18: Spectroscopic Binary Stars
- Page ID
- 6909
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)There are many binary stars whose angular separation is so small that we cannot distinguish the two components even with a large telescope – but we can detect the fact that there are two stars from their spectra. In favourable circumstances, two distinct spectra can be seen. It might be that the spectral types of the two components are very different – perhaps a hot A-type star and a cool K-type star, and it is easy to recognize that there must be two stars there. But it is not necessary that the two spectral types should be different; a system consisting of two stars of identical spectral type can still be recognized as a binary pair. As the two components orbit around each other (or, rather, around their mutual centre of mass) the radial components of their velocities with respect to the observer periodically change. This results in a periodic change in the measured wavelengths of the spectra of the two components. By measuring the change in wavelengths of the two sets of spectrum lines over a period of time, we can construct a radial velocity curve (i.e. a graph of radial velocity versus time) and from this it is possible to deduce some of the orbital characteristics. Often one component may be significantly brighter than the other, with the consequence that we can see only one spectrum, but the periodic Doppler shift of that one spectrum tells us that we are observing one component of a spectroscopic binary system. Thus we have to distinguish between a double-lined spectroscopic binary system and a single-lined spectroscopic binary system. As with all topics in this series of notes, there has accumulated over centuries a vast body of experience, knowledge and technical facility, and this chapter is intended only as a first introduction to the basic principles. But all of us, whether beginners or experienced practitioners, have to know these!
- 18.1: Introduction to Spectroscopic Binary Stars
- This page examines the orbital elements of binary star systems, focusing on the difficulties in measuring certain parameters through spectroscopic and visual observations. It explains that while radial velocity measurements indicate the motion of binary components, they do not determine the position angle of ascending nodes. Visual binaries are more challenging to analyze due to longer orbital periods, while spectroscopic binaries offer insights but are generally closer with shorter periods.
- 18.2: The Velocity Curve from the Elements
- This page explores the calculation of expected velocity curves for stars based on orbital elements, introducing key concepts such as the "plane of the sky" and parameters like semi-major axis and angular momentum. It focuses on deriving radial velocity expressions and includes examples differentiating between eccentricities.
- 18.3: Preliminary Elements from the Velocity Curve
- This page covers the inverse problem of deducing orbital elements from a radial velocity curve, assuming accurate observations and knowledge of the orbital period. It highlights estimating parameters like systemic velocity (V0), semiamplitude (K1), eccentricity (e), and argument of periastron (ω) from the curve's shape. K1 can be calculated from velocity extremes, and the time of periastron passage (T) can also be estimated. Future sections will provide further refinements on these techniques.
- 18.4: Masses
- This page explores binary star systems, focusing on the semi-amplitude of the velocity curve (K1) and its role in determining orbital characteristics. It describes how to approximate a1 sin i using mean motion, eccentricity, and K1, leading to a mass function for unseen companions.
- 18.5: Refinement of the Orbital Elements
- This page explains the process of refining orbital elements by comparing theoretical and observed radial velocities. It outlines the relevant parameters used in the calculations and emphasizes the importance of adjusting these estimates through an iterative method. Supervision by an experienced orbit computer is advised to account for observational errors and distribution. Experts must carefully decide on fixing specific parameters, as these decisions significantly impact the results.
- 18.6: Finding the Period
- This page addresses the difficulties of measuring radial velocity in celestial mechanics, highlighting the contrast between the straightforward calculation of orbital elements and the practical challenges posed by inconsistent observation intervals. It discusses the complexities in determining the orbital period due to sparse data, which can result in 'stroboscopic effects.
- 18.7: Measuring the Radial Velocity
- This page covers techniques for measuring radial velocity using stellar spectra, focusing on wavelength comparisons between stars and laboratory examples. It points out difficulties in measurements caused by spectral line broadening and blending in different star types.
Thumbnail: Algol B orbits Algol A. This animation was assembled from 55 images of the CHARA interferometer in the near-infrared H-band, sorted according to orbital phase. (CC BY-SA 3.0; Dr. Fabien Baron, Dept. of Astronomy, University of Michigan, Ann Arbor, MI 48109-1090, labels indicating phase added by Stigmatella aurantiaca).