21May2019

Why You Can’t See Extrasolar Planets With Your Telescope

The most powerful telescopes in the world are unable to see most of the planets orbiting other stars. One rare exception to this required the European Southern Observatory’s 8.2 meter Yepun Very Large Telescope.

That’s a 26.9 foot aperture, or opening to let in light. The one scope has an angular resolution of 0.05 arc-second. That’s an angle equal to one part in 72,000 of one degree of arc—a very tiny angle, indeed. The dimmest star visible with such a telescope is about 21.4 visual (apparent) magnitude.

In the case of this one particular exception, the planet (2M1207b) is huge—thought to be 3.3 times the mass of Jupiter, while its “sun” is not even a full-fledged star. Instead, it is merely a dim, brown dwarf, or failed star with insufficient mass to trigger its own nuclear furnace. But the brown dwarf has enough heat from gravitational compression to glow sufficiently to be seen in the near infrared.

There are 3 key factors which prevent us from using our personal telescope from seeing, tiny, dim objects like extrasolar planets.

  • Limiting magnitude—the dimmest possible apparent magnitude visible with a specific telescope. This is measured on the standard magnitude scale where negative numbers are very bright and positive, larger numbers are very dim. Our sun, viewed from a distance of 10 parsecs (32.6 light years) would be +4.83. Viewed from Earth, our sun has an apparent magnitude of –26.74. The full Moon has an apparent magnitude of –12.9. And the brightest star in our night sky, Sirius, has an apparent magnitude of –1.47.
  • Resolving power—the smallest angle separating two objects, like two stars or a star and a planet. This is typically measured in arc-seconds (seconds of arc). Our sun has an angular diameter of about 32 minutes of arc (1 degree = 60 minutes; 1 minute = 60 seconds of arc). The angular diameter of Jupiter, as seen from Earth ranges from 29.8–50.1 arc-seconds.
  • Relative brightness—the difference in brightness of a planet and its sun. This is sometimes listed as a brightness factor, like “300,000x brighter,” but more frequently is given as a difference in apparent magnitudes (Δm). From the distance of the Earth from the sun, for instance, we’ve already seen that the sun has an apparent magnitude of –26.74, while the Earth from that same distance has an apparent magnitude of –3.49. The magnitude difference (Δm) between the Earth and sun is about –23.25.

Limiting Magnitude

Every telescope has a limiting magnitude. Stars dimmer than this limit simply won’t be visible. For example, a 300 mm aperture scope (roughly 12 inches) with 250x magnification will allow us to see stars as dim as 15.3 apparent magnitude. Any star (or planet) dimmer than this simply won’t be visible.

From our closest neighboring star system—Alpha Centauri (α Cen)—our Earth would have a maximum apparent magnitude of about 28.72. This would be a “full” Earth, from the far side of our sun from Alpha Centauri. The separation, however, would be virtually zero. In other words, our Earth’s light would be lost in the glare of the sun as seen from our neighboring system. At maximum separation, the Earth would be in half-phase as seen from Alpha Centauri, or about 1 magnitude dimmer (~30). As we can see, this is roughly 15 magnitudes too dim for the 300 mm (or 12-inch) telescope.

Resolving Power

Our next factor involves the resolving power of a telescope which determines the smallest angle the device can detect. For light in the middle of the visible spectrum (about 550 nm, or bright yellowish green) and a scope aperture of 0.3 meters (300 mm), the smallest angle is 0.38 arc-second. In other words, we would be able to discern two stars separated by 0.38 arc-second or more. If the stars were any closer, they would appear as one star in that telescope. A wide range of telescopes are available at various apertures.

For our example of Earth as seen from Alpha Centauri, the maximum separation of Earth from our sun would be 0.748 arc-second. So, if Earth were able to reflect far more light, it might be visible at this separation. As we can see, the resolving power is sufficient, but the limiting magnitude makes it impossible.

Relative Brightness

When we look at stars with our telescope, we see objects of various brightness which appear larger or smaller in our field of view, depending on that brightness. In actual fact, all of the stars we view are considered point sources. In other words, there is no apparent width visible with any of the telescopes commercially available. This means that the brighter a star is, the more the light flares out from that point.

The width of that brightness is not the size of the star. Any planets relatively close to its parent star would thus be drowned out by all that brightness, even though the star itself would be a point of zero actual width. Because planets are huddled in close to their parent suns, seeing the dim world against the powerful glare of its star ma kes the problem of seeing an extrasolar planet even more difficult.

 

Consider for a moment this analogy: Imagine someone shining a Klieg light directly into our face from a dozen meters away. A Klieg light is a carbon arc lamp like those used at a Hollywood movie premier. They’ve also been used to spot bombers at night during war. They are blindingly bright. Now, imagine trying to see the LED face of a digital watch of the person pointing the Klieg light at us. Besides being blinded by the spotlight, our eyes would find it impossible to see the dim, LED numbers on the face of their wristwatch. With the spotlight removed or turned off, we could readily see the LED wristwatch.

In order to improve this condition, we would need to decrease the apparent brightness of the system primary (the planet’s sun) with our telescope. But dimming the star would also dim the planet, making it even harder to see because of the telescope’s limiting magnitude. Using a larger aperture would let in more light making the planet more visible, but also making the parent star far brighter, drowning out the feeble reflection from the planet.

Conclusion

So, though the resolving power of a commercially available telescope may be sufficient to separate a planet from its parent star, the limiting magnitude and relative brightness of star and planet, work against our ability to see extrasolar planets. 

Article Written and Supplied By: Peter Thompson

‘References:

Astronomy for Beginners. (ND). “Best Telescopes Per Aperture Size.” Retrieved on May 4, 2019 from https://astronomyforbeginners.com/

Hawks, Chuck, and Landers, Gordon. (2010). “Telescope Focal Length: Pros and Cons.” Retrieved on May 4, 2019 from https://chuckhawks.com/

telescope_focal_length.htm

Houdart, Robert. (2010). “Telescope Limiting Magnitude Calculator.” Retrieved on May 9, 2019 from http://cruxis.com/scope/limitingmagnitude.htm

Vcalc.com. (Oct. 12, 2018). “Resolving Power of a Telescope.” Retrieved on May 4, 2019 from https://vcalc.com/wiki/sspickle/Resolving+Power+of+a+Telescope

Ventrudo, Brian. (May 4, 2016). “The Five Numbers That Explain a Telescope.” Retrieved on May 4, 2019 from https://cosmicpursuits.com/943/telescopes-explained/

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