Posts Tagged ‘Doppler’

Could there be as many as 17 billion Earth-like planets in our Milky Way galaxy?
This has been suggested in a paper presented in this last few weeks at the semi-annual meeting of the American Astronomical Society. The lead author of the papaer is Dr. Francois Fressin, who was part of the team that discovered the first Earth-sized planets in late 2011.

An artist's representation of exoplanets

An artist’s representation of extra-solar planets

Dr. Fressin has analysed data from the Kepler mission to come up with his startling figure. But, it should be pointed out that a lot of assumptions come into this number, so I thought I would explain what some of these assumptions are, as well as explaining a little about the Kepler mission.

Wobbling stars

The history of detecting extra-solar planets (exoplanets) goes back to the mid 1990s. The detection technique used for the vast majority of the early discoveries was to detect the wobble that an orbiting planet produces in the position of its host star. When a planet orbits a star they in fact both orbit the system’s centre of mass. This may be a point actually within the body of the star. The larger the ratio between the mass of the star and the mass of the orbiting planet, the closer the centre of mass will be to the centre of the host star.

The dopper shift in the spectrum of a star produced as an unseen planet orbits it

The dopper shift in the spectrum of a star produced as an unseen planet orbits it

Our Earth produces a wobble in the Sun, but it is too small a wobble for us to be able to detect. However, Jupiter, the most massive planet in our Solar System, produces a wobble in the Sun’s position that is detectable.

If we are looking at a star with a Jupiter-mass planet going around it then, as long as this planet is not too far from its host star, we should be able to detect the wobble in the position of the host star. But, only if we are looking at it with the right orientation. This is because we do not directly see the wobble in the host star, what we observe is a rhythmic Doppler shift in the spectral lines of the star, which shows that it is moving towards and away from us in a regular manner.

If we were to look at such a system face-on (at right angles to the plane of orbit of the planet) we would not detect any wobble, as the wobble would be side-to-side. The effect is maximum when we view the system edge-on, and will be less for other angles. More precisely, if \theta is the angle between the plane of orbit of the planet and our line of sight, then the observed wobble to our line of sight will vary as \cos\theta, maximum when \theta=0^{\circ} (edge-on) and zero when \theta=90^{\circ} (face-on).

Because of the accuracy with which we can measure Doppler shifts, this technique for finding exoplanets tends to predominantly find planets with masses as large or larger than Jupiter orbiting often much closer than our Earth orbits the Sun.

The Kepler mission

The Kepler mission was launched in 2009 and uses an entirely different technique, known as the transit technique. If a planet passes in front of its host star, the light coming from the star will be reduced a small amount as the planet passes across the disk of its host star. Often the amount can be less than 1%, but with our modern-day high accuracy cameras we can detect such tiny dips in brightness.

The dip in light from a star when a planet passes in front of it.

The dip in light from a star when a planet passes in front of it.

Of course, we will only see such a dip if we are viewing the system edge-on or close to edge-one. Depending on how close the planet is to its host star, once the viewing angle is more than a few degrees away from being edge-on, the planet will no longer be seen to pass across the disk of its host star and so no dip in light will be observed.

Although this is a severe limitation, Kepler gets around this by viewing many stars simultaneously. Kepler constantly stares at the same small patch of the sky (some 1/400th of the sky), but in its field of view there are over 150,000 stars. To date, Kepler has found some 2,740 candiate exoplanets, a much larger figure than the number of exoplanets found using the wobble technique.

The Kepler mission telescope, which was launched in 2009.

The Kepler mission telescope, which was launched in 2009.

I should also point out that not only orbiting planets can cause a dip in a star’s light. Some stars are intrinsically variable, but we know which kinds of stars these are so can ignore those. Also, something else could come between us and the star, such as a clould of gas and dust, or another passing star. So, the dip in light of a particular star needs to be observed to be repeating for us to know that it is due to a planet in orbit about it.

In addition to its greater number of detections, the transit technique is able to observe planets as small as the Earth orbiting their host star, because we are capable of detecting even such tiny dips in the light of the host star. In late 2011, Dr.Fressin and his team made the first announcement of the detection of Earth-sized exoplanets which were detected by the Kepler mission.

What can we learn from the dips of light

It turns out that we can learn quite a lot about the exoplanet from observing the dip in light. First, by observing the time between the dips in the star’s light we can determine how long the planet takes to orbit its host star (the period of orbit). Also, by analysing the amount the host star’s light dims, we can work out the physical size of the planet as we know from the spectral type of the star what it’s physical size is.

In order to confirm that a transit event is indeed an orbiting planet we need to follow up the observation using the Doppler-shift technique to see its radial wobble. The Doppler-shift technique allows us to determine the mass of the exoplanet, because we know from the host star’s spectral type what its mass is, and so the size of the host star’s wobble is related to the ratio of the host star’s mass to the exoplanet’s mass.

By combining the two techniques we can also determine the exoplanet’s density, as the transit technique tells us its size and the Doppler-shift technique tells us its mass. The density allows us to say whether the exoplanet is gaseous or rocky.

Is 17 billion reasonable?

So far Kepler has detected some 2,740 possible exoplanets, from the more than 150,000 stars that it is observing. As scientists only recently announced a 461 new candidates, clearly new detections are still being made. Dr. Fressin calculates that 17% of stars host a planet up to 1.25 times the size of the Earth. This figure is based on several steps of calculations – including how many of the 2,740 detections are Earth-sized planets and how many of the approximately 150,000 stars in the field of view have the correct orientation for us to see a transit event. The figure of 17% that Dr. Fressin has determined is then multiplied by the calculation that there are 100 billion stars in our Galaxy to come up with the figure of 17 billion Earth-like planets.

By anyone’s reckoning, 17 billion Earth-like planets is a lot! Even if the figure is found to be too high, it is unlikely to be out by more than a factor or 10, probably much less. This still leaves more than 2 billion Earth-like planets in our Milky Way galaxy, a very large number. Not all of these Earth-like planets would be suitable places for life to have evolved; they may be orbiting high-mass stars whose lifetimes are too brief for life to evolve, or they may be too close or too far from their host star to be suitable.

It seems to me that there is every likelyhood of not only life but intelligent life elsewhere in our Galaxy. Whether we ever make contact with extra-terrestrial civilisations is a whole different matter.


This interesting histogram has recently been produced by NASA, as their Astronomy Picture of the Day (APOD) for Saturday the 12th of January 2013.

A histogram produced by NASA showing the percentages of different types of exoplanets.

A histogram produced by NASA showing the percentages of different types of exoplanets.

As the caption to the image on NASA’s APOD page says, these percentages are for predominantly planets in orbits close to the host star, within the equivalent of Mercury’s orbit. This is because Kepler is more likely to detect a transit event when the exoplanet is in a close orbit, because a larger range of viewing angles will still lead to our seeing a transit event.

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