Chapter 11Chapter 11

Surveying The StarsSurveying The Stars

Properties of StarsProperties of Stars Distance

Speed

Radius

Brightness (Intensity)

Temperature

Luminosity ( L ) - the amount of energy a star radiates per unit time = power (e.g. Lsun= 4 x 1026 Watts.)

Intensity ( I ) – Power per unit area (Power/Area) Intensity is measured in Watts/m2.

Stefan-Boltzmann Law - a star of temperature T radiates an amount of energy each second (Power) equal to T4 per square meter ( Intensity )

I = Power/area = T4.

L = Power output of the star.

I = (Luminosity)/(surface area of a sphere).

I = L/4d2

Definitions

Measuring A Star’s “Brightness”Measuring A Star’s “Brightness” Inverse-Square Law - the apparent brightness

(Intensity) of a star decreases with increasing distance from Earth

24 d

LIB

424 TRL R

The Luminosity of the star can be written as:

Where:

L = Luminosity

R = Radius of the star

= Stefan-Bolzmann constant

T = Surface temperature in K

The Inverse Square Law for Light

24 d

Larea

powerI

d

area = 4d2

The Magnitude SystemThe Magnitude System

Apparent Magnitude - logarithmic scale of brightness for stars (e.g. the size of the dots on star charts)

Absolute Magnitude - the apparent magnitude that a star would have if it were 10 parsecs away from Earth

Measuring a Star’s DistanceMeasuring a Star’s Distance

Parallax - the apparent change in the position of a star due to the motion of the Earth

Nearby objects exhibit more parallax that remote ones.

pd

1

AngleParallax

1= Parsecsin Distance

Stellar Parallax

Stellar Parallax

Stellar DistancesStellar Distances Parsec - the distance corresponding to a parallax angle

of exactly 1” (1 arc second) and the baseline is 1A.U. (distance between the earth and sun)

1 parsec = 3.26 light years

1 arc second = 1/3600 degrees

Light-year - the distance that light travels in one year.

Proxima Centauri is 4.2 light years from Earth (24 trillion miles).

Stellar Motion

Measuring A Star’s TemperatureMeasuring A Star’s Temperature

A star’s surface temperature can be determined from its color using Wien’s Law.

• Red coolest star• Orange• Yellow• White• Blue hottest star

Hubble Space Telescope view through the Galaxy reveals that stars come in different colors

Stellar SpectroscopyStellar Spectroscopy

Stellar Spectroscopy - the study of the properties of stars by measuring absorption line strengths

Spectral Class - classification of star according to the appearance of their spectra

O B A F G K M

Binary StarsBinary Stars Optical Double - two stars that just happen

to lie in the same direction as seen from Earth

Visual Binary - two stars that are orbiting one another and can both be seen from Earth

Binary StarsBinary Stars Spectroscopic Binary - two stars that are found to

orbit one another through observations of the Doppler effect in their spectral lines

Eclipsing Binary - two stars that regularly eclipse one another causing a periodic variation in brightness

Light Curve - a plot of a variable star's apparent magnitude versus time

Sirius A and Sirius B at ten year intervals reveals a binary system

Apparent Brightness Of An Eclipsing Binary System

Spectral Lines of a Binary System – Alternating Doppler Shift

Compare these spectra.

Spectrum of Hydrogen in Lab

Spectrum a Star

What do these spectra tell us about the star?

Compare these spectra.

Spectrum of Hydrogen in Lab

Spectrum a Star

What do these spectra tell us about the star?

Compare these spectra.

Spectrum of Hydrogen in Lab

Spectrum a Star…..Day 1

What do these spectra tell us about the star?

Spectrum a Star…..Day 2

Spectrum a Star…..Day 3

Spectrum a Star…..Day 4

Mystery Star PropertiesMystery Star Properties1. The star appears as a point of light through a telescope.

2. The absorption lines appear split and move over a

4 day period.

3. The brightness of the star also varies over 4 days.

Question: Why do you think the brightness of the

star is varying?

Answer: This could be an eclipsing binary star

system that cannot be resolved by a

telescope!

The H-R DiagramThe H-R Diagram

Hertzsprung-Russell Diagrams - plots of luminosity versus temperature known stars

Most stars on the H-R diagram lie along a diagonal curve called the main sequence.

Stellar Luminosity Classes

CLASS DESCRIPTION Ia Bright supergiants IbSupergiants II Bright giants III Giants IV Subgiants V Main-sequence stars/dwarfs

Along the main sequence, more massive stars are brighter and hotter but have shorter lifetimes

Stellar Lifetimes Star Spectral Mass Central Luminosity Estimated

Type (Solar) Temp(K) (Solar Lum) Lifetime

• (106 Years)

Rigel B8Ia 10 30 44,000 20 Sirius A1V 2.3 20 23 1,000 -Centauri G2V 1.1 17 1.4 7,000 Sun G2V 1.0 15 1.0 10,000 P-Centauri M5V 0.1 5.0 0.00006 >1,000,000

Variable StarsVariable Stars

Stars that have a change in brightness over time are called variable stars.

Examples:– Eclipsing binary stars– Cepheid variables– RR Lyra variables

A Typical Light Curve For A Cepheid Variable Star.

~ 15 days

H-R diagram with the instability strip highlighted

Star Clusters

Open Clusters: Loosely bound collection of tens to hundreds of stars, a few parsecs across, generally found in the plane of the Milky Way.

Globular Clusters: Tightly bound, roughly spherical collection of hundreds of thousands , and sometimes millions, of stars spanning about 50 parsecs. Globular Clusters are distributed in the halos around the Milky Way and other galaxies.

H-R Diagram for the Pleiades.

Missing upper main

sequence stars

Main Sequence turn off –

Pleiades ~ 100 million yrs old

B6

Star Clusters

Open Cluster Globular Cluster

H-R Diagram for the globular cluster Palomar 3.

Main sequence turnoff indicates age ~ 12-14 billion years

Matching Questions

1. The temperature of a star can be determined from its_____________.

2. The pattern of the absorption spectral lines for a star contains information about a star’s________________.

3. The Doppler shift of a star's spectral lines tells us something about the star’s_______________.

4. The distance of a star from Earth can be determined from the star’s_______________.

5. The radius of a star can be determined from its ________________.

(a) composition.(b) parallax shift.(c) motion.(d) luminosity and temperature.(e) color.

H-R Diagram Questions1. What property is measure along

the horizontal axis?

2. … along the vertical axis?

3. Where are the red giants?

4. … the white dwarfs?

5. … the hottest stars?

6. … the coolest stars?

7. … the largest stars?

8. … the smallest stars?

H-R Diagram Questions9. Where are O class stars?

10. … M class stars?

11. … G class stars?

12. Where is the Sun?

13. Where are the high-mass main-

sequence stars?

14. Where are the low-mass main-

sequence stars?

15. Where are the oldest stars?

16. Which stars along the main-sequence

live the longest?

End of Chapter 13