The document discusses astrophysics concepts related to stars, including: 1. The main energy source of stars is hydrogen fusion, which occurs through either the proton-proton chain or CNO cycle depending on the star's core temperature. 2. A star's luminosity, temperature, radius, mass, chemical composition, and age can be used to characterize it. Its luminosity can be calculated using the Stefan-Boltzmann law. 3. A star's spectrum provides information about its surface temperature, chemical composition, and whether it is part of a binary system.

1. IB Physics Power Points
www.pedagogics.ca
Option E
Astrophysics
E2. Stellar Radiation
& Stellar Types

2. E.2.1 State that fusion is the main energy source
of stars
The source of all energy in stars is hydrogen “burning”.
TWO fusion reaction pathways for hydrogen (which
pathway occurs depends on core temperature of the
star)
1. proton-proton chain – in stars like our Sun (core
temperature < 16 x 106 K)
2. carbon-nitrogen-oxygen (CNO) cycle (hotter core
temperatures) - not in the syllabus

3. Energy release in fusion comes from mass defect in the
fusion reaction (products have less mass than reactants)
The proton-proton chain consists of three steps (each
step liberates energy)
1. 1
1 H 1
1 H 2
1 H 0
1 e ν (1.19MeV)
1 2 3
2. 1 H 1 H 2 He (5.49MeV)
3 3 4 1 1
3. 2 He 2 He 2 He 1 H 1 H (12.85MeV)
Overall 1 4 0
4H
1 2 He 2 e 2 1

5. Practice Problem
Determine the energy (in Joules) released in the
following reaction:
2 2 3 1
1 H H
1 2 He 0n
Given the following nuclide masses
Deuteron = 2.015 u
Helium-3 = 3.017 u click for solution
Neutron = 1.009 u
m (1.009 3.017) 2(2.015)
0.004
E 0.004 931.5
E 3.73 MeV

6. As a result of fusion, stars lose mass! The rate of
mass loss by our Sun to fusion reactions is about
4.33 × 109 kg s-1.
Estimate the power output of our Sun.
click for solution
2
E mc (for 1 second)
9 2
E (4.33 10 )c
26
E 3.90 10 W

7. Star Stability
E.2.2 Explain that in a stable star (for example, our Sun) there
is an equilibrium between radiation pressure and
gravitational pressure.
In stars . . .
An outward force exists due to emitted radiation “pressure”
(the energy emitted by fusion reactions)
Gravity pulls the outer part of the star inward towards the
core.
In a stable star these two forces are a balanced equilibrium

8. Nature of core changes as star ages

9. Observing Stars – Key Characteristics
There are six principle characteristics used to describe
stars. They are:
1. Luminosity
2. Temperature
3. Radius
4. Mass
5. Chemical composition
6. Age
STUDY TIP: Stellar characteristics are often measured indirectly (like
using brightness to determine luminosity, or peak wavelength to
find surface temperature) AND these characteristics are often
mathematically interrelated.

10. Luminosity and Brightness
E.2.3 Define the luminosity of a star
Luminosity (L) is an absolute value that measures the
total power radiated by a star (in all directions).
• Luminosity is measured in watts
• our Sun has a luminosity of about 3.90 x 1026 W.
Luminosity is very important in providing information
about star structure and age.

11. Luminosity and Brightness
E.2.4 Define apparent brightness and state how it is
measured.
Apparent brightness (l) is a relative value.
• we measure apparent star brightness as the fraction
of the luminosity received by us.
• brightness is measured in watts per square meter.

12. L
b 2
4 d
Apparent brightness b depends on two variables:
Apparent brightness is proportional to the
luminosity L of the star.
Apparent brightness is inversely proportional to
the square of the distance d between the star
and the observer.

13. This can be misleading . . . .
This means that a brighter star is not necessarily closer
to Earth, or larger, or hotter.
A high luminosity star that is farther
from Earth can appear brighter.

14. What you can conclude . . . .
For two stars the same distance from Earth, the star
with the greatest luminosity will appear brighter.
Note: both the surface
temperature and size of a
star affect luminosity.

15. E.2.5 Apply the Stefan-Boltzmann law to compare
the luminosities of different stars.
The Stefan-Boltzmann law states:
4
Total Power Radiated A T
surface surface
8 2 4
where 5.67 10 Wm K
NOTE:
Total Power Radiated = LUMINOSITY
2
Surface area of a sphere A 4 r

16. Sample problem: F1 (c) M02 exam
Antares A has a surface temperature of 3000 K and is part of
a binary star system. The companion star Antares B has a
surface temperature of 15 000 K and a luminosity that is
1/40 of that of Antares A. Calculate the ratio of the radius
of Antares A to Antares B.
Click for solution
STUDY TIP: Many problems are encountered like the one above
where the answer is a ratio of two variables. Get used to
working with variables and not always looking for a “plug and
chug” type of solution strategy.

17. LA
LB use Stefan-Boltzmann Law
40
2 4
2 4 (4 rA )TA
(4 rB )TB
40
40rB2 (15000) 4 rA (3000) 4
2
18 2 13 2
2.025 10 r B 8.1 10 r A
rA
160 (2 SF)
rB

18. E.2.6 State Wien’s (displacement) law and apply it to explain
the connection between the color and temperature of stars.
The color of a star is determined by the intensity of the
wavelengths of visible light emitted by the star.
Recall – in the visible spectrum
RED light (longer wavelength, lower frequency)
VIOLET light (shorter wavelength, higher frequency)

19. A star’s emission spectra is similar to a
theoretical blackbody spectra
Peak wavelength emission
gives an idea of surface
temperature.
The shorter the peak
wavelength, the hotter
the blackbody.

20. Wein’s displacement law relates the peak wavelength
(in metres) of an emission spectrum to surface
temperature (in Kelvin).
3
T
max surface a constant (2.9 10 m K )
shorter peak wavelength = higher surface temperature.
Determine the surface temperature of our Sun if the
peak wavelength is 500 nm. Click for solution
3
2.9 10
T 9
5800 K
500 10

21. E.2.7 Explain how atomic spectra may be used to
deduce chemical and physical data for stars
Stellar Spectra – Star Data
Recall: what important characteristic of stars can be
estimated from stellar spectra? Click for answer
Surface temperature can be
determined from peak wavelength
In addition, wavelengths missing from stellar spectra
indicate chemical nature of the outer layers of a star. Think
resonance, and relate this idea to greenhouse gases.

22. E.2.7 Explain how atomic spectra may be used to
deduce chemical and physical data for stars
Stellar Spectra – Star Data
Recall: what important characteristic of stars can be
estimated from stellar spectra? Click for answer
In addition, wavelengths missing from stellar spectra
indicate chemical nature of the outer layers of a star. Think
resonance, and relate this idea to greenhouse gases.

24. 5 minute physics concept – the Doppler Effect
Surface temperature can be
determined from peak wavelength
If a wave source is moving towards or away from an
observer, what the observer detects depends on their
position relative to the wave source.

25. Applied to stellar spectra
Red shifts in the position of absorption lines indicate
motion away from us
Blue shifts indicate motion towards us

26. E.2.8
Describe the overall classification system of spectral classes
Class Surface Temp. K Colour
O 28000 - 50000 Blue
B 9900 - 28000 Blue-white
A 7400 - 9900 White
F 6000 - 7400 Yellow-white
G 4900 - 6000 Yellow
K 3500 - 4900 Orange
M 2000 - 3500 Orange-red
Oh be a fine girl/guy, kiss me!

28. E.2.9 Describe the different types of stars
Stellar Spectra – Star Data
Ursa Major : The Big Dipper

30. Mizar

31. Types of Stars – Binary Stars
- two stars in orbit about their mutual centre of mass
Visual binary stars can be distinguished as separate stars
using a telescope.

32. Spectroscopic Binary Stars
- identified by spectral analysis – look at absorption lines
- spectral frequency of each star will shift depending on
orbit position.
B
A B B A
A
A B A+B B A
 Blue Red 

33. Interpreting Spectrum Shifts – The Doppler Effect
A higher frequency than the source is observed if the source
is approaching the observer i.e. a BLUE SHIFT.
If the light source is receding from the observer, a RED SHIFT
is observed.
The “shift” in wavelength can be used to
determine the speed the source is
travelling. v c
ref

34. observer

35. observer
B A

36. A
B

37. observer

38. Sample problem: F2 M02 exam
20 days
B
B A
A
B+A B A
Day 1 Day 6
Day 6 and 26 are at the same phase of the cycle.
On Day 6, the lines in the spectra from Star A are
red shifted (right) and those for Star B are blue
shifted (left)

39. Sample problem: F2 M02 exam
Circular or elliptical orbits drawn around the centre of
mass.
Star spectra shifts towards blue when moving towards
Earth and towards red when moving away. As one star
is moving towards Earth while the other moves away, a
red shift in a binary system is always accompanied by a
blue shift.
No shift occurs when stars are moving perpendicular to
Earth.

40. 0.26 5 -1
v c c 1.74 10 ms
ref 448.3
Mass of star / system

42. Eclipsing Binaries
In an eclipsing binary system, the binary brightness shows
regular variation. This occurs because one star gets between
the other and the observer blocking some of the emitted
radiation.

43. Eclipsing binary information gives astronomers information
about orbital period and the separation of the stars.

44. Background information - apparent brightness

45. The Hertzsprung-Russell Diagram
A Hertzsprung-Russell diagram is a
plot of luminosity against surface
temperature.

46. When plotted this way, a diagonal band appears that
contains the majority of stars. These are called main
sequence stars.
main sequence stars
• are stable
• derive their energy from hydrogen fusion.
• comprise 90% of stars visible in the night sky
The two fundamental factors that determine a star's
position in the main sequence its mass and
evolutionary state.

47. high luminosity,
High mass 20 days low temperature
short life giant stars
Low luminosity, low mass
high temperature long life
dwarf stars

49. L
Apparent
brightness if
10 pc away

50. L
Apparent
brightness if
10 pc away

51. L
Apparent
brightness if
10 pc away

52. L

54. Practice Problem 1
A parsec (pc) is a unit of distance (see Data Booklet)

55. Practice Problem 1
A parsec (pc) is a unit of distance (see Data Booklet)

56. Practice Problem 2
Suppose that the distances to two nearby stars can be
reasonably estimated and this data, together with
measured apparent brightness suggests that the two
stars have a similar luminosity. The peak wavelength for
one star is 700 nm (reddish) while for the other it is 350
nm (bluish). Determine a) the surface temperature of
each star and b) how much larger one star is than the
other.

58. Summary
Luminosity is the total power output of a star. Luminosity
can measured as a absolute value (in Watts) or relative to
the Sun (in L where L = 3.90 x 1026 W)
Apparent brightness (or intensity) is a relative value and
represents the portion (measured in W m-2) of a star’s
luminosity that is observed on Earth. Apparent brightness,
stellar distance and luminosity are related by:
L
b 2
4 d

59. Stars emit a radiation spectrum similar to that of a
theoretical black-body. This allows the surface temperature
of a star to be estimated from the peak wavelength in a
spectrum using Wien’s Law
maxTsurface 2.9 10 3 m K
The temperature can be related to the luminosity
and size of a star using the Stefan-Boltzmann Law
4
L A T
surface surface
8 2 4
where 5.67 10 Wm K
2
Recalling that Asurface 4 r

60. Stellar spectra are very important for a number of reasons
1. Most peak wavelength indicates surface temperature
(and color of star)
2. The area under a stellar spectrum is an indication of total
power emitted i.e. luminosity.
3. Absorption lines in stellar spectra give an indication of
what elements are present in the atmosphere of the star
and therefore an idea of what fusion reactions are taking
place (helps with star age etc)
4. Stellar spectra give us important information about
binaries