1. Usually, what we know is how bright the star looks to us here on Earth… We call this its Apparent Magnitude “What you see is what you get…”

2. The 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 earthquake  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 earthquake This is the “8.9” earthquake off of Sumatra Betelgeuse and Rigel, stars in Orion with apparent magnitudes 0.3 and 0.9

3.  In the 2 nd century BC, Hipparchus invented the Magnitude Scale.  Stars are placed on the following scale  These are often referred to as apparent magnitudes because the value depends on  Distance from Earth  Luminosity  In the 2 nd century BC, Hipparchus invented the Magnitude Scale.  Stars are placed on the following scale  These are often referred to as apparent magnitudes because the value depends on  Distance from Earth  Luminosity aka apparent brightness MagnitudeDescription 1stThe 20 brightest stars 2ndstars less bright than the 20 brightest 3rdand so on... 4thgetting dimmer each time 5thand more in each group, until 6ththe dimmest stars (depending on your eyesight) The Magnitude Scale

4.  On the scale a 1 star is approx. 100 times brighter than a 6 star. in other words it takes 100 Mag. 6 stars to be equally as bright as a Mag. 1 star.  On the scale a 1 star is approx. 100 times brighter than a 6 star. in other words it takes 100 Mag. 6 stars to be equally as bright as a Mag. 1 star.

5.  To make calculations easier, a new scale was developed in the nineteenth century.  In this scale a magnitude difference of 5 exactly corresponds to a factor of 100 in brightness according to the following equation  To make calculations easier, a new scale was developed in the nineteenth century.  In this scale a magnitude difference of 5 exactly corresponds to a factor of 100 in brightness according to the following equation The Magnitude Scale (m) – revised

6. Brighter = Smaller magnitudes Fainter = Bigger magnitudes  Magnitudes can even be negative for really bright stuff! ObjectApparent Magnitude The Sun-26.8 Full Moon-12.6 Venus (at brightest)-4.4 Sirius (brightest star)-1.5 Faintest naked eye stars6 to 7 Faintest star visible from Earth telescopes ~25

7. Ratio of apparent brightness Difference in apparent magnitudes of stars

8.  The Star Cluster Pleiades is 117 pc from Earth in the constellation Taurus. Determine the ratio of apparent brightness for the two stars selected

9. 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

10. …we need to know its distance! In order to get from how bright something looks… to how much energy it’s putting out…

11. The whole point of knowing the distance using the parallax method (and other methods to be discussed later) is to figure out luminosity… It is often helpful to put luminosity on the magnitude scale… Absolute Magnitude: The magnitude an object would have if we put it 10 parsecs away from Earth Once we have both brightness and distance, we can do that!

12. Absolute Magnitude (M)  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 magnitude  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 magnitude Remember magnitude scale is “backwards” removes the effect of distance and puts stars on a common scale

13. The “Distance Modulus” gives ratio of apparent brightness  “light ratio”  The difference between the apparent magnitude and the absolute magnitude. m - M = Distance Modulus  2.512 m-M = “light ratio”  Now can use our definition of apparent brightness in a useful way.  d 1 = 10Pc  b 1 = brightness at 10Pc  The difference between the apparent magnitude and the absolute magnitude. m - M = Distance Modulus  2.512 m-M = “light ratio”  Now can use our definition of apparent brightness in a useful way.  d 1 = 10Pc  b 1 = brightness at 10Pc

14. Example Problem  A star has an apparent magnitude of 2.0 and an absolute magnitude of 6.0. What is the distance to the star?

15. Solution:  Distance modulus m – M = 2 – 6 = -4  2.512 4 = 40, so the light ratio is 40:1  The fact that the distance modulus is negative means the star is closer than 10Pc.  Use the ratio of apparent brightness  Distance modulus m – M = 2 – 6 = -4  2.512 4 = 40, so the light ratio is 40:1  The fact that the distance modulus is negative means the star is closer than 10Pc.  Use the ratio of apparent brightness

16. Example Problem  A star has an apparent magnitude of 4.0 and an absolute magnitude of -3.0. What is the distance to the star?

17. Solution:  Distance modulus m – M = 4 – -3 = 7  2.512 7 = 631, so the light ratio is 631:1  The fact that the distance modulus is positive means the star is farther away than 10Pc.  Use the ratio of apparent brightness  Distance modulus m – M = 4 – -3 = 7  2.512 7 = 631, so the light ratio is 631:1  The fact that the distance modulus is positive means the star is farther away than 10Pc.  Use the ratio of apparent brightness

18. Absolute Magnitude (M) Knowing the apparent magnitude (m) and the distance in pc (d) of a star its absolute magnitude (M) can be found using the following equation: Example: 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 Answer = +4.8

19. So we have three ways of talking 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  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