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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