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18.2 Measuring Stellar Masses

3 min read•june 12, 2024

are cosmic duos that dance together through space. These stellar pairs come in different flavors: visual, spectroscopic, and eclipsing. Each type offers unique insights into the stars' properties, allowing astronomers to unravel their secrets.

Measuring stellar is a key application of binary star observations. By analyzing orbital motions and using , scientists can determine star masses. This information is crucial for understanding and the that governs a star's brightness and lifespan.

Binary Star Systems and Stellar Mass Measurement

Types of binary star systems

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    • Two stars that can be resolved separately through a telescope ( in Cygnus)
    • Orbital motions can be observed over time reveals
    • Allows direct calculation of the combined mass using Newton's version of Kepler's third law
    • Two stars that are too close together to be resolved visually ( in Ursa Major)
    • Periodic in the stars' spectra indicate orbital motion
    • measurements allow calculation of the stars' masses
    • provides additional information about the stars' compositions and temperatures
    • Two stars that periodically eclipse each other from Earth's perspective ( in Perseus)
    • Light curve analysis reveals information about the stars' sizes and orbital properties
    • Combined with spectroscopic data, allows determination of individual stellar masses

Mass calculation in binary stars

  • Newton's version of Kepler's third law: a3P2=G(M1+M2)4π2\frac{a^3}{P^2} = \frac{G(M_1 + M_2)}{4\pi^2}
    • aa: of the orbit in AU
    • PP: in years
    • GG: gravitational constant
    • M1M_1 and M2M_2: masses of the two stars in solar masses
  • Measure the (PP) and semi-major axis (aa) of a system
    1. Observe the binary system over an extended period to determine PP
    2. Measure the angular separation and distance to calculate aa
      • can be used to determine the distance to nearby binary systems
  • Substitute values into the equation and solve for the combined mass (M1+M2M_1 + M_2)
  • principles are applied to analyze the motion of binary star systems

Mass-luminosity relationship for stars

  • The mass-luminosity relationship: LL⊙≈(MM⊙)3.5\frac{L}{L_{\odot}} \approx (\frac{M}{M_{\odot}})^{3.5}
    • LL: luminosity of the star
    • L⊙L_{\odot}: luminosity of the Sun
    • MM: mass of the star
    • M⊙M_{\odot}: mass of the Sun
  • More massive stars have higher luminosities due to increased gravitational compression
    • Higher core temperatures and fusion rates ( vs )
  • Determine a star's luminosity through observations
    • Measure apparent brightness and distance to calculate absolute luminosity
  • Use the mass-luminosity relationship to estimate the star's mass based on its luminosity
  • Mass influences other physical properties
    • Radius: more massive stars are generally larger
    • Surface temperature: more massive stars are hotter (O and B stars vs M stars)
    • Evolutionary path and lifetime: massive stars evolve faster and have shorter lifespans

Stellar Evolution and Mass

  • is closely tied to a star's initial mass
  • More massive stars progress through evolutionary stages more rapidly
  • Mass loss through stellar winds affects a star's evolutionary path

Key Terms to Review (31)

Albireo: Albireo is a binary star system located in the constellation Cygnus. It is one of the most famous double stars visible to the naked eye, known for its contrasting colors and its importance in the study of stellar masses.
Alcor: Alcor is a star in the constellation Ursa Major, often associated with Mizar as part of a visual double star system. It is located approximately 81 light-years from Earth and is visible to the naked eye.
Algol: Algol is a well-known eclipsing binary star system, where two stars orbit each other and periodically eclipse one another from our perspective on Earth. This phenomenon is closely tied to the topics of measuring stellar masses and diameters of stars.
Binary Star Systems: A binary star system is a system of two stars that orbit around a common center of mass. These two stars are gravitationally bound and revolve around each other, forming a single astronomical object. Binary star systems are important in the context of measuring stellar masses, as the motion and properties of the two stars can provide valuable information about their individual masses.
Binary stars: Binary stars are systems in which two stars orbit around a common center of mass. They provide crucial information for determining stellar masses and understanding stellar evolution.
Doppler Shifts: Doppler shifts refer to the change in the observed frequency or wavelength of a wave due to the relative motion between the source of the wave and the observer. This phenomenon is widely used in astronomy to study the motion and properties of celestial objects.
Eclipsing Binary Stars: Eclipsing binary stars are a type of binary star system where the two stars orbit each other in a plane that is oriented edge-on relative to the observer. This results in one star passing in front of the other, causing a periodic decrease in the total brightness of the system that can be observed and measured.
Gravitational Interaction: Gravitational interaction is the attractive force between objects with mass that governs the motion and behavior of celestial bodies, from stars and planets to entire galaxies. This fundamental force is central to understanding various astronomical phenomena.
Mass: Mass is a measure of the amount of matter in an object and is typically measured in kilograms. It is a fundamental property that influences gravitational attraction and inertia.
Mass-luminosity relation: The mass-luminosity relation describes the relationship between the mass of a star and its luminosity. Generally, more massive stars are significantly more luminous than less massive stars.
Mass-Luminosity Relationship: The mass-luminosity relationship is a fundamental connection between the mass and the luminosity (brightness) of a star. It describes the empirical observation that more massive stars tend to be more luminous than less massive stars.
Mizar: Mizar is a star system located in the constellation Ursa Major, known for being part of the Big Dipper's handle. It is one of the first binary stars discovered through telescopic observation.
Mizar A: Mizar A is a binary star system located in the constellation Ursa Major, also known as the Big Dipper. It is a prominent and easily observable component of the Mizar-Alcor double star system, which has been studied extensively to understand the nature of binary star systems and measure stellar masses.
Newton's version of Kepler's third law: Newton's version of Kepler's third law describes the relationship between the orbital period and the semi-major axis of a planet or satellite orbiting a central body, such as a star or a planet. This law provides a mathematical expression that allows for the calculation of the mass of the central body based on the observed orbital properties of the orbiting object.
Orbital Mechanics: Orbital mechanics, also known as celestial mechanics, is the study of the motion of objects around other objects, such as planets, stars, or other celestial bodies. It is a fundamental concept in astronomy that describes the complex interactions and trajectories of objects in space.
Orbital period: The orbital period is the time it takes for a celestial object to complete one full orbit around another object. It is commonly measured in Earth days, months, or years depending on the context of the objects involved.
Orbital Period: The orbital period is the time it takes for a celestial body, such as a planet or a moon, to complete one full revolution around its parent body or another celestial object. This term is crucial in understanding the motion and dynamics of objects within a gravitational system.
Parallax Measurement: Parallax measurement is a technique used in astronomy to determine the distance to nearby stars by observing their apparent shift in position against more distant celestial objects as the Earth orbits the Sun. This method provides a fundamental way to measure the scale of the universe by establishing a reliable distance scale for the nearest stars.
Pickering: Pickering was an astronomer known for his work in the classification of stellar spectra and contributing to our understanding of stellar masses. He also founded the Harvard College Observatory's program that led to significant advancements in astronomy.
Proxima Centauri: Proxima Centauri is the closest star to the Sun, located just over 4 light-years away in the constellation of Centaurus. It is a small, low-mass red dwarf star that is part of the Alpha Centauri triple star system, which is the closest stellar system to our solar system.
Radial velocity: Radial velocity is the component of a star's or other celestial object's velocity that is directed along the line of sight of an observer. It can be measured by observing Doppler shifts in the object's spectral lines.
Radial Velocity: Radial velocity refers to the component of an object's velocity that is directed along the line of sight between the object and the observer. It is a crucial concept in astronomy, as it allows for the detection and study of exoplanets, the measurement of stellar properties, and the exploration of the dynamics of our universe.
Rigel: Rigel is a prominent blue supergiant star located in the Orion constellation. It is one of the brightest stars in the night sky and holds significance in various aspects of stellar astronomy, including the brightness of stars, stellar census, measuring stellar masses, diameters of stars, the Hertzsprung-Russell (H-R) diagram, and the study of stellar evolution.
Semi-major Axis: The semi-major axis is a fundamental parameter that defines the size and shape of an elliptical orbit, such as the orbit of a planet around the Sun or a star around another star. It represents the average distance between the two objects in an elliptical system.
Spectral Analysis: Spectral analysis is the study and interpretation of the spectrum of light or other electromagnetic radiation emitted, reflected, or absorbed by a substance. It is a powerful tool used in various fields, including astronomy, to gather information about the physical and chemical properties of celestial objects and their compositions.
Spectroscopic binary: A spectroscopic binary is a binary star system in which the stars are too close together to be resolved individually through a telescope. Instead, their presence is inferred by observing Doppler shifts in their spectral lines as they move around their common center of mass.
Spectroscopic Binary Stars: Spectroscopic binary stars are a type of binary star system where the two stars are too close together to be resolved visually, but their presence can be detected through the analysis of their spectra. These binary systems exhibit periodic shifts in the wavelengths of the absorption lines in their spectra, indicating that the stars are orbiting a common center of mass.
Stellar evolution: Stellar evolution is the process by which a star changes over the course of time. It encompasses the formation, life cycle, and eventual fate of stars.
Stellar Evolution: Stellar evolution is the process by which a star changes over the course of its lifetime, from birth to death. This term encompasses the various stages and transformations a star undergoes, driven by the complex interplay of gravitational, thermal, and nuclear forces within the star. Understanding stellar evolution is crucial in astronomy, as it provides insights into the life cycle of stars and their impact on the broader cosmic landscape.
Visual binary: A visual binary is a binary star system where the two stars can be individually resolved through a telescope. This allows astronomers to observe their orbital motion directly over time.
Visual Binary Stars: Visual binary stars are a type of binary star system where the two stars can be directly observed and their orbits around a common center of mass can be measured. This allows for the determination of the masses of the individual stars, a crucial aspect of studying stellar properties.
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18.3 Diameters of Stars