Eric Agol

Finding Black Holes with Microlensing

The MACHO and OGLE collaborations have argued that the three longest duration bulge microlensing events are likely caused by nearby black holes, given the small velocities measured with microlensing parallax and nondetection of the lenses. However, these events may be due to lensing by more numerous lower mass stars at greater distances. We find a posteriori probabilities of 76%, 16%, and 4% that the three longest events are black holes, assuming a Salpeter initial mass function (IMF) and a 40 M☉ cutoff for neutron star progenitors; the numbers depend strongly on the assumed mass function but favor a black hole for the longest event for most standard IMFs. The longest events (>600 days) have an a priori ~26% probability of being black holes for a standard mass function. We propose a new technique for measuring the lens mass function using the mass distribution of long events measured with the Advanced Camera for Surveys on the Hubble Space Telescope, the Very Large Telescope Interferometer, the Space Interferometry Mission, or the Global Astrometric Interferometer for Astrophysics.

Analytic Light Curves for Planetary Transit Searches

We present exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening. In the limit that the planet radius is less than a tenth of the stellar radius, we show that the exact light curve can be well approximated by assuming the region of the star blocked by the planet has constant surface brightness. We apply these results to the Hubble Space Telescope observations of HD 209458, showing that the ratio of the planetary to stellar radii is 0.1207 ± 0.0003. These formulae give a fast and accurate means of computing light curves using limb-darkening coefficients from model atmospheres that should aid in the detection, simulation, and parameter fitting of planetary transits.

A map of the day-night contrast of the extrasolar planet HD 189733b

‘Hot Jupiter’ extrasolar planets are expected to be tidally locked because they are close (<0.05 astronomical units, where 1 au is the average Sun–Earth distance) to their parent stars, resulting in permanent daysides and nightsides. By observing systems where the planet and star periodically eclipse each other, several groups have been able to estimate the temperatures of the daysides of these planets. A key question is whether the atmosphere is able to transport the energy incident upon the dayside to the nightside, which will determine the temperature at different points on the planet’s surface. Here we report observations of HD 189733, the closest of these eclipsing planetary systems, over half an orbital period, from which we can construct a ‘map’ of the distribution of temperatures. We detected the increase in brightness as the dayside of the planet rotated into view. We estimate a minimum brightness temperature of 973 ± 33 K and a maximum brightness temperature of 1,212 ± 11 K at a wavelength of 8 μm, indicating that energy from the irradiated dayside is efficiently redistributed throughout the atmosphere, in contrast to a recent claim for another hot Jupiter. Our data indicate that the peak hemisphere-integrated brightness occurs 16 ± 6° before opposition, corresponding to a hotspot shifted east of the substellar point. The secondary eclipse (when the planet moves behind the star) occurs 120 ± 24 s later than predicted, which may indicate a slightly eccentric orbit.

On detecting terrestrial planets with timing of giant planet transits

In order to contain the COVID-19 pandemic, several countries enforced extended social distancing measures for several weeks, effectively pausing the majority of economic activities. In an effort to resume economic activity safely, several Digital Contact Tracing applications and protocols have been introduced with success. However, DCT is a reactive method, as it aims to break existing chains of disease transmission in a population. Therefore DCT is not suitable for proactively preventing the spread of a disease; an approach that relevant to certain use cases, such as international tourism, where individuals travel across borders. In this work, we first identify the limitations characterising DCT related to privacy issues, unwillingness of the public to use DCT mobile apps due to privacy concerns, lack of interoperability among different DCT applications and protocols, and the assumption that there is limited, local mobility in the population. We then discuss the concept of a Health Passport as a means of verifying that individuals are disease risk-free and how it could be used to resume the international tourism sector. Following, we present the DHP Framework that uses a private blockchain and Proof of Authority for issuing Digital Health Passports. The framework provides a distributed infrastructure supporting the issuance of DHPs by foreign health systems and their verification by relevant stakeholders, such as airline companies and border control authorities. We discuss the attributes of the system in terms of its usability and performance, security and privacy. Finally, we conclude by identifying future extensions of our work on formal security and privacy properties that need to be rigorously guaranteed via appropriate security protocols.

Architecture of Kepler's Multi-transiting Systems: II. New investigations with twice as many candidates

We report on the orbital architectures of Kepler systems having multiple-planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. (2013). These data show 899 transiting planet candidates in 365 multiple-planet systems and provide a powerful means to study the statistical properties of planetary systems. Using a generic mass–radius relationship, we find that only two pairs of planets in these candidate systems (out of 761 pairs total) appear to be on Hill-unstable orbits, indicating ~96% of the candidate planetary systems are correctly interpreted as true systems. We find that planet pairs show little statistical preference to be near mean-motion resonances. We identify an asymmetry in the distribution of period ratios near first-order resonances (e.g., 2:1, 3:2), with an excess of planet pairs lying wide of resonance and relatively few lying narrow of resonance. Finally, based upon the transit duration ratios of adjacent planets in each system, we find that the interior planet tends to have a smaller transit impact parameter than the exterior planet does. This finding suggests that the mode of the mutual inclinations of planetary orbital planes is in the range 1°.0–2°.2, for the packed systems of small planets probed by these observations.

Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1

One aim of modern astronomy is to detect temperate, Earth-like exoplanets that are well suited for atmospheric characterization. Recently, three Earth-sized planets were detected that transit (that is, pass in front of) a star with a mass just eight per cent that of the Sun, located 12 parsecs away. The transiting configuration of these planets, combined with the Jupiter-like size of their host star—named TRAPPIST-1—makes possible in-depth studies of their atmospheric properties with present-day and future astronomical facilities. Here we report the results of a photometric monitoring campaign of that star from the ground and space. Our observations reveal that at least seven planets with sizes and masses similar to those of Earth revolve around TRAPPIST-1. The six inner planets form a near-resonant chain, such that their orbital periods (1.51, 2.42, 4.04, 6.06, 9.1 and 12.35 days) are near-ratios of small integers. This architecture suggests that the planets formed farther from the star and migrated inwards. Moreover, the seven planets have equilibrium temperatures low enough to make possible the presence of liquid water on their surfaces.

Validation of Kepler's Multiple Planet Candidates. III. Light Curve Analysis and Announcement of Hundreds of New Multi-planet Systems

The Kepler mission has discovered more than 2500 exoplanet candidates in the first two years of spacecraft data, with approximately 40% of those in candidate multi-planet systems. The high rate of multiplicity combined with the low rate of identified false positives indicates that the multiplanet systems contain very few false positive signals due to other systems not gravitationally bound to the target star. False positives in the multi-planet systems are identified and removed, leaving behind a residual population of candidate multi-planet transiting systems expected to have a false positive rate less than 1%. We present a sample of 340 planetary systems that contain 851 planets that are validated to substantially better than the 99% confidence level; the vast majority of these have not been previously verified as planets. We expect ~two unidentified false positives making our sample of planet very reliable. We present fundamental planetary properties of our sample based on a comprehensive analysis of Kepler light curves, ground-based spectroscopy, and high-resolution imaging. Since we do not require spectroscopy or high-resolution imaging for validation, some of our derived parameters for a planetary system may be systematically incorrect due to dilution from light due to additional stars in the photometric aperture. Nonetheless, our result nearly doubles the number verified exoplanets.

Kepler-36: A Pair of Planets with Neighboring Orbits and Dissimilar Densities

So Close and So Different In our solar system, the rocky planets have very distinct orbits from those of the gas giants. Carter et al. (p. 556, published online 21 June) report on a planetary system where this pattern does not apply, posing a challenge to theories of planet formation. Data from the Kepler space telescope reveal two planets with radically different densities orbiting the same star with very similar orbital periods. One planet has a rocky Earth-like composition and the other is akin to Neptune. The Kepler spacecraft detected a super-Earth and a Neptune-like planet in very tightly spaced orbits around the same star. In the solar system, the planets’ compositions vary with orbital distance, with rocky planets in close orbits and lower-density gas giants in wider orbits. The detection of close-in giant planets around other stars was the first clue that this pattern is not universal and that planets’ orbits can change substantially after their formation. Here, we report another violation of the orbit-composition pattern: two planets orbiting the same star with orbital distances differing by only 10% and densities differing by a factor of 8. One planet is likely a rocky “super-Earth,” whereas the other is more akin to Neptune. These planets are 20 times more closely spaced and have a larger density contrast than any adjacent pair of planets in the solar system.

Kepler-47: A Transiting Circumbinary Multiplanet System

A Pair of Planets Around a Pair of Stars Most of the planets we know about orbit a single star; however, most of the stars in our galaxy are not single. Based on data from the Kepler space telescope, Orosz et al. (p. 1511, published online 28 August) report the detection of a pair of planets orbiting a pair of stars. These two planets are the smallest of the known transiting circumbinary planets and have the shortest and longest orbital periods. The outer planet resides in the habitable zone—the “goldilocks” region where the temperatures could allow liquid water to exist. This discovery establishes that, despite the chaotic environment around a close binary star, a system of planets can form and persist. Data from the Kepler space telescope reveal two small planets orbiting a pair of two low-mass stars. We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of Earth, respectively. The binary star consists of a Sun-like star and a companion roughly one-third its size, orbiting each other every 7.45 days. With an orbital period of 49.5 days, 18 transits of the inner planet have been observed, allowing a detailed characterization of its orbit and those of the stars. The outer planet’s orbital period is 303.2 days, and although the planet is not Earth-like, it resides within the classical “habitable zone,” where liquid water could exist on an Earth-like planet. With its two known planets, Kepler-47 establishes that close binary stars can host complete planetary systems.

Infrared Transmission Spectroscopy of the Exoplanets HD 209458b and XO-1b Using the Wide Field Camera-3 on the Hubble Space Telescope

Exoplanetary transmission spectroscopy in the near-infrared using the Hubble Space Telescope (HST) NICMOS is currently ambiguous because different observational groups claim different results from the same data, depending on their analysis methodologies. Spatial scanning with HST/WFC3 provides an opportunity to resolve this ambiguity. We here report WFC3 spectroscopy of the giant planets HD 209458b 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% (XO-1) and 26% (HD 209458b) of the photon-limit at a resolving power of λ/δλ ~ 70, and are better than 0.01% per spectral channel. Both planets exhibit water absorption of approximately 200 ppm at the water peak near 1.38 μm. Our result for XO-1b contradicts the much larger absorption derived from NICMOS spectroscopy. The weak water absorption we measure for HD 209458b is reminiscent of the weakness of sodium absorption in the first transmission spectroscopy of an exoplanet atmosphere by Charbonneau et al. Model atmospheres having uniformly distributed extra opacity of 0.012 cm2 g−1 account approximately for both our water measurement and the sodium absorption. Our results for HD 209458b support the picture advocated by Pont et al. 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 HD 209458b is grayer than for HD 189733b, with a weaker Rayleigh component.