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DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON E-3 STELLAR OBJECTS IB Assessment Statements Option E-3, Stellar Distances: Parallax Method E.3.1. Define the parsec. E.3.2. Describe the stellar parallax method of determining the distance to a star. E.3.3. Explain why the method of stellar parallax is limited to measuring stellar distances less than several hundred parsecs. E.3.4. Solve problems involving stellar parallax. IB Assessment Statements Option E-3, Stellar Distances: Absolute and Apparent Magnitudes E.3.5. Describe the apparent magnitude scale. E.3.6. Define absolute magnitude. E.3.7. Solve problems involving apparent magnitude, absolute magnitude and distance. E.3.8. Solve problems involving apparent brightness and apparent magnitude. IB Assessment Statements Option E-3, Stellar Distances: Spectroscopic Parallax E.3.9. State that the luminosity of a star may be estimated from its spectrum. E.3.10. Explain how stellar distance may be determined using apparent brightness and luminosity. E.3.11. State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc. E.3.12. Solve problems involving stellar distances, apparent brightness and luminosity. IB Assessment Statements Option E-3, Stellar Distances: Cepheid Variables E.3.13. Outline the nature of a Cepheid variable. E.3.14. State the relationship between period and absolute magnitude for Cepheid variables. E.3.15. Explain how Cepheid variables may be used as “standard candles”. E.3.16. Determine the distance to a Cepheid variable using the luminosity-period relationship. Objectives Describe the method of parallax, d (in parsecs) = 1/p (in arcseconds), the method of spectroscopic parallax and the Cepheids method for determining distances in astronomy Define the parsec State the definitions of apparent brightness, b = L/4πd2 , and apparent and absolute magnitude, b/b0 = 100-m/5 = 2.512-m Objectives Solve problems using apparent brightness and luminosity Use the magnitude-distance formula Parallax Method When an object is viewed from two different positions, it appears to move relative to a fixed background We can use this fact to measure distances to stars Parallax Method Make two measurements of a star six months apart The distance between the two positions is equal to the diameter of the earth’s orbit around the sun The distance to the star, d, is given by R tan p d R d tan p Parallax Method R tan p d R d tan p R d p Since the parallax angle is very small, tan p ≈ p where p is measured in radians Parallax Method Parallax angle is the angle from the position of the star that subtends a distance equal to the radius of the earth’s orbit of the sun R d p Parallax Method The radius of the earth’s orbit is defined as one astronomical unit (AU) 1 AU = 1.5 x 1011 m R d p Parallax Method Parallax angle measurements are quite accurate provided the angles are not too small Parallax angles down to 1 arcsecond (1” = 1/3600 of a degree) are easily measured from earth R d p Parallax Method Parallax method fails if the angle is less than 1 arcsecond Parallax allows measurements up to 300 ly (≈ 100 parsec) from earth Satellites can measure distances greater than 500 parsecs R d p Parallax Method 1 parsec = 3.26 ly = 3x1016 m 1 parsec = 1 parallax second One parsec is the distance to a star whose parallax angle is one arcsecond R d p Parallax Method 1AU 1 pc 1arc sec ond 11 1.5 x10 1 pc m 1 2 360 3600 15 1ly 9.46 x10 m d par sec s 1 pc 3.09 x10 m 1 pc 3.26ly 16 1 parc sec onds Parallax Method 5 stars nearest to earth Apparent Magnitude Apparent magnitude (m) derived from a scale devised by ancient astronomers The higher the apparent magnitude, the dimmer the star Classification based on a factor of 100 using apparent brightness b m / 5 m 100 2.512 b0 8 b0 2.52 x10 W 5 b m log 2 b0 m 2 Apparent Magnitude What is the apparent magnitude of a star whose apparent brightness is 6.43 x 10-9 W/m2? b m / 5 m 100 2.512 b0 8 b0 2.52 x10 W 5 b m log 2 b0 m 2 Apparent Magnitude What is the apparent magnitude of a star whose apparent brightness is 6.43 x 10-9 W/m2? 5 6.43x10 m log 8 2 2.52 x10 9 m 2.5 log 0.2552 m 1.48 b m / 5 m 100 2.512 b0 8 b0 2.52 x10 W 5 b m log 2 b0 m 2 Apparent Magnitude What is the apparent brightness of a star whose apparent magnitude is 4.35? b m / 5 m 100 2.512 b0 b0 2.52 x10 8 W 5 b m log 2 b0 m 2 Apparent Magnitude What is the apparent brightness of a star whose apparent magnitude is 4.35? b m / 5 m 100 2.512 b0 b0 2.52 x10 8 W b 2.512 m b0 b 4.35 2 . 512 8 2.52 x10 b 2.52 x10 8 2.512 4.35 b 4.58 x10 10 5 b m log 2 b0 m 2 Apparent Magnitude Magnitude scale is defined so that the larger the magnitude, the dimmer the star! b m / 5 m 100 2.512 b0 b0 2.52 x10 8 W 5 b m log 2 b0 m 2 Absolute Magnitude Apparent magnitude is based on view from earth Two stars may have the same apparent magnitude but very different actual brightness depending on their distances from earth Absolute Magnitude Absolute magnitude (M) is equal to the apparent magnitude the star would have if it were 10 parsecs from earth Comparison of apparent and absolute magnitude is given by d m M 5 log 10 m M / 5 d 10 x10 pc where d is given in parsecs! Apparent and Absolute Magnitude Apparent Absolute Spectroscopic Parallax Using the star’s luminosity and apparent brightness to determine its distance Parallax is not involved – it’s just there to mess with your head Luminosity is the power output of a star and is based on temperature and surface area L b 2 4d L d 4b L Spectroscopic Parallax b 2 4d So how do you determine L d luminosity? 4b From the emission spectrum, we can determine temperature using Wien’s Law From temperature and the HR diagram (knowing what kind of star) we can determine luminosity The Cepheids Stars whose luminosity varies periodically over time Periods range from days to months Brightness increases rapidly and fades gradually The Cepheids The interaction of radiation and matter in the outer layers of the star’s atmosphere causes it to expand (brightest) and contract (dimmest) The Cepheids The longer the period, the larger the luminosity Measuring a Cepheid’s period allows you to determine luminosity which in turn allows you to determine distance The Cepheids The period of the Cepheid in the lower diagram is about 22 days The luminosity from the upper diagram is 7000 solar luminosities or 2.73 x 1030 W The Cepheids The peak apparent magnitude (m) from the diagram is 3.7 Apparent brightness (b) is found to be b 3. 7 2.512 x10 8 2.52 x10 10 W b 8.34 x10 2 m L The Cepheids b 2 4d L d 4b So the distance is, 30 2.73 x10 d 10 4 8.34 x10 d 1.6 x10 m d 1700ly d 520 pc 19 The Cepheids Once you know the distance to the Cepheid, you can approximate the distance to its galaxy Using Cepheids to determine distance is useful up to a few Mpc and that is why they are referred to as ‘standard candles’ Summary Review Can you describe the method of parallax, d (in parsecs) = 1/p (in arcseconds), the method of spectroscopic parallax and the Cepheids method for determining distances in astronomy? Can you define the parsec? Can you state the definitions of apparent brightness, b = L/4πd2 , and apparent and absolute magnitude, b/b0 = 100-m/5 = 2.512-m? Summary Review Can you solve problems using apparent brightness and luminosity? Can you use the magnitude-distance formula IB Assessment Statements Option E-3, Stellar Distances: Parallax Method E.3.1. Define the parsec. E.3.2. Describe the stellar parallax method of determining the distance to a star. E.3.3. Explain why the method of stellar parallax is limited to measuring stellar distances less than several hundred parsecs. E.3.4. Solve problems involving stellar parallax. IB Assessment Statements Option E-3, Stellar Distances: Absolute and Apparent Magnitudes E.3.5. Describe the apparent magnitude scale. E.3.6. Define absolute magnitude. E.3.7. Solve problems involving apparent magnitude, absolute magnitude and distance. E.3.8. Solve problems involving apparent brightness and apparent magnitude. IB Assessment Statements Option E-3, Stellar Distances: Spectroscopic Parallax E.3.9. State that the luminosity of a star may be estimated from its spectrum. E.3.10. Explain how stellar distance may be determined using apparent brightness and luminosity. E.3.11. State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc. E.3.12. Solve problems involving stellar distances, apparent brightness and luminosity. IB Assessment Statements Option E-3, Stellar Distances: Cepheid Variables E.3.13. Outline the nature of a Cepheid variable. E.3.14. State the relationship between period and absolute magnitude for Cepheid variables. E.3.15. Explain how Cepheid variables may be used as “standard candles”. E.3.16. Determine the distance to a Cepheid variable using the luminosity-period relationship. QUESTIONS? Homework #1-17