Monthly Archives: September 2013

Mapping the Galaxy

The Milky Way Galaxy

The Milky Way Galaxy (Source)

Measuring the distance to a star makes use of astrometry – the careful monitoring of a position of a star over time. As Earth orbits the sun, it has a maximum displacement from any given position along its orbit of about 2 AU (i.e., being on the other side of the orbit). By observing the angular change in the apparent position of a star 2 AU apart, simple trigonometry can allow you to calculate the distance to the star.

In the middle of the last century (not terribly long ago from a historical perspective), we knew the distances to very few stars and knew their positions with much poorer accuracy. The FK4 catalogue catalogued the position of stars in the year 1950 with a precision of position of about 0.04 arcsec in the northern hemisphere, and a dismal 0.08 arcsec precision in the southern hemisphere. It was suggested that using a network of astrolabes over ten years could reduce the errors to about 0.03 arcsec, only marginally better. Major obstacles to the advance of stellar cartography was the typical issues that plague amateur astronomers now — atmospheric distortion of stellar images, instrumental instability, and inability for a ground-based observatory to view the entire sky.

In 1966, Pierre Lacroute came up with an idea (that he himself called “weird”) of performing the necessary measurements from a spacecraft, orbiting Earth outside the atmosphere. The idea was presented in 1967 to the IAU where it received a great deal of interest, but the technological capacity at the time (and available rocketry in France) was not accommodating to the idea. The satellite, a 140 kg spacecraft designed to observe 700 stars all over the sky with a precision of 0.01 arcsec, had stability requirements that could not be met by the Diamant rocket used by France at the time.

The idea of a spacecraft to catalogue the distances and positions of a large number of stars evolved over time and was revised and improved for the next decade, while the rest of astrophysics advanced and continued running into the problem of distance scales being poorly known.

“The determination of the extragalactic distance scale, like so many problems that occupy astronomers attention, is essentially an impossible task. The methods, the data, and the understanding are all too fragmentary at this time to allow a reliable result to be obtained. It would probably be a wise thing to stop trying for the time being and to concentrate on better establishing such things as the distance scale in our Galaxy.” — Hodge (1981)

Support for a space-based astrometry mission continued to grow and recognising that France alone did not have the resources necessary to complete the task, the European Space Agency planned and devised a new spacecraft, Hipparcos, to catalogue the positions of 100,000 stars and to determine their positions with an accuracy of 0.001 arcsec (1 milliarcsec).

Hipparcos

Hipparcos

Hipparcos was launched on August 8, 1989 on a 3.5 year mission. It determined the positions of stars, monitored the position over the course of a half year to determine the parallax and thus distance to the star, monitored the position over the course of the entire mission to determine the proper motion of the star in space, measured the spectrum of stars to determine their composition, and performed radial velocity measurements on these stars to determine their motion toward or away from Earth. In total, 118,200 stars were observed with high precision observations (published in 1997), with another 2.5 million stars observed with lower precision (published in 2000).

Hipparcos data has practically revolutionised astronomy. With the knowledge of the positions and motions of over a hundred thousand stars in hand, we’ve been able to understand the structure and dynamics of nearby clusters, understand the local structure of the Galaxy, understand the orbits and true orientations of binary star systems, and more. Even an extrasolar planet transit was observed (though it was not known until the planet was discovered later).

This brings us to today. This Hipparcos catalogue remains as the best available source of uniform parallaxes and positions. It is time, however, to take another step forward, with greater precision, a larger sample, and newer science. The successor to Hipparcos is called GAIA – Global Astrometric Interferometer for Astrophysics – however it will not use interferometry due to a design change.

Gaia will essentially do exactly what Hipparcos did, but better. Whereas Hipparcos only measured a hundred thousand stars down to brightnesses of V = 9, Gaia will observe over a billion stars with brightnesses down to V = 20. Gaia will measure the angular position of all stars of magnitude 5.7 – 20. For stars brighter than V = 10, it will determine the position with a precision of 7 µas (microarcseconds), a precision of 12 – 25 µas down to V = 15, and 100 – 300 µas down to V = 20. It will acquire their spectrum (from 320 – 1000 nm) to determine their temperature, age, mass, and composition. It will also measure the radial velocity of stars with a precision of 1 km s-1 for V = 11.5, and 30 km s-1 for V = 17.5. Tangential velocities for 40 million stars will be measured with a precision better than 0.5 km s-1.

Gaia

Gaia (Source: ESA)

While the stellar astrophysics enabled by Gaia will be revolutionary in its own right, the unprecedented astrometric precision also makes the mission interesting from an extrasolar planet perspective. Hipparcos was not able to discover any planets on its own, but it was marginally helpful for extrasolar planet science. Planets detected with radial velocity have unknown true masses. The greater the true mass of the planet, the greater the astrometric amplitude of the barycentric motion of the star is (see this post where astrometry is discussed in the context of planet detection). Planets of especially high true masses would therefore have a chance of having their star’s barycentric motion detectable to Hipparcos. Otherwise, Hipparcos data could be used to set upper limits to the true mass of the planet, by knowing that it’s astrometric effect must be sufficiently low so as to not have been detected by Hipparcos (an upper limit to the astrometric amplitude and thus the planetary mass).

The astrometric precision and vast number of targets available to Gaia will allow for the detection of a large number of planets. Astrometry is, of course, less biased toward high values of the planetary orbital inclination, and will permit us to know the true mass of the planet and orientation of the orbit in 3D space. Still, several complications are expected to arise based on nearly two decades of radial velocity experience.

Just like with radial velocity (and, actually, science in general), models will need to be fitted to data points to yield high-quality fits, however as Doppler spectroscopy has shown us, planetary systems can often feature several components all contributing to the barycentric velocity profile of the star, complicating radial velocity fitting in the same way it can be expected to complicate astrometric fitting. Radial velocity surveys can often produce more than one model that fit the data nicely, where both models may disagree on certain aspects of the orbit, or even number of planets. Astrometry is likely to be prone to the same problems. In the case of astrometry, it may even be harder because of the greater number of free parameters – ascending node, inclination, etc, issues that need to be modelled for an astrometric fit that could usually be ignored for a radial velocity fit.

These challenges can be addressed and handled, and the Gaia data will be wonderfully productive to extrasolar planet science. It is hard to know how many planets we can expect Gaia to discover, because statistics for planets in intermediate-period orbits are still unconstrained, but with the accuracy and large number of stars Gaia will observe, it is likely that Gaia will discover thousands of giant planets. It will be sensitive to Jupiter analogues out to 200 parsecs.

Gaia Results

Gaia Results (Source: Sozzetti (2010)

What about transiting planets? A transit of HD 209458 b was squeezed out of Hipparcos data, which was not at all optimised for transiting planet science. Can Gaia be expected to detect transiting planets? As far as photometric precision, Gaia is expected to achieve 1 mmag precision for most objects Gaia will observe, down to V ~ 15, and 10 mmag precision at the worst case of V ~ 20. For most hot Jupiter systems, mmag precision is indeed sufficient for transit detections. The next major issue is cadence.

Focused transit searches tend to be high-cadence, narrow field observations, whereas Gaia is an all-sky, low cadence observatory. On average, each star will be observed by Gaia 70 times, giving us 70 measurements for a light curve of any given star with a baseline of five years. While 70 measurements spread out over five years seems dismal (and let’s not sugar-coat the issue — for a transit search, it is dismal, but Gaia is not designed to be a transit search mission), but for a planet in a short period orbit, perhaps three or four measurements may occur while the planet is transiting. Obviously, the longer the orbital period, the less a fraction of the planet’s orbital period is spent in-transit, and the fewer transits will be observed by Gaia. Since only 70 measurements will be taken, Gaia is severely biased toward short-period transiting planets.

Early studies suggested wildly fantastic transiting planet yields. Høg (2002) estimated over a half million hot Jupiters and thousands of planets in longer periods would be found, based on the (unrealistic) assumption that a transit could be identified based on a single data point and other oversimplifications. Robichon (2002) suggested that Gaia will detect 4,000 – 40,000 transiting hot Jupiters under the assumption that each star would receive an average of 130 measurements, however the currently planned Gaia mission has instead 70 measurements per star.

Dzigan & Zucker suggest that Gaia could potentially detect sub-Jupiter-sized planets around smaller stars, and that a ground-based follow-up campaign can easily observe hints of transiting planets that show up in Gaia data. They also suggest that a few hundred to a few thousand hot Jupiters could be found in Gaia photometry.

While Gaia will perform km s-1 radial velocity measurements on millions of stars, this precision level is simply not sufficient to detect even hot Jupiters. It will, however, be able to tell if a transiting planet candidate is a brown dwarf instead, or an eclipsing binary star, allowing for one method of ruling out false positives. Interestingly, the astrometric fit to the orbit of a planet will have the inclination of the planetary orbit sufficiently well-characterised that a list of planets that are likely to transit can be compiled and followed-up with ground-based radial velocity and photometry. These long-period transiting planets will certainly prove valuable – they will be likely to host detectable rings and moons.

ESA will launch Gaia on a Soyuz ST-B rocket in November of this year. It will take five years after a commissioning phase for the total extrasolar planets science results to become known. It will be very exciting to see what giant planets exist in the solar neighbourhood. They will attract interest in follow-up observations to discover smaller, inner worlds that may exist. Gaia has the potential for flagging the first solar system analogues in the solar neighbourhood for dedicated study.