Download astrophysics - The University of Sydney

Science Teachers’ Workshop 2010
ASTROPHYSICS
Helen Johnston
School of Physics
The University of Sydney
[email protected]
Introduction
In this workshop, we look at the links between the different topics in option 9.7 Astrophysics
of the NSW Stage 6 Physics syllabus. Concentrating on the Hertzsprung-Russell diagram, we
examine how each of the other topics -- photometry, spectroscopy, astrometry, binary stars -feeds into the central story of the life cycle of stars. We try out some ideas, activities and
analogies which can help to illustrate the concepts involved.
Syllabus requirement
This paper uses the amended NSW Board of Studies Stage 6 Physics Syllabus of October 2002.
The Hertzsprung-Russell (H-R) diagram and the evolution of stars is covered in topic 6 (p. 65),
but each of the other topics is used as necessary input to our understanding of stellar evolution. Syllabus topics from option 9.7 are indicated as footnotes as they are discussed.
The central thread of the story is the over-arching importance of gravity in the cycle of life of
stars. The Hertzsprung-Russell diagram is our main tool in elucidating this story; but in order
to construct it, we need inputs from many different sources. In what follows, the “input” sections are set off from the main thread discussing the H-R diagram and stellar evolution with
narrow margins; activities to do in the classroom are indicated by bold headers.
Constructing the H-R diagram
The H-R diagram was discovered as an observed relationship between the properties of stars
Discovered independently in about 1911 by Ejnar Hertzsprung and Henry Norris Russell, it is a
graph of the luminosity of stars plotted against their temperature. Because the diagram was
originally constructed as a plot of absolute magnitude against colour, the temperature scale
goes the wrong way, increasing to the left. For historical consistency, this has never been
changed.
H. Johnston: Astrophysics!
1
Science Teachers’ Workshop 2010
Figure 1: The Hertzsprung-Russe#
diagram, showing the main regions,
as we# as a few representative stars.
(From the Australia Telescope Outreach and Education website: Astrophysics)
Input #1: Luminosity, brightness and distance 1
In order to be able to construct a H-R diagram, we need to be able to measure the luminosity of stars accurately. What we observe, however, is the brightness of the star, so in order to determine the luminosity, we need to know the distance to the star. If stars all had
the same intrinsic brightness, we could use their apparent brightness to determine their
distances. However, stars have very different intrinsic brightnesses, so distance and luminosity effects need to be disentangled.
There are many simple ideas you can use in the classroom to illustrate the connection
between luminosity, brightness and distance.
1. Light bulb “shell game” 2 Using three or four standard lightbulbs of different wattages in a socket at the end of a long extension cord, show the students how bright each
appears when standing at the front of the classroom. Ask individual students to name the
wattage of a random bulb; this is easy, as long as the distance to the bulbs remains constant. Next, ask a student to identify the bulb while moving around the classroom with
the bulb. This is much harder, and shows that when distance is mixed up with brightness,
luminosity is harder to determine. Point out that real stars are point sources (so you can’t
use the size of the bulb to help judge the distance) and the range of both brightnesses and
distances are orders of magnitude greater for real stars.
1 Topic
2
4, Photometry and Topic 2: Astrometry
from Pompea, “Great Ideas for Teaching Astronomy”, p. 116
H. Johnston: Astrophysics!
2
Science Teachers’ Workshop 2010
γ Crux (1.6)
β Crux (1.2)
β Cen (0.6)
α Cen (0.1)
δ Crux (2.8)
α Crux (0.7)
Figure 2: The Southern Cross and Pointers, showing the apparent magnitudes in brackets.
Image credit: Mike Besse# http://www.mso.anu.edu.au/~besse#/
2. Star fields. The confusion between luminosity and brightness is well illustrated by
looking at real star fields. Figure 2 shows an image of the Southern Cross and pointers;
there’s a poster called The Southern Cross and the “Pointers” by Akira Fujii available from
CSIRO Parkes Observatory. Ask students to order the stars by brightness, then show
them the actual distances to the stars as shown in Figure 3. Alpha and Beta Centauri are
almost the same brightness, but Beta Cen is 120 times further away, which means it must
be intrinsically much brighter.
3. Grease-spot photometer. Once students understand that the distance needs to be
known in order to determine the luminosity, they can try to determine the brightness of
an unknown source by using the inverse-square law. The inverse-square law can be easily
and effectively demonstrated using an overhead projector or slide projector. Project a rec-
Figure 3: Distances to the stars in Figure 2. Image credit: Peter Caldwe#,
http://users.netconnect.com.au/~astronet/dist.html.
H. Johnston: Astrophysics!
3
Science Teachers’ Workshop 2010
Table 1: The brightest stars
Table 2: The nearest stars
apparent
d (pc)
magnitude
apparent
magnitude
d (pc)
Sirius
–1.50
2.6
Proxima Centauri
11.5
1.3
Canopus
–0.73
96
α Centauri
0.1
1.3
α Centauri
+0.10
1.3
Barnard’s Star
9.5
1.8
Vega
+0.04
7.9
Wolf 359
13.5
2.3
Arcturus
+0.00
11.6
Lalande 21185
7.5
2.5
Capella
+0.05
13.1
Sirius
–1.5
2.6
Rigel
+0.08
184
Luyten 726–8
12.5
2.7
Procyon
+0.34
3.5
Ross 154
10.6
2.9
Betelgeuse
+0.41
131
Ross 248
12.2
3.2
Achernar
+0.47
45
Epsilon Eridani
3.7
32
star
star
tangle of light on the blackboard, then draw around the area and note the brightness.
Move the projector twice as far away and note the new area and brightness. This demonstrates that when the distance doubles, the light is spread over four times the area so is
only a quarter the intensity.
A grease-spot photometer 3 (Figure 4) uses the inverse-square law and a source of known
brightness to measure the brightness of an unknown source. A sheet of brown or white
paper with a drop of olive oil is placed between a bulb of known brightness and an unknown bulb. When the illumination is the same on both sides of the sheet, the greasespot “disappears”; the ratio of the distances of the two bulbs can then be used to calculate
the luminosity of the unknown bulb.
4. Comparison of bright and nearby stars. Students may find it illuminating to
compare a list of the ten brightest stars and the ten nearest stars (Tables 1 and 2). Only
two stars are common to both lists. Some bright stars are at enormous distances, and
some near stars are very faint. This is why the apparent brightness of a star is not a very
useful quantity
So once we know the distances to the stars, we can finally plot an observed HertzsprungRussell diagram. Figure 5 shows the B–V colours and absolute magnitudes of stars with dis-
see http://members.ozemail.com.au/[email protected]/scifun/slight.htm#bunsengrease, or
http://www.phy6.org/outreach/edu/greaspot.htm for a detailed explanation.
3
H. Johnston: Astrophysics!
4
Science Teachers’ Workshop 2010
Figure 5: Observed H-R diagram, showing
the colours and absolute magnitudes of stars
as measured by Hipparcos
tances measured by the Hipparcos satellite 4. Colour corresponds closely to the temperature of
the star, while absolute magnitude is related to luminosity. Clearly there are patterns apparent
in where the stars are located. 90% of stars are found to lie in a narrow band running roughly
diagonally across the diagram, from hot and bright (top left) to cool and dim (bottom right).
Stars do not fall randomly in the diagram: they are apparently only allowed to have some values
of temperature and luminosity. This indicates that there is an underlying physical link between
these properties.
Patterns in the H-R diagram. Students can plot data-sets and find that there is a correlation, indicating a single underlying factor. The easiest underlying factor is usually time; thus a
plot of (for instance) someone’s age versus the All Ords index will yield an almost perfect correlation. A better example would be plotting height versus weight for a sample of children, preferably over a wide age range. While there is a considerable amount of scatter about the mean,
there is general trend that the taller a child is, the heavier he or she is; and the underlying factor linking the two is age – both height and weight increase as a child grows.
Thus the existence of a correlation indicates the existence of a link between the two. For stars,
however, the main sequence is not an age sequence: unlike children, stars do not trace out the
main sequence as they age. In fact, the main sequence is a mass sequence.
4 data available at http://astro.estec.esa.nl/Hipparcos/
H. Johnston: Astrophysics!
5
Science Teachers’ Workshop 2010
Input #2: Spectral type and mass5
Because the main sequence is so linear, it is possible to characterise the properties of
stars along it using a very simple classification: the famous spectral sequence OBAFGKM
(using the mnemonic Oh Be A Fine Girl (or Guy), Kiss Me). The CLEA project6 has an
excellent activity called “The Classification of Stellar Spectra”, which enables students to
try their hand at classifying stars.
In order to determine the masses of stars, we need to study binary systems. The period,
orbital radius and total mass of the system are related by Kepler’s law
mA + mB =
4π 2 r3
GT 2
so if we can measure any two of these we can derive the third. In practice, we use this to
derive the masses of stars from the observed periods and radii or velocities.
Understanding the H-R diagram7
The reason that mass is so important is because the whole of a star’s life is a sequence of attempts to hold off gravity. Gravity compresses the matter in the centre of the star until it is
hot enough to fuse hydrogen into helium. This produces enough energy and hence pressure to
counteract gravity: the star is in equilibrium.
Fusion requires a temperature of 10 million K to start. Above this, a small increase in temperature results in a large increase in the
rate of fusion. This explains why
heavier stars are brighter than lowmass stars. More mass leads to more
compression in the star’s core, which
leads to higher temperature, which
in turn leads to much higher rates of
fusion and thus much higher luminosity. A small increase in mass leads
to a large change in the luminosity
(Figure 7). If we plot a star’s mass
against its luminosity, we find a relation
Figure 6: How a star maintains equilibrium
5 Topic
3, Spectroscopy and Topic 5: Binaries
http://www3.gettysburg.edu/~marschal/clea/CLEAhome.html
7 Topic 6, Evolution
6
H. Johnston: Astrophysics!
6
Science Teachers’ Workshop 2010
L ∝ M 3.5
which means that if we increase the mass of the star by a factor of 10, we increase its luminosity by a factor of 3000: massive stars are a lot brighter than their lower-mass siblings.
How long a star can stay on the min sequence burning hydrogen depends on two things: how
much hydrogen it has, and how fast it burns it. The first is just the star’s mass, and the second
the star’s luminosity. Thus the lifetime of a star goes like
t∝
M
M
∝ 3.5 = M −2.5
L
M
In other words, a factor of 10 increase in mass corresponds to a decrease in the lifetime of the
star by a factor of 300. So massive stars live for much shorter times than low-mass stars. This
explains the shape of the H-R diagrams for clusters: the more massive stars leave the main sequence earlier, so the main sequence gets progressively eroded, like a candle burning down.
Using the H-R diagram
We can use the H-R diagram as a tool for understanding the internal evolution of stars. As the
internal structure of the star changes, the temperature and luminosity change, and we can
plot these changes and show them as tracks in the H-R diagram. As the star evolves, it moves
to different regions of the diagram, so we can determine the evolutionary state of a star from
its current position.
When the star runs out of hydrogen, fusion stops, so the star is no longer producing the energy
which counteracts gravity. The core starts to collapse, and in doing so, heats up. Two things
then happen. Unburnt hydrogen around the core ignites for the first time, causing the outer
layers of the star to puff up. The star becomes enormously large and red : a red giant. Meanwhile, the core contracts until it becomes hot enough to ignite helium. This halts the collapse
for a while, as the star burns helium in its core, just as it burnt hydrogen on the main sequence.
Figure 7: The mass-luminosity relation for main sequence stars. From
http://www.astronomy.org.nz/aas/MonthlyMeetings
/MeetingMay2002.asp
H. Johnston: Astrophysics!
7
Science Teachers’ Workshop 2010
Figure 8: Evolutionary track of an
intermediate mass star, showing
how the temperature and luminosity change as the star evolves.
Pressure-temperature link. There are several demonstrations to show that the temperature goes up as the pressure increases. A simple bicycle pump will do: have students pump it
several times, and feel how the pump gets noticeably hot.
The cycle then repeats itself. Helium is fused to carbon and oxygen in the star’s core, but eventually the core runs out of helium. Fusion stops, and the core resumes its collapse. This heats
up the layer of helium just outside the core, which begins fusing in a shell of its own, inside the
hydrogen burning shell. This extra energy forces the star to expand again, and the star begins a
second ascent of the giant branch: the asymptotic giant branch (Figure 8).
We can predict what happens next: the cycle repeats again and again, each time starting to fuse
heavier and heavier elements to stave off the next collapse. The core reaches temperatures by
converting gravitational energy into thermal energy. Each time the star runs out of fuel, the inexorable collapse due to gravity begins again.
The fate of stars from this point depends on their mass. Low mass stars cannot reach temperatures high enough to fuse carbon in their cores, so once the helium is all burnt, the outer layers
are ejected and the core collapses to form a white dwarf. High mass stars (greater than about 6
solar masses) continue to burn all elements up to iron. During this time, the star zigzags across
the H-R diagram.
After iron, however, there is no more energy to extract from fusion. Once the silicon in the
core has fused to make iron, the star can no longer support itself against collapse. The iron
core, now weighing about 1.4 times the mass of the Sun, collapses inwards again; but this time
there is no new fusion process to stop the collapse. The end is sudden and violent: a supernova
explosion. The outer layers of the star “bounce” off the core at enormous speeds, propelling
them into space as a fireball which we see as the supernova.
H. Johnston: Astrophysics!
8
Science Teachers’ Workshop 2010
Core bounce.8 The transfer of momentum from the heavy core to the light overlying layers in
a supernova explosion can be illustrated by dropping a tennis ball on top of a basketball. The
tennis ball bounces astonishingly high, and it’s a very effective demonstration.
The inner core collapses to form a neutron star, where the neutrons are squeezed so tightly together than they can resist the gravitational pressure. Finally, the star has reached a truly stable
state: it can exist forever, without the need for fuel to hold itself up.
Conclusion
I have tried to provide suggestions for uniting the disparate topics in the Astrophysics option
into a unifying framework, based on the the Hertzsprung-Russell diagram and the central role
of gravity in determining the fate of a star. I hope the ideas presented here can help students
gain a deeper understanding of the topic.
H. Johnston: Astrophysics!
9
Science Teachers’ Workshop 2010
Resources
• Stephen M. Pompea, "Great Ideas for Teaching Astronomy" (Brooks/Cole 2000), ISBN 0534-37301-1 has lots of fantastic ideas, some of which I’ve included here
• “The Collapsing Universe” by Isaac Asimov (no longer in print, but lots of second hand copies around) is now 25 years old, but I have a very soft spot for it. He does a marvellous job of
explaining the competing forces within stars, in his own highly readable style. The last section is very out-of-date, but the rest is as readable an introduction to stellar evolution as any.
• The grease-spot photometer is described at
http://members.ozemail.com.au/[email protected]/scifun/slight.htm#bunsengrease
with a more detailed explanation at http://www.phy6.org/outreach/edu/greaspot.htm
• The CLEA project – Contemporary Laboratory Experiences in Astronomy – is a collection
of computer-based exercises that allow students to experience real astronomical data. The
“Classification of Stellar Spectra” lets students attempt to classify real spectra by comparison
with known stars. There’s a online exercise to do the same thing at
http://astro.wku.edu/astr106/spectra.html.
• The Australia Telescope Outreach and Education website http://outreach.atnf.csiro.au has a
wealth of useful information. The “HR Diagram Activities” page
http://outreach.atnf.csiro.au/education/senior/astrophysics/stellarevolution_hractivity.html
has links to several sites which allow you to explore stellar evolution in the HertzsprungRussell diagram.
• “Astronomy 162 Digital Movie Gallery” by Richard Pogge,
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/ has a nice collection of
simulations of different types of binaries.
• NASA has a set of nice tutorials about stars at the Observatorium,
http://observe.arc.nasa.gov/nasa/space/space_index.shtml.html
H. Johnston: Astrophysics!
10