Properties of Stars

Distances Parallax (“Triangulation”):

- observe object from two separate points - use orbit of the Earth (1 AU)

- measure angular “shift” of object - angle depends on distance to object

more distant objects = smaller parallax angle

p *

p *

Measuring distances to stars: http://sci2.esa.int/interactive/media/flashes/2_1_1.htm http://css-tricks.com/examples/StarryNight/

Other examples of parallax: http://muffi.pl/en/, http://www.noleath.com/noleath/

http://www.intacto10years.com/index_start.php

Distance (d): - if parallax angle measured in arcsec (“)

d = 1/p

d = distance in parsecs

New Unit of Distance: Parsec

1 pc = the distance when angle is exactly 1”

( = 3.26 light years or 206265 AU’s)

Practical limit: 0.01” from ground telescopes 0.001” from space (Hipparcos)

Baseline (1 AU) Parallax Angle (p)

Distance (d)

Luminosity and Brightness

Luminosity (L): - total energy output of an object

Brightness (b): - amount of energy received by observer

- depends on luminosity and distance

Magnitude Scale to describe brightness - developed by Hipparchus (190 – 120 B.C)

Brightest stars = 1st Magnitude ½ as bright stars = 2nd Magnitude

Faintest stars = 6th Magnitude

BUT, Scale is backwards Brighter stars smaller magnitude Fainter stars larger magnitude

http://www.london2012.com/weightlifting/event/men-56kg/index.html

Response of human eye What we see as twice (2 times) as bright

100 Watt 250 Watt

= 2.512 times as much energy!

Apparent Magnitude (m) - measure of how bright object appears

- depends on luminosity and distance

“Oooh! Bright stars !! “

Absolute Magnitude (M) - how bright star would appear IF the

distance to star is exactly 10 parsecs - depends only on luminosity

Relation between M, m, and distance

m – M = 5 log d - 5 Brightness (m) Distance (d)

Luminosity (M)

This one’s not so bright.

This one is REALLY bright!!

10 pc

Spectral Classification

Classification of stars into spectral types

Spectral Types: determined by temperature

O, B, A, F, G, K, M hottest coolest

“Oh, Be A Fine Girl/Guy Kiss Me!”

Subdivisions of Spectral Types: 0 - 9

…, F8, F9, G0, G1, G2, … , G8, G9, K0, K1, … hotter > > > > > > > cooler

http://www.noao.edu/image_gallery/html/im0649.html Our Sun: Surface Temperature: 5778 K (= 5500oC or 9940oF)

Spectral Type: G2 Spectral Lines Spectral Type

Temperature

Diameters of Stars - cannot be determined directly

from observations

But, can be found from luminosity, temperature. Temp amount of E per square meter (flux) Lum. total energy output from entire surface

Energy from each m2

X number of m2

= Total Energy output

L = ( 4 R2 ) X ( T4 ) Stefan - Boltzmann Law where:

R = radius of star (size), = Stef-Boltz Constant

Temperature Size (Radius)

Luminosity

Properties of Stars - Examples

(1) Two stars with the same temperature, different diameters.

A. 5000 K B. 5000 K Which has the higher luminosity? (2) Two stars with the same diameter, different temperatures.

A. 5000 K B. 10000 K Which has the higher luminosity? (3) Two stars with the same luminosity, different temperatures.

A. B. 5000 K 10000 K

Which star is larger?

Stefan – Boltzmann Law with money

(1) Two sheets (stars) with the same denomination (temperature), different size (diameters).

A. B. 1 dollar bills 1 dollar bills

Which has the higher total value $ (luminosity)? (2) Two sheets (stars) with the same size (diameter), different denominations (temperatures).

A. B. 1 dollar bills 20 dollar bills

Which has the higher total value $ (luminosity)? (3) Two sheets (stars) with the same total value $ (luminosity), different denomination (temperatures).

A. B.

1 dollar bills 20 dollar bills

Which sheet (star) has a larger size (diameter)?

The Hertzsprung – Russell Diagram

Henry N. Russell, Ejnar Hertzsprung -made a simple plot of stars -M vs. Spectral Type -to see if properties are related

RESULTS: The H-R Diagram “most important correlation between stellar properties discovered to date” (Mihalas & Binney, Galactic Astronomy)

High L Luminosity or M Low L High T Low T Temperature or Spectral Type or Color

In general: (90% of all stars) Hotter stars are more luminous Main Sequence

But, some stars are cool & very luminous some stars are hot with low luminosity

Groups on the HR diagram:

- Main Sequence - Red Giants - White Dwarfs - Supergiants

Luminosity Class - separate groups on HR diagram

Luminosity Class Type of Star I Supergiant II Bright Giant III Red Giant IV Subgiant V Main Sequence

Mass of Stars

Use binary star systems - two stars that orbit around each other

Finding mass of stars: - depends on orbital properties

- size of orbit, time to complete orbit (period) - depends on center of mass (balance point)

Two equal mass stars:

Center of mass – exactly in the middle

Two unequal mass stars:

Center of mass – closer to more massive star

http://csep10.phys.utk.edu/guidry/java/binary/binary.html http://astro.unl.edu/naap/ebs/animations/ebs.html

Example: Total Mass: 6 M

Based on CM: if M1 = M2 What are M1, M2 ?

Based on CM: if M1 = 2M2 What are M1, M2 ?

Size of Orbit

+ Period of orbit MASS

+

Center of Mass

Mass – Luminosity Relation - developed by studying binary stars - can be applied to all Main Sequence stars

- but not to other stars

L related to (mass)3

Stellar Models

based on: Hydrostatic Equilibrium Thermal Equilibrium Heat Transport

Russell - Vogt Theorem: - all the properties of a star are uniquely

determined by:

Mass

Chemical Composition

Difference between stars along the main sequence: Difference in Mass

Difference between main sequence and other groups:

Difference in Composition