hertzsprung-russell diagram - college of charlestonneffj.people.cofc.edu/astr130/notes/lec13.pdf ·...
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Lec 13: 21 FEB 12 ASTR 130 - Introductory Astronomy II (Chapter 17) LAST WEEK - Cataloging Basic Properties of Stars
Position, Distance, Motion Luminosity, Radius, Temperature Spectral Classification (O B A F G K M)
TODAY - The HR Diagram • The HR Diagram • Spectroscopic Parallax • Binary Stars and Measuring Mass • Mass-Luminosity Relationship; Ages of Stars
Lab This Week: M & B (finish) and Spectral Classification Lab Next Week: HR Diagram THURSDAY: Chapter 18 – (start) Star Formation
An “H-R Diagram” for Automobiles and People
weight v. power
basic properties
weight v. height
related to aging
Hertzsprung-Russell Diagram • X-axis:
– spectral type – color – temperature – [mass ??]
• Y-axis: – luminosity – absolute magnitude
• “Log-Log” plot • note that higher
temperatures to the left
“HR” Diagram of the nearest stars (w/ measured distances)
• Most stars “cooler” than the Sun
• Stars confined to the lower right end of a narrow strip (“main sequence”
• or below and to the left of the main sequence (“white dwarfs”)
“HR” Diagram of the brightest stars (w/ measured distances)
• Most bright stars “hotter” than the Sun
• Stars confined to narrow strip (upper left of “main sequence”)
• or above and to the right of the main sequence (“red giants”)
L = 4πR2 σ T4
L
T
R
Stars of same Temperature can have very different Luminosity!
What if we don’t know the distance?
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How Can We Infer Size From Spectrum?
Giant stars (top) have narrower lines than main sequence stars (bottom) of the same spectral type
2nd dimension to spectral type: LUMINOSITY CLASS (I – V)
Distance Modulus (Lab) apparent brightness depends on true (“absolute”)
brightness and how far away it is a.b. = L / 4πd2 (Watt/m2)
the equivalent statement using magnitudes is:
m - M = 5 log(d/10)
m=“apparent” magnitude M=“absolute” magnitude (luminosity)
= apparent magnitude if 10 pc away d in parsecs; magnitude has no unit
Spectroscopic Parallax • we can combine absolute magnitude with apparent
magnitude to determine distance – but we needed distance to determine absolute magnitude,
so isn’t this circular?
• yes, but if we make an HR diagram of just stars with known distances then we can ...
• use spectral type and apparent magnitude to infer absolute magnitude (and therefore distance)
• not as accurate as parallax – “spread” in main sequence – uncertainty in luminosity class
Spectroscopic Parallax • stars are confined to narrow strips defined by spectral type and luminosity class
• given MK classification, we know approximately what absolute magnitude (luminosity) should be
• with apparent magnitude, we can determine distance (from the distance modulus)
How Can We Measure MASS? mass will prove to be the most distinguishing property of a
star, but it is one of the hardest properties to measure
• Binary Systems; can sometimes measure the masses using Kepler’s Second and Third Laws: Total Mass: m1+m2 = (4π/G) a3 /P2
Mass Ratio: m1/m2 = a2/a1 (visual binaries) or m1/m2 = v2/v1 (spectroscopic binaries)
Visual m1a1 = m2 a2
m1/m2 = a2/a1
Spectroscopic m1v1 = m2 v2
m1/m2 = v2/v1
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Visual Binary
measure separation between 2 stars
period and semimajor axis of separation ellipse gives us m1+m2
if we are lucky, we can also see the motion of the center of mass, which gives us a1 and a2, so m1/m2
caution: orbital plane could be tipped in any orientation
Spectroscopic Binary
do not directly measure separation (a) between 2 stars, but period is easy to measure
velocity ratio, v1 and v2, gives m1/m2
if orbits are circular and system eclipses, we can get m1+m2
caution: orbital plane could be tipped in any orientation
Eclipsing Binary
velocity ratio, v1 and v2, gives m1/m2
if orbits are circular, we can get m1+m2
light curve --> radius and temperature of each star!
caution: orbital plane could be tipped in any orientation