB is detected. At longer wavelengths, where the zodiacal contamination is weaker, we detect the CIB at surprisingly high flux levels of 32 ± 13 nW m-2 sr-1 at 140 μm and of 17 ± 4 nW m-2 sr-1 at 240 μm (95% confidence). This integrated flux ~2 times that extrapolated from optical galaxies in the Hubble Deep Field. The primary use of these maps is likely to be as a new estimator of Galactic extinction. To calibrate our maps, we assume a standard reddening law and use the colors of elliptical galaxies to measure the reddening per unit flux density of 100 μm emission. We find consistent calibration using the B-R color distribution of a sample of the 106 brightest cluster ellipticals, as well as a sample of 384 ellipticals with B-V and Mg line strength measurements. For the latter sample, we use the correlation of intrinsic B-V versus Mg2 index to tighten the power of the test greatly. We demonstrate that the new maps are twice as accurate as the older Burstein-Heiles reddening estimates in regions of low and moderate reddening. The maps are expected to be significantly more accurate in regions of high reddening. These dust maps will also be useful for estimating millimeter emission that contaminates cosmic microwave background radiation experiments and for estimating soft X-ray absorption. We describe how to access our maps readily for general use.

15,988 citations


"Kepler-432: a red giant interacting..." refers background in this paper

  • ...The mean of the reddening values reported by Schlafly & Finkbeiner (2011) and Schlegel et al. (1998) –...

    [...]

Journal ArticleDOI
TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.
Abstract: SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed. For numerical problems in a large number of dimensions, Monte Carlo methods are often more efficient than conventional numerical methods. However, implementation of the Monte Carlo methods requires sampling from high dimensional probability distributions and this may be very difficult and expensive in analysis and computer time. General methods for sampling from, or estimating expectations with respect to, such distributions are as follows. (i) If possible, factorize the distribution into the product of one-dimensional conditional distributions from which samples may be obtained. (ii) Use importance sampling, which may also be used for variance reduction. That is, in order to evaluate the integral J = X) p(x)dx = Ev(f), where p(x) is a probability density function, instead of obtaining independent samples XI, ..., Xv from p(x) and using the estimate J, = Zf(xi)/N, we instead obtain the sample from a distribution with density q(x) and use the estimate J2 = Y{f(xj)p(x1)}/{q(xj)N}. This may be advantageous if it is easier to sample from q(x) thanp(x), but it is a difficult method to use in a large number of dimensions, since the values of the weights w(xi) = p(x1)/q(xj) for reasonable values of N may all be extremely small, or a few may be extremely large. In estimating the probability of an event A, however, these difficulties may not be as serious since the only values of w(x) which are important are those for which x -A. Since the methods proposed by Trotter & Tukey (1956) for the estimation of conditional expectations require the use of importance sampling, the same difficulties may be encountered in their use. (iii) Use a simulation technique; that is, if it is difficult to sample directly from p(x) or if p(x) is unknown, sample from some distribution q(y) and obtain the sample x values as some function of the corresponding y values. If we want samples from the conditional dis

14,965 citations


"Kepler-432: a red giant interacting..." refers methods in this paper

  • ...…identified both visually and via periodogram analysis), they were fit with two Keplerian orbits using a Markov Chain Monte Carlo (MCMC) algorithm with the Metropolis-Hastings rule (Metropolis et al. 1953; Hastings 1970) and a Gibbs sampler (a review of which can be found in Casella & George 1992)....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors presented a reprocessed composite of the COBE/DIRBE and IRAS/ISSA maps, with the zodiacal foreground and confirmed point sources removed.
Abstract: We present a full sky 100 micron map that is a reprocessed composite of the COBE/DIRBE and IRAS/ISSA maps, with the zodiacal foreground and confirmed point sources removed. Before using the ISSA maps, we remove the remaining artifacts from the IRAS scan pattern. Using the DIRBE 100 micron and 240 micron data, we have constructed a map of the dust temperature, so that the 100 micron map can be converted to a map proportional to dust column density. The result of these manipulations is a map with DIRBE-quality calibration and IRAS resolution. To generate the full sky dust maps, we must first remove zodiacal light contamination as well as a possible cosmic infrared background (CIB). This is done via a regression analysis of the 100 micron DIRBE map against the Leiden- Dwingeloo map of H_I emission, with corrections for the zodiacal light via a suitable expansion of the DIRBE 25 micron flux. For the 100 micron map, no significant CIB is detected. In the 140 micron and 240 micron maps, where the zodiacal contamination is weaker, we detect the CIB at surprisingly high flux levels of 32 \pm 13 nW/m^2/sr at 140 micron, and 17 \pm 4 nW/m^2/sr at 240 micron (95% confidence). This integrated flux is ~2 times that extrapolated from optical galaxies in the Hubble Deep Field. The primary use of these maps is likely to be as a new estimator of Galactic extinction. We demonstrate that the new maps are twice as accurate as the older Burstein-Heiles estimates in regions of low and moderate reddening. These dust maps will also be useful for estimating millimeter emission that contaminates CMBR experiments and for estimating soft X-ray absorption.

14,295 citations

Journal ArticleDOI
TL;DR: The Two Micron All Sky Survey (2MASS) as mentioned in this paper collected 25.4 Tbytes of raw imaging data from two dedicated 1.3 m diameter telescopes located at Mount Hopkins, Arizona and CerroTololo, Chile.
Abstract: Between 1997 June and 2001 February the Two Micron All Sky Survey (2MASS) collected 25.4 Tbytes of raw imagingdatacovering99.998%ofthecelestialsphereinthenear-infraredJ(1.25 � m),H(1.65 � m),andKs(2.16 � m) bandpasses. Observations were conducted from two dedicated 1.3 m diameter telescopes located at Mount Hopkins, Arizona,andCerroTololo,Chile.The7.8sofintegrationtimeaccumulatedforeachpointontheskyandstrictquality control yielded a 10 � point-source detection level of better than 15.8, 15.1, and 14.3 mag at the J, H, and Ks bands, respectively, for virtually the entire sky. Bright source extractions have 1 � photometric uncertainty of <0.03 mag and astrometric accuracy of order 100 mas. Calibration offsets between any two points in the sky are <0.02 mag. The 2MASS All-Sky Data Release includes 4.1 million compressed FITS images covering the entire sky, 471 million source extractions in a Point Source Catalog, and 1.6 million objects identified as extended in an Extended Source Catalog.

12,126 citations

Related Papers (5)
Frequently Asked Questions (8)
Q1. What are the contributions in "Kepler-432: a red giant interacting with one of its two long-period giant planets" ?

The authors report the discovery of Kepler-432b, a giant planet ( = + M M 5. 41 b 0. 18 0. 32 Jup, = + R R 1. 145 b 0. 039 0. 036 Jup ) transiting an evolved star (   = = + +   M M R R 1. 32, 4. 06 0. 07 0. 10 0. 08 0. 12 ) with an orbital period of = + P 52. 501129 b 0. 000053 0. 000067 days. 5 day orbit may have been shaped by star–planet interaction in a manner similar to hot Jupiter systems, and the authors present observational and theoretical evidence to support this scenario. Finally, as a short-period outlier among giant planets orbiting giant stars, study of Kepler-432b may help explain the distribution of massive planets orbiting giant stars interior to 1 AU. Analysis of the rotational splitting of the oscillation modes additionally reveals the stellar spin axis to be nearly edge-on, which suggests that the stellar spin is likely well aligned with the orbit of the transiting planet. 

Because of its unprecedented photometric sensitivity,duty cycle, and time coverage, companions that are intrinsically rare or otherwise difficult to detect are expected to be found by Kepler, and detailed study of such discoveries can lead to characterization of poorly understood classes of objects and physical processes. 

Twelve parameters were included in the fit: for each planet, the times of inferior conjunction T0, orbital periods P, radial-velocity semi-amplitudes K, and the orthogonal quantities the authors sin and the authors cos , where e is orbital eccentricity and ω is the longitude of periastron; the systemic velocity, grel, in the arbitrary zero point of the TRES relative RV data set; and the FIES RV offset, DRVFIES. 

The nightly observations of RV standards were used to correct for systematic velocity shifts between runs and to estimate the instrumental precision. 

Rauch & Holman (1999) demonstrated that ∼20 time steps per innermost orbit is sufficient to ensure numerical stability in symplectic integrations. 

The stellar model best fit to the derived stellar properties provides color indices that may be compared against measured values as a consistency check and as a means to determine a photometric distance to the system. 

The authors do caution that their v isin measurement for this slowly rotating giant could be biased, for example, due to the unknown macroturbulent velocity of Kepler-432. 

This means that the heights of the m = ±1 components relative to the m = 0 component will change in opposite directions, so the effect can be mitigated by forcing the m = ±1 components to have the same height in the fit, as well as by performing a global fit to all modes, as the authors have done.