Doppler spectroscopy
Doppler spectroscopy (also known as the radial-velocity method, or colloquially, the wobble method) is an
History
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
In November 1995, the scientists published their findings in the journal
Beginning in the early 2000s, a second generation of planet-hunting spectrographs permitted far more precise measurements. The
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
If an extrasolar planet is detected, a
The Bayesian Kepler periodogram is a mathematical
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.[12][13] The method is also applied to the HD 11964 system, where it found an apparent planet with a period of approximately 1 year. However, this planet was not found in re-reduced data,[14][15] suggesting that this detection was an artifact of the Earth's orbital motion around the Sun.[citation needed]
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.[16]
Example
The graph to the right illustrates the
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
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 , the velocity of the planet around the star can be calculated using
where is the velocity of planet.
The mass of the planet can then be found from the calculated velocity of the planet:
where is the velocity of parent star. The observed Doppler velocity, , where i is the
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
Planet Mass | Distance AU
|
Star's Radial Velocity Due to the Planet (vradial) |
Notice |
---|---|---|---|
Jupiter | 5 | 12.7 m/s | |
Neptune | 0.1 | 4.8 m/s | |
Neptune | 1 | 1.5 m/s | |
Super-Earth (5 M🜨) | 0.1 | 1.4 m/s | |
L 98-59 b (0.4 M🜨) | 0.02 | 0.46 m/s | [17] |
Super-Earth (5 M🜨) | 1 | 0.45 m/s | |
Earth | 0.09 | 0.30 m/s | |
Earth | 1 | 0.09 m/s |
Ref:[18]
Planet | Planet Type |
Semimajor Axis (AU) |
Orbital Period |
Star's Radial Velocity Due to the Planet (m/s) |
Detectable by: |
---|---|---|---|---|---|
51 Pegasi b | Hot Jupiter | 0.05 | 4.23 days | 55.9[19] | First-generation spectrograph |
55 Cancri d | Gas giant | 5.77 | 14.29 years | 45.2[20] | First-generation spectrograph |
Jupiter | Gas giant | 5.20 | 11.86 years | 12.4[21] | First-generation spectrograph |
Gliese 581c | Super-Earth | 0.07 | 12.92 days | 3.18[22] | Second-generation spectrograph |
Saturn | Gas giant | 9.58 | 29.46 years | 2.75 | Second-generation spectrograph |
L 98-59 b | Terrestrial planet | 0.02 | 2.25 days | 0.46[17] | Third-generation spectrograph |
Neptune | Ice giant | 30.10 | 164.79 years | 0.281 | Third-generation spectrograph |
Earth | Habitable planet
|
1.00 | 365.26 days | 0.089 | Third-generation spectrograph (likely) |
Pluto | Dwarf planet | 39.26 | 246.04 years | 0.00003 | Not detectable |
For MK-type stars with planets in the habitable zone
Stellar mass (M☉) |
Planetary mass (ME) |
Lum. (L0) |
Type | RHAB (AU) |
RV (cm/s) |
Period (days) |
---|---|---|---|---|---|---|
0.10 | 1.0 | 8×10−4 | M8 | 0.028 | 168 | 6 |
0.21 | 1.0 | 7.9×10−3 | M5 | 0.089 | 65 | 21 |
0.47 | 1.0 | 6.3×10−2 | M0 | 0.25 | 26 | 67 |
0.65 | 1.0 | 1.6×10−1 | K5 | 0.40 | 18 | 115 |
0.78 | 2.0 | 4.0×10−1 | K0 | 0.63 | 25 | 209 |
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
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.[4]
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.
See also
References
- . Retrieved 4 April 2022.
- ^ "Exoplanet and Candidate Statistics". NASA Exoplanet Archive. NASA Exoplanet Science Institute. Retrieved 27 November 2022.
- ^
Bibcode:1952Obs....72..199S.
- ^ a b c "Radial velocity method". The Internet Encyclopedia of Science. Retrieved 2007-04-27.
- ^
Penn State University. Archived from the original(PDF) on 2008-12-17. Retrieved 2009-04-19.
- ^ "A user's guide to Elodie archive data products". Haute-Provence Observatory. May 2009. Retrieved 26 October 2012.
- ^ S2CID 4339201.
- ^ Brennan, Pat (July 7, 2015). "Will the real 'first exoplanet' please stand up?". Exoplanet Exploration: Planets Beyond our Solar System. Retrieved 28 February 2022.
- S2CID 119067572. Archived from the original(PDF) on 2007-07-07.
- Bibcode:2003Msngr.114...20M.
- ^ "ESPRESSO – Searching for other Worlds". Centro de Astrofísica da Universidade do Porto. 2009-12-16. Archived from the original on 2010-10-17. Retrieved 2010-10-26.
- ^
P.C. Gregory (2007). "A Bayesian Kepler periodogram detects a second planet in HD 208487". S2CID 8220838.
- ^
Wright, J. T.; Marcy, G. W.; Fischer, D. A; Butler, R. P.; Vogt, S. S.; Tinney, C. G.; Jones, H. R. A.; Carter, B. D.; et al. (2007). "Four New Exoplanets and Hints of Additional Substellar Companions to Exoplanet Host Stars". S2CID 35682784.
- ^
P.C. Gregory (2007). "A Bayesian periodogram finds evidence for three planets in HD 11964". S2CID 16796923.
- ^
Wright, J.T.; Upadhyay, S.; Marcy, G. W.; Fischer, D. A.; Ford, Eric B.; Johnson, John Asher (2009). "Ten New and Updated Multi-planet Systems, and a Survey of Exoplanetary Systems". The Astrophysical Journal. 693 (2): 1084–1099. S2CID 18169921.
- ^ Weighing The Non-Transiting Hot Jupiter Tau BOO b, Florian Rodler, Mercedes Lopez-Morales, Ignasi Ribas, 27 June 2012
- ^ S2CID 236957385.
- ^ a b "ESPRESSO and CODEX the next generation of RV planet hunters at ESO". Chinese Academy of Sciences. 2010-10-16. Archived from the original on 2011-07-04. Retrieved 2010-10-16.
- ^ "51 Peg b". Exoplanets Data Explorer.
- ^ "55 Cnc d". Exoplanets Data Explorer.
- ^ Endl, Michael. "The Doppler Method, or Radial Velocity Detection of Planets". University of Texas at Austin. Retrieved 26 October 2012.[permanent dead link]
- ^ "GJ 581 c". Exoplanets Data Explorer.
- ^ "An NIR laser frequency comb for high precision Doppler planet surveys". Chinese Academy of Sciences. 2010-10-16. Retrieved 2010-10-16.[dead link]