Doppler spectroscopy

Doppler spectroscopy

Overview
Doppler spectroscopy, also known as radial velocity
Radial velocity
Radial velocity is the velocity of an object in the direction of the line of sight . In astronomy, radial velocity most commonly refers to the spectroscopic radial velocity...

measurement, is a spectroscopic
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 method for finding extrasolar planets. It involves the observation of Doppler shifts in the spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

 of the star around which the planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

 orbits.

It is extremely difficult to directly observe extrasolar planets because they are very faint at interstellar distances, although the first claims of direct observations were made in 2004 and 2005.
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Encyclopedia
Doppler spectroscopy, also known as radial velocity
Radial velocity
Radial velocity is the velocity of an object in the direction of the line of sight . In astronomy, radial velocity most commonly refers to the spectroscopic radial velocity...

measurement, is a spectroscopic
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 method for finding extrasolar planets. It involves the observation of Doppler shifts in the spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

 of the star around which the planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

 orbits.

It is extremely difficult to directly observe extrasolar planets because they are very faint at interstellar distances, although the first claims of direct observations were made in 2004 and 2005. As a result, planets outside of our solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

 are usually discovered using indirect methods, through the effect of the planet on an object that is easier to observe, such as the parent star. Successful methods include Doppler spectroscopy, astrometry
Astrometry
Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of our Solar System and our Galaxy, the Milky...

, pulsar
Pulsar
A pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...

 timing, transits
Astronomical transit
The term transit or astronomical transit has three meanings in astronomy:* A transit is the astronomical event that occurs when one celestial body appears to move across the face of another celestial body, hiding a small part of it, as seen by an observer at some particular vantage point...

, and gravitational microlensing
Gravitational microlensing
Gravitational microlensing is an astronomical phenomenon due to the gravitational lens effect. It can be used to detect objects ranging from the mass of a planet to the mass of a star, regardless of the light they emit. Typically, astronomers can only detect bright objects that emit lots of light ...

. As of September 15, 2011, over 90% of the known extrasolar planets have been discovered using Doppler spectroscopy.

History




Otto Struve
Otto Struve
Otto Struve was a Russian astronomer. In Russian, his name is sometimes given as Otto Lyudvigovich Struve ; however, he spent most of his life and his entire scientific career in the United States...

 proposed in 1952 the use of powerful spectrograph
Spectrograph
A spectrograph is an instrument that separates an incoming wave into a frequency spectrum. There are several kinds of machines referred to as spectrographs, depending on the precise nature of the waves...

s to detect distant planets. He described how a very large planet, as large as Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

, for example, would cause its parent star to wobble slightly as the two objects orbit around their center of mass. He predicted that the small Doppler shifts to the light emitted by the star, caused by its continuously varying radial velocity, would be detectable by the most sensitive spectrographs as tiny red shift
Red shift
-Science:* Redshift, the increase of wavelength of detected electromagnetic radiation with respect to the original wavelength of the emission* Red shift, an informal term for a bathochromic shift...

s and blue shift
Blue shift
A blueshift is any decrease in wavelength ; the opposite effect is referred to as redshift. In visible light, this shifts the colour from the red end of the spectrum to the blue end...

s in the star's emission. However, the technology of the time produced radial velocity measurements with errors of 1,000 m/s or more, making them useless for the detection of orbiting planets. The expected changes in radial velocity are very small – Jupiter causes the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 to change velocity by about 13 m/s over a period of 12 years, and the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

's effect is only 0.1 m/s over a period of 1 year – so long-term observations by instruments with a very high resolution
Optical resolution
Optical resolution describes the ability of an imaging system to resolve detail in the object that is being imaged.An imaging system may have many individual components including a lens and recording and display components...

 are required.

Advances in spectrometer technology and observational techniques in the 1980s and 1990s produced instruments capable of detecting the first of many new extrasolar planets. 51 Pegasi b
51 Pegasi b
51 Pegasi b , sometimes though unofficially named Bellerophon, is an extrasolar planet approximately 50 light-years away in the constellation of Pegasus...

, the first extrasolar planet to be detected, was discovered in October 1995 using Doppler spectroscopy. Since that date, nearly 300 exoplanet candidates have been identified, and most have been detected by Doppler search programs based at
the Keck, Lick
Lick Observatory
The Lick Observatory is an astronomical observatory, owned and operated by the University of California. It is situated on the summit of Mount Hamilton, in the Diablo Range just east of San Jose, California, USA...

, and Anglo-Australian
Anglo-Australian Observatory
The Australian Astronomical Observatory , formerly the Anglo-Australian Observatory, is an optical/near-infrared astronomy observatory with its headquarters in suburban Sydney, Australia...

 Observatories (respectively, the California, Carnegie and Anglo-Australian planet searches), and teams based at the Geneva Extrasolar Planet Search
Geneva Extrasolar Planet Search
The Geneva Extrasolar Planet Search is a variety of observational programs run by M. Mayor, D. Naef, F. Pepe, D. Queloz, N.C. Santos, and S. Udry. The program is located at the site of Sauverny in Versoix, a small town near Geneva, Switzerland...

.

The Bayesian Kepler periodogram is a mathematical algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

, used to detect single or multiple extrasolar planets from successive radial velocity
Radial velocity
Radial velocity is the velocity of an object in the direction of the line of sight . In astronomy, radial velocity most commonly refers to the spectroscopic radial velocity...

 measurements of the star they are orbiting. It involves a Bayesian statistical analysis of the radial velocity data, using a prior
Prior probability
In Bayesian statistical inference, a prior probability distribution, often called simply the prior, of an uncertain quantity p is the probability distribution that would express one's uncertainty about p before the "data"...

 probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

 over the space determined by one or more sets of Keplerian orbital parameters. This analysis may be implemented using the Markov chain
Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the...

 Monte Carlo
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...

 (MCMC) method.

The method has been applied to the HD 208487
HD 208487
HD 208487 is a 7th magnitude G-type main sequence star located approximately 144 light-years away in the constellation of Grus. It has the same spectral type as our sun, G2V. However, it is probably slightly less massive and more luminous, indicating that it is slightly older...

 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. The method is also applied to the HD 11964
HD 11964
HD 11964 is a yellow subgiant star approximately 107 light-years away in the constellation of Cetus. The star is more massive and luminous than our Sun and is barely visible to the naked eye. A wide binary companion star was discovered in 2000...

 system, where it found an apparent planet with a period of approximately 1 year. However, this planet was not found in re-reduced data, suggesting that this detection was an artifact of the Earth's orbital motion around the Sun.

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
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

 of characteristic spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

s in the spectrum increasing and decreasing regularly over a period of time. These variations may be indicative of the radial velocity of the star being altered by the presence of planet orbiting the star, causing Doppler shifts in the light emitted by the star.

If an extrasolar planet is detected, its mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 can be determined from the changes in the star's radial velocity. 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 planet's mass to be calculated.

Example




The graph to the right illustrates the sine curve created 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
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...

 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
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

, 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 () using the following equation:



where:
  • r is the distance of the planet from the star
  • G is the gravitational constant
    Gravitational constant
    The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

  • 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 Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's law of gravitation, and the orbit equation
Orbit equation
In astrodynamics an orbit equation defines the path of orbiting body m_2\,\! around central body m_1\,\! relative to m_1\,\!, without specifying position as a function of time...

:



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 inclination
Inclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...

 of the planet's orbit to the line perpendicular to the line-of-sight
Line-of-sight propagation
Line-of-sight propagation refers to electro-magnetic radiation or acoustic wave propagation. Electromagnetic transmission includes light emissions traveling in a straight line...

.

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.

Problems



The major problem 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
True mass
The term true mass is synonymous with the term mass, but is used in astronomy to differentiate the measured mass of a planet from the lower limit of mass usually obtained from radial velocity techniques...

 will be higher than expected.

To correct for this effect, and so determine the true mass of an extrasolar planet, radial velocity measurements must be combined with astrometric
Astrometry
Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of our Solar System and our Galaxy, the Milky...

 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 dwarf
Brown dwarf
Brown dwarfs are sub-stellar objects which are too low in mass to sustain hydrogen-1 fusion reactions in their cores, which is characteristic of stars on the main sequence. Brown dwarfs have fully convective surfaces and interiors, with no chemical differentiation by depth...

s.

A further problem is that the gas envelope around certain types of stars can expand and contract, and some stars are variable
Variable star
A star is classified as variable if its apparent magnitude as seen from Earth changes over time, whether the changes are due to variations in the star's actual luminosity, or to variations in the amount of the star's light that is blocked from reaching Earth...

. 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 Jupiter
Hot Jupiter
Hot Jupiters are a class of extrasolar planet whose mass is close to or exceeds that of Jupiter...

s" – which have the greatest gravitational effect on the parent star, and so cause the largest changes in its radial velocity. 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

  • Methods of detecting extrasolar planets
    Methods of detecting extrasolar planets
    Any planet is an extremely faint light source compared to its parent star. In addition to the intrinsic difficulty of detecting such a faint light source, the light from the parent star causes a glare that washes it out...

  • Systemic (amateur extrasolar planet search project)
    Systemic (amateur extrasolar planet search project)
    Systemic is a research project designed to search data for extrasolar planets using amateur astronomers. The project utilizes a downloaded console provided on the Systemic web site allowing users to sort through data sets in search of characteristics which may reveal the presence of a planet within...


External links