The Transit and Light Curve Modeller Csizmadia, Sz
Monthly notices of the Royal Astronomical Society,
08/2020, Letnik:
496, Številka:
4
Journal Article
Recenzirano
Odprti dostop
ABSTRACT
Transit and Light Curve Modeller (TLCM), a computer code with the purpose of analysing photometric time series of transits simultaneously with the out-of-transit light variations and radial ...velocity curves of transiting/eclipsing binary systems, is presented here. Joint light-curve and radial velocity fits are possible with it. The code is based on the combination of a genetic algorithm and simulated annealing. Binning, beaming, reflection, and ellipsoidal effects are included. Both objects may have their own luminosities and therefore one can use TLCM to analyse the eclipses of both exoplanet and well-detached binary systems. A simplified Rossiter–McLaughlin effect is included in the radial velocity fit, and drifts and offsets of different instruments can also be fitted. The impact of poorly known limb darkening on the Rossiter–McLaughlin effect is shortly studied. TLCM is able to manage red-noise effects via wavelet analysis. It is also possible to add parabolic or user-defined baselines and features to the code. I also predict that light variations due to beaming in some systems exhibiting radial velocity drift should be observed by, e.g. PLATO. The fit of the beaming effect is improved by invoking a physical description of the ellipsoidal effects, which has an impact on the modelling of the relativistic beaming; I also point out the difficulties that are stemming from the fact that beaming and first-order reflection effects have the same form of time dependence. Recipe is given, which describes how to analyse grazing transit events. The code is freely available.
Context.
The direct imaging of exoplanets in reflected starlight will represent a major advance in the study of cold and temperate exoplanet atmospheres. Understanding how basic planet and ...atmospheric properties may affect the measured spectra is key to their interpretation.
Aims.
We have investigated the information content in reflected-starlight spectra of exoplanets. We apply our analysis to Barnard’s Star b candidate super-Earth, for which we assume a radius 0.6 times that of Neptune, an atmosphere dominated by H
2
–He, and a CH
4
volume mixing ratio of 5 × 10
−3
. The main conclusions of our study are however planet-independent.
Methods.
We set up a model of the exoplanet described by seven parameters including its radius, atmospheric methane abundance, and basic properties of a cloud layer. We generated synthetic spectra at zero phase (full disc illumination) from 500 to 900 nm and a spectral resolution
R
~ 125–225. We simulated a measured spectrum with a simplified, wavelength-independent noise model at a signal-to-noise ratio of 10. With a retrieval methodology based on Markov chain Monte Carlo sampling, we analysed which planet and atmosphere parameters can be inferred from the measured spectrum and the theoretical correlations amongst them. We considered limiting cases in which the planet radius is either known or completely unknown, and intermediate cases in which the planet radius is partly constrained.
Results.
If the planet radius is known, we can generally discriminate between cloud-free and cloudy atmospheres, and constrain the methane abundance to within two orders of magnitude. If the planet radius is unknown, new correlations between model parameters occur and the accuracy of the retrievals decreases. Without a radius determination, it is challenging to discern whether the planet has clouds, and the estimates on methane abundance degrade. However, we find the planet radius is constrained to within a factor of two for all the cases explored. Having a priori information on the planet radius, even if approximate, helps improve the retrievals.
Conclusions.
Reflected-starlight measurements will open a new avenue for characterizing long-period exoplanets, a population that remains poorly studied. For this task to be complete, direct-imaging observations should be accompanied by other techniques. We urge exoplanet detection efforts to extend the population of long-period planets with mass and radius determinations.
Context. The radius of an exoplanet is one of its most important parameters. Studies of planetary interiors and their evolution require 1% precision in the radius determination. Transiting exoplanets ...offer a unique oppurtunity to measure the radius of exoplanets in stellar units. These radius measurements and their precision are strongly affected by our knowledge of limb darkening. Aims. We study how the precision of the exoplanet radius determination is affected by our present knowledge of limb darkening in two cases: when we fix the limb darkening coefficients and when we adjust them. We also investigate the effects of spots in one-colour photometry. Methods. We study the effect of limb darkening on the planetary radius determination both via analytical expressions and by numerical experiments. We also compare some of the existing limb darkening tables. When stellar spots affect the fit, we replace the limb darkening coefficients, calculated for the unspotted cases, with effective limb darkening coefficients to describe the effect of the spots. Results. There are two important cases. (1) When one fixes the limb darkening values according to some theoretical predictions, the inconsistencies of the tables do not allow us to reach accuracy in the planetary radius of better than 1−10% (depending on the impact parameter) if the host star’s surface effective temperature is higher than 5000 K. Below 5000 K the radius ratio determination may contain even 20% error. (2) When one allows adjustment of the limb darkening coefficients, the a/Rs ratio, the planet-to-stellar radius ratio, and the impact parameter can be determined with sufficient accuracy (<1%), if the signal-to-noise ratio is high enough. However, the presence of stellar spots and faculae can destroy the agreement between the limb darkening tables and the fitted limb darkening coefficients, but this does not affect the precision of the planet radius determination. We also find that it is necessary to fit the contamination factor, too. Conclusions. We conclude that the present inconsistencies of theoretical stellar limb darkening tables suggests one should not fix the limb darkening coefficients. When one allows them to be adjusted, then the planet radius, impact parameter, and the a/Rs can be obtained with the required precision.
Context. Love numbers measure the reaction of a celestial body to perturbing forces, such as the centrifugal force caused by rotation, or tidal forces resulting from the interaction with a companion ...body. These parameters are related to the interior density profile. The non-point mass nature of the host star and a planet orbiting around each other contributes to the periastron precession. The rate of this precession is characterized mainly by the second-order Love number, which offers an opportunity to determine its value. When it is known, the planetary interior structure can be studied with one additional constraint beyond the mass, radius, and orbital parameters. Aims. We aim to re-determine the orbital period, eccentricity, and argument of the periastron for WASP-19Ab, along with a study of its periastron precession rate. We calculated the planetary Love number from the observed periastron precession rate, based on the assumption of the stellar Love number from stellar evolutionary models. Methods. We collected all available radial velocity (RV) data, along with the transit and occultation times from the previous investigations of the system. We supplemented the data set with 19 new RV data points of the host star WASP-19A obtained by HARPS. Here, we summarize the technique for modeling the RV observations and the photometric transit timing variations (TTVs) to determine the rate of periastron precession in this system for the first time. Results. We excluded the presence of a second possible planet up to a period of ~4200 d and with a radial velocity amplitude bigger than ≃ 1 m s −1 . We show that a constant period is not able to reproduce the observed radial velocities. We also investigated and excluded the possibility of tidal decay and long-term acceleration in the system. However, the inclusion of a small periastron precession term did indeed improve the quality of the fit. We measured the periastron precession rate to be 233 −35 +25 ″d −1 . By assuming synchronous rotation for the planet, it indicates a k 2 Love number of 0.20 −0.03 +0.02 for WASP-19Ab. Conclusions. The derived k 2,p value of the planet has the same order of magnitude as the estimated fluid Love number of other Jupiter-sized exoplanets (WASP-18Ab, WASP-103b, and WASP-121b). A low value of k 2,p indicates a higher concentration of mass toward the planetary nucleus.
Context.
The theory of remote sensing shows that observing a planet at multiple phase angles (
α
) is a powerful strategy to characterize its atmosphere. Here, we study this observing strategy as ...applied to future disc-integrated direct imaging of exoplanets in reflected starlight.
Aims.
We analyse how the information contained in reflected-starlight spectra of exoplanets depends on the phase angle and the potential of multi-phase measurements to better constrain the atmospheric properties and the planet radius (
R
p
).
Methods.
We simulate spectra (500−900 nm) at
α
= 37°, 85°, and 123° with a spectral resolution of
R
~ 125−225 and signal-to-noise ratio (
S
∕
N
) = 10, consistent with the expected capabilities of future direct-imaging space telescopes. Assuming a H
2
-He atmosphere, we use a seven-parameter model that includes the atmospheric methane abundance (
f
CH
4
), the optical properties of a cloud layer and
R
p
. All these parameters are assumed to be unknown a priori and are explored with a Markov chain Monte Carlo retrieval method.
Results.
No single-phase observation can robustly identify whether the atmosphere has clouds or not. A single-phase observation at
α
= 123° and
S
∕
N
= 10 can constrain
R
p
with a maximum error of 35%, regardless of the cloud coverage. We find that combining small (37°) and large (123°) phase angles is a generally effective strategy to break multiple parameter degeneracies. This enables us to determine the presence or absence of a cloud and its main properties,
f
CH
4
and
R
p
, with higher confidence in all the explored scenarios. Other strategies, such as doubling
S
∕
N
to 20 for a single-phase observation or combining small (37°) and moderate (85°) phase angles, fail to achieve this. We show that the improvements in multi-phase retrievals are associated with the shape of the scattering phase function of the cloud aerosols and that the improvement is more modest for isotropically scattering aerosols. We finally discuss that misidentifying the background gas in the retrievals of super-Earth observations leads to systematic underestimation of the absorbing gas abundance.
Conclusions.
Exoplanets with wide ranges of observable phase angles should be prioritized for atmospheric characterization in reflected starlight.
TOI-1416 (BD+42 2504, HIP 70705) is a
V
=10 late G- or early K-type dwarf star. TESS detected transits in its Sectors 16, 23, and 50 with a depth of about 455 ppm and a period of 1.07 days. Radial ...velocities (RVs) confirm the presence of the transiting planet TOI-1416
b
, which has a mass of 3.48 ± 0.47
M
⊕
and a radius of 1.62 ± 0.08
R
⊕
, implying a slightly sub-Earth density of 4.50
−0.83
+0.99
g cm
−3
. The RV data also further indicate a tentative planet,
c
, with a period of 27.4 or 29.5 days, whose nature cannot be verified due to strong suspicions of contamination by a signal related to the Moon’s synodic period of 29.53 days. The nearly ultra-short-period planet TOI-1416
b
is a typical representative of a short-period and hot (
T
eq
≈ 1570 K) super-Earth-like planet. A planet model of an interior of molten magma containing a significant fraction of dissolved water provides a plausible explanation for its composition, and its atmosphere could be suitable for transmission spectroscopy with JWST. The position of TOI-1416
b
within the radius-period distribution corroborates the idea that planets with periods of less than one day do not form any special group. It instead implies that ultra-short-period planets belong to a continuous distribution of super-Earth-like planets with periods ranging from the shortest known ones up to ≈30 days; their period-radius distribution is delimited against larger radii by the Neptune Desert and by the period-radius valley that separates super-Earths from sub-Neptune planets. In the abundance of small, short-periodic planets, a notable plateau has emerged between periods of 0.6–1.4 days, which is compatible with the low-eccentricity formation channel. For the Neptune Desert, its lower limits required a revision due to the increasing population of short-period planets; for periods shorter then 2 days, we establish a radius of 1.6
R
⊕
and a mass of 0.028
M
jup
(corresponding to 8.9
M
⊕
) as the desert’s lower limits. We also provide corresponding limits to the Neptune Desert against the planets’ insolation and effective temperatures.
Abstract
We report the discovery in K2's Campaign 10 of a transiting terrestrial planet in an ultra-short-period orbit around an M3-dwarf. K2-137 b completes an orbit in only 4.3 h, the second ...shortest orbital period of any known planet, just 4 min longer than that of KOI 1843.03, which also orbits an M-dwarf. Using a combination of archival images, adaptive optics imaging, radial velocity measurements, and light-curve modelling, we show that no plausible eclipsing binary scenario can explain the K2 light curve, and thus confirm the planetary nature of the system. The planet, whose radius we determine to be 0.89 ± 0.09 R⊕, and which must have an iron mass fraction greater than 0.45, orbits a star of mass 0.463 ± 0.052 M⊙ and radius 0.442 ± 0.044 R⊙.
Context. Multiplanet systems are excellent laboratories to test planet formation models as all planets are formed under the same initial conditions. In this context, systems transiting bright stars ...can play a key role, since planetary masses, radii, and bulk densities can be measured. Aims. GJ 9827 (K2-135) has recently been found to host a tightly packed system consisting of three transiting small planets whose orbital periods of 1.2, 3.6, and 6.2 days are near the 1:3:5 ratio. GJ 9827 hosts the nearest planetary system (~30 pc) detected by NASA’s Kepler or K2 space mission. Its brightness (V = 10.35 mag) makes the star an ideal target for detailed studies of the properties of its planets. Methods. Combining the K2 photometry with high-precision radial-velocity measurements gathered with the FIES, HARPS, and HARPS-N spectrographs we revised the system parameters and derive the masses of the three planets. Results. We find that GJ 9827 b has a mass of Mb = 3.69−0.46+0.48 M⊕ $M_{\mathrm{b}}\,{=}\,3.69 _{ - 0.46 } ^ { + 0.48 }\, M_{\oplus}$ Mb = 3.69−0.46+0.48 M⊕ and a radius of Rb = 1.58−0.13+0.14 R⊕ $R_{\mathrm{b}}=\,1.58 _{ - 0.13 } ^ { + 0.14 }\,R_{\oplus}$Rb= 1.58−0.13+0.14 R⊕, yielding a mean density of ρb = 5.11−1.27+1.74 g cm−3 $\rho_{\mathrm{b}}=\,5.11_{ - 1.27 }^{ + 1.74}\,\textrm{g\,cm}^{-3}$ρb= 5.11−1.27+1.74 g cm−3. GJ 9827 c has a mass of Mc = 1.45−0.57+0.58 M⊕ $M_{\mathrm{c}}=\,1.45 _{ - 0.57 } ^ { + 0.58 }\,M_{\oplus}$Mc= 1.45−0.57+0.58 M⊕, radius of Rc = 1.24−0.11+0.11 R⊕ $R_{\mathrm{c}}=\,1.24 _{ - 0.11 } ^ { + 0.11 }\,R_{\oplus}$Rc= 1.24−0.11+0.11 R⊕, and a mean density of ρc = 4.13−1.77+2.31 g cm−3 $\rho_{\mathrm{c}}\,{=}\,4.13 _{ - 1.77 } ^ { + 2.31 }\,\textrm{g\,cm}^{-3}$ρc = 4.13−1.77+2.31 g cm−3. For GJ 9827 d, we derive Md = 1.45−0.57+0.58 M⊕ $M_{\mathrm{d}}\,{=}\,1.45 _{ - 0.57 } ^ { + 0.58 }\,M_{\oplus}$Md = 1.45−0.57+0.58 M⊕, Rd = 1.24−0.11+0.11 R⊕ $R_{\mathrm{d}}\,{=}\,1.24 _{ - 0.11 } ^ { + 0.11 }\,R_{\oplus}$Rd = 1.24−0.11+0.11 R⊕, and ρd = 1.51−0.53+0.71 g cm−3 $\rho_{\mathrm{d}}\,{=}\,1.51 _{ - 0.53 } ^ { + 0.71 }\,\textrm{g\,cm}^{-3}$ρd = 1.51−0.53+0.71 g cm−3. Conclusions. GJ 9827 is one of the few known transiting planetary systems for which the masses of all planets have been determined with a precision better than 30%. This system is particularly interesting because all three planets are close to the limit between super-Earths and sub-Neptunes. The planetary bulk compositions are compatible with a scenario where all three planets formed with similar core and atmosphere compositions, and we speculate that while GJ 9827 b and GJ 9827 c lost their atmospheric envelopes, GJ 9827 d maintained its primordial atmosphere, owing to the much lower stellarirradiation. This makes GJ 9827 one of the very few systems where the dynamical evolution and the atmosphericescape can be studied in detail for all planets, helping us to understand how compact systems form and evolve.
ABSTRACT
We report the discovery of two transiting planets orbiting K2-290 (EPIC 249624646), a bright (V = 11.11) late F-type star residing in a triple-star system. It was observed during Campaign 15 ...of the K2 mission, and in order to confirm and characterize the system, follow-up spectroscopy and AO imaging were carried out using the FIES, HARPS, HARPS-N, and IRCS instruments. From AO imaging and Gaia data we identify two M-dwarf companions at a separation of 113 ± 2 and $2467_{-155}^{+177}$ au. From radial velocities, K2 photometry, and stellar characterization of the host star, we find the inner planet to be a mini-Neptune with a radius of 3.06 ± 0.16 R⊕ and an orbital period of P = 9.2 d. The radius of the mini-Neptune suggests that the planet is located above the radius valley, and with an incident flux of F ∼ 400 F⊕, it lies safely outside the super-Earth desert. The outer warm Jupiter has a mass of 0.774 ± 0.047 MJ and a radius of 1.006 ± 0.050 RJ, and orbits the host star every 48.4 d on an orbit with an eccentricity e < 0.241. Its mild eccentricity and mini-Neptune sibling suggest that the warm Jupiter originates from in situ formation or disc migration.
ABSTRACT
We report new photometric and spectroscopic observations of the K2-99 planetary system. Asteroseismic analysis of the short-cadence light curve from K2’s Campaign 17 allows us to refine the ...stellar properties. We find K2-99 to be significantly smaller than previously thought, with R⋆ = 2.55 ± 0.02 R⊙. The new light curve also contains four transits of K2-99 b, which we use to improve our knowledge of the planetary properties. We find the planet to be a non-inflated warm Jupiter, with Rb = 1.06 ± 0.01 $\mathrm{R_{\rm Jup}}$. 60 new radial velocity measurements from HARPS, HARPS-N, and HIRES enable the determination of the orbital parameters of K2-99 c, which were previously poorly constrained. We find that this outer planet has a minimum mass Mcsin ic = 8.4 ± 0.2 $\mathrm{M_{\rm Jup}}$, and an eccentric orbit (ec = 0.210 ± 0.009) with a period of 522.2 ± 1.4 d. Upcoming TESS observations in 2022 have a good chance of detecting the transit of this planet, if the mutual inclination between the two planetary orbits is small.
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