Monday, July 27, 2015

A Population of Extremely Long Duration Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are among the most energetic events in the universe. There are three classes of GRBs - short gamma-ray bursts (SGRBs) with durations less than ~2 seconds, long gamma-ray bursts (LGRBs) with durations extending to ~1,000 seconds and ultra-long gamma-ray bursts (ULGRBs) with durations of ~10,000 seconds. SGRBs originate from the mergers of neutron star binaries or neutron star-black hole binaries, while LGRBs are created when the cores of massive stars collapse to form black holes.

ULGRBs have such long burst durations that their progenitors are unlikely to be the same as those for LGRBs. Instead, ULGRBs probably originate from the collapse of giant or supergiant stars into black holes. These stars are orders of magnitude larger than the progenitors of LGRBs, resulting in much longer collapse times. Additionally, these stars have lower densities, resulting in lower mass in-fall rates. The continuous in-fall of material into the nascent black hole drives a GRB with an extremely long duration, leading to an ULGRB. Alternatively, ULGRBs can also be created when white dwarfs get tidally shredded by intermediate mass black holes (IMBH).

Figure 1: Artist’s impression of a gamma-ray burst.

Figure 2: Parameter space for GRBs and other high energy transient phenomena plotted as a function of burst duration versus average luminosity. The classes of events are - soft gamma repeaters (SGRs), short gamma-ray bursts (SGRBs), low-luminosity and long gamma-ray bursts (LLGRBs), long gamma-ray bursts (LGRBs), ultra-long gamma-ray bursts (ULGRBs) and tidal disruption events (TDEs). Andrew Levan (2015).

Recent observations by NASA’s Swift Gamma-Ray Burst Mission have revealed what could be a new population of GRBs with extremely long durations that exceed 100,000 seconds. These extremely long duration GRBs may represent the tidal disruption of main sequence stars by supermassive black holes (SMBHs). When a main sequence star comes too close to a SMBH, the gravitational pull on the star’s outer layers from the SMBH can be stronger than the star’s own gravity. This can cause the star to be completely or partly disrupted.

Material stripped from the star forms an accretion disk around the SMBH and a small fraction of the material may be expelled at relativistic velocities, driving a tidal disruption flare (TDF) that is observed as an extremely long duration GRB. Tidal disruption events (TDEs) involving the tidal shredding of main sequence stars by SMBHs are likely to be the progenitors of extremely long duration GRBs.

Andrew Levan (2015), “Swift discoveries of new populations of extremely long duration high energy transient”, arXiv:1506.03960 [astro-ph.HE] 

Sunday, July 26, 2015

Ultra-Diffuse Galaxies in the Virgo Cluster

Recently, a large number of low surface brightness (LSB) galaxies were discovered in the Coma Cluster - a large cluster of galaxies located over 300 million light years away. Galaxies do not possess well defined boundaries. They simply get fainter and fainter towards their outer regions. As a result, the size of a galaxy is defined by its effective radius, also known as the half-light radius. The effective radius is the radius within which half of the galaxy’s luminosity is emitted.

Many of the LSB galaxies in the Coma Cluster are large, with effective radii between 2 to 5 kpc. One kpc (kiloparsec) is equivalent to 3,260 light years, and for comparison, the effective radius of the Milky Way galaxy is estimated to be ~3.6 kpc. They are also extremely diffuse galaxies with central surface brightnesses between 24 to 26 mag/arcsec². LSB galaxies are vulnerable to tidal perturbations as they move through the cluster and interact with other galaxies. Tidal disruption of a LSB galaxy can strip the galaxy down to only its dense nucleus, leading to the formation of an ultra-compact dwarf (UCD) galaxy.

Mihos et al. (2015) present the discovery of three LSB galaxies in the Virgo Cluster - a much nearer cluster of galaxies located ~50 million light years away. The three LSB galaxies are dubbed VLSB-A, VLSB-B and VLSB-C. They are extremely diffuse galaxies with central surface brightnesses around 27 mag/arcsec² and effective radii between 3 to 10 kpc. All three LSB galaxies appear quite diverse in their physical properties.

VLSB-A appears as a nucleated LSB galaxy with a tidal stream extending off it. This indicates that VLSB-A is presently experiencing tidal perturbations and its diffuse component is currently being stripped away. Since the nucleus of VLSB-A shares the same structural properties as UCD galaxies, VLSB-A will most likely become a new UCD galaxy after its diffuse component is stripped away.

The properties of VLSB-B and VLSB-C are not as clear compared to VLSB-A. However, both VLSB-B and VLSB-C do show a lack of obvious tidal distortion. This suggests they may lie in the outskirts of the Virgo Cluster or may be “falling” into the Virgo Cluster for the first time. Alternatively, they may be highly dominated by dark matter, making them less susceptible to tidal stripping. Interestingly, VLSB-B is appears to host a small population of globular clusters. These globular clusters may indicate the presence of a massive halo of dark matter around the galaxy which means that the galaxy has stronger self-gravity and is therefore more protected against tidal stripping.

Surface brightness of the three LSB galaxies in the Virgo Cluster. Mihos et al. (2015).

Structural properties of the three LSB galaxies in the Virgo Cluster compared with other stellar systems, including early type galaxies in the Virgo Cluster and Fornax Cluster, and in the Local Group, as well as globular clusters and UCD galaxies in the Virgo Cluster, and the LSB galaxies found in the Coma Cluster. The dashed orange lines show the globular cluster selection box, while lines of constant surface brightness are shown in green. Mihos et al. (2015).

Mihos et al. (2015), “Galaxies at the extremes: Ultra-diffuse galaxies in the Virgo Cluster”, arXiv:1507.02270 [astro-ph.GA]

Saturday, July 25, 2015

WOH G64 is a Stellar Behemoth with a Thick Disk

Artist’s impression of WOH G64. Credit: ESO.

WOH G64 is a remarkable red supergiant (RSG) star located 163,000 light years away in the Large Magellanic Cloud (LMC), a satellite galaxy of the Milky Way. The “WHO” in the star’s name comes from the initials of its discoverers - Westerlund, Olander and Hedin; and “G64” indicates that it is the 64th entry in the catalogue published in 1981. The physical properties of WOH G64 are extreme. The star has a relatively cool surface temperature of 3,400 K, but it shines roughly 300,000 times more brightly than does the Sun. With that, WOH G64 is estimated to be 1,540 times larger in size than the Sun, making it one of the largest known RSG stars. If placed at the position of the Sun in the Solar System, the surface of WOH G64 would extend almost to the orbit of Saturn.

Observations of WHO G64 made with the Very Large Telescope Interferometer (VLTI) operated by the European Southern Observatory (ESO) in Chile revealed the presence of an enormous and thick disk of gas and dust around the star. The inner edge of the disk is at ~15 stellar radii from WOH G64, about 120 times the distance of Earth from the Sun. The rest of the disk extends far out from WHO G64, reaching almost one light year in total size. Between 3 to 9 solar masses worth of material is estimated to be in the disk of gas and dust. WHO G64 is at an advance stage of its evolution and is experiencing violent, unstable mass loss. WHO G64 started out with ~25 times the Sun’s mass, but it has since lost between one tenth and a third of its original mass. This stellar behemoth is nearing its final fate as a supernova.

- Levesque et al. (2009), “The Physical Properties of the Red Supergiant WOH G64: The Largest Star Known?”, arXiv:0903.2260 [astro-ph.SR]
- Ohnaka et al. (2009), “Spatially resolved dusty torus toward the red supergiant WOH G64 in the Large Magellanic Cloud”, arXiv:0803.3823 [astro-ph]
- Westerlund, Olander & Hedin (1981), “Supergiant and giant M type stars in the Large Magellanic Cloud”, Astronomy & Astrophysics Supplement Series 43: 267-295

Friday, July 24, 2015

Properties of a Newly Discovered Super-Neptune

Bakos et al. (2015) present the discovery of HATS-7b, a transiting Super-Neptune with an orbital period of 3.185 days around a K dwarf star. The host star of HATS-7b has an effective temperature of 4,990 K, 85 percent the Sun’s mass, 82 percent the Sun’s diameter and shines with 37 percent the luminosity of the Sun. Being a K dwarf star, it is somewhat cooler and less luminous than the Sun - a G dwarf star. The detection of HATS-7b was made using the HATSouth network, comprised of a number of fully automated telescopes in the Southern Hemisphere. The primary goal of the HATSouth network is to search for transiting exoplanets.

Figure 1: Artist’s impression of a Neptune-like planet.

By measuring how much HATS-7b dims its host star when it transits in front, the planet is estimated to be 0.563 times the size of Jupiter. As HATS-7b circles its host star, it also gravitationally perturbs its host star, causing its host star to wobble back and forth. The magnitude of wobbling depends on the planet’s mass. Radial velocity measurements of the host star’s wobbling motion indicate that HATS-7b has 0.120 times the mass of Jupiter, placing it in the mass regime of super-Neptunes. For comparison, the planet Neptune has 0.054 times the mass of Jupiter, or 17.147 times the mass of Earth.

Figure 2: Transit light curve of HATS-7b phase folded to the planet’s orbital period of 3.185 days. The lower panel zooms in on the transit. Bakos et al. (2015).

Figure 3: Radial velocity measurements for the host star of HATS-7b. The gravitational perturbation from HATS-7b induces radial velocity semi-amplitude of 18.4 ± 1.9 m/s on its host star. Bakos et al. (2015).

Knowing the size and mass of HATS-7b allows the planet’s bulk composition to be constrained. Interior models of HATS-7b indicate a hydrogen-helium (H2-He) mass fraction of 18 ± 4 percent if the planet has a rock-iron core and a H2-He envelope, or a H2-He mass fraction of 9 ± 4 percent if the planet has an ice core and a H2-He envelope. If HATS-7b has a rock-iron core and a hydrogen-helium envelope, the best fit models give a core mass of 31 ± 4 Earth-masses and an envelope mass of 7 ± 1.5 Earth-masses. If instead HATS-7b has a ice core and a hydrogen-helium envelope, the best fit models give a core mass of 34.5 ± 4 Earth-masses and an envelope mass of 3.5 ± 1.5 Earth-masses.

The composition of HATS-7b is broadly similar to that of Uranus and Neptune, but quite different from Jupiter and Saturn, which are both predominantly comprised of hydrogen and helium. Super-Neptunes like HATS-7b and the recently discovered HATS-8b (also by the HATSouth network) are important for understanding the transition from ice giants (i.e. Uranus and Neptune) to gas giants (i.e. Jupiter and Saturn). HATS-7b circles in a close-in orbit around its host star at a distance of only 6 million km. This is 25 times closer than Earth is from the Sun. The dayside of HATS-7b is heated to a temperature of over 1,000 K.

Figure 4: Mass-radius diagram of super-Neptunes (planets with less than 0.18 times Jupiter’s mass) and super-Earths with accurately measured masses and radii (less than 20 percent uncertainties). Colour indicates equilibrium temperature. HATS-7b is marked with a box and Neptune is marked with a blue triangle. Abbreviations are: K: Kepler, H: HAT, HS: HATSouth, C: Corot. Bakos et al. (2015).

- Bakos et al. (2015), “HATS-7b: A Hot Super Neptune Transiting a Quiet K Dwarf Star”, arXiv:1507.01024 [astro-ph.EP]
- Bayliss et al. (2015), “HATS-8b: A Low-Density Transiting Super-Neptune”, arXiv:1506.01334 [astro-ph.EP]

Thursday, July 23, 2015

Properties of Oxygen Sequence Wolf-Rayet Stars

Oxygen sequence Wolf-Rayet (WO) stars are some of the rarest stars in the universe. To date, only nine WO stars are known, two of which are in binary systems. WO stars are remarkably hot, with surface temperatures ranging from 150,000 K to 210,000 K. For comparison, the Sun’s surface temperature is only 5,778 K. Core-helium burning is the process where helium in a star’s core undergoes nuclear fusion, leading to the production of oxygen and carbon. WO stars are massive stars that have passed the end of core-helium burning and have shed their outer envelopes through powerful stellar winds to reveal hotter underlying layers. Also, after a massive star exhausts the helium in its core, it naturally contracts and heats up. This is consistent with the high surface temperatures observed for WO stars.

WO stars are extremely luminous objects with hundreds of thousands of times the Sun’s luminosity. Despite their extreme luminosities, WO stars are generally smaller in size than the Sun. For example, the WO star WR102 is almost 300,000 times more luminous than the Sun, but its diameter is only 40 percent of the Sun’s. The intensely hot surfaces of WO stars are observed to be enriched with the products from core-helium burning, particularly carbon and oxygen. The helium surface mass fraction on WO stars is usually between 20 to 30 percent, but ranges from 44 percent for the least hot WO star to as low as 14 percent for the hottest known WO star. Observations have shown that the oxygen and carbon surface mass fractions can be as high as 24 and 62 percent, respectively, as in the case for the WO star WR102.

WO stars represent a very brief stage in the evolution of massive stars, predicted to be the final evolutionary stage of massive stars with initial masses between 40 to 60 times the Sun’s mass. These remarkable stars are likely to explode as type Ic supernovae in ~1,000 to 10,000 years. Type Ic supernovae are a class of stellar explosions caused by the core collapse of massive stars that have shed their outer envelopes of hydrogen and helium. As a result, type Ic supernovae do not contain hydrogen and helium. For comparison, type Ib supernovae are another class of stellar explosions involving massive stars that have only shed their outer envelope of hydrogen.

Locations of several WO stars on the Hertzsprung-Russell diagram. Also indicated are several WC stars (i.e. carbon sequence Wolf-Rayet stars). Tramper et al. (2015).

Model showing the evolution of the surface mass fractions of the WO star WR102 since the onset of core-helium burning. Tramper et al. (2015).

Tramper et al. (2015), “Massive stars on the verge of exploding: the properties of oxygen sequence Wolf-Rayet stars”, arXiv:1507.00839 [astro-ph.SR]

Wednesday, July 22, 2015

A Saturn-Mass Planet beyond the Snowline of an M Dwarf Star

Gravitational microlensing is a powerful technique for detecting exoplanets that orbit their host stars beyond the snowline (i.e. the distance from a star where temperatures are cool enough for water-ice and other volatiles to condense). Beyond the snowline, a protoplanetary disk around a star is expected to contain more material, allowing for the formation of more massive planets. When a foreground star crosses the line-of-sight to a background star, the gravity of the foreground star can act as a lens, magnifying the light from the background star. The change in the brightness of the background star with time is measured in the form of a light curve. If the background star hosts a planet, the planet’s own gravity can induce a “spike” in the light curve of the background star.

Using the technique of gravitational microlensing, Fukui et al. (2015) present the discovery of a Saturn-mass planet with ~0.34 times the mass of Jupiter orbiting an M dwarf star with ~0.39 times the Sun’s mass at a projected separation of either ~0.74 AU (close model) or ~4.3 AU (wide model). The planet is identified as OGLE-2012-BLG-0563Lb and it is the 5th sub-Jupiter-mass (i.e. between 0.2 to 1.0 times the mass of Jupiter) to be found around an M dwarf star through gravitational microlensing. Although it is clear that there is a population of sub-Jupiter-mass planets around M dwarf stars, there appears to be a paucity of Jupiter-mass planets (i.e. planets with ~1 to 2 times the mass of Jupiter) around the same type of star. This suggests that planet formation via the core-accretion mechanism rarely produces Jupiter-mass planets around M dwarf stars due to the lack of material in the protoplanetary disk.

Fukui et al. (2015), “OGLE-2012-BLG-0563Lb: a Saturn-mass Planet around an M Dwarf with the Mass Constrained by Subaru AO imaging”, arXiv:1506.08850 [astro-ph.EP

Tuesday, July 21, 2015

Two Record-Breaking Compact Stellar Systems

Following the discovery of the densest known galaxy, M60-UCD1, Sandoval et al. (2015) present the discovery of M59-UCD3 and M85-HCC1 - two record-breaking compact stellar systems. Since the density of stars in a galaxy decreases gradually away from the center, one way to express the size of a galaxy is by its half-light radius. The half-light radius is basically the size of the volume of space that is contributing to half the galaxy’s brightness and it can also apply to other stellar systems.

M59-UCD3 is an ultracompact dwarf (UCD) galaxy similar in size to M60-UCD1. It has a half-light radius of roughly 70 light years, but it is 40 percent more luminous than M60-UCD1. This makes M59-UCD3 the new densest known galaxy. M59-UCD3 is estimated to contain roughly ~180 million times the Sun’s mass and this means an average density of roughly 30 solar masses per volume of space one light year across. For comparison, an observer on Earth can see ~6,000 stars with unaided eyes under “typical” dark sky conditions. However, an observer in the core of M59-UCD3 would see roughly a million stars in the sky.

M85-HCC1 is an extremely compact stellar system with a half-light radius of roughly 6 light years, similar in size to a typical globular cluster. It is estimated to contain ~12 million times the Sun’s mass and has an average density of roughly 3,000 solar masses per volume of space one light year across. This is ~100 times the density of M59-UCD3. For comparison, the nearest star to the Sun is Proxima Centauri, located 4.24 light years away.

M59-UCD3 and M85-HCC1 are estimated to be ~9 billion and ~3 billion years old, respectively. They are most likely the remnant cores of what were once much larger galaxies that got tidally-stripped. This scenario can be tested for M59-UCD3 by looking to see if it contains an “overweight” supermassive black hole (SMBH) since almost all massive galaxies host SMBHs. M60-UCD1, the previous record holder for the densest known galaxy, is known to host an “overweight” SMBH comprising a whopping ~15 percent of the galaxy’s total mass.

- Sandoval et al. (2015), “Hiding in plain sight: record-breaking compact stellar systems in the Sloan Digital Sky Survey”, arXiv:1506.08828 [astro-ph.GA]
- Strader et al. (2014), “The Densest Galaxy”, arXiv:1307.7707 [astro-ph.CO]
- Seth et al. (2014), “A Supermassive Black Hole in an Ultracompact Dwarf Galaxy”, arXiv:1409.4769 [astro-ph.GA]

Monday, July 20, 2015

Properties of a Pair of Juvenile Brown Dwarfs

Observations of DE0823-49 indicated that it is a system composed of a pair of brown dwarfs identified as DE0823-49A (primary) and DE0823-49B (secondary) with spectral types L1.5 ± 0.6 and L5.5 ± 1.1, respectively. Both objects orbit each other every ~248 days. The estimated effective temperatures of DE0823-49A and DE0823-49B are 2,150 ± 100 K and 1,670 ± 140 K, respectively. Models predict that both objects have masses between 0.028 to 0.063 times the Sun’s mass for DE0823-49A and between 0.018 to 0.045 times the Sun’s mass for DE0823-49B, with a mass ratio (i.e. mass of DE0823-49A relative to DE0823-49B) of 0.64 to 0.74. This places both objects in the brown dwarf mass regime and also below the lithium-burning mass limit of 0.065 times the Sun’s mass.

The age DE0823-49 is estimated to be between 80 million to 500 million years. This is consistant with the presence of lithium detected on DE0823-49A which implies it has a mass of less than 0.065 times the Sun’s mass. An object more massive that that is expected to burn away its lithium. Given that DE0823-49A is less than 0.065 times the Sun’s mass and still relatively hot, and that brown dwarfs cool gradually as they age, the age of DE0823-49A cannot exceed 500 million years. Since both DE0823-49A and DE0823-49B formed together, they should have the same age. With an age of less than 500 million years, DE0823-49 is a pair of juvenile brown dwarfs. It is also relatively nearby, located only 67.5 light years away.

Sahlmann et al. (2015), “DE0823-49 is a juvenile binary brown dwarf at 20.7 pc”, arXiv:1505.07972 [astro-ph.SR]

Sunday, July 19, 2015

Hot-Neptune GJ 436b has a Comet-Like Tail

GJ 436b is a Neptune-mass exoplanet in a close-in orbit around its parent star. The planet is so intensely irradiated by its parent star that its own gravity is not strong enough to hold on to the hydrogen in its atmosphere, causing the hydrogen to escape into space to form a large exospheric cloud which surrounds and trails the planet. This discovery was made in the ultraviolet band with the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST).

Artist’s impression of GJ 436b. Image credit: Mark Garlick/University of Warwick.

GJ 436b transits in front of its parent star every 2.64 days. The transit depth in the ultraviolet band is 56.3 ± 3.5 percent (1σ), far deeper than the transit depth of 0.69 percent in the optical band. This means that over half the disk of the star is eclipsed in the ultraviolet band. Furthermore, in the ultraviolet band, the transit of GJ 436b starts ~2 hours before and ends more than 3 hours after the ~1 hour optical transit. Such a transit signature is believed to be due to the passage of a large cloud of hydrogen surround and trailing the planet.

The mass-loss rate of GJ 436b is estimated to be between ~10² to 10³ tons per second. At this rate, the planet loses only ~0.1 percent of its atmosphere per billion years, far too small to deplete the planet’s atmosphere over the lifetime of its parent star. However, planets similar to GJ 436b that orbit closer to their host stars can experience much more dramatic mass-loss, possibly even causing them to erode down to their rocky cores.

Ehrenreich et al., “A giant comet-like cloud of hydrogen escaping the warm Neptune-mass exoplanet GJ 436b”, Nature 522, 459-461 (25 June 2015)

Saturday, July 18, 2015

Illuminating the Dark Sides of Tidally-Locked Planets

Figure 1: Artist’s impression of a habitable planet.

Red dwarf stars are by far the most common stars in the Universe. Observations by NASA’s Kepler space telescope have shown that Earth-sized planets are ubiquitous around red dwarf stars. Red dwarf stars are much smaller and much less luminous than stars like the Sun. For a planet around a red dwarf star to receive as much insolation as Earth gets from the Sun, the planet needs to orbit much closer to the star. As a result, the planet is likely tidally-locked, with a permanent dayside hemisphere and a permanent nightside hemisphere.

If an extraterrestrial civilisation evolved from such a planet or migrated in from elsewhere, it may wish to make better use of the planet’s surface by illuminating the permanent nightside. The most obvious way is to place mirrors in space to illuminate the planet’s dark side. Either a single large mirror could be stationed at the L2 Lagrange point or a fleet of smaller mirrors could be placed into orbit around the planet (Figure 2). From a feasibility standpoint, a fleet of smaller mirrors is less technically challenging than a single large mirror at the L2 Lagrange point.

Figure 2: Schematic illustration of three methods of dark-side illumination (not to scale). Planetary grayscale bands indicate different levels in stellar illumination. In the three cross-sectional drawings, (a) shows a large circular or annular mirror stationed at the L2 Lagrange point, (b) shows multiple small mirrors in circular orbits, (c) shows multiple small mirrors in elliptical orbits designed to maximise the duty cycle of the mirrors.

Illuminating the dark side of a tidally-locked planet with a fleet of orbiting mirrors will warm up the planet’s dark side and lead to a smaller day-night temperature contrast on the planet. This will slow the transfer of heat from the dayside to the nightside, causing the dayside to warm up. However, the mirrors can obscure some of the starlight falling on the planet’s dayside and this can keep the dayside from warming up excessively.

To provide sufficient illumination, a fleet of orbiting mirrors is expected to have a total reflective surface area comparable to the cross-sectional area of the planet. As a result, if the planet were to transit its parent star, the presence of such a fleet of orbiting mirrors could be detected from the unique transit light curve. In order to model and understand such a transit light curve, the fleet of mirrors orbiting the planet can be approximated as a translucent annulus around the planet.

During the initial phases of the transit (i.e. ingress), only the mirrors block starlight, so the light curve decreases relatively gradually. When the planet itself starts to transit, the light curve begins to decrease more steeply. The light curve decreases gradually again when the planet is completely in front of the star and the remaining fleet of mirrors, approximated as a translucent annulus around the planet, blocks more starlight. Once the fleet of mirrors are completely in front of the star, the transit light curve resembles that of a larger planet. 

A fleet of orbiting mirrors basically lengthens the transit duration and deepens the transit depth. If the fleet of orbiting mirrors is designed for maximum efficiency such that all the reflected starlight is directed to illuminate the planet’s dark side, then the eclipse duration (i.e. duration where the planet passes behind the star) will be smaller than the transit duration. A fleet of orbiting mirrors around a planet, if present, could be detectable by the James Webb Space Telescope (JWST).

Figure 3: Transit light curves for a planet with 2 Earth radii orbiting an M5 red dwarf star (dashed line: planet alone), the same planet surrounded by a fleet of orbiting mirrors extending to 3 planetary radii (solid line: mirror + planet), and a planet without mirrors but large enough to produce a light curve with the same depth of transit (dotted line: large planet). Korpela, Sallmen & Greene (2015).

Figure 4: Transit light curves that result when a planet with 2 Earth radii, located in the middle of an M5 red dwarf star’s habitable zone, transits in front of the star. In all cases, the planet is surrounded by a fleet of orbiting mirrors extending to 3 planetary radii (solid), 2 planetary radii (dotted) and 10 planetary radii (dashed). Korpela, Sallmen & Greene (2015).

Korpela, Sallmen & Greene (2015), “Modeling Indications of Technology in Planetary Transit Light Curves -- Dark-side illumination”, arXiv:1505.07399 [astro-ph.EP]