Analytic Light Curves for Planetary Transit Searches

Mandel, Kaisey S.; Agol, Eric

doi:10.1086/345520

Cited by 2,159 publications

(2,696 citation statements)

References 19 publications

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“…In brief, we analyzed the Kepler long-cadence data from Q1 through Q15 (a total of 3.7 years of nearly continuous observations) to construct a filtered, phase-folded light curve with a final cadence of 2 minutes. The light curve is modeled with a combination of a transit model 35 , a model for the out-of-transit modulations, and an occultation model. The most relevant transit parameters are the impact parameter, the ratio of stellar radius to orbital distance, and the zero-limb-darkening transit depth.…”

Section: Methodsmentioning

confidence: 99%

A rocky composition for an Earth-sized exoplanet

Howard

Sanchis-Ojeda

Marcy

et al. 2013

Nature

195

157

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Planets with sizes between that of Earth (with radius R ⊕ ) and Neptune (about 4 R ⊕ ) are now known to be common around Sun-like stars 1,2,3 . Most such planets have been discovered through the transit technique, by which the planet's size can be determined from the fraction of starlight blocked by the planet as it passes in front of its star. Measuring the planet's mass-and hence its density, which is a clue to its composition-is more difficult. Planets of size 2-4 R ⊕ have proven to have a wide range of densities, implying a diversity of compositions 4,5 , but these measurements did not extend down to planets as small as Earth. Here we report Doppler spectroscopic measurements of the mass of the Earth-sized planet Kepler-78b, which orbits its host star every 8.5 hours (ref. 6). Given a radius of 1.20 ± 0.09 R ⊕ and mass of 1.69 ± 0.41 M ⊕ , the planet's mean density of 5.3 ± 1.8 g cm -3 is similar to the Earth's, suggesting a composition of rock and iron.Kepler-78 is one of approximately 150,000 stars whose brightness was precisely measured at 30-minute intervals for four years by the NASA Kepler spacecraft 7 . This star is somewhat smaller, less massive, and younger than the Sun (Table 1). Every 8.5 hours the star's brightness declines by 0.02% as the planet Kepler-78b transits (passes in front of) the stellar disk. The planet's radius was originally measured 6 to be 1.16 !!.!" !!.!" R ⊕ . The mass could not be measured, although masses >8 M ⊕ could be ruled out because the planet's gravity would have deformed the star and produced brightness variations that were not detected.We measured the mass of Kepler-78b by tracking the line-of-sight component of the host star's motion (the radial velocity, RV) due to the gravitational force of the planet. The RV analysis is challenging not only because the signal is expected to be small (~1-3 m s -1 ) but also because the apparent Doppler shifts due to rotating starspots are much larger (~50 m s -1 peak-to-peak). Nevertheless the detection proved to be possible, thanks to the precisely known orbital period and phase of Kepler-78b that cleanly separated the timescale of spot variations (P rot ≈ 12.5 days) from the much shorter timescale of the planetary orbit (P ≈ 8.5 hours). We adopted a strategy of intensive Doppler measurements spanning 6-8 hours per night, long enough to cover nearly the entire orbit and short enough for the spot variations to be nearly frozen out.We measured RVs using optical spectra of Kepler-78 that we obtained from the High Resolution Echelle Spectrometer (HIRES) 8 on the 10-m Keck I Telescope. These Doppler shifts were computed relative to a template spectrum with a standard algorithm 9 that uses a spectrum of molecular iodine superposed on the stellar spectrum as a reference for the wavelength scale and instrumental profile of HIRES (Supplementary Table 1). Exposures lasted 15-30 minutes depending on conditions and produced RVs with 1.5-2.0 m s -1 uncertainties. The time series of RVs spans 38 days, with large velocity offsets between nights ...

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Section: Methodsmentioning

confidence: 99%

A rocky composition for an Earth-sized exoplanet

Howard

Sanchis-Ojeda

Marcy

et al. 2013

Nature

195

157

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“…The transit signal was modeled following the formalism of Mandel & Agol (2002), which accounts for the effect of limb darkening via a quadratic law of the form…”

Section: General Proceduresmentioning

confidence: 99%

ACCESS I. AN OPTICAL TRANSMISSION SPECTRUM OF GJ 1214b REVEALS A HETEROGENEOUS STELLAR PHOTOSPHERE

Rackham

Espinoza

Apai

et al. 2017

ApJ

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GJ1214b is the most studied sub-Neptune exoplanet to date. Recent measurements have shown its near-infrared transmission spectrum to be flat, pointing to a high-altitude opacity source in the exoplanetʼs atmosphere, either equilibrium condensate clouds or photochemical hazes. Many photometric observations have been reported in the optical by different groups, though simultaneous measurements spanning the entire optical regime are lacking. We present an optical transmission spectrum (4500-9260Å) of GJ1214b in 14 bins, measured with Magellan/IMACS repeatedly over three transits. We measure a mean planet-to-star radius ratio of ( ) in the spectral bins. The optical transit depths are shallower on average than observed in the near-infrared. We present a model for jointly incorporating the effects of a composite photosphere and atmospheric transmission through the exoplanetʼs limb (the CPAT model), and use it to examine the cases of absorber and temperature heterogeneities in the stellar photosphere. We find the optical and near-infrared measurements are best explained by the combination of (1) photochemical haze in the exoplanetary atmosphere with a mode particle size r=0.1μm and haze-forming efficiency = f 10% haze and (2) faculae in the unocculted stellar disk with a temperature contrast D = -+ T 354 46 46 K, assuming 3.2% surface coverage. The CPAT model can be used to assess potential contributions of heterogeneous stellar photospheres to observations of exoplanet transmission spectra, which will be important for searches for spectral features in the optical.

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“…Where T (r p (λ)) is an analytical transit model (Mandel & Agol, 2002) and r p (λ), a 1,4 (λ) are the free fit parameters for each wavelength channel, respectively. WASP-31b: For WASP-31b we used the approach recently suggested by Waldmann (2012), which is based on the assumption that the systematic noise can be described as a linear combination of several noise signals, all contributing to the signal measured in each wavelength channel data with different weights.…”

Section: Discussionmentioning

confidence: 99%

On the Current State of Ground-based Transmission Spectroscopy of Planet Atmospheres

Nortmann¹,

Bean²

2012

Proc. IAU

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Abstract. In response to the large number of exoplanet detections, the characterization of these planets has become a major focus of exoplanet science. Transiting planets are of particular interest as they allow us to investigate the transmission of their atmospheres. Our group uses ground-based facilities like the ESO/VLT to probe the atmosphere of hot Jupiters with the technique of spectrophotometry. In our preliminary results for the hot Jupiters WASP-17b and WASP-31b we find the reachable precision to be limited by instrumental systematic noise rather than photon noise. We discuss the source of the noise and suggest two approaches to correct it.

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Analytic Light Curves for Planetary Transit Searches

Cited by 2,159 publications

References 19 publications

A rocky composition for an Earth-sized exoplanet

A rocky composition for an Earth-sized exoplanet

ACCESS I. AN OPTICAL TRANSMISSION SPECTRUM OF GJ 1214b REVEALS A HETEROGENEOUS STELLAR PHOTOSPHERE

On the Current State of Ground-based Transmission Spectroscopy of Planet Atmospheres

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