arXiv subjects

Adam Burrows

Publications and source records attributed to Adam Burrows.

At least 127 records · Page 7Linked to original sources

arXiv2014

CHARIS Science: Performance Simulations for the Subaru Telescope's Third-Generation of Exoplanet Imaging Instrumentation

We describe the expected scientific capabilities of CHARIS, a high-contrast integral-field spectrograph (IFS) currently under construction for the Subaru telescope. CHARIS is part of a new generation of instruments, enabled by extreme adaptive optics (AO) systems (including SCExAO at Subaru), that promise greatly improved contrasts at small angular separation thanks to their ability to use spectral information to distinguish planets from quasistatic speckles in the stellar point-spread function (PSF). CHARIS is similar in concept to GPI and SPHERE, on Gemini South and the Very Large Telescope, respectively, but will be unique in its ability to simultaneously cover the entire near-infrared $J$, $H$, and $K$ bands with a low-resolution mode. This extraordinarily broad wavelength coverage will enable spectral differential imaging down to angular separations of a few $λ/D$, corresponding to $\sim$$0.\!\!''1$. SCExAO will also offer contrast approaching $10^{-5}$ at similar separations, $\sim$$0.\!\!''1$--$0.\!\!''2$. The discovery yield of a CHARIS survey will depend on the exoplanet distribution function at around 10 AU. If the distribution of planets discovered by radial velocity surveys extends unchanged to $\sim$20 AU, observations of $\sim$200 mostly young, nearby stars targeted by existing high-contrast instruments might find $\sim$1--3 planets. Carefully optimizing the target sample could improve this yield by a factor of a few, while an upturn in frequency at a few AU could also increase the number of detections. CHARIS, with a higher spectral resolution mode of $R \sim 75$, will also be among the best instruments to characterize planets and brown dwarfs like HR 8799 cde and $κ$ And b.

astro-ph.IM↗

arXiv2014

Gemini Planet Imager Spectroscopy of the HR 8799 planets c and d

During the first-light run of the Gemini Planet Imager (GPI) we obtained K-band spectra of exoplanets HR 8799 c and d. Analysis of the spectra indicates that planet d may be warmer than planet c. Comparisons to recent patchy cloud models and previously obtained observations over multiple wavelengths confirm that thick clouds combined with horizontal variation in the cloud cover generally reproduce the planets' spectral energy distributions. When combined with the 3 to 4 um photometric data points, the observations provide strong constraints on the atmospheric methane content for both planets. The data also provide further evidence that future modeling efforts must include cloud opacity, possibly including cloud holes, disequilibrium chemistry, and super-solar metallicity.

astro-ph.EP↗

arXiv2014

Deep Thermal Infrared Imaging of HR 8799 bcde: New Atmospheric Constraints and Limits on a Fifth Planet

We present new $L^\prime$ (3.8 $μm$) and Br-$α$ (4.05 $μm$) data and reprocessed archival $L^\prime$ data for the young, planet-hosting star HR 8799 obtained with Keck/NIRC2, VLT/NaCo and Subaru/IRCS. We detect all four HR 8799 planets in each dataset at a moderate to high signal-to-noise (SNR $\gtrsim$ 6-15). We fail to identify a fifth planet, "HR 8799 f", at $r$ $<$ 15 $AU$ at a 5-$σ$ confidence level: one suggestive, marginally significant residual at 0.2" is most likely a PSF artifact. Assuming companion ages of 30 $Myr$ and the Baraffe (Spiegel \& Burrows) planet cooling models, we rule out an HR 8799 f with mass of 5 $M_{J}$ (7 $M_{J}$), 7 $M_{J}$ (10 $M_{J}$), and 12 $M_{J}$ (13 $M_{J}$) at $r_{proj}$ $\sim$ 12 $AU$, 9 $AU$, and 5 $AU$, respectively. All four HR 8799 planets have red early T dwarf-like $L^\prime$ - [4.05] colors, suggesting that their SEDs peak in between the $L^\prime$ and $M^\prime$ broadband filters. We find no statistically significant difference in HR 8799 cde's colors. Atmosphere models assuming thick, patchy clouds appear to better match HR 8799 bcde's photometry than models assuming a uniform cloud layer. While non-equilibrium carbon chemistry is required to explain HR 8799 bc's photometry/spectra, evidence for it from HR 8799 de's photometry is weaker. Future, deep IR spectroscopy/spectrophotometry with the Gemini Planet Imager, SCExAO/CHARIS, and other facilities may clarify whether the planets are chemically similar or heterogeneous.

astro-ph.EP↗

arXiv2014

Atmospheric Characterization of the Hot Jupiter Kepler-13Ab

Kepler-13Ab (= KOI-13.01) is a unique transiting hot Jupiter. It is one of very few known short-period planets orbiting a hot A-type star, making it one of the hottest planets currently known. The availability of Kepler data allows us to measure the planet's occultation (secondary eclipse) and phase curve in the optical, which we combine with occultations observed by warm Spitzer at 4.5 mic and 3.6 mic and a ground-based occultation observation in the Ks band (2.1 mic). We derive a day-side hemisphere temperature of 2,750 +- 160 K as the effective temperature of a black body showing the same occultation depths. Comparing the occultation depths with one-dimensional planetary atmosphere models suggests the presence of an atmospheric temperature inversion. Our analysis shows evidence for a relatively high geometric albedo, Ag= 0.33 +0.04 -0.06. While measured with a simplistic method, a high Ag is supported also by the fact that the one-dimensional atmosphere models underestimate the occultation depth in the optical. We use stellar spectra to determine the dilution, in the four wide bands where occultation was measured, due to the visual stellar binary companion 1.15 +- 0.05" away. The revised stellar parameters measured using these spectra are combined with other measurements leading to revised planetary mass and radius estimates of Mp = 4.94 - 8.09 Mjup and Rp = 1.406 +- 0.038 Rjup. Finally, we measure a Kepler mid-occultation time that is 34.0 +- 6.9 s earlier than expected based on the mid-transit time and the delay due to light travel time, and discuss possible scenarios.

astro-ph.EP↗

arXiv2014

A First-Look Atmospheric Modeling Study of the Young Directly-Imaged Planet-Mass Companion, ROXs 42Bb

We present and analyze $J$$K_{s}$$L^\prime$ photometry and our previously published $H$-band photometry and $K$-band spectroscopy for ROXs 42Bb, an object Currie et al. (2014) first reported as a young directly imaged planet-mass companion. ROXs 42Bb exhibits IR colors redder than field L dwarfs but consistent with other planet-mass companions. From the H$_{2}$O-2 spectral index, we estimate a spectral type of L0 $\pm$ 1; weak detections/non-detections of the $CO$ bandheads, $Na I$, and $Ca I$ support evidence for a young, low surface gravity object primarily derived from the $H_{2}$(K) index. ROXs 42Bb's photometry/K-band spectrum are inconsistent with limiting cases of dust-free atmospheres ($COND$) and marginally inconsistent with the AMES/DUSTY models and the BT-SETTL models. However, ROXS 42Bb data are simultaneously fit by atmosphere models incorporating several micron-sized dust grains entrained in thick clouds, although further modifications are needed to better reproduce the $K$-band spectral shape. ROXs 42Bb's best-estimated temperature is $T_{eff}$ $\sim$ 1950--2000 $K$, near the low end of the empirically-derived range in Currie et al. (2014). For an age of $\sim$ 1--3 $Myr$ and considering the lifetime of the protostar phase, ROXs 42Bb's luminosity of log($L$/$L_{\odot}$) $\sim$ -3.07 $\pm$ 0.07 implies a mass of 9$^{+3}_{-3}$ $M_{J}$, making it one of the lightest planetary mass objects yet imaged.

astro-ph.EP↗

arXiv2014

Expectations for the Hard X-ray Continuum and Gamma-ray Line Fluxes from the Type Ia supernova SN 2014J in M82

The hard X-ray continuum and gamma-ray lines from a Type Ia supernova dominate its integrated photon emissions and can provide unique diagnostics of the mass of the ejecta, the $^{56}$Ni yield and spatial distribution, its kinetic energy and expansion speed, and the mechanism of explosion. Such signatures and their time behavior "X-ray" the bulk debris field in direct fashion, and do not depend upon the oftimes problematic and elaborate UV, optical, and near-infrared spectroscopy and radiative transfer that have informed the study of these events for decades. However, to date no hard photons have ever been detected from a Type Ia supernova in explosion. With the advent of the supernova SN 2014J in M82, at a distance of $\sim$3.5 Mpc, this situation may soon change. Both NuSTAR and INTEGRAL have the potential to detect SN 2014J, and, if spectra and light curves can be measured, would usefully constrain the various explosion models published during the last $\sim$thirty years. In support of these observational campaigns, we provide predictions for the hard X-ray continuum and gamma-line emissions for fifteen Type Ia explosion models gleaned from the literature. The model set, containing as it does deflagration, delayed detonation, merger detonation, pulsational delayed detonation, and sub-Chandrasekhar helium detonation models, collectively spans a wide range of properties and, hence, signatures. We provide a brief discussion of various diagnostics (with examples), but importantly make the spectral and line results available electronically to aid in the interpretation of the anticipated data.

astro-ph.HE↗

arXiv2014

The Gemini Planet Imager: First Light

The Gemini Planet Imager (GPI) is a dedicated facility for directly imaging and spectroscopically characterizing extrasolar planets. It combines a very high-order adaptive optics system, a diffraction-suppressing coronagraph, and an integral field spectrograph with low spectral resolution but high spatial resolution. Every aspect of GPI has been tuned for maximum sensitivity to faint planets near bright stars. During first light observations, we achieved an estimated H band Strehl ratio of 0.89 and a 5-sigma contrast of $10^6$ at 0.75 arcseconds and $10^5$ at 0.35 arcseconds. Observations of Beta Pictoris clearly detect the planet, Beta Pictoris b, in a single 60-second exposure with minimal post-processing. Beta Pictoris b is observed at a separation of $434 \pm 6$ milli-arcseconds and position angle $211.8 \pm 0.5$ deg. Fitting the Keplerian orbit of Beta Pic b using the new position together with previous astrometry gives a factor of three improvement in most parameters over previous solutions. The planet orbits at a semi-major axis of $9.0^{+0.8}_{-0.4}$ AU near the 3:2 resonance with the previously-known 6 AU asteroidal belt and is aligned with the inner warped disk. The observations give a 4% posterior probability of a transit of the planet in late 2017.

astro-ph.EP↗

arXiv2014

The Emergent 1.1-1.7 Micron Spectrum of the Exoplanet CoRoT-2b as Measured Using the Hubble Space Telescope

We have used Hubble/WFC3 and the G141 grism to measure the secondary eclipse of the transiting very hot Jupiter CoRoT-2b in the 1.1-1.7$μ$m spectral region. We find an eclipse depth averaged over this band equal to $395^{+69}_{-45}$ parts per million, equivalent to a blackbody temperature of $1788\pm18$K. We study and characterize several WFC3 instrumental effects, especially the "hook" phenomenon described by Deming et al. (2013). We use data from several transiting exoplanet systems to find a quantitative relation between the amplitude of the hook and the exposure level of a given pixel. Although the uncertainties in this relation are too large to allow us to develop an empirical correction for our data, our study provides a useful guide for optimizing exposure levels in future WFC3 observations. We derive the planet's spectrum using a differential method. The planet-to-star contrast increases to longer wavelength within the WFC3 bandpass, but without water absorption or emission to a $3σ$ limit of 85 ppm. The slope of the WFC3 spectrum is significantly less than the slope of the best-fit blackbody. We compare all existing eclipse data for this planet to a blackbody spectrum, and to spectra from both solar abundance and carbon-rich (C/O=1) models. A blackbody spectrum is an acceptable fit to the full dataset. Extra continuous opacity due to clouds or haze, and flattened temperature profiles, are strong candidates to produce quasi-blackbody spectra, and to account for the amplitude of the optical eclipses. Our results show ambiguous evidence for a temperature inversion in this planet.

astro-ph.EP↗

arXiv2014

The Astronomical Reach of Fundamental Physics

Using basic physical arguments, we derive by dimensional and physical analysis the characteristic masses and sizes of important objects in the Universe in terms of just a few fundamental constants. This exercise illustrates the unifying power of physics and the profound connections between the small and the large in the Cosmos we inhabit. We focus on the minimum and maximum masses of normal stars, the corresponding quantities for neutron stars, the maximum mass of a rocky planet, the maximum mass of a white dwarf, and the mass of a typical galaxy. To zeroth order, we show that all these masses can be expressed in terms of either the Planck mass or the Chandrasekar mass, in combination with various dimensionless quantities. With these examples we expose the deep interrelationships imposed by Nature between disparate realms of the Universe and the amazing consequences of the unifying character of physical law.

astro-ph.SR↗

arXiv2013

Warm Spitzer and Palomar Near-IR Secondary Eclipse Photometry of Two Hot Jupiters: WASP-48b and HAT-P-23b

We report secondary eclipse photometry of two hot Jupiters, WASP-48b and HAT-P-23b, at 3.6 and 4.5 um taken with the InfraRed Array Camera aboard the Spitzer Space Telescope during the warm Spitzer mission and in the H and Ks bands with the Wide Field IR Camera at the Palomar 200-inch Hale Telescope. WASP-48b and HAT-P-23b are Jupiter-mass and twice Jupiter-mass objects orbiting an old, slightly evolved F star and an early G dwarf star, respectively. In the H, Ks, 3.6 um, and 4.5 um bands, respectively, we measure secondary eclipse depths of 0.047% +/- 0.016%, 0.109% +/- 0.027%, 0.176% +/- 0.013%, and 0.214% +/- 0.020% for WASP-48b. In the Ks, 3.6 um, and 4.5 um bands, respectively, we measure secondary eclipse depths of 0.234% +/- 0.046%, 0.248% +/- 0.019%, and 0.309% +/- 0.026% for HAT-P-23b. For WASP-48b and HAT-P-23b, respectively, we measure delays of 2.6 +/- 3.9 minutes and 4.0 +/- 2.4 minutes relative to the predicted times of secondary eclipse for circular orbits, placing 2-sigma upper limits on |e cos(omega)| of 0.0053 and 0.0080, both of which are consistent with circular orbits. The dayside emission spectra of these planets are well-described by blackbodies with effective temperatures of 2158 +/- 100 K (WASP-48b) and 2154 +/- 90 K (HAT-P-23b), corresponding to moderate recirculation in the zero albedo case. Our measured eclipse depths are also consistent with one-dimensional radiative transfer models featuring varying degrees of recirculation and weak thermal inversions or no inversions at all. We discuss how the absence of strong temperature inversions on these planets may be related to the activity levels and metallicities of their host stars.

astro-ph.EP↗

arXiv2013

Spectra as Windows into Exoplanet Atmospheres

Understanding a planet's atmosphere is a necessary condition for understanding not only the planet itself, but also its formation, structure, evolution, and habitability, This puts a premium on obtaining spectra, and developing credible interpretative tools with which to retrieve vital planetary information. However, for exoplanets these twin goals are far from being realized. In this paper, I provide a personal perspective on exoplanet theory and remote sensing via photometry and low-resolution spectroscopy. Though not a review in any sense, this paper highlights the limitations in our knowledge of compositions, thermal profiles, and the effects of stellar irradiation, focussing on, but not restricted to, transiting giant planets. I suggest that the true function of the recent past of exoplanet atmospheric research has been not to constrain planet properties for all time, but to train a new generation of scientists that, by rapid trial and error, is fast establishing a solid future foundation for a robust science of exoplanets.

astro-ph.EP↗

arXiv2013

Exoplanet Transit Spectroscopy Using WFC3: WASP-12 b, WASP-17 b, and WASP-19 b

We report analysis of transit spectroscopy of the extrasolar planets WASP-12 b, WASP-17 b, and WASP-19 b using the Wide Field Camera 3 on the HST. We analyze the data for a single transit for each planet using a strategy similar in certain aspects to the techniques used by Berta et al. (2012), but we extend their methodology to allow us to correct for channel- or wavelength-dependent instrumental effects by utilizing the band-integrated time series and measurements of the drift of the spectrum on the detector over time. We achieve almost photon-limited results for individual spectral bins, but the uncertainties in the transit depth for the the band-integrated data are exacerbated by the uneven sampling of the light curve imposed by the orbital phasing of HST's observations. Our final transit spectra for all three objects are consistent with the presence of a broad absorption feature at 1.4 microns potentially due to water. However, the amplitude of the absorption is less than that expected based on previous observations with Spitzer, possibly due to hazes absorbing in the NIR or non-solar compositions. The degeneracy of models with different compositions and temperature structures combined with the low amplitude of any features in the data preclude our ability to place unambiguous constraints on the atmospheric composition without additional observations with WFC3 to improve the S/N and/or a comprehensive multi-wavelength analysis.

astro-ph.EP↗

arXiv2013

Transport Equations for Oscillating Neutrinos

We derive a suite of generalized Boltzmann equations, based on the density-matrix formalism, that incorporates the physics of neutrino oscillations for two- and three-flavor oscillations, matter refraction, and self-refraction. The resulting equations are straightforward extensions of the classical transport equations that nevertheless contain the full physics of quantum oscillation phenomena. In this way, our broadened formalism provides a bridge between the familiar neutrino transport algorithms employed by supernova modelers and the more quantum-heavy approaches frequently employed to illuminate the various neutrino oscillation effects. We also provide the corresponding angular-moment versions of this generalized equation set. Our goal is to make it easier for astrophysicists to address oscillation phenomena in a language with which they are familiar. The equations we derive are simple and practical, and are intended to facilitate progress concerning oscillation phenomena in the context of core-collapse supernova theory.

hep-ph↗

arXiv2013

A Combined VLT and Gemini Study of the Atmosphere of the Directly-Imaged Planet, beta Pictoris b

We analyze new/archival VLT/NaCo and Gemini/NICI high-contrast imaging of the young, self-luminous planet $β$ Pictoris b in seven near-to-mid IR photometric filters, using advanced image processing methods to achieve high signal-to-noise, high precision measurements. While $β$ Pic b's near-IR colors mimick that of a standard, cloudy early-to-mid L dwarf, it is overluminous in the mid-infrared compared to the field L/T dwarf sequence. Few substellar/planet-mass objects -- i.e. $κ$ And b and 1RXJ 1609B -- match $β$ Pic b's $JHK_{s}L^\prime$ photometry, and its 3.1 $μm$ and 5 $μm$ photometry are particularly difficult to reproduce. Atmosphere models adopting cloud prescriptions and large ($\sim$ 60 $μm$) dust grains fail to reproduce the $β$ Pic b spectrum. However, models incorporating thick clouds similar to those found for HR 8799 bcde but also with small (a few microns) modal particle sizes yield fits consistent with the data within uncertainties. Assuming solar abundance models, thick clouds, and small dust particles ($ $ = 4 $μm$) we derive atmosphere parameters of log(g) = 3.8 $\pm$ 0.2 and $T_{eff}$ = 1575--1650 $K$, an inferred mass of 7$^{+4}_{-3}$ $M_{J}$, and a luminosity of log(L/L$_{\odot}$) $\sim$ -3.80 $\pm$ 0.02. The best-estimated planet radius, $\approx$ 1.65 $\pm$ 0.06 $R_{J}$, is near the upper end of allowable planet radii for hot-start models given the host star's age and likely reflects challenges with constructing accurate atmospheric models. Alternatively, these radii are comfortably consistent with hot-start model predictions if $β$ Pic b is younger than $\approx$ 7 Myr, consistent with a late formation, well after its host star's birth $\sim$ 12$^{+8}_{-4}$ Myr ago.

astro-ph.EP↗

arXiv2013

Spectral and Photometric Diagnostics of Giant Planet Formation Scenarios

Gas-giant planets that form via core accretion might have very different characteristics from those that form via disk-instability. Disk-instability objects are typically thought to have higher entropies, larger radii, and (generally) higher effective temperatures than core-accretion objects. We provide a large set of models exploring the observational consequences of high-entropy (hot) and low-entropy (cold) initial conditions, in the hope that this will ultimately help to distinguish between different physical mechanisms of planet formation. However, the exact entropies and radii of newly-formed planets due to these two modes of formation cannot, at present, be precisely predicted. We introduce a broad range of "Warm Start" gas-giant planet models. Between the hottest and the coldest models that we consider, differences in radii, temperatures, luminosities, and spectra persist for only a few million to a few tens of millions of years for planets that are a few times Jupiter's mass or less. For planets that are ~five times Jupiter's mass or more, significant differences between hottest-start and coldest-start models persist for on the order of 100 Myrs. We find that out of the standard infrared bands (J, H, K, L', M, N) the K and H bands are the most diagnostic of the initial conditions. A hottest-start model can be from ~4.5 magnitudes brighter (at Jupiter's mass) to ~9 magnitudes brighter (at ten times Jupiter's mass) than a coldest-start model in the first few million years. In more massive objects, these large differences in luminosity and spectrum persist for much longer than in less massive objects. We consider the influence of atmospheric conditions on spectra, and find that the presence or absence of clouds, and the metallicity of an atmosphere, can affect an object's apparent brightness in different bands by up to several magnitudes.

astro-ph.EP↗

arXiv2013

Infrared Transmission Spectroscopy of the Exoplanets HD209458b and XO-1b Using the Wide Field Camera-3 on the Hubble Space Telescope

Exoplanetary transmission spectroscopy in the near-infrared using Hubble/NICMOS is currently ambiguous because different observational groups claim different results from the same data, depending on their analysis methodologies. Spatial scanning with Hubble/WFC3 provides an opportunity to resolve this ambiguity. We here report WFC3 spectroscopy of the giant planets HD209458b and XO-1b in transit, using spatial scanning mode for maximum photon-collecting efficiency. We introduce an analysis technique that derives the exoplanetary transmission spectrum without the necessity of explicitly decorrelating instrumental effects, and achieves nearly photon-limited precision even at the high flux levels collected in spatial scan mode. Our errors are within 6-percent (XO-1) and 26-percent (HD209458b) of the photon-limit at a spectral resolving power of 70, and are better than 0.01-percent per spectral channel. Both planets exhibit water absorption of approximately 200 ppm at the water peak near 1.38 microns. Our result for XO-1b contradicts the much larger absorption derived from NICMOS spectroscopy. The weak water absorption we measure for HD209458b is reminiscent of the weakness of sodium absorption in the first transmission spectroscopy of an exoplanet atmosphere by Charbonneau et al. (2002). Model atmospheres having uniformly-distributed extra opacity of 0.012 cm^2 per gram account approximately for both our water measurement and the sodium absorption in this planet. Our results for HD209458b support the picture advocated by Pont et al. (2013) in which weak molecular absorptions are superposed on a transmission spectrum that is dominated by continuous opacity due to haze and/or dust. However, the extra opacity needed for HD209458b is grayer than for HD189733b, with a weaker Rayleigh component.

astro-ph.EP↗

arXiv2013

Secondary Eclipse Photometry of the Exoplanet WASP-5b with Warm Spitzer

We present photometry of the extrasolar planet WASP-5b in the 3.6 and 4.5 micron bands taken with the Spitzer Space Telescope's Infrared Array Camera as part of the extended warm mission. By examining the depth of the planet's secondary eclipse at these two wavelengths, we can place joint constraints on the planet's atmospheric pressure-temperature profile and chemistry. We measure secondary eclipse depths of 0.197% +/- 0.028% and 0.227% +/- 0.025% in the 3.6 micron and 4.5 micron bands, respectively. Our observations are best matched by models showing a hot dayside and, depending on our choice of model, a weak thermal inversion or no inversion at all. We measure a mean offset from the predicted center of eclipse of 0.078 +/- 0.032 hours, translating to ecos(omega) = 0.0031 +/- 0.0013 and consistent with a circular orbit. We see no evidence for any eclipse timing variations comparable to those reported in a previous transit study.

astro-ph.EP↗

arXiv2013

Thermal Processes Governing Hot-Jupiter Radii

There have been many proposed explanations for the larger-than-expected radii of some transiting hot Jupiters, including either stellar or orbital energy deposition deep in the atmosphere or deep in the interior. In this paper, we explore the important influences on hot-Jupiter radius evolution of (i) additional heat sources in the high atmosphere, the deep atmosphere, and deep in the convective interior; (ii) consistent cooling of the deep interior through the planetary dayside, nightside, and poles; (iii) the degree of heat redistribution to the nightside; and (iv) the presence of an upper atmosphere absorber inferred to produce anomalously hot upper atmospheres and inversions in some close-in giant planets. In particular, we compare the radius expansion effects of atmospheric and deep-interior heating at the same power levels and derive the power required to achieve a given radius increase when night-side cooling is incorporated. We find that models that include consistent day/night cooling are more similar to isotropically irradiated models when there is more heat redistributed from the dayside to the nightside. In addition, we consider the efficacy of ohmic heating in the atmosphere and/or convective interior in inflating hot Jupiters. Among our conclusions are that (i) the most highly irradiated planets cannot stably have uB > (10 km/s Gauss) over a large fraction of their daysides, where u is the zonal wind speed and B is the dipolar magnetic field strength in the atmosphere, and (ii) that ohmic heating cannot in and of itself lead to a runaway in planet radius.

astro-ph.EP↗