1. Devil physics The baddest class on campus IB Physics

2. Tsokos Lesson E-3 Stellar objects

3. 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.

4. 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.

5. 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 Explain how stellar distance may be determined using apparent brightness and luminosity. E State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc. E Solve problems involving stellar distances, apparent brightness and luminosity.

6. IB Assessment Statements
Option E-3, Stellar Distances:
Cepheid Variables
E Outline the nature of a Cepheid variable.
E State the relationship between period and absolute magnitude for Cepheid variables.
E Explain how Cepheid variables may be used as “standard candles”.
E Determine the distance to a Cepheid variable using the luminosity-period relationship.

7. 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 = m

8. Objectives Solve problems using apparent brightness and luminosity
Use the magnitude-distance formula

9. 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

10. 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

11. Parallax Method
Since the parallax angle is very small, tan p ≈ p where p is measured in radians

12. 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

13. Parallax Method
The radius of the earth’s orbit is defined as one astronomical unit (AU)
1 AU = 1.5 x 1011 m

14. 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

15. Parallax Method
Parallax method fails if the angle is less than 1 arcsecond
Parallax allows measurements up to ly (≈ 100 parsec) from earth
Satellites can measure distances greater than 500 parsecs

16. 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

17. Parallax Method

18. Parallax Method
5 stars nearest to earth

19. 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

20. Apparent Magnitude
What is the apparent magnitude of a star whose apparent brightness is 6.43 x W/m2?

21. Apparent Magnitude
What is the apparent magnitude of a star whose apparent brightness is 6.43 x W/m2?

22. Apparent Magnitude
What is the apparent brightness of a star whose apparent magnitude is 4.35?

23. Apparent Magnitude
What is the apparent brightness of a star whose apparent magnitude is 4.35?

24. Apparent Magnitude
Magnitude scale is defined so that the larger the magnitude, the dimmer the star!

25. 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

26. 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
where d is given in parsecs!

27. Apparent and Absolute Magnitude

28. 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

29. Spectroscopic Parallax
So how do you determine luminosity?
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

30. The Cepheids Stars whose luminosity varies periodically over time
Periods range from days to months
Brightness increases rapidly and fades gradually

31. 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)

32. 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

33. The Cepheids
The period of the Cepheid in the lower diagram is about 22 days
The luminosity from the upper diagram is solar luminosities or 2.73 x 1030 W

34. The Cepheids The peak apparent magnitude (m) from the diagram is 3.7
Apparent brightness (b) is found to be

35. The Cepheids
So the distance is,

36. 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’

37. 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 = m?

38. Summary Review
Can you solve problems using apparent brightness and luminosity?
Can you use the magnitude-distance formula

39. 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.

40. 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.

41. 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 Explain how stellar distance may be determined using apparent brightness and luminosity. E State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc. E Solve problems involving stellar distances, apparent brightness and luminosity.

42. IB Assessment Statements
Option E-3, Stellar Distances:
Cepheid Variables
E Outline the nature of a Cepheid variable.
E State the relationship between period and absolute magnitude for Cepheid variables.
E Explain how Cepheid variables may be used as “standard candles”.
E Determine the distance to a Cepheid variable using the luminosity-period relationship.

43. Questions?

44. Homework
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