Sunrise on TRAPPIST-1d
Earlier this month, Belgian astronomers from the University of Liege announced the discovery of the first Earth-Like planetary system found in the solar neighborhood. Originally published in the Journal Nature for 2 May, 2016, the announcement describes the initial discovery as the result of a methodical, organized program of searching designated regions of the sky with sub-meter class telescopes located atop ESO’s La Silla Observatory in Chile’s high Atacama desert, 600 kilometers north of the Chilean capital, Santiago de Chile.
TRAPPIST (TRAnsiting Planets and Planetesimals Small Telescope)
TRAPPIST consists of two robotic 0.6 meter telescopes located atop ESO’s La Silla Observatory and at the Oukaïmden Observatory in Morocco. The observations that led to this exciting new discovery were made from the La Silla station between September and December, 2015 followed by the 2 May, 2016 publication of the results in the science journal Nature.
The Transit Method
Using the same technique as the Kepler Space Telescope, the TRAPPIST-1 system was discovered using the Transit Method where the transiting planets cause a reduction in the host star’s total flux as they transit. In the case of all three planets of the TRAPPIST-1 system, a change in flux of one part in 131 is required to detect an Earth size planet transiting its host star. This threshold is certainly attainable for a limited platform unlike the technical requirement of Kepler whose prime directive is to detect Earth-like planets orbiting sun-like stars in their habitable zone, where a change in flux of one part in 10,000 is required to detect a transiting planet. The irradiance of any star is a measure of its output from its total area thus, the output from a section that is eclipsed will reduce the total observed output by the area of the object that is between the star and the observer. Follow-up observations with larger telescopes were made that included the HAWK-I instrument on ESO’s 8 meter Very Large Telescope on Paranal, also on Chile’s Atacama high desert plateau. These observations have determined that the planets orbiting TRAPPIST-1 have sizes very similar to that of Earth with the two inner planets having orbital periods of about 1.5 days and 2.4 days respectively. The third planet, TRAPPIST-1d (pictured above), has a less well determined period in the range of 4.5 to 73 days and a correspondingly uncertain orbital distance of 0.022 – 0.146 AU.
Design and Philosophy
Given their relatively small size and low luminosity compared to the sun, cool, Red Dwarf Stars lend themselves to detection of transiting Earth-size planets. Unlike the requirements of Kepler, where the relative area of an Earth-size planet is one part in 10,000 compared to a sun-like star, the relative areas of an Earth-like planet and a cool, Red Dwarf is one part in 131. Add to that, the relative brilliance of the sun, the technical requirements become substantial in detecting Earth-like planets orbiting sun-like stars. This speaks to the relatively large proportion of planets detected by Kepler as being relatively large, Jupiter-scale planets. Given the abundance of low-mass, cool, Red Dwarf stars, their longevity and low relative luminosity, a new philosophy and approach to detecting Earth-like planets has been adopted. It is now thought that our best chance of finding our analog, our reflection in the cosmos will be on a planet orbiting one such star, a cool, low-mass star such as TRAPPIST-1. The TRAPPIST telescope network joins other network of other such robotic telescopes, targeting cool, low-mass stars, looking for transiting, Earth-scale planets given the lower technical threshold and demand in detecting transiting Earth-scale planets orbiting cool, low-mass stars.
At 39 light years distant in the constellation Aquarius, TRAPPIST-1 is the first system found using the TRAPPIST network, hence the designation ‘1’. Exoplanet naming convention is such that any planets found orbiting a star bear the star’s name followed by a letter starting with “b” for the first planet, with each subsequent planet being assigned the next letter in the alphabet.
Stellar Condensation Theory
Stellar condensation theory teaches us that stars form from collapsing pockets of cold gas and dust of higher relative density in the Interstellar Medium (ISM) between 10 and 100 solar masses. As the pocket collapses its core heats up and if it reaches at least 10 Million Kelvin, thermonuclear reactions begin in the core and a star is born; the minimum mass required for this to occur is 7.2% the sun’s mass. A star at this lower threshold is said to be at the “Hydrogen Burning Mass Limit” and is classified as a Red Dwarf; TRAPPIST-1 is such a star. Red Dwarf stars are the most abundant in the universe and will live hundreds of times longer than stars in the sun’s mass range with lifetimes measured in trillions of years, not billions such as the sun’s. An object that does not achieve thermonuclear ignition in its core is said to be substellar and is classified as a “Brown Dwarf”. TRAPPIST-1 is barely above the Hydrogen Burning Mass Limit at 8% the sun’s mass; such stars have an additional designation, being regarded as “ultracool“. The property specifics for TRAPPIST-1 are:
- Effective temperature: 2,550 K compared to the sun’s 5,780 K. This is essentially the average temperature of the star’s photosphere not to be confused with the star’s internal temperature
- Luminosity: 5/10,000 of the sun’s or 5 parts in 10,000 = 0.0005 solar
- Mass: 8% solar = 1.592E-29 Kg (1.592 with 26 zeros following) or 84 Jupiter masses
- Radius: 11.5% Solar = 80,040 kilometers compared to Jupiter’s 69,911 equatorial radius.
- Projected hydrogen burning lifetime: 160 solar or 3.03 trillion years. This means that the sun could live and die 160 times during this star’s productive lifetime. This aspect of any star is derived from what is known as the Mass/Luminosity relation. These ultracool stars need to expend very little hydrogen fuel to maintain the equilibrium state between outward gas pressure from the nuclear fusion occurring in the core and the inward crush of gravity. Luminosity increases as the forth power of the mass with hydrogen fuel consumption quickly increasing as the star’s mass increases.
- Average density: 74,157 Kg/M^3 which is 53 solar! The sun’s average density is 1,410 Kg/M^3, so the average density of TRAPPIST-1 is 53 times that of the sun! This result is consistent with an object that is 83 Jupiter masses occupying a volume 1.5x that of Jupiter. As a reference, the density of water is 1,000 Kg/M^3.
The following chart compares the distances of the system’s planets and our inner solar system and the prevailing temperatures at those distances for both TRAPPIST-1 and the sun. Distances are measured in terms of Astronomical Units (AU), the distance from the Earth to the sun. The labels HZ1 and HZ2 indicate the inner and outer limits of the star’s habitable zone, the region around any star where the prevailing temperature from the star’s irradiance is such that water can exist in a liquid state. Take note of how hot it would be on those planets if they orbited the sun. Also note the temperature for a planet in orbit around TRAPPIST-1 at 1 AU, the distance from the earth to the sun; this the prevailing temperature at Pluto in our own solar system! The prevailing temperature for a planet orbiting TRAPPIST-1 at Mercury’s orbital radius is the prevailing temperature at Uranus in our own solar system! The chart is color coded to indicate if the planet is in the habitable zone for either the sun or TRAPPIST-1. Note the red coloration for the prevailing temperature at 1 AU, the distance from the Earth to the sun, suggesting that we are inside the inner boundary of the sun’s habitable zone; this is in fact true. Also note, the prevailing temperature at Mars’ distance from the sun of 1.5 AU. Since the orbital radius (distance to the host star) of planet 1d has a significant uncertainty, a value of 0.030 AU was chosen so as to keep it within the habitable zone while still being within the acceptable range given of 0.022 and 0.146 AU. Anything beyond 0.046 AU places 1d outside the habitable zone creating the situation where the first two planets are two hot and the third, 1d, is too cold.
Green indicates the prevailing temperature is within the freezing and boiling points of water (this is where water would be in a liquid state), red, above boiling and blue, below freezing. All temperatures are in Kelvin with a legend on the right. Note: the sun’s power output of 3.85 E-26 watts (3.85 with 24 zeros following), water boils at 373 Kelvin and freezes at 273 Kelvin. The Kelvin temperature scale is widely used in astronomy and relates temperature to absolute zero where zero Kelvin would be absolute zero. Note that the prevailing temperatures scale beautifully with our own solar system in terms of position and temperature relative to the host star and that the only planet in the habitable zone is 1d, the third planet from the host star! This chart highlights the dramatic difference the host star’s luminosity has on its planetary environment.
TRAPPIST-1 Planetary System
The following chart illustrates and compares the macro properties of each of the system’s planets. Note the mass of each of the planets is in kilograms and has yet to be determined experimentally and the mass listed is a theoretical value based on a density of 5, 000 Kg/M^3, where the average density of Earth is 5,510 Kg/M^3. It would be safe to say that the mass listed is probably +/- 10% of its actual value. As a reference, the mass of the Earth is 5.98 E-24 kg. The published study indicated the most probable orbital period for planet ‘d’ is 18.2 days, corresponding to a distance of 0.0588 AU, a distance that places TRAPPIST-1d outside the Habitable Zone. A nominal orbit of 0.030 AU places it comfortably within the Habitable Zone for the star. In the study, they characterize the orbit as ‘circular’, an inference suggesting a very small eccentricity for the orbit, approaching that of a circle (e = 0). Truly circular orbits don’t exist in nature due to the mutual gravitation of all bodies in a particular system.
The TRAPPIST-1 system will be an excellent target for the James Webb Space Telescope when it is deployed in 2018.
ESO Journey Through The TRAPPIST-1 System
Imagination is more important than knowledge
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