Chapter 11 Surveying The Stars Surveying The Stars

Properties of Stars t Distance t Speed t Radius t Brightness (Intensity) t Temperature

t Luminosity ( L ) - the amount of energy a star radiates per unit time = power (e.g. L sun = 4 x Watts.) t Intensity ( I ) – Power per unit area (Power/Area) Intensity is measured in Watts/m 2.  Stefan-Boltzmann Law - a star of temperature T radiates an amount of energy each second (Power) equal to  T 4 per square meter ( Intensity )

I = Power/area =  T 4. L = Power output of the star. I = (Luminosity)/(surface area of a sphere). I = L/4  d 2 Definitions

Measuring A Star’s “Brightness” t Inverse-Square Law - the apparent brightness (Intensity) of a star decreases with increasing distance from Earth

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 d area = 4  d 2

The Magnitude System t Apparent Magnitude - logarithmic scale of brightness for stars (e.g. the size of the dots on star charts) t Absolute Magnitude - the apparent magnitude that a star would have if it were 10 parsecs away from Earth

Measuring a Star’s Distance t Parallax - the apparent change in the position of a star due to the motion of the Earth t Nearby objects exhibit more parallax that remote ones.

StellarParallax

Stellar Parallax

Stellar Distances t 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) t 1 parsec = 3.26 light years t 1 arc second = 1/3600 degrees t Light-year - the distance that light travels in one year. t Proxima Centauri is 4.2 light years from Earth (24 trillion miles).

Stellar Motion

Measuring A Star’s Temperature t 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 Spectroscopy t Stellar Spectroscopy - the study of the properties of stars by measuring absorption line strengths t Spectral Class - classification of star according to the appearance of their spectra O B A F G K M

Binary Stars t Optical Double - two stars that just happen to lie in the same direction as seen from Earth t Visual Binary - two stars that are orbiting one another and can both be seen from Earth

Binary Stars t Spectroscopic Binary - two stars that are found to orbit one another through observations of the Doppler effect in their spectral lines t Eclipsing Binary - two stars that regularly eclipse one another causing a periodic variation in brightness t 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 Properties 1. 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 Diagram t Hertzsprung-Russell Diagrams - plots of luminosity versus temperature known stars t Most stars on the H-R diagram lie along a diagonal curve called the main sequence.

Stellar Luminosity Classes t CLASSDESCRIPTION t IaBright supergiants t IbSupergiants t IIBright giants t IIIGiants t IVSubgiants t VMain-sequence stars/dwarfs t

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

Stellar Lifetimes t Star Spectral Mass Central Luminosity Estimated Type (Solar) Temp(K) (Solar Lum) Lifetime (10 6 Years) t Rigel B8Ia , t Sirius A1V ,000 t  -Centauri G2V ,000 t Sun G2V ,000 t P-Centauri M5V >1,000,000

Variable Stars t Stars that have a change in brightness over time are called variable stars. t 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 t Open Clusters: Loosely bound collection of tens to hundreds of stars, a few parsecs across, generally found in the plane of the Milky Way. t 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 ClusterGlobular Cluster

H-R Diagram for the globular cluster Palomar 3. Main sequence turnoff indicates age ~ 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 Questions 1. 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 Questions 9. 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