Questions: Binary Stars and Multiple Stellar Systems

Question 1

Stellar masses are difficult to determine directly. What is the primary method astronomers use to measure the masses of stars?

• A. Measuring luminosity and applying the mass-luminosity relation
• B. Analyzing the elemental abundances in a star's spectrum
• C. Applying Kepler's third law to the orbital parameters of binary stars
• D. Measuring the parallax shift over a known time baseline

Answer: (C)

Kepler's third law (modified for two massive bodies) relates orbital period and semi-major axis to the combined mass of the system. For binary stars with measured periods and separations, this gives the only direct mass determination. The mass-luminosity relation is empirical and relies on masses already derived from binaries.

Question 2

A nova observed in a binary star system means at least one of the two stars has been destroyed in the explosion.

• T. True
• F. False

Answer: False

A nova occurs when hydrogen accreted from a companion star onto the surface of a white dwarf reaches the temperature and pressure needed for a thermonuclear runaway. Only the accumulated surface layer explodes. The white dwarf survives, and if mass transfer continues, the process can repeat (recurrent novae). Neither star is destroyed. A Type Ia supernova is different: it occurs if the white dwarf accumulates enough mass to exceed the Chandrasekhar limit (~1.4 solar masses) and collapses/explodes entirely.

Question 3

A binary system shows no Doppler shifts in its spectrum and the two stars cannot be resolved telescopically, but its total brightness dips periodically. What type of binary is this, and what can be inferred from the shape of the light curve?

Model answer: This is an eclipsing binary. The periodic brightness dips occur when one star passes in front of the other. The depths of the primary and secondary eclipses reveal the relative sizes and surface temperatures (luminosities) of the two stars; the duration of each eclipse constrains the stellar radii relative to the orbital separation; and the orbital inclination must be nearly edge-on.

Eclipsing binaries are especially valuable because the geometry of the eclipses encodes physical dimensions that are otherwise unobservable. Combined with radial velocity measurements from spectroscopy (when possible), eclipsing binaries yield the most complete set of stellar parameters — mass, radius, luminosity — of any measurement technique.