Usually, what we know is how bright the star looks to us here on Earth…

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…”

The Magnitude ScaleThe 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

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

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

aka apparent brightness

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)

The Magnitude ScaleThe Magnitude Scale

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.

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( . )2 512 1005

2 512 2 512 2 512 2 512 2 512 2 512 1005. . . . . ( . )x x x x

The Magnitude Scale (m) – revised The Magnitude Scale (m) – revised

Brighter = Smaller magnitudesFainter = Bigger magnitudes

Brighter = Smaller magnitudesFainter = Bigger magnitudes Magnitudes can even be negative

for really bright stuff! 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

( . )2 512 2 1m m

Ratio of apparent brightness

Difference in apparent magnitudes of stars

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

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

( . )2 512 2 1m m

However: knowing how bright a star looks doesn’t really tell us anything about the star itself!

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’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!

…we need to know its distance!

In order to get from how bright something looks…

to how much energy it’s putting out…

The whole point of knowing the distance using the parallax method (and other methods to be discussed later) is to figure out luminosity…

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: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!

Absolute Magnitude (M)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 magnitudeRemember magnitude scale is “backwards”

removes the effect of distanceand

puts stars on a common scale

The “Distance Modulus” gives ratio of apparent brightness “light ratio”

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

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 2

1

22

2

1

d

d

b

b

Example ProblemExample Problem

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

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

Solution: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

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

21

22

2

1

d

d

b

b

Example ProblemExample Problem

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

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

Solution: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

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

21

22

2

1

d

d

b

b

Absolute Magnitude (M)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:

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:

10

log5d

Mm

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: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