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…”

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

The Magnitude Scale In the 2nd 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 Magnitude Description 1st The 20 brightest stars 2nd stars less bright than the 20 brightest 3rd and so on... 4th getting dimmer each time 5th and more in each group, until 6th the dimmest stars (depending on your eyesight) aka apparent brightness

Apparent Magnitude 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.

The Magnitude Scale (m) – revised 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

Brighter = Smaller magnitudes Fainter = 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 Earth telescopes ~25

using Apparent Magnitude to calculate ratios of apparent brightness Difference in apparent magnitudes of stars Ratio of apparent brightness

using Apparent Magnitude to calculate ratios of apparent brightness The Star Cluster Pleiades is 117 pc from Earth in the constellation Taurus. Determine the ratio of apparent brightness for the two stars selected

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

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

Once we have both brightness and distance, we can do that! 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… Once we have both brightness and distance, we can do that! Absolute Magnitude: The magnitude an object would have if we put it 10 parsecs away from Earth

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 magnitude Remember magnitude scale is “backwards”

The “Distance Modulus” gives ratio of apparent brightness  “light ratio” The difference between the apparent magnitude and the absolute magnitude. m - M = Distance Modulus 2.512m-M = “light ratio” Now can use our definition of apparent brightness in a useful way. d1= 10Pc b1 = brightness at 10Pc

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?

Solution: Distance modulus m – M = 2 – 6 = -4 2.5124 = 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

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?

Solution: Distance modulus m – M = 4 – -3 = 7 2.5127 = 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

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

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