Goal: To understand how to find the brightness of stars and what they mean.

1. Goal: To understand how to find the brightness of stars and what they mean. Objectives: To learn about Absolute brightness To learn about the Magnitude system To learn about Apparent brightness To understand Apparent magnitude To understand Absolute Magnitude To explore what we can learn about stars by comparing their Apparent and Absolute brightnesses

2. Absolute brightness • Absolute brightness is how bright an object really is. • Absolute brightness does not change with distance as it is the amount of light the thing actually radiates. • The sun has an absolute brightness of 2 * 1033 erg/sec (which is enough to power the entire USA for 3 million years!). • The earth in the infrared has an absolute brightness of about 1 * 1024 erg/sec (which is still enough energy to power the USA for a day).

3. Luminosity • A more common turn for an objects actual brightness is Luminosity • An object’s luminosity depends only on the temperature and size of the object (as it radiates like a blackbody). • You don’t need to memorize or use this equation, just understand how it works: • L = 4πσ R2 T4 (σ is called the Stefan-Boltzmann constant)

4. Magnitude • However, it is usually difficult to measure an objects actual brightness. • We have to know how far away it is as well as how hot and how big it is. • Also, as we have seen, brightness can greatly differ from star to star (by factors of trillions). • So, we need a convention to be able to scale this down to something that we can fit on a single scale. • We do this by using magnitudes.

5. Ancient “magnitude” scale • Ancient astronomers had no way to measure directly how bright an object was. • So, they devised a way to give comparative estimates for how bright in the sky objects looked. • The brightest star in a constellation was defined to be first magnitude. • The next brightest was 2nd magnitude. • And so on – and we can see down to about 6 or 7th magnitude in a “dark” sky with our naked eye.

6. Modern “magnitude” scale • However we have long since calibrated the scale to make it more exact. • To do this we have defined the “apparent” brightness of the star Vega to be magnitude 0 in all colors and wavelengths (it should be noted that some # of ergs per second will have a different magnitude in different colors/wavelengths). • After that we use a logarithmic scale. • Like in ancient times, we made smaller #s be brighter objects.

7. logarithmic scale • A logarithmic scale is a scale that instead of going up by adding 1 we go up by multiplying a factor. • So, instead of 1,2,3, we go by X1, X2,X3. • X can be anything. • For stars, X is about 2.5. • So, 5 orders of magnitude is a factor of 2.55 (which turns out to be about a factor of 100) • Some scales also have logarithmic scales for both axis. These are called log-log plots.

8. Apparent Brightness • What do you think apparent brightness means? • A) The brightness of an object from a distance of 10 parsecs • B) How bright the object actually is • C) How bright the object appears to be from your perspective • D) The time it takes light to get from the object to us.

9. Apparent Brightness • What do you think apparent brightness means? • C) How bright the object appears to be from your perspective • So, apparent brightness depends on how bright the object actually is AND how far away it is.

10. Further away • Imagine a campfire. • The campfire emits heat – which is just infrared light. • The fire emits this heat in all directions – in a sphere. • If you move twice as far away from the fire, by what factor doe the amount of heat you get from the fire decrease? • A) 4 • B) 2 • C) 1.4 • D) you no longer get any heat

11. Further away • Imagine a campfire. • The campfire emits heat – which is just infrared light. • The fire emits this heat in all directions – in a sphere. • If you move twice as far away from the fire, by what factor doe the amount of heat you get from the fire decrease? • A) 4 • Light emitted spreads out over an area, and the area of a sphere depends on the radius squared. • So, the light drops as the radius squared. • So, you get 4 times less light. • If you went 3 times further away it would be a ninth, ect.

12. Apparent Magnitude • So, the further away a star is, the dimmer it will appear to be. • Our sun is much closer to us than any other star, so it appears to be very bright. • If you scale the brightness logarithmically, then how bright a star appears to be is its Apparent Magnitude. • But if a star gets 10 time further away, then it would be 100X dimmer (or 5 magnitudes).

13. Some examples • The sun from viewed from the earth has a apparent magnitude of -26. • The brightest star in the night time sky is Sirius at -1 (that is a factor of 10 billion times dimmer than the sun). • The Hubble Space Telescope can see to about magnitude 30 (which is about a trillion times dimmer than Sirius). • So, larger #s are dimmer. • Pluto is 14th magnitude. • Alpha Centauri A/B (Rigel) are magnitudes 0/1. • Alpha Centauri Proxima (the red dwarf) has a magnitude of 10.7

14. Apparent vs Absolute • Do apparent and/or absolute magnitudes depend on how far the star is from us? (answers are by apparent, absolute) • A) yes, yes • B) yes, no • C) no, yes • D) no, no

15. Apparent vs Absolute • Do apparent and/or absolute magnitudes depend on how far the star is from us? (answers are by apparent, absolute) • B) yes, no • Apparent magnitudes depend on distance (if the star is further away it appears dimmer). • However absolute magnitudes do not depend on distance. • Absolute magnitude is how bright the star actually is.

16. Absolute Magnitude • The Absolute Magnitude of a star is how bright the star would be if it was place at a distance of 10 parsecs. • This magnitude is independent of distance from earth. • Example, the absolute magnitude of our sun is about +5.

17. Why is this all important? • Well, if you know how bright a star is supposed to be and how bright it appears to be you can tell how far away it is. • If you know how far away a star is, how bright it appears to be, and what its temperature is, then you can find what its actual brightness is, and with it how big it is (in size, not mass). • Also, as we will see later, from the size and distance you can get other values such as a possible age and what type of star it is.

18. On the horizon • As we will see in the coming weeks, the changes in brightness of an object can tell us a great deal about it also.

19. Conclusion • The brightness of a star depend on its temperature and radius. • The apparent brightness of a star depends on its absolute brightness and its distance from us. • The absolute brightness is independent of distance. • From all this we can find distances and sizes of stars.