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The Apparent Brightness and Size of Exoplanets and their Stars

posted Oct 12, 2011, 11:53 AM by Abel Mendez   [ updated Jun 30, 2012, 12:10 PM ]
One thing that we are trying to reproduce for the Habitable Exoplanets Catalog is the visual appearance of exoplanets and stars. This includes the color, brightness, and size of the star and exoplanet from the point of view of the exoplanet and a hypothetical moon, respectively. We decided to use the Earth-Moon distance as the reference distance because this is a something we can relate too, everybody knows how big and bright is the Moon in the night sky. We are developing the Scientific Exoplanets Renderer (SER) to create the visualizations, including potential colors. Here we will just discuss how big and bright are exoplanets as seen from moons

    The relative brightness of stars and exoplanets can be conveniently measure with the apparent magnitude scale where +6.5 is close to the visual limit and -27 is the brightness of the Sun. This logarithmic scale tries to match the visual response of the eye to light in a similar way as the intensity level scale is used for sound. The brightness and size of exoplanets and their stars can be calculated from
where ms and mp are the apparent magnitude of the star and exoplanet, respectively, Ls is the visual luminosity of the star (in solar units), dp is the distance from the exoplanet to the star (in AU), do is the distance of the observer from the planet or star (in AU), a is the planet's geometric albedo (usually ~0.3), rp its radius (in Earth radii units), and p(zeta) the phase integral (a value from zero, dark side, to one, full phase), ∂ is the planet or star apparent size (in degrees), and r is the radius of the planet or star (in Earth radii units). All distance in the equations are in astronomical units (AU). Figure 1 shows a visual comparison of these parameters for Solar System planets at a variable distance (to appear the same size) and Table 1 shows values for a fixed Earth-Moon distance.


Figure 1. Relative brightness to the human eye of planets of the Solar System as seem from a distance of three times their radii (hence they appear to be the same size). The intensity scale for the image was adjusted to show brightness between -14 to -25 apparent magnitudes. Even Neptune (last) is still brighter than the Moon in this scale so this is like looking at the planets from orbit with sunglasses (otherwise they will be to bright for the screen). A similar graphic will help to compare exoplanets visualizations for the Habitable Exoplanets Catalog.

Table 1. Comparison of the Relative Moon Size (RMS) and Relative Moon Magnitude (RMM) for Solar System objects. The RMS and RMM compares the apparent size and brightness, respectively, of any planet with the Moon as seen from an Earth-Moon distance. A RMS value of one means equal apparent size as the Moon (31 arcseconds) and a RMM of zero as bright as the Moon (-12.7 apparent magnitude) with negative values brighter and positive values dimmer (the RMM is just a Moon-fixed apparent magnitude scale). Almost all Solar System planets will look larger and brighter than the Moon as observed from an Earth-Moon distance at their respective positions. Only Neptune will appear larger but as bright of the Moon. Other planetary properties shown are mass (M), radius (R), period (P), distance from the Sun (d), equilibrium temperature (Teq), Habitable Zone Distance (HZD), geometric albedo (gA), apparent size (∂), and apparent magnitude (m).

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    Name   M(EU)   R(EU)  P(yrs)   d(AU)  Teq(K)     HZD      gA    ∂(°)       m     RMS     RMM

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 Mercury    0.06    0.38    0.24    0.39    434.   -1.46   0.106     0.7   -15.7     1.4    -2.9

   Venus    0.81    0.95    0.62    0.72    184.   -0.93   0.650     1.8   -18.3     3.5    -5.6

   Earth    1.00    1.00    1.00    1.00    254.   -0.50   0.367     1.9   -17.1     3.7    -4.3

    Mars    0.11    0.53    1.88    1.52    210.    0.33   0.150     1.0   -13.8     1.9    -1.1

 Jupiter  318.00   10.97   11.86    5.20    110.    6.12   0.520    21.0   -19.1    40.6    -6.3

  Saturn   95.20    9.14   29.45    9.54     81.   12.95   0.470    17.4   -17.3    33.7    -4.5

  Uranus   14.50    3.98   84.02   19.19     58.   28.15   0.510     7.6   -14.0    14.6    -1.3

 Neptune   17.10    3.87  164.79   30.07     47.   45.28   0.410     7.4   -12.7    14.2     0.0

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    TrES-2b (or Kepler-1b) is an exoplanet orbiting the star GSC 03549-02811 located 718 light years away in the constellation of Draco. TrES-2b is a gas giant with a bulk composition similar to that of Jupiter but located much closer to a star similar to our Sun. It is the darkest known exoplanet, reflecting less than 1% of its star light (Kipping & Spiegel, 2011). However, if we were in a moon around TrES-2b and at the same Earth-Moon distance it will have a huge 27° apparent size in the sky and a magnitude of up to -27 (full phase), or as bright as the Sun looks now from Earth. The star will be of a scorching -34 magnitude. So even that this is a relatively dark planet, and depicted incorrectly as a very dark sphere in many artistic representations, it is still very bright due to its proximity to the star.

    The presented information can be used to compare the relative size and brightness of stars and exoplanets from a desired vantage point, or give a sense of how bright might be a day on the surface of known exoplanets. For example, Kelpler-16 (AB) b, aka "Tatooine," is a planet in the habitable zone that orbits two stars albeit far away. How bright will be a day in this exoplanets? How it will look in the sky from its potential moons? This type of questions will be later answered for the Habitable Exoplanets Catalog.