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