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DEVIL PHYSICS
THE BADDEST CLASS ON CAMPUS
IB PHYSICS
TSOKOS LESSON E-3
STELLAR OBJECTS
IB Assessment Statements
Option E-3, Stellar Distances:
Parallax Method
E.3.1. Define the parsec.
E.3.2. Describe the stellar parallax method of
determining the distance to a star.
E.3.3. Explain why the method of stellar
parallax is limited to measuring stellar
distances less than several hundred
parsecs.
E.3.4. Solve problems involving stellar parallax.
IB Assessment Statements
Option E-3, Stellar Distances:
Absolute and Apparent Magnitudes
E.3.5. Describe the apparent magnitude scale.
E.3.6. Define absolute magnitude.
E.3.7. Solve problems involving apparent
magnitude, absolute magnitude and
distance.
E.3.8. Solve problems involving apparent
brightness and apparent magnitude.
IB Assessment Statements
Option E-3, Stellar Distances:
Spectroscopic Parallax
E.3.9. State that the luminosity of a star may be
estimated from its spectrum.
E.3.10. Explain how stellar distance may be
determined using apparent brightness and
luminosity.
E.3.11. State that the method of spectroscopic
parallax is limited to measuring stellar
distances less than about 10 Mpc.
E.3.12. Solve problems involving stellar distances,
apparent brightness and luminosity.
IB Assessment Statements
Option E-3, Stellar Distances:
Cepheid Variables
E.3.13. Outline the nature of a Cepheid variable.
E.3.14. State the relationship between period and
absolute magnitude for Cepheid variables.
E.3.15. Explain how Cepheid variables may be used
as “standard candles”.
E.3.16. Determine the distance to a Cepheid
variable using the luminosity-period
relationship.
Objectives
 Describe the method of parallax, d (in
parsecs) = 1/p (in arcseconds), the method of
spectroscopic parallax and the Cepheids
method for determining distances in
astronomy
 Define the parsec
 State the definitions of apparent brightness,
b = L/4πd2 , and apparent and absolute
magnitude, b/b0 = 100-m/5 = 2.512-m
Objectives
 Solve problems using apparent brightness
and luminosity
 Use the magnitude-distance formula
Parallax Method
 When an object is viewed from two different
positions, it appears to move relative to a
fixed background
 We can use this fact to measure distances to
stars
Parallax Method
 Make two
measurements of
a star six months apart
 The distance between
the two positions is
equal to the diameter
of the earth’s orbit
around the sun
 The distance to the
star, d, is given by
R
tan p 
d
R
d
tan p
Parallax Method
R
tan p 
d
R
d
tan p
R
d
p
 Since the parallax angle is very
small, tan p ≈ p where p is
measured in radians
Parallax Method
 Parallax angle is the
angle from the position
of the star that
subtends a distance
equal to the radius of
the earth’s orbit of the
sun
R
d
p
Parallax Method
 The radius of the earth’s
orbit is defined as one
astronomical unit (AU)
 1 AU = 1.5 x 1011 m
R
d
p
Parallax Method
 Parallax angle
measurements are quite
accurate provided the
angles are not too small
 Parallax angles down to 1
arcsecond (1” = 1/3600 of a
degree) are easily
measured from earth
R
d
p
Parallax Method
 Parallax method fails if the
angle is less than 1
arcsecond
 Parallax allows
measurements up to
300 ly (≈ 100 parsec) from
earth
 Satellites can measure
distances greater than 500
parsecs
R
d
p
Parallax Method
 1 parsec = 3.26 ly = 3x1016 m
 1 parsec = 1 parallax second
 One parsec is the distance to
a star whose parallax angle
is one arcsecond
R
d
p
Parallax Method
1AU
1 pc 
1arc sec ond
11
1.5 x10
1 pc 
m
1
2
 360 
3600
15
1ly  9.46 x10 m d  par sec s  
1 pc  3.09 x10 m
1 pc  3.26ly
16
1
parc sec onds 
Parallax Method
5 stars nearest to earth
Apparent Magnitude
 Apparent magnitude
(m) derived from a
scale devised by
ancient astronomers
 The higher the apparent
magnitude, the dimmer
the star
 Classification based on a
factor of 100 using
apparent brightness
b
m / 5
m
 100
 2.512
b0
8
b0  2.52 x10 W
5 b
m   log  
2  b0 
m
2
Apparent Magnitude
 What is the apparent
magnitude of a star
whose apparent
brightness is 6.43 x 10-9
W/m2?
b
m / 5
m
 100
 2.512
b0
8
b0  2.52 x10 W
5 b
m   log  
2  b0 
m
2
Apparent Magnitude
 What is the apparent
magnitude of a star
whose apparent
brightness is 6.43 x 10-9
W/m2?
5  6.43x10 

m   log 
8 
2  2.52 x10 
9
m  2.5 log 0.2552
m  1.48
b
m / 5
m
 100
 2.512
b0
8
b0  2.52 x10 W
5 b
m   log  
2  b0 
m
2
Apparent Magnitude
 What is the apparent
brightness of a star
whose apparent
magnitude is 4.35?
b
m / 5
m
 100
 2.512
b0
b0  2.52 x10 8 W
5 b
m   log  
2  b0 
m
2
Apparent Magnitude
 What is the apparent
brightness of a star
whose apparent
magnitude is 4.35?
b
m / 5
m
 100
 2.512
b0
b0  2.52 x10 8 W
b
 2.512  m
b0
b
 4.35

2
.
512
8
2.52 x10
b  2.52 x10 8 2.512  4.35

b  4.58 x10

10

5 b
m   log  
2  b0 
m
2
Apparent Magnitude
 Magnitude scale
is defined so that
the larger the
magnitude, the
dimmer the star!
b
m / 5
m
 100
 2.512
b0
b0  2.52 x10 8 W
5 b
m   log  
2  b0 
m
2
Absolute Magnitude
 Apparent magnitude is based on view from earth
 Two stars may have the same apparent
magnitude but very different actual brightness
depending on their distances from earth
Absolute Magnitude
 Absolute magnitude (M) is equal to the apparent
magnitude the star would have if it were 10
parsecs from earth
 Comparison of apparent and absolute magnitude
is given by
d 
m  M  5 log  
 10 
m M / 5
d  10
x10 pc
where d is given in parsecs!
Apparent and Absolute Magnitude
Apparent
Absolute
Spectroscopic Parallax
 Using the star’s luminosity
and apparent brightness to
determine its distance
 Parallax is not involved –
it’s just there to mess with
your head
 Luminosity is the power
output of a star and is
based on temperature and
surface area
L
b
2
4d
L
d
4b
L
Spectroscopic Parallax b 
2
4d
 So how do you determine
L
d
luminosity?
4b
 From the emission spectrum, we
can determine temperature using
Wien’s Law
 From temperature and the HR
diagram (knowing what kind of
star) we can determine luminosity
The Cepheids
 Stars whose luminosity varies periodically over
time
 Periods range from days to months
 Brightness increases rapidly and fades gradually
The Cepheids
 The interaction of radiation and matter in the
outer layers of the star’s atmosphere causes it to
expand (brightest) and contract (dimmest)
The Cepheids
 The longer the
period, the larger
the luminosity
 Measuring a
Cepheid’s period
allows you to
determine
luminosity which
in turn allows you
to determine
distance
The Cepheids
 The period of the
Cepheid in the
lower diagram is
about 22 days
 The luminosity
from the upper
diagram is 7000
solar luminosities
or 2.73 x 1030 W
The Cepheids
 The peak apparent
magnitude (m) from
the diagram is 3.7
 Apparent brightness
(b) is found to be
b
 3. 7
 2.512 x10
8
2.52 x10
10 W
b  8.34 x10
2
m
L
The Cepheids b 
2
4d
L
d
4b
 So the distance is,
30
2.73 x10
d
10
4  8.34 x10

d  1.6 x10 m
d  1700ly
d  520 pc
19

The Cepheids
 Once you know the distance to the Cepheid, you
can approximate the distance to its galaxy
 Using Cepheids to determine distance is useful
up to a few Mpc and that is why they are
referred to as ‘standard candles’
Summary Review
 Can you describe the method of parallax, d
(in parsecs) = 1/p (in arcseconds), the method
of spectroscopic parallax and the Cepheids
method for determining distances in
astronomy?
 Can you define the parsec?
 Can you state the definitions of apparent
brightness, b = L/4πd2 , and apparent and
absolute magnitude, b/b0 = 100-m/5 = 2.512-m?
Summary Review
 Can you solve problems using apparent
brightness and luminosity?
 Can you use the magnitude-distance formula
IB Assessment Statements
Option E-3, Stellar Distances:
Parallax Method
E.3.1. Define the parsec.
E.3.2. Describe the stellar parallax method of
determining the distance to a star.
E.3.3. Explain why the method of stellar
parallax is limited to measuring stellar
distances less than several hundred
parsecs.
E.3.4. Solve problems involving stellar parallax.
IB Assessment Statements
Option E-3, Stellar Distances:
Absolute and Apparent Magnitudes
E.3.5. Describe the apparent magnitude scale.
E.3.6. Define absolute magnitude.
E.3.7. Solve problems involving apparent
magnitude, absolute magnitude and
distance.
E.3.8. Solve problems involving apparent
brightness and apparent magnitude.
IB Assessment Statements
Option E-3, Stellar Distances:
Spectroscopic Parallax
E.3.9. State that the luminosity of a star may be
estimated from its spectrum.
E.3.10. Explain how stellar distance may be
determined using apparent brightness and
luminosity.
E.3.11. State that the method of spectroscopic
parallax is limited to measuring stellar
distances less than about 10 Mpc.
E.3.12. Solve problems involving stellar distances,
apparent brightness and luminosity.
IB Assessment Statements
Option E-3, Stellar Distances:
Cepheid Variables
E.3.13. Outline the nature of a Cepheid variable.
E.3.14. State the relationship between period and
absolute magnitude for Cepheid variables.
E.3.15. Explain how Cepheid variables may be used
as “standard candles”.
E.3.16. Determine the distance to a Cepheid
variable using the luminosity-period
relationship.
QUESTIONS?
Homework
#1-17