We analyze solutions drawn from the recently published posterior distribution of the TRAPPIST-1 system, which consists of seven Earth-size planets appearing to be in a resonant chain around a red ...dwarf. We show that all the planets are simultaneously in two-planet and three-planet resonances, apart from the innermost pair for which the two-planet resonant angles circulate. By means of a frequency analysis, we highlight that the transit-timing variation (TTV) signals possess a series of common periods varying from days to decades, which are also present in the variations of the dynamical variables of the system. Shorter periods (e.g., the TTVs characteristic timescale of 1.3 yr) are associated with two-planet mean-motion resonances, while longer periods arise from three-planet resonances. By use of
N
-body simulations with migration forces, we explore the origin of the resonant chain of TRAPPIST-1 and find that for particular disc conditions, a chain of resonances – similar to the observed one – can be formed which accurately reproduces the observed TTVs. Our analysis suggests that while the 4-yr collected data of observations hold key information on the two-planet resonant dynamics, further monitoring of TRAPPIST-1 will soon provide signatures of three-body resonances, in particular the 3.3 and 5.1 yr periodicities expected for the current best-fit solution. Additional observations would help to assess whether the innermost pair of planets is indeed resonant (its proximity to the 8:5 resonance being challenging to explain), and therefore give additional constraints on formation scenarios.
Abstract
We report on the properties of eclipsing binaries (EBs) from the Kepler mission with a newly developed photometric modelling code, which uses the light curve, spectral energy distribution of ...each binary, and stellar evolution models to infer stellar masses without the need for radial velocity (RV) measurements. We present solutions and posteriors to orbital and stellar parameters for 728 systems, forming the largest homogeneous catalogue of full Kepler binary parameter estimates to date. Using comparisons to published RV measurements, we demonstrate that the inferred properties (e.g. masses) are reliable for well-detached main-sequence (MS) binaries, which make up the majority of our sample. The fidelity of our inferred parameters degrades for a subset of systems not well described by input isochrones, such as short-period binaries that have undergone interactions, or binaries with post-MS components. Additionally, we identify 35 new systems which show evidence of eclipse timing variations, perhaps from apsidal motion due to binary tides or tertiary companions. We plan to subsequently use these models to search for and constrain the presence of circumbinary planets in Kepler EB systems.
Context.
With more than 1000 h of observation from Feb. 2016 to Oct. 2019, the
Spitzer
Exploration Program Red Worlds (ID: 13067, 13175 and 14223) exclusively targeted TRAPPIST-1, a nearby (12 pc) ...ultracool dwarf star, finding that it is orbited by seven transiting Earth-sized planets. At least three of these planets orbit within the classical habitable zone of the star, and all of them are well-suited for a detailed atmospheric characterization with the upcoming JWST.
Aims.
The main goals of the
Spitzer
Red Worlds program were (1) to explore the system for new transiting planets, (2) to intensively monitor the planets’ transits to yield the strongest possible constraints on their masses, sizes, compositions, and dynamics, and (3) to assess the infrared variability of the host star. In this paper, we present the global results of the project.
Methods.
We analyzed 88 new transits and combined them with 100 previously analyzed transits, for a total of 188 transits observed at 3.6 or 4.5
μ
m. For a comprehensive study, we analyzed all light curves both individually and globally. We also analyzed 29 occultations (secondary eclipses) of planet b and eight occultations of planet c observed at 4.5
μ
m to constrain the brightness temperatures of their daysides.
Results.
We identify several orphan transit-like structures in our
Spitzer
photometry, but all of them are of low significance. We do not confirm any new transiting planets. We do not detect any significant variation of the transit depths of the planets throughout the different campaigns. Comparing our individual and global analyses of the transits, we estimate for TRAPPIST-1 transit depth measurements mean noise floors of ~35 and 25 ppm in channels 1 and 2 of
Spitzer
/IRAC, respectively. We estimate that most of this noise floor is of instrumental origins and due to the large inter-pixel inhomogeneity of IRAC InSb arrays, and that the much better interpixel homogeneity of JWST instruments should result in noise floors as low as 10 ppm, which is low enough to enable the atmospheric characterization of the planets by transit transmission spectroscopy. Our analysis reveals a few outlier transits, but we cannot conclude whether or not they correspond to spot or faculae crossing events. We construct updated broadband transmission spectra for all seven planets which show consistent transit depths between the two
Spitzer
channels. Although we are limited by instrumental precision, the combined transmission spectrum of planet b to g tells us that their atmospheres seem unlikely to be CH
4
-dominated. We identify and model five distinct high energy flares in the whole dataset, and discuss our results in the context of habitability. Finally, we fail to detect occultation signals of planets b and c at 4.5
μ
m, and can only set 3-
σ
upper limits on their dayside brightness temperatures (611 K for b 586 K for c).
We use gravitational microlensing of the four images of the z = 0.658 quasar RXJ 1131-1231 to measure the sizes of the optical and X-ray emission regions of the quasar. The (face-on) scale length of ...the optical disk at rest frame 400 nm is R{sub l}ambda{sub ,O} = 1.3 x 10{sup 15} cm, while the half-light radius of the rest frame 0.3-17 keV X-ray emission is R{sub 1/2,X} = 2.3 x 10{sup 14} cm. The formal uncertainties are factors of 1.6 and 2.0, respectively. With the exception of the lower limit on the X-ray size, the results are very stable against any changes in the priors used in the analysis. Based on the Hbeta line width, we estimate that the black hole mass is M{sub 1131} approx = 10{sup 8} M{sub sun}, which corresponds to a gravitational radius of r{sub g} approx = 2 x 10{sup 13} cm. Thus, the X-ray emission is emerging on scales of approx10r{sub g} and the 400 nm emission on scales of approx70r{sub g} . A standard thin disk of this size should be significantly brighter than observed. Possible solutions are to have a flatter temperature profile or to scatter a large fraction of the optical flux on larger scales after it is emitted. While our calculations were not optimized to constrain the dark matter fraction in the lens galaxy, dark matter-dominated models are favored. With well-sampled optical and X-ray light curves over a broad range of frequencies, there will be no difficulty in extending our analysis to completely map the structure of the accretion disk as a function of wavelength.
Transit timing variations (TTVs) can be a very efficient way of constraining masses and eccentricities of multi-planet systems. Recent measurements of the TTVs of TRAPPIST-1 have led to an estimate ...of the masses of the planets, enabling an estimate of their densities and their water content. A recent TTV analysis using data obtained in the past two years yields a 34 and 13% increase in mass for TRAPPIST-1b and c, respectively. In most studies to date, a Newtonian
N
-body model is used to fit the masses of the planets, while sometimes general relativity is accounted for. Using the Posidonius
N
-body code, in this paper we show that in the case of the TRAPPIST-1 system, non-Newtonian effects might also be relevant to correctly model the dynamics of the system and the resulting TTVs. In particular, using standard values of the tidal Love number
k
2
(accounting for the tidal deformation) and the fluid Love number
k
2
f
(accounting for the rotational flattening) leads to differences in the TTVs of TRAPPIST-1b and c that are similar to the differences caused by general relativity. We also show that relaxing the values of tidal Love number
k
2
and the fluid Love number
k
2
f
can lead to TTVs which differ by as much as a few 10 s on a 3−4-yr timescale, which is a potentially observable level. The high values of the Love numbers needed to reach observable levels for the TTVs could be achieved for planets with a liquid ocean, which if detected might then be interpreted as a sign that TRAPPIST-1b and TRAPPIST-1c could have a liquid magma ocean. For TRAPPIST-1 and similar systems the models to fit the TTVs should potentially account for general relativity, for the tidal deformation of the planets, for the rotational deformation of the planets, and to a lesser extent for the rotational deformation of the star, which would add up to 7 × 2 + 1 = 15 additional free parameters in the case of TRAPPIST-1.
The transits of a distant star by a planet on a Keplerian orbit occur at time intervals exactly equal to the orbital period. If a second planet orbits the same star, the orbits are not Keplerian and ...the transits are no longer exactly periodic. We compute the magnitude of the variation in the timing of the transits, δt. We investigate analytically several limiting cases: (i) interior perturbing planets with much smaller periods; (ii) exterior perturbing planets on eccentric orbits with much larger periods; (iii) both planets on circular orbits with arbitrary period ratio but not in resonance; (iv) planets on initially circular orbits locked in resonance. Using subscripts ‘out’ and ‘in’ for the exterior and interior planets, μ for planet-to-star mass ratio and the standard notation for orbital elements, our findings in these cases are as follows. (i) Planet–planet perturbations are negligible. The main effect is the wobble of the star due to the inner planet, and therefore δt ∼ µin(ain/aout)Pout. (ii) The exterior planet changes the period of the interior planet by µout(ain/rout)3Pin. As the distance of the exterior planet changes due to its eccentricity, the inner planet's period changes. Deviations in its transit timing accumulate over the period of the outer planet, and therefore δt ∼ µouteout(ain/aout)3Pout. (iii) Halfway between resonances the perturbations are small, of the order of µouta2in/(ain − aout)2Pin for the inner planet (switch ‘out’ and ‘in’ for the outer planet). This increases as one gets closer to a resonance. (iv) This is perhaps the most interesting case because some systems are known to be in resonances and the perturbations are the largest. As long as the perturber is more massive than the transiting planet, the timing variations would be of the order of the period regardless of the perturber mass. For lighter perturbers, we show that the timing variations are smaller than the period by the perturber-to-transiting-planet mass ratio. An earth-mass planet in 2 : 1 resonance with a three-dimensional period transiting planet (e.g. HD 209458b) would cause timing variations of the order of 3 min, which would be accumulated over a year. This signal of a terrestrial planet is easily detectable with current ground-based measurements. For the case in which both planets are on eccentric orbits, we compute numerically the transit timing variations for several known multiplanet systems, assuming they are edge-on. Transit timing measurements may be used to constrain the masses, radii and orbital elements of planetary systems, and, when combined with radial velocity measurements, provide a new means of measuring the mass and radius of the host star.
Early 2017 observations of TRAPPIST-1 with Spitzer Delrez, L; Gillon, M; Triaud, A H M J ...
Monthly notices of the Royal Astronomical Society,
04/2018, Letnik:
475, Številka:
3
Journal Article, Web Resource
Recenzirano
Odprti dostop
Abstract
The recently detected TRAPPIST-1 planetary system, with its seven planets transiting a nearby ultracool dwarf star, offers the first opportunity to perform comparative exoplanetology of ...temperate Earth-sized worlds. To further advance our understanding of these planets’ compositions, energy budgets, and dynamics, we are carrying out an intensive photometric monitoring campaign of their transits with the Spitzer Space Telescope. In this context, we present 60 new transits of the TRAPPIST-1 planets observed with Spitzer/Infrared Array Camera (IRAC) in 2017 February and March. We combine these observations with previously published Spitzer transit photometry and perform a global analysis of the resulting extensive data set. This analysis refines the transit parameters and provides revised values for the planets’ physical parameters, notably their radii, using updated properties for the star. As part of our study, we also measure precise transit timings that will be used in a companion paper to refine the planets’ masses and compositions using the transit timing variations method. TRAPPIST-1 shows a very low level of low-frequency variability in the IRAC 4.5-μm band, with a photometric RMS of only 0.11 per cent at a 123-s cadence. We do not detect any evidence of a (quasi-)periodic signal related to stellar rotation. We also analyse the transit light curves individually, to search for possible variations in the transit parameters of each planet due to stellar variability, and find that the Spitzer transits of the planets are mostly immune to the effects of stellar variations. These results are encouraging for forthcoming transmission spectroscopy observations of the TRAPPIST-1 planets with the James Webb Space Telescope.
Galactic stellar‐population‐synthesis models, chemical‐enrichment models, and possibly gravitational microlensing indicate that about Ntot=108–109 stellar‐mass black holes reside in our Galaxy. We ...study X‐ray emission from accretion from the interstellar medium on to isolated black holes. Although black holes may be fewer in number than neutron stars, NNS∼109, their higher masses, 〈M〉∼9 M⊙, and smaller space velocities, σv∼40 km s‐1, result in Bondi–Hoyle accretion rates ∼4×103 times higher than for neutron stars. Given a total number of black holes Ntot=N9109 within the Milky Way, we estimate that ∼103N9 should accrete at M˙>1015 g s‐1, comparable to accretion rates inferred for black hole X‐ray binaries. If black holes accrete at the Bondi–Hoyle rate with efficiencies only ∼10−4(NNS/Ntot)0.8 of the neutron‐star accretion efficiency, a comparable number of each may be detectable. We make predictions for the number of isolated accreting black holes in our Galaxy that can be detected with X‐ray surveys as a function of efficiency, concluding that all‐sky surveys at a depth of F=F‐1510‐15 erg cm‐2 s‐1 dex‐1 can find N(>F)∼104N9(F‐15/ε‐5)‐1.2 isolated accreting black holes for a velocity dispersion of 40 km s−1 and an X‐ray accretion efficiency of ε=ε‐510‐5. Deeper surveys of the Galactic plane with Chandra or XMM‐Newton may find tens of these objects per year, depending on the efficiency. We argue that a mass estimate can be derived for microlensing black hole candidates with an X‐ray detection.
Abstract
The TRAPPIST-1 planetary system provides an exceptional opportunity for the atmospheric characterization of temperate terrestrial exoplanets with the upcoming
James Webb Space Telescope
(
...JWST
). Assessing the potential impact of stellar contamination on the planets’ transit transmission spectra is an essential precursor to this characterization. Planetary transits themselves can be used to scan the stellar photosphere and to constrain its heterogeneity through transit depth variations in time and wavelength. In this context, we present our analysis of 169 transits observed in the optical from space with
K2
and from the ground with the SPECULOOS and Liverpool telescopes. Combining our measured transit depths with literature results gathered in the mid-/near-IR with
Spitzer
/IRAC and
HST
/WFC3, we construct the broadband transmission spectra of the TRAPPIST-1 planets over the 0.8–4.5
μ
m spectral range. While planet b, d, and f spectra show some structures at the 200–300 ppm level, the four others are globally flat. Even if we cannot discard their instrumental origins, two scenarios seem to be favored by the data: a stellar photosphere dominated by a few high-latitude giant (cold) spots, or, alternatively, by a few small and hot (3500–4000 K) faculae. In both cases, the stellar contamination of the transit transmission spectra is expected to be less dramatic than predicted in recent papers. Nevertheless, based on our results, stellar contamination can still be of comparable or greater order than planetary atmospheric signals at certain wavelengths. Understanding and correcting the effects of stellar heterogeneity therefore appears essential for preparing for the exploration of TRAPPIST-1 with
JWST
.
We present results from Spitzer Space Telescope observations of the mid-infrared phase variations of three short-period extrasolar planetary systems: HD 209458, HD 179949 and 51 Peg. We gathered ...Infrared Array Camera (IRAC) images in multiple wavebands (3.6 or 4.5 and 8 μm) at eight phases of each planet's orbit. We find the uncertainty in relative photometry from one epoch to the next to be significantly larger than the photon counting error at 3.6 and 4.5 μm. We are able to place 2σ upper limits of only ∼2 per cent on the phase variations at these wavelengths. At 8 μm, the epoch-to-epoch systematic uncertainty is comparable to the photon counting noise and we detect a phase function for HD 179949 which is in phase with the planet's orbit and with a relative peak-to-trough amplitude of 0.001 41 (33). Assuming that HD 179949b has a radius RJ < Rp < 1.2RJ, it must recirculate less than 21 per cent of incident stellar energy to its night side at the 1σ level (less than 26 per cent at the 2σ level, where 50 per cent signifies full recirculation). If the planet has a small Bond albedo, it must have a mass less than 2.4MJ(1σ). We do not detect phase variations for the other two systems but we do place the following 2σ upper limits: 0.0007 for 51 Peg and 0.0015 for HD 209458. Due to its edge-on configuration, the upper limit for HD 209458 translates, with appropriate assumptions about Bond albedo, into a lower limit on the recirculation occuring in the planet's atmosphere. HD 209458b must recirculate at least 32 per cent of incident stellar energy to its night side, at the 1σ level (at least 16 per cent at the 2σ level), which is consistent with other constraints on recirculation from the depth of secondary eclipse depth at 8 μm and the low optical albedo. These data indicate that different hot Jupiter planets may experience different recirculation efficiencies.
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