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Chapter 11 Surveying The Stars Properties 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 sT4 per square meter ( Intensity ) Definitions I = Power/area = sT4. L = Power output of the star. I = (Luminosity)/(surface area of a sphere). I = L/4d2 Measuring A Star’s “Brightness” Inverse-Square Law - the apparent brightness (Intensity) of a star decreases with increasing distance from Earth L BI 2 4d The Luminosity of the star can be written as: L 4R sT 2 4 Where: L = Luminosity R = Radius of the star s= Stefan-Bolzmann constant T = Surface temperature in K The Inverse Square Law for Light power I area L 2 4d area = 4d2 The 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 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. Distance in Parsecs = 1 Parallax Angle d 1 p Stellar Parallax Stellar Parallax Stellar 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 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 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 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 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 Spectrum a Star…..Day 2 Spectrum a Star…..Day 3 Spectrum a Star…..Day 4 What do these spectra tell us about the star? 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 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 Ia Ib II III IV V DESCRIPTION Bright supergiants Supergiants Bright giants Giants Subgiants 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 • Rigel Sirius -Centauri Sun P-Centauri (106 Years) B8Ia A1V G2V G2V M5V 10 2.3 1.1 1.0 0.1 30 20 17 15 5.0 44,000 23 1.4 1.0 0.00006 20 1,000 7,000 10,000 >1,000,000 Variable 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 B6 Main Sequence turn off – Pleiades ~ 100 million yrs old Open Cluster Globular Cluster Star Clusters 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) (b) (c) (d) (e) composition. parallax shift. motion. luminosity and temperature. 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 mainsequence stars? 14. Where are the low-mass mainsequence stars? 15. Where are the oldest stars? 16. Which stars along the main-sequence live the longest? End of Chapter 13