Measuring Properties of Stars

Important Slides marked with a

Measurable Properties of Stars

• Position• Apparent Brightness• Color• Distance

– many methods• Velocity

– Doppler Shift, proper motion

• Luminosity– Distance + Apparent

Brightness

• Temperature – Color

• Composition– Spectral Lines

• Size (radius)– Stephan-Boltzmann

Law

• Mass– Binary star orbit

• Age

Measuring Distance

• Parallax• Angular Diameter Method• Standard Candle Method

Measuring Distance - Parallax

Parallax is the change in position of a star, relative to other stars, based on change in the observer’s position.

One parsec (pc) = distance of an object with a parallax of one arc-second = 3.26 ly

Measuring Distance - Parallax

Only good out to ~300 ly

Or d (pc)=1/p(arcsec)

Measuring Distance - Angular Diameter Method

Measuring Distance - Angular Diameter Method

• Angular diameter is easy to measure• D (distance) = L (real size) x A

(angular diameter, in radians)• If you somehow know real size, you

can calculate distance• Does not work for stars (too small)• Humans judge long distances with

this method

Measuring Distance - Standard Candle Method

• Apparent Brightness– How bright something looks from the Earth– Easily measured– Measured as Apparent Magnitude

• Luminosity– How bright something really is– Units of power (energy/sec emitted, or watts)– Also called Absolute Magnitude (App Mag at

10pc)

Measuring Distance - Standard Candle Method

• Distance relates Apparent Brightness and Luminosity

• Inverse-square Law shows this• “Apparent Brightness-Luminosity-

Distance”– Any two yield the third

You should review pages 365-366 “Explorations, Third Edition by Arny – Class Text”

“Apparent Magnitude” was defined by Hipparachus in 150 BC. He devised a magnitude scale based on:

Magnitude Constellation Star

1 (Orion) Betelgeuse

2 Big Dipper various

6 stars just barely seen

However, he underestimated the magnitudes. Therefore, many very bright stars today have negative magnitudes.

Magnitude Difference is based on the idea that the difference between the magnitude of a first magnitude star to a 6th magnitude star is a factor of 100. Thus a 1st mag star is 100 times brighter than a 6th mag star. This represents a range of 5 so that 2.512 = the fifth root of 100. Thus the table hierarchy is the following.

Magnitude Difference of 1 is 2.512:1, 2 is 2.5122:1 or 6.31:1, 3 is 2.5123 = 15.85:1 etc.

(2) Astronomy Magazine Sept. 2002 issue defines the faintest naked eye star at 6.5 apparent magnitude.

Absolute Magnitude is defined as how bright a star would appear if it were of certain apparent magnitude but only 10 parsecs distance.

Images courtesy of Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

Images courtesy of Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

Measuring Distance - Standard Candle Method

• Standard Candle– An object with a luminosity that can be

found without knowing its distance

• We will cover many types over the semester

• Examples: 75W light bulb, second brightest galaxy in a cluster, main sequence star spectral type, Cepheid Variables

If luminosity and temperatureare known, we can find radius

F = T 4

Spectral Types

• Around 1901 Annie Jump Cannon finished Henry Draper’s work categorizing stars by the strength of their Hydrogen lines

• Categories: A,B,C,D,…,M,N,O,P• A-> strong lines, P-> weak/no lines • No physical basis for these

categories (“stamp collecting”)

Spectral Types

• Around 1920 M. Saha realized temperature determines strength of lines– All stars made of Hydrogen– Spectral Types -> temperature

• Cecilia Payne made the modern system– Spectral Sequence OBAFGKM– Hottest to coolest– Letters still represent strength of H-lines

Other Properties

• Composition– Spectral lines

• Velocity– Doppler-shifts and proper motion

• Mass– Weigh the star with a form of Kepler’s

3rd Law

Summary of Spectral Lines

Putting it Together - The Herztsprung-Russell

Diagram• Measure surface temperature from

color or spectral-type• Measure distance from parallax (or

other method)• Calculate luminosity from apparent

brightness and distance• Plot luminosity vs. surface

temperature

Radius From Stephan-Boltzmann Law

Shows three groups of stars.

Luminosity=Mass3

This was empirical and is now supported by computer models.

Masses come from binary stars

Herztsprung-Russell Diagram

• Plot Luminosity vs. Temperature • Showed three classes of stars

– Main Sequence, Red Giants, White Dwarfs

• For MS stars Temperature -> Luminosity– MS stars are ‘standard candles’

• Binaries show variations between Main Sequence stars are due to mass

Binary Systems

• At least 70% of all stars are binaries or multiple-star systems

• Optical Doubles: Not actual binaries

• Visual binaries: Two stars seen as binaries

• Spectroscopic binaries– Two sets of spectral lines seen, or– One set of Doppler-shifting lines

• Eclipsing binaries: Stars eclipse each other

Algol - An Eclipsing Binary• This blue ‘star’ turns red

every ~3 days• Arabic: Algol

– ‘Demon’s Head’

• Chinese: Tseih-She– ‘Piled-up corpses’

• Hebrew: Rosh he Satan– “Satan’s Head”

• Hebrew: Lillith– Adam’s first, demonic

wife