Doppler spectroscopy

History

Otto Struve proposed in 1952 the use of powerful spectrographs to detect distant planets. He described how a very large planet, as large as Jupiter, for example, would cause its parent star to wobble slightly as the two objects orbit around their center of mass. |author-link=Otto Struve |access-date=2007-04-27 |access-date = 2009-04-19 |url-status = dead |archive-url = https://web.archive.org/web/20081217034658/http://www.astro.psu.edu/users/alex/astro497_2.pdf |archive-date = 2008-12-17 |author-link = Alex Wolszczan

Advances in spectrometer technology and observational techniques in the 1980s and 1990s produced instruments capable of detecting the first of many new extrasolar planets. The ELODIE spectrograph, installed at the Haute-Provence Observatory in Southern France in 1993, could measure radial-velocity shifts as low as 7 m/s, low enough for an extraterrestrial observer to detect Jupiter's influence on the Sun.{{cite web | access-date = 26 October 2012}} Using this instrument, astronomers Michel Mayor and Didier Queloz identified 51 Pegasi b, a "Hot Jupiter" in the constellation Pegasus. Although planets had previously been detected orbiting pulsars, 51 Pegasi b was the first planet ever confirmed to be orbiting a main-sequence star, and the first detected using Doppler spectroscopy.

In November 1995, the scientists published their findings in the journal Nature; the paper has since been cited over 1,000 times. Since that date, thousands of exoplanet candidates have been identified, many of which have been detected by Doppler search programs based at the Keck, Lick, and Anglo-Australian Observatories (respectively, the California, Carnegie and Anglo-Australian planet searches), and teams based at the Geneva Extrasolar Planet Search.{{cite journal |display-authors = etal |url-status = dead |archive-url = https://web.archive.org/web/20070707104318/http://exoplanets.org/cne.pdf |archive-date = 2007-07-07 |author-link = R. Paul Butler

Beginning in the early 2000s, a second generation of planet-hunting spectrographs permitted far more precise measurements. The HARPS spectrograph, installed at the La Silla Observatory in Chile in 2003, can identify radial-velocity shifts as small as 0.3 m/s, enough to locate many possibly rocky, Earth-like planets.{{cite journal | display-authors=etal

Procedure

A series of observations is made of the spectrum of light emitted by a star. Periodic variations in the star's spectrum may be detected, with the wavelength of characteristic spectral lines in the spectrum increasing and decreasing regularly over a period of time. Statistical filters are then applied to the data set to cancel out spectrum effects from other sources. Using mathematical best-fit techniques, astronomers can isolate the tell-tale periodic sine wave that indicates a planet in orbit.

If an extrasolar planet is detected, a minimum mass for the planet can be determined from the changes in the star's radial velocity. To find a more precise measure of the mass requires knowledge of the inclination of the planet's orbit. A graph of measured radial velocity versus time will give a characteristic curve (sine curve in the case of a circular orbit), and the amplitude of the curve will allow the minimum mass of the planet to be calculated using the binary mass function.

The Bayesian Kepler periodogram is a mathematical algorithm, used to detect single or multiple extrasolar planets from successive radial-velocity measurements of the star they are orbiting. It involves a Bayesian statistical analysis of the radial-velocity data, using a prior probability distribution over the space determined by one or more sets of Keplerian orbital parameters. This analysis may be implemented using the Markov chain Monte Carlo (MCMC) method.

The method has been applied to the HD 208487 system, resulting in an apparent detection of a second planet with a period of approximately 1000 days. However, this may be an artifact of stellar activity. |doi-access=free |display-authors=8 |doi-access=free

Although radial-velocity of the star only gives a planet's minimum mass, if the planet's spectral lines can be distinguished from the star's spectral lines then the radial-velocity of the planet itself can be found and this gives the inclination of the planet's orbit and therefore the planet's actual mass can be determined. The first non-transiting planet to have its mass found this way was Tau Boötis b in 2012 when carbon monoxide was detected in the infrared part of the spectrum.

Example

The graph to the right illustrates the sine curve using Doppler spectroscopy to observe the radial velocity of an imaginary star which is being orbited by a planet in a circular orbit. Observations of a real star would produce a similar graph, although eccentricity in the orbit will distort the curve and complicate the calculations below.

This theoretical star's velocity shows a periodic variance of ±1 m/s, suggesting an orbiting mass that is creating a gravitational pull on this star. Using Kepler's third law of planetary motion, the observed period of the planet's orbit around the star (equal to the period of the observed variations in the star's spectrum) can be used to determine the planet's distance from the star (r) using the following equation:

:r^3=\frac{GM_\mathrm{star}}{4\pi^2}P_\mathrm{star}^2,

where:

• r is the distance of the planet from the star
• G is the gravitational constant
• Mstar is the mass of the star
• Pstar is the observed period of the star

Having determined r, the velocity of the planet around the star can be calculated using Newton's law of gravitation, and the orbit equation:

:V_\mathrm{PL}=\sqrt{GM_\mathrm{star}/r},

where V_\mathrm{PL} is the velocity of planet.

The mass of the planet can then be found from the calculated velocity of the planet:

:M_\mathrm{PL}=\frac{M_\mathrm{star}V_\mathrm{star}}{V_\mathrm{PL}},

where V_\mathrm{star} is the velocity of parent star. The observed Doppler velocity, K = V_\mathrm{star}\sin(i), where i is the inclination of the planet's orbit to the line perpendicular to the line-of-sight.

Thus, assuming a value for the inclination of the planet's orbit and for the mass of the star, the observed changes in the radial velocity of the star can be used to calculate the mass of the extrasolar planet.

Radial-velocity comparison tables

Ref:

For MK-type stars with planets in the habitable zone

Limitations

The major limitation with Doppler spectroscopy is that it can only measure movement along the line-of-sight, and so depends on a measurement (or estimate) of the inclination of the planet's orbit to determine the planet's mass. If the orbital plane of the planet happens to line up with the line-of-sight of the observer, then the measured variation in the star's radial velocity is the true value. However, if the orbital plane is tilted away from the line-of-sight, then the true effect of the planet on the motion of the star will be greater than the measured variation in the star's radial velocity, which is only the component along the line-of-sight. As a result, the planet's true mass will be greater than measured.

To correct for this effect, and so determine the true mass of an extrasolar planet, radial-velocity measurements can be combined with astrometric observations, which track the movement of the star across the plane of the sky, perpendicular to the line-of-sight. Astrometric measurements allows researchers to check whether objects that appear to be high mass planets are more likely to be brown dwarfs.

A further disadvantage is that the gas envelope around certain types of stars can expand and contract, and some stars are variable. This method is unsuitable for finding planets around these types of stars, as changes in the stellar emission spectrum caused by the intrinsic variability of the star can swamp the small effect caused by a planet.

The method is best at detecting very massive objects close to the parent star – so-called "hot Jupiters" – which have the greatest gravitational effect on the parent star, and so cause the largest changes in its radial velocity. Hot Jupiters have the greatest gravitational effect on their host stars because they have relatively small orbits and large masses. Observation of many separate spectral lines and many orbital periods allows the signal-to-noise ratio of observations to be increased, increasing the chance of observing smaller and more distant planets, but planets like the Earth remain undetectable with current instruments.

Another limitation in radial velocity measurements is the impact of stellar activity from the host star, which can drown out or even mimic planetary signals. A method of addressing stellar activity is by utilizing Gaussian Process modeling to model the radial velocity time series alongside stellar activity indicators, which later can be used to untangle the stellar activity from the planetary signals within the time series.

Right: In this case none of the star's movement is along the viewer's line-of-sight and the Doppler spectroscopy method will not detect the planet at all.

References

References

1. (10 October 2019). "Lessons from scorching hot weirdo-planets". Annual Reviews.
2. "Exoplanet and Candidate Statistics". [[NASA Exoplanet Science Institute]].
3. (1995). "A Jupiter-mass companion to a solar-type star". [[Nature (journal).
4. (July 7, 2015). "Will the real 'first exoplanet' please stand up?". Exoplanet Exploration: Planets Beyond our Solar System.
5. (2009-12-16). "ESPRESSO – Searching for other Worlds". Centro de Astrofísica da Universidade do Porto.
6. (2012). "WEIGHING THE NON-TRANSITING HOT JUPITER τ Boo B". The Astrophysical Journal.
7. (2010-10-16). "ESPRESSO and CODEX the next generation of RV planet hunters at ESO". [[Chinese Academy of Sciences]].
8. (2010-10-16). "An NIR laser frequency comb for high precision Doppler planet surveys". [[Chinese Academy of Sciences]].
9. (2015-06-24). "A Gaussian process framework for modelling stellar activity signals in radial velocity data". Monthly Notices of the Royal Astronomical Society.