Transcript Lesson 6 - Magnitudes of Stars

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 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
 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
5
(2.512)  100
2.512 x2.512 x2.512 x2.512 x2.512  (2.512)  100
5
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
(2.512)
m2  m1

Difference in apparent magnitudes
of stars
Ratio 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
(2.512)
m2  m1

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
In order to get from how
bright something looks…
to how much energy
it’s putting out…
…we need to know its distance!
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.
b1
 d1= 10Pc

 b1 = brightness at 10Pc
b2
2
d2
2
d1
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
b1 d 22
 2
b2 d1
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
b1 d 22
 2
b2 d1
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:
d 
m  M  5 log  
 10 
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