BINARIES Read Your Textbook: Foundations of Astronomy

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Presentation transcript:

BINARIES Read Your Textbook: Foundations of Astronomy Chapter 10 Homework Problems Chapter 9 Review Questions: 1, 4, 5, 7 Review Problems: 1-5 Web Inquiries: 1 Homework Problems Chapter 10 Review Questions: 1, 2, 4, 6-8 Review Problems: 1-4, 8 Web Inquiries: 2

Binary Center of Mass Balance point

Binary Separation a = rA + rB Visual Binary Star

Spectroscopic Binary From Doppler Shift

Spectroscopic Orbit This represents the orbit of the star that is farthest from the center of mass. Its velocity amplitude is higher. It is the lower mass star. Velocity Time

Spectroscopic Orbit This represents the orbit of the star that is closest to the center of mass. Its velocity amplitude is smaller. It is the higher mass star. Velocity Time

Spectroscopic Parameters Center of Mass Low Mass Star Velocity Amplitude High Mass Star Velocity Amplitude Velocity Time

Inclination K velocity = amplitude of radial velocity (m/s) Doppler effect is maximized for an “edge-on” system; non-existent for a “pole-on” system. Inclination ~ 90o Inclination ~ 0o

Inclination K velocity = amplitude of radial velocities v sin(i) v = velocity i = 90 degrees, edge on i = 0 degrees, pole face

Spectroscopic Parameters g velocity = velocity of Center of Mass (CoM) K velocity = amplitude of radial velocity (v sin i) P = period Mass ratio M2/M1 = K1/K2 Smaller star orbits farther from the CoM, Larger star is closer from the CoM. Smaller star has large K velocity.

Center of Mass Velocity? Spectroscopic Orbit Center of Mass Velocity?

Spectroscopic Orbit Orbital Period?

Spectroscopic Orbit

Spectroscopic Orbit K velocities?

Spectroscopic Orbit K2 = 115 - 40 = 75

Spectroscopic Orbit K1 = 65 - 40 = 25

One Star is 3 times more massive than the other. K2/K1= M1/M2 = 75/25 = 3 One Star is 3 times more massive than the other. Spectroscopic Orbit

Eclipsing Binary Light Intensity variations are observed because of blocking of light by each of the stars in the system if inclination is large enough. Systems are edge-on or nearly edge-on as seen from earth. (i.e. inclinations are ~ 90 degrees)

Algol (b Perseus) Light Curve Light Intensity versus Time

Eclipsing Binary Light Curve

Eclipsing Binary Light Curve LA + LB LA + LB LB + f LA LA Only

Eclipsing Binary Light Curve LA + LB LA + LB LB + f LA LA Only

Eclipsing Binary Light Curve LA + LB LA + LB LB + f LA LA Only

Eclipsing Binary Light Curve LA + LB LA + LB LB + f LA LA Only

Simple Eclipsing Binary

Unequal Temperature and Size

Star Spots

Light Curve Fit

Light Curve Varieties

Light Curve Contacts

Light Curve Contacts Time interval (t2 - t1) ~ size of “orange” star

Light Curve Contacts Time interval (t3 - t1) ~ size of “yellow” star

Size Determinations 2 RA = (VA+VB ) ( t2 - t1 ) 2 RB = (VA+VB ) ( t3 - t1 ) Velocities obtained from spectroscopic orbit. Contact times obtained from eclipse light curve. The radii of the stars are then calculated to yield their size.

Determining Radii

Intrinsic Luminosity L = 4pR2sT4 Radius obtained from spectroscopic orbit with eclipse light curve. Temperature obtained from observations of spectrum.

Fundamental Stellar Parameters Spectra Distance Temperature Chemical Composition Luminosity (if distance is known) Velocity Binaries Orbital Velocities Sizes Masses Luminosity

Fundamental Stellar Parameters

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