Radial Velocity & Extrasolar Planets: Investigating Systematic Errors

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In summary, the conversation discusses the use of a spectrograph to record the Radial velocity of a star and its potential error. It is noted that the equipment has an intrinsic systematic error of 4ms^{-1} and additional error from experimentation is added in quadrature. The data is then fitted to a 7 parameter function through nonlinear regression. The question is posed, how will reducing the intrinsic systematic error to 1ms^{-1} impact a single fitted parameter? To investigate this, a mathematical model of the spectrograph and its data must be used, such as differential equations, linear algebra, or statistical software. The impact of reducing the systematic error on the fitted function's parameters must be calculated using the chosen method.
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NoobixCube
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Hi,
I need some help getting started with a problem I have.
A spectrograph records the Radial velocity of a star to find if it has a planet. It has an intrinsic systematic error of say [tex] 4ms^{-1}[/tex]. The error of experimentation such as 'stellar jitter' is added in quadrature to this systematic error. The data is fitted to a 7 parameter function through nonlinear regression. How will the error change on a single fitted parameter if the intrinsic systematic error of the equipment is reduced to say [tex] 1ms^{-1}[/tex]?
Where do I begin to investigate this?
 
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To investigate this, you will need to use a mathematical model of the spectrograph and its data. This could be done using differential equations, linear algebra, or statistical software. Depending on which method you use, you will need to calculate the impact of reducing the systematic error on the parameters of the fitted function. For example, if you use linear algebra to model the system, you would need to examine how changes in the systematic error affect the coefficients of the equation that describes the fit. If you use statistical software, you would need to look at how the error terms in the model are affected by changes in the systematic error.
 

1. What is radial velocity and how is it used to detect extrasolar planets?

Radial velocity is a measurement of the speed at which a star is moving towards or away from us. It can be measured by observing the Doppler shift in the star's spectrum. When an extrasolar planet orbits a star, it causes the star to wobble slightly due to the gravitational pull between the two bodies. This wobble can be detected through changes in the star's radial velocity, allowing us to infer the presence of an orbiting planet.

2. What are some of the systematic errors that can affect radial velocity measurements?

Some of the systematic errors that can affect radial velocity measurements include instrumental errors, such as telescope and spectrograph imperfections, as well as noise from the Earth's atmosphere. Stellar jitter, caused by activity on the star's surface, can also contribute to errors in radial velocity measurements. Additionally, errors can arise from the data analysis techniques used to extract the radial velocity signal from the observations.

3. How do scientists account for systematic errors in radial velocity measurements?

Scientists use a variety of methods to account for systematic errors in radial velocity measurements. These can include calibrating and regularly monitoring the instruments, using advanced data analysis techniques to filter out noise, and conducting follow-up observations to confirm the presence of an extrasolar planet. Additionally, scientists often run simulations and tests to identify and correct for any systematic errors in their data.

4. How accurate are radial velocity measurements in detecting extrasolar planets?

The accuracy of radial velocity measurements in detecting extrasolar planets depends on various factors, including the quality of the instruments and data, as well as the characteristics of the star and planet being observed. In general, radial velocity measurements have been able to detect planets with masses as small as a few Earth masses and with orbital periods ranging from a few days to several years.

5. How does the study of radial velocity and extrasolar planets contribute to our understanding of the universe?

The study of radial velocity and extrasolar planets has greatly expanded our understanding of the universe and our place in it. By detecting and characterizing these distant worlds, scientists are able to learn more about the formation and evolution of planetary systems, as well as the prevalence and diversity of other habitable worlds in our galaxy. Additionally, the study of extrasolar planets can provide valuable insights into the conditions necessary for life to exist, potentially guiding our search for life beyond Earth.

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