scholarly journals Analytic solutions to the maximum and average exoplanet transit depth for common stellar limb darkening laws

2019 ◽  
Vol 623 ◽  
pp. A137 ◽  
Author(s):  
René Heller
Keyword(s):  
Light Curve ◽  
Impact Parameter ◽  
Extrasolar Planets ◽  
Analytic Solutions ◽  
Radius Ratio ◽  
Average Intensity ◽  
The Mean ◽  
Impact Parameters ◽  
In Transit ◽  
Limb Darkening

Context. The depth of an exoplanetary transit in the light curve of a distant star is commonly approximated as the squared planet-to-star radius ratio, (Rp/Rs)2. Stellar limb darkening, however, can result in significantly deeper transits. An analytic solution would be worthwhile to illustrate the principles of the problem and predict the actual transit signal required for the planning of transit observations with certain signal-to-noise requirements without the need of computer-based transit simulations. Aims. We calculate the overshoot of the mid-transit depth caused by stellar limb darkening compared to the (Rp/Rs)2 estimate for arbitrary transit impact parameters. In turn, this allows us to compute the true planet-to-star radius ratio from the transit depth for a given parameterization of a limb darkening law and for a known transit impact parameter. Methods. We compute the maximum emerging specific stellar intensity covered by the planet in transit and derive analytic solutions for the transit depth overshoot. Solutions are presented for the linear, quadratic, square-root, logarithmic, and nonlinear stellar limb darkening with arbitrary transit impact parameters. We also derive formulae to calculate the average intensity along the transit chord, which allows us to estimate the actual transit depth (and therefore Rp∕Rs) from the mean in-transit flux. Results. The transit depth overshoot of exoplanets compared to the (Rp/Rs)2 estimate increases from about 15% for main-sequence stars of spectral type A to roughly 20% for sun-like stars and some 30% for K and M stars. The error in our analytical solutions for Rp∕Rs from the small planet approximation is orders of magnitude smaller than the uncertainties arising from typical noise in real light curves and from the uncertain limb darkening. Conclusions. Our equations can be used to predict with high accuracy the expected transit depth of extrasolar planets. The actual planet radius can be calculated from the measured transit depth or from the mean in-transit flux if the stellar limb darkening can be properly parameterized and if the transit impact parameter is known. Light curve fitting is not required.

scholarly journals High spin temperatures at large impact parameters: Ionisation in the outskirts of galaxies

2020 ◽  
Vol 635 ◽  
pp. A166
Author(s):  
S. J. Curran
Keyword(s):  
Temperature Distribution ◽  
High Resolution ◽  
Impact Parameter ◽  
Column Density ◽  
Milky Way ◽  
Spiral Galaxies ◽  
Neutral Hydrogen ◽  
Spin Temperature ◽  
The Mean ◽  
Impact Parameters

By including the most recent observations of H I 21-cm absorption through nearby galactic discs, we confirm our previous assertion that there is an anti-correlation between the abundance of cool neutral atomic gas and impact parameter. In comparing the measured neutral hydrogen column densities of the sample with the absorption strength, we find a peak in the mean spin temperature of ⟨Tspin/f ⟩ ≈ 2310 K at an impact parameter of ρ ≈ 14 kpc, with ⟨Tspin/f ⟩≳1000 K in the remainder of the disc. This is significantly different to the spin temperature distribution in the Milky Way, which exhibits a constant ≈250 − 400 K over ρ = 8 − 25 kpc. The measured column densities may, however, suffer from beam dilution, which we show appears to be the case for the observations of H I 21-cm emission in which the beam subtends radii of ≳10 kpc. We therefore applied the column density profile of the Milky Way, in addition to the mean of the sample, observed at sufficiently high resolution, and the mean profile for the nearby ∼1012 M⊙ galaxies in the IllustrisTNG simulations. All of the models yield a peak in the mean spin temperature at similar impact parameters (r ≈ 10 − 15 kpc) as the measured column densities. These radii are similar to those of the spiral arms where H II regions are often concentrated. We therefore suggest that the elevated spin temperatures trace the H II regions observed in the outer disc of many spiral galaxies.

scholarly journals Fast and precise light-curve model for transiting exoplanets with rings

2019 ◽  
Vol 490 (1) ◽  
pp. 1111-1119 ◽  
Author(s):  
Edan Rein ◽  
Aviv Ofir
Keyword(s):  
Solar System ◽  
Light Curve ◽  
Source Code ◽  
Light Curves ◽  
Small Range ◽  
Silicate Material ◽  
Computationally Efficient ◽  
Curve Model ◽  
In Transit ◽  
Limb Darkening

ABSTRACT The presence of silicate material in known rings in the Solar system raises the possibility of ring systems existing even within the snow line – where most transiting exoplanets are found. Previous studies have shown that the detection of exoplanetary rings in transit light curves is possible, albeit challenging. To aid such future detection of exoplanetary rings, we present the Polygon + Segments model for modelling the light curve of an exoplanet with rings. This high-precision model includes full ring geometry as well as possible ring transparency and the host star’s limb darkening. It is also computationally efficient, requiring just a 1D integration over a small range, making it faster than existing techniques. The algorithm at its core is further generalized to compute the light curve of any set of convex primitive shapes in transit (e.g. multiple planets, oblate planets, moons, rings, combination thereof, etc.) while accounting for their overlaps. The python source code is made available.

scholarly journals The stellar variability noise floor for transiting exoplanet photometry with PLATO

2020 ◽  
Vol 493 (4) ◽  
pp. 5489-5498 ◽  
Author(s):  
Brett M Morris ◽  
Monica G Bobra ◽  
Eric Agol ◽  
Yu Jin Lee ◽  
Suzanne L Hawley
Keyword(s):  
Impact Parameter ◽  
Solar Dynamics Observatory ◽  
Depth Measurement ◽  
Stellar Oscillations ◽  
Mission Duration ◽  
Intensity Images ◽  
Solar Dynamics ◽  
In Transit ◽  
Limb Darkening ◽  
The Impact

ABSTRACT One of the main science motivations for the ESA PLAnetary Transit and Oscillations (PLATO) mission is to measure exoplanet transit radii with 3 per cent precision. In addition to flares and starspots, stellar oscillations and granulation will enforce fundamental noise floors for transiting exoplanet radius measurements. We simulate light curves of Earth-sized exoplanets transiting continuum intensity images of the Sun taken by the Helioseismic and Magnetic Imager (HMI) instrument aboard the Solar Dynamics Observatory (SDO) to investigate the uncertainties introduced on the exoplanet radius measurements by stellar granulation and oscillations. After modelling the solar variability with a Gaussian process, we find that the amplitude of solar oscillations and granulation is of order 100 ppm – similar to the depth of an Earth transit – and introduces a fractional uncertainty on the depth of transit of 0.73 per cent assuming four transits are observed over the mission duration. However, when we translate the depth measurement into a radius measurement of the planet, we find a much larger radius uncertainty of 3.6 per cent. This is due to a degeneracy between the transit radius ratio, the limb darkening, and the impact parameter caused by the inability to constrain the transit impact parameter in the presence of stellar variability. We find that surface brightness inhomogeneity due to photospheric granulation contributes a lower limit of only 2 ppm to the photometry in-transit. The radius uncertainty due to granulation and oscillations, combined with the degeneracy with the transit impact parameter, accounts for a significant fraction of the error budget of the PLATO mission, before detector or observational noise is introduced to the light curve. If it is possible to constrain the impact parameter or to obtain follow-up observations at longer wavelengths where limb darkening is less significant, this may enable higher precision radius measurements.

scholarly journals STUDY OF A MA16-BASED VERTEX TRIGGER FOR THE CDF EXPERIMENT

1995 ◽  
Vol 06 (05) ◽  
pp. 681-692
Author(s):  
R. ODORICO
Keyword(s):  
Neural Network ◽  
Response Time ◽  
Impact Parameter ◽  
Electronic Components ◽  
The Neural Network ◽  
Viable Solution ◽  
Impact Parameters ◽  
Input Variables ◽  
Better Than

A Neural Network trigger for [Formula: see text] events based on the SVT microvertex processor of experiment CDF at Fermilab is presented. It exploits correlations among track impact parameters and azimuths calculated by the SVT from the SVX microvertex detector data. The neural trigger is meant for implementation on the systolic Siemens microprocessor MA16, which has already been used in a neural-network trigger for experiment WA92 at CERN. A suitable set of input variables is found, which allows a viable solution for the preprocessing task using standard electronic components. The response time of the neural-network stage of the trigger, including preprocessing, can be estimated ~10 μs. Its precise value depends on the quantitative specifications of the output signals of the SVT, which is still in development. The performance of the neural-network trigger is found to be significantly better than that of a conventional trigger exclusively based on impact parameter data.

scholarly journals Comparison of the power-2 limb-darkening law from the STAGGER-grid to Kepler light curves of transiting exoplanets

2018 ◽  
Vol 616 ◽  
pp. A39 ◽  
Author(s):  
P. F. L. Maxted
Keyword(s):  
Light Curve ◽  
Probability Distributions ◽  
Binary Star ◽  
Magnetic Activity ◽  
Light Curves ◽  
Practical Implementation ◽  
Light Curve Analysis ◽  
Stagger Grid ◽  
Least Squares Fit ◽  
Limb Darkening

Context. Inaccurate limb-darkening models can be a significant source of error in the analysis of the light curves for transiting exoplanet and eclipsing binary star systems, particularly for high-precision light curves at optical wavelengths. The power-2 limb-darkening law, Iλ(µ) = 1 − c(1−µα), has recently been proposed as a good compromise between complexity and precision in the treatment of limb-darkening. Aims. My aim is to develop a practical implementation of the power-2 limb-darkening law and to quantify the accuracy of this implementation. Methods. I have used synthetic spectra based on the 3D stellar atmosphere models from the STAGGER-grid to compute the limb-darkening for several passbands (UBVRI, CHEOPS, TESS, Kepler, etc.). The parameters of the power-2 limb-darkening laws are optimized using a least-squares fit to a simulated light curve computed directly from the tabulated Iλ(μ) values. I use the transformed parameters h1 = 1 − c(1 − 2−α) and h2 = c2−α to directly compare these optimized limb-darkening parameters to the limb darkening measured from Kepler light curves of 16 transiting exoplanet systems. Results. The posterior probability distributions (PPDs) of the transformed parameters h1 and h2 resulting from the light curve analysis are found to be much less strongly correlated than the PPDs for c and α. The agreement between the computed and observed values of (h1, h2) is generally very good but there are significant differences between the observed and computed values for Kepler-17, the only star in the sample that shows significant variability between the eclipses due to magnetic activity (star spots). Conclusions. The tabulation of h1 and h2 provided here can be used to accurately model the light curves of transiting exoplanets. I also provide estimates of the priors that should be applied to transformed parameters h1 and h2 based on my analysis of the Kepler light curves of 16 stars with transiting exoplanets.

scholarly journals The Eclipses of the Close Binary Star BE UMa

1996 ◽  
Vol 158 ◽  
pp. 471-472
Author(s):  
Janet H. Wood ◽  
E. L. Robinson ◽  
E.-H. Zhang
Keyword(s):  
Light Curve ◽  
High Speed ◽  
Binary Star ◽  
Light Curves ◽  
Close Binary ◽  
Primary Star ◽  
Secondary Star ◽  
Different Depths ◽  
The Mean ◽  
Close Binary Star

BE UMa is a close binary star, not transferring mass, with an extremely hot primary star irradiating the inner face of the cool secondary star. The light curve shows a large-amplitude, sinusoidal variation with a period of 2.29 d, and an eclipse that is centered on the minimum of the variation [1], [3]. According to [1], the eclipse is partial, not total. However, it has been argued [2] that the eclipse was really flat bottomed and thus total. This has important repercussions for the deduced model of the system. To resolve this issue we obtained simultaneous UBVR photometry of BE UMa using the Stiening 4-channel, high-speed photometer on the 82-inch telescope at McDonald Observatory. The mean light curves are shown in Fig. 1. The eclipse in all colours is round bottomed and partial. The different depths are caused by the different contribution from the red secondary star in each bandpass.

scholarly journals IUE Spectra of The by Dra/Flare Star AU Mic

1983 ◽  
Vol 71 ◽  
pp. 249-250
Author(s):  
C.J. Butler ◽  
A.D. Andrews ◽  
J.G. Doyle ◽  
P.B. Byrne ◽  
J.L. Linsky ◽  
...  
Keyword(s):  
Light Curve ◽  
Emission Line ◽  
Flare Star ◽  
Emission Lines ◽  
Spectral Variation ◽  
Strong Emission ◽  
Line Intensities ◽  
The Mean ◽  
Phase Interval

A coordinated series of ground-based optical and IUE observations of BY Dra variables was undertaken to follow the spectral variation of these stars over one cycle. In the first series 20 LWR and 19 SWP trailed spectra were taken of AU Mic over a three day period 4-6 August 1980 .In Figure 1 we show the mean integrated fluxes for the strong emission lines in the SWP spectra of AU Mic over the observed phase interval of 0.14 to 0.8 together with an approximate V light curve determined by the FES on IUE. From comparison of the emission line intensities and FES magnitudes in Figure 1 several points emerge.

scholarly journals Benzo[<i>a</i>]pyrene in urban environments of eastern Moscow: pollution levels and critical loads

2017 ◽  
Vol 17 (3) ◽  
pp. 2217-2227 ◽  
Author(s):  
Nikolay S. Kasimov ◽  
Natalia E. Kosheleva ◽  
Elena M. Nikiforova ◽  
Dmitry V. Vlasov
Keyword(s):  
Land Use ◽  
Critical Loads ◽  
Significant Contribution ◽  
Urban Environments ◽  
Anthropogenic Sources ◽  
Average Intensity ◽  
Pollution Levels ◽  
Local Background ◽  
Polycyclic Aromatic ◽  
The Mean

Abstract. Polycyclic aromatic hydrocarbons (PAHs), particularly benzo[a]pyrene (BaP), are toxic compounds emitted from various anthropogenic sources. Understanding the BaP concentrations, dynamics and decomposition in soil is required to assess the critical loads of BaP in urban environments. This study is the first attempt to evaluate all major input and output components of benzo[a]pyrene (BaP) balance and to calculate the permissible load on the urban environment in different land-use zones in the Eastern district of Moscow. BaP contamination of the snow cover in the Eastern district of Moscow was related to daily BaP fallout from the atmosphere. In 2010, the mean content of the pollutant in the snow dust was 1942 ng g−1, whereas the average intensity of its fallout was 7.13 ng m−2 per day. Across the territory, BaP winter fallout intensities varied from 0.3 to 1100 ng m−2 per day. The average BaP content in the surface (0–10 cm) soil horizons was 409 ng g−1, which is 83 times higher than the local background value and 20 times higher than the maximum permissible concentration (MPC) accepted in Russia. The variations in soil and snow BaP concentrations among different land-use zones were examined. A significant contribution of BaP from the atmosphere to urban soils was identified. Based on the measurements of BaP atmospheric fallout and BaP reserves in the soils, the critical loads of BaP for the land-use zones in the Eastern district were calculated for different values of degradation intensity and different exposure times. It was established that at an annual degradation intensity of 1–10 %, ecologically safe BaP levels in the soils of all land-use zones, excluding the agricultural zone, will only be reached after many decades or centuries.

scholarly journals New near-infrared JHKs light-curve templates for RR Lyrae variables

2019 ◽  
Vol 625 ◽  
pp. A1 ◽  
Author(s):  
V. F. Braga ◽  
P. B. Stetson ◽  
G. Bono ◽  
M. Dall’Ora ◽  
I. Ferraro ◽  
...  
Keyword(s):  
Light Curve ◽  
Near Infrared ◽  
Large Magellanic Cloud ◽  
Light Curves ◽  
Anchor Point ◽  
Phase Point ◽  
Pulsation Period ◽  
Rr Lyrae ◽  
The Mean ◽  
The Difference

We provide homogeneous optical (UBVRI) and near-infrared (NIR, JHK) time series photometry for 254 cluster (ω Cen, M 4) and field RR Lyrae (RRL) variables. We ended up with more than 551 000 measurements, of which only 9% are literature data. For 94 fundamental (RRab) and 51 first overtones (RRc) we provide a complete optical/NIR characterization (mean magnitudes, luminosity amplitudes, epoch of the anchor point). The NIR light curves of these variables were adopted to provide new light-curve templates for both RRc and RRab variables. The templates for the J and the H bands are newly introduced, together with the use of the pulsation period to discriminate among the different RRab templates. To overcome subtle uncertainties in the fit of secondary features of the light curves we provide two independent sets of analytical functions (Fourier and periodic Gaussian series). The new templates were validated by using 26 ω Cen and Bulge RRLs. We find that the difference between the measured mean magnitude along the light curve and the mean magnitude estimated by using the template on a single randomly extracted phase point is better than 0.01 mag (σ = 0.04 mag). We also validated the template on variables for which at least three phase points were available, but without information on the phase of the anchor point. We find that the accuracy of the mean magnitudes is also ∼0.01 mag (σ = 0.04 mag). The new templates were applied to the Large Magellanic Cloud (LMC) globular cluster Reticulum and by using literature data and predicted PLZ relations we find true distance moduli μ = 18.47 ± 0.10 (rand.) ± 0.03 (syst.) mag (J) and 18.49 ± 0.09 ± 0.05 mag (K). We also used literature optical and mid-infrared data and we found a mean μ of 18.47 ± 0.02 ± 0.06 mag, suggesting that Reticulum is ∼1 kpc closer than the LMC.

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