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# E3 - Stellar Distances

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Topic E3 of IB Physics Astrophysics

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### E3 - Stellar Distances

1. 1. E3 Astronomical distancesThe SI unit for length, the metre, is a very small unitto measure astronomical distances. There units usuallyused is astronomy:The Astronomical Unit (AU) – this is the average distancebetween the Earth and the Sun. This unit is more used withinthe Solar System.1 AU = 150 000 000 km or 1 AU = 1.5x1011m
2. 2. E3 Astronomical distancesThe light year (ly) – this is the distance travelled by thelight in one year. c = 3x108 m/s t = 1 year = 365.25 x 24 x 60 x 60= 3.16 x 107 s Speed =Distance / Time Distance = Speed x Time = 3x108 x 3.16 x 107 = 9.46 x 1015 m 1 ly = 9.46x1015 m
3. 3. E3.1 Astronomical distancesThe parsec (pc) – this is thedistance at which 1 AU subtends anangle of 1 arcsencond. “Parsec” is short for parallax arcsecond 1 pc = 3.086x1016 m or 1 pc = 3.26 ly
4. 4. E3.1 Angular sizes 360 degrees (360o) in a circle 60 arcminutes (60’) in a degree 60 arcseconds (60”) in an arcminute
5. 5. E3.11 parsec = 3.086 X 1016 metres  Nearest Star 1.3 pc (206,000 times further than the Earth is from the Sun)
6. 6. E3.2 ParallaxBjork’s Eyes Where star/ball Space appears relative to background Angle star/ball appears to shift Distance to star/ball “Baseline”
7. 7. E3.2 Parallax Parallax, more accuratelymotion parallax, is the change ofangular position of twoobservations of a single objectrelative to each other as seen byan observer, caused by themotion of the observer. Simply put, it is the apparentshift of an object against thebackground that is caused by achange in the observers position.
8. 8. E3.2 ParallaxWe know how big the Earth’s orbit is, we measure the shift(parallax), and then we get the distance… Parallax - p (Angle) Distance to Star - d Baseline – R (Earth’s orbit)
9. 9. E3.2 Parallax R (Baseline) tan p (Parallax) d (Distance)For very small angles tan p ≈ p R p dIn conventional units it means that 11 1.5 x 10 16 1 pc m 3.086 x 10 m 2 1 360 3600
10. 10. E3.2 Parallax 11 1.5 x 10 161 pc m 3.086 x 10 m 2 1 360 3600 R R p d d p 1 d (parsec) p ( arcsecond)
11. 11. E3.3 Parallax has its limits The farther away an object gets, the smaller its shift.Eventually, the shiftis too small to see.
12. 12. Another thing we can figure out about stars is their colors… We’ve figured out brightness, but stars don’t put out an equal amount of all light… …some put out more blue light, while others put out more red light!
13. 13. Usually, what we know is how E3.5bright the star looks to us hereon Earth… We call this its Apparent Magnitude “What you see is what you get…”
14. 14. E3.5The Magnitude Scale  Magnitudes are a way of assigning a number to a star so we know how bright it is  Similar to how the Richter scale assigns a number to the strength of an earthquakeBetelgeuse and Rigel, stars in Orion withapparent magnitudes This is the “8.9” 0.3 and 0.9 earthquake off of Sumatra
15. 15. E3.5The historical magnitude scale… Greeks ordered the Magnitude Description stars in the sky 1st The 20 brightest from brightest to stars faintest… 2nd stars less bright than the 20 brightest 3rd and so on... …so brighter stars 4th getting dimmer have smaller each time magnitudes. 5th and more in each group, until 6th the dimmest stars (depending on your eyesight)
16. 16. E3.5Later, astronomers quantified this system. Because stars have such a wide range in brightness, magnitudes are on a “log scale” Every one magnitude corresponds to a factor of 2.5 change in brightness Every 5 magnitudes is a factor of 100 change in brightness (because (2.5)5 = 2.5 x 2.5 x 2.5 x 2.5 x 2.5 = 100)
17. 17. E3.5Brighter = Smaller magnitudesFainter = Bigger magnitudes  Magnitudes can even be negative for really bright stuff! Object Apparent Magnitude The Sun -26.8 Full Moon -12.6 Venus (at brightest) -4.4 Sirius (brightest star) -1.5 Faintest naked eye stars 6 to 7 Faintest star visible from ~25 Earth telescopes
18. 18. E3.5 However: knowing how bright a star looks doesn’t really tell us anything about the star itself!We’d really like to know things that are intrinsic properties of the star like: Luminosity (energy output) and Temperature
19. 19. In order to get from howbright something looks… to how much energy it’s putting out… …we need to know its distance!
20. 20. E3.6The whole point of knowing thedistance using the parallax method isto figure out luminosity… Once we have both brightness and distance, It is often helpful to put we can do that! luminosity on the magnitude scale… Absolute Magnitude: The magnitude an object would have if we put it 10 parsecs away from Earth
21. 21. E3.6 Absolute Magnitude (M) removes the effect of distance and puts stars on a common scale  The Sun is -26.5 in apparent magnitude, but would be 4.4 if we moved it far away  Aldebaran is farther than 10pc, so it’s absolute magnitude is brighter than its apparent magnitudeRemember magnitude scale is “backwards”
22. 22. E3.6 Absolute Magnitude (M)Knowing the apparent magnitude (m) and thedistance in pc (d) of a star its absolute magnitude (M)can be found using the following equation: m M 5log 10 dExample: Find the absolute magnitude of the Sun. The apparent magnitude is -26.7 The distance of the Sun from the Earth is 1 AU = 4.9x10-6 pc Therefore, M= -26.7 – log (4.9x10-6) + 5 = = +4.8
23. 23. E3.6So we have three ways oftalking about brightness: Apparent Magnitude - How bright a star looks from Earth Luminosity - How much energy a star puts out per second Absolute Magnitude - How bright a star would look if it was 10 parsecs away
24. 24. E3.9 Spectroscopic parallax Spectroscopic parallax is an astronomical method for measuring the distances to stars. Despite its name, it does not rely on the apparent change in the position of the star. This technique can be applied to any main sequence star for which a spectrum can be recorded.
25. 25. E3.9 Spectroscopic parallaxThe Luminosity of a star can be found using anabsorption spectrum.Using its spectrum a star can be placed in a spectralclass.Also the star’s surface temperature can determinedfrom its spectrum (Wien’s law)Using the H-R diagram and knowing bothtemperature and spectral class of the star, itsluminosity can be found.
26. 26. E3.13 Types of Stars (review) Cepheid variables Cepheid variables are stars of variable luminosity. The luminosity increases sharply and falls of gently with a well-defined period. The period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star. A Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity. The luminosity of Cepheid stars range from 103 to 104 times that of the Sun.
27. 27. E3.13 Cepheid variables The relationship between a Cepheidvariables luminosity and variability period isquite precise, and has been used as astandard candle (astronomical object that hasa know luminosity) for almost a century. This connection wasdiscovered in 1912 byHenrietta Swan Leavitt.She measured thebrightness of hundredsof Cepheid variablesand discovered adistinct period-luminosity relationship.
28. 28. E3.13
29. 29. E3.14 Cepheid variablesA three-day period Cepheid has a luminosity of about 800times that of the Sun.A thirty-day period Cepheid is 10,000 times as bright as theSun.The scale has been calibrated using nearby Cepheid stars, forwhich the distance was already known.This high luminosity, and the precision with which theirdistance can be estimated, makes Cepheid stars the idealstandard candle to measure the distance of clusters andexternal galaxies.
30. 30. E3.14Cepheid variables
31. 31. E3.14
32. 32. E3 SummaryDistance measured by parallax: Distancemeasurement apparent spectrum by parallax brightness Chemical composition Wien’s Law of corona Luminosity d=1/p (surface L = 4πd2 b temperature T) L = 4πR2 σT4 Stefan-Boltzmann Radius
33. 33. E3 SummaryDistance measured by spectroscopic parallax / Cepheid variables: Apparent Luminosity spectrum Chemical brightness class composition Spectral type Cepheid variable H-R Surface temperature (T) Period diagram Wien’s Law Luminosity (L) Stefan-Boltzmann b = L / 4πd2 L = 4πR2 σT4 Distance (d) Radius