Download Physics- HSC- Module 9.7 Astrophysics

HSC
Physics
Module 9.7
Astrophysics
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
9.7
Astrophysics
(28 indicative hours)
Contextual Outline
The wonders of the Universe are revealed through technological advances based on tested principles of physics.
Our understanding of the cosmos draws upon models, theories and laws in our endeavour to seek explanations
for the myriad of observations made by various instruments at many different wavelengths. Techniques, such as
imaging, photometry, astrometry and spectroscopy, allow us to determine many of the properties and
characteristics of celestial objects. Continual technical advancement has resulted in a range of devices extending
from optical and radio-telescopes on Earth to orbiting telescopes, such as Hipparcos, Chandra and HST.
Explanations for events in our spectacular Universe, based on our understandings of the electromagnetic
spectrum, allow for insights into the relationships between star formation and evolution (supernovae), and
extreme events, such as high gravity environments of a neutron star or black hole.
This module increases students’ understanding of the nature and practice of physics and the implications of
physics for society and the environment.
Concept Map
Sensitivity
Adaptive Optics
Telescopes
Interferometry
Black
Body
Radiation
Resolution
Electromagnetic
Radiation
Magnitude
Parallax
parsec
Light
year
Spectra
Astronomical
Objects
Astrometry
Satellites
Emission
Spectra
Absorption
Spectra
Stellar
Spectra
Colour
Index
surface temperature,
rotational and
translational velocity,
density and chemical
composition of stars
HR Diagram
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
Astrophysics Module Plan
Module Length: 7 weeks
Focus Area
1. Our understanding
of celestial objects
depends upon
observations made
from Earth or from
space near the Earth
Time
½
½
1
1
1
2. Careful
measurement of a
celestial object’s
position, in the sky,
(astrometry) may be
used to determine its
distance
1
1
1
Concept
1. discuss Galileo’s
utlisation of the
telescope to identify
features of the Moon.
2. discuss why some
wavebands can be more
easily detected from
space
3. define the terms
resolution and sensitivity
of telescopes.
4. discuss the problems
associated with groundbased astronomy in terms
of resolution and
absorption of radiation
and atmospheric
distortion.
5. outline methods by
which the resolution
and/or sensitivity of
ground-based systems
can be improved,
including:
– adaptive optics
– interferometry
- active optics.
1. define the terms
parallax, parsec, light
year
2. explain how
trigonometric parallax
can be used to determine
the distance to stars
3. discuss the limitations
of trigonometric parallax
measurements
Text Summary
Practical
1. (Exp 1) identify data sources, plan, choose
equipment or resources for, and perform an
investigation to demonstrate why it is desirable
for telescopes to have a large diameter objective
lens or mirror in terms of both sensitivity and
resolution
2. (Act 2) gather, process and present
information on new generation optical
telescopes
1. (Act 3) solve problems and analyse
information to calculate the distance to a star
given its trigonometric parallax using d = 1/p
2. (Act 4) gather and process information to
determine the relative limits to trigonometric
parallax distance determinations using recent
ground-based and space-based telescopes.
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
Focus Area
3. Spectroscopy is a
vital tool for
astronomers and
provides a wealth of
information
Time
1
1
1
1
1
4. Photometric
measurements can be
used for determining
distance and
comparing objects
1
2
Concept
1. account for the
production of emission
and absorption spectra
and compare these with a
continuous blackbody
spectrum
2. describe the
technology needed to
measure astronomical
spectra
3. identify the general
types of spectra produced
by stars, emission
nebulae, galaxies and
quasars
4. describe the key
features of stellar spectra
and describe how this is
used to classify stars
5. describe how spectra
can provide information
on surface temperature,
rotational and
translational velocity,
density and chemical
composition of stars
1. define absolute and
apparent magnitude
2. explain how the
concept of magnitude can
be used to determine the
distance to a celestial
object
Text Summary
Practical
1. (Act 5) perform a first-hand investigation to
examine a variety of spectra produced by
discharge tubes, reflected sunlight, incandescent
filaments
3. (Act 6) analyse information to predict the
surface temperature of a star from its
intensity/wavelength graph
1. (Act 7) solve problems and analyse
information using:
M  m  5log(
d
)
10
and
IA
 100(M B  M A ) / 5
IB
to calculate the absolute or apparent magnitude
of stars using data and a reference star
1
1
1
3. outline spectroscopic
parallax
4. explain how twocolour values (ie colour
index, B-V) are obtained
and why they are useful
5. describe the
advantages of
photoelectrictechnologies
over photographic
methods for photometry
2. (Exp 8) perform an investigation to
demonstrate the use of filters for photometric
measurements.
3. (Act 9) identify data sources, gather, process
and present information to assess the impact of
improvements in measurement technologies on
our understanding of celestial objects
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
Focus Area
5. The study of binary
and variable stars
reveals vital
information about
stars
Time
1
2
Concept
1. describe binary stars in
terms of the means of
their detection: visual,
eclipsing, spectroscopic
and astrometric
2. explain the importance
of binary stars in
determining stellar
masses
Text Summary
Practical
1. (Exp 10) perform an investigation to model
the light curves of eclipsing binaries using
computer simulation
2. (Act 11) solve problems and analyse
information by applying Kepler’s Third Law:
m1  m2 
42 r 3
GT
to calculate the mass of a star system
1
1
6. Stars evolve and
eventually ‘die’
2
2
1
1
2
2
3. classify variable stars
as either intrinsic or
extrinsic and periodic or
non-periodic
4. explain the importance
of the period-luminosity
relationship for
determining the distance
of Cepheids
1. describe the processes
involved in stellar
formation
2. outline the key stages
in a star’s life in terms of
the physical processes
involved
3. describe the types of
nuclear reactions
involved in mainsequence and post-main
sequence stars
4. discuss the synthesis
of elements in stars by
fusion.
5. explain how the age of
a globular cluster can be
determined from its zeroage main sequence plot
for a HR diagram
6. explain the concept of
star death in relation
to:
– planetary nebula
– supernovae
– white dwarfs
– neutron stars/pulsars
– black holes
1. (Act 12) present information by plotting
Hertzsprung-Russell diagrams for: nearby or
brightest stars; stars in a young open cluster;
stars in a globular cluster
2. (Act 13) analyse information from a H-R
diagram and use available evidence to determine
the characteristics of a star and its evolutionary
stage
3. (Act 14) present information by plotting on a
H-R diagram the pathways of stars of 1, 5 and
10 solar masses during their life cycle.
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
HSC Physics E3: Astrophysics Experiment 1: Sensitivity and Resolution
Aim: To identify data sources, plan, choose equipment or resources for, and perform an investigation to demonstrate
why it is desirable for telescopes to have a large diameter objective lens or mirror in terms of both sensitivity
and resolution
You must devise a method using equipment listed below and/or any other equipment you bring in.
Equipment Available
Any equipment that is reasonable (arrange with your teacher beforehand)
You should consider the following points:
 Does the experiment satisfy the aim above?
 The safety of the experiment. Any safety notes need to be explicit.
 Design your own result table. Have you repeated the experiment several times to validate the results and to
calculate a mean?
 Did you show your working?
 What are some possible sources of error? How could these errors be minimised or eliminated?
HSC Physics E3: Astrophysics Activity 2: New Optical Telescopes
Aim: To gather, process and present information on new generation optical telescopes
Write a 400 word report on this issue, including relevant diagrams.
A bibliography must be included and in-text referencing used.
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
HSC Physics E3: Astrophysics Activity 3: Stellar Parallax
Aim: To solve problems and analyse information to calculate the distance to a star given its trigonometric parallax
using d = 1/p
Measuring by Parallax
Stellar distances can be measured by a trigonometric method called parallax. This technique is very similar to
surveying.
In surveying, the distance to object O is determined by measuring the angles a and b and knowing the length of the
baseline PQ.
SINE a = l / ½PQ
Since a is measured and the distance PQ is known, the perpendicular distance to O can be determined.
Parallax uses the diameter of Earth's orbit as the known distance. The angles a and b are measured when the Earth
is at opposite position in its orbit (i.e. the measurements are taken 6 months apart).
The average radius of Earth's orbit is 1.5 X 108 km. This distance is also referred to as one astronomical unit A.U.
As the Earth rotates about the Sun the aspect of a nearby star will appear to change by a small angle 2p. p is called
the parallax of a star. As the distance to the star increases p decreases. p is so small for most stars that this method
can only really be used for relatively close stars (i.e. within 100 light-years from Earth). p is measured in arcseconds
where one arcsecond (1") is equal to 1/3600 th of a degree.
The nearest star to Earth (excluding the Sun) is Proxima Centauri, which has a parallax of 0.765".
When p = 1" the star is at a distance known as a parsec.
One parsec = 3 X 1013 km or 3.26 light-years
If the parallax angle of a star is p, then the distance to that star is equal to 1/p parsecs.
1. Calculate the distance to Proxima Centauri in parsecs and in light years.
1. Do Humphrey’s Set 75
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
Below is a list of parallax measurements of nine of the brightest stars in the southern skies. It is you task to convert
these angular measurements into distance measurement from Earth.
Remember:
An angle of 1" (arcsecond)
= 1/3600 degree.
1 parsec
= 3 X 1013 km
1 parsec
= 3.26 light-years
1 A.U.
= 1.5 X 108 km
Star
Systematic Name
Sirius
-Canis Major
Parallax Angle Distance
(parsecs)
0.3678”
Canopus
-Carina
0.1778”
Rigil Kent
-Centauri 
0.7650”
Rigel
ß-Orion
0.00364”
Hadar
ß-Centauri 
0.00762”
Betelgeuse
-Orion
0.00542”
Antares
-Scorpio
0.00757”
Acrux
-Crus
0.01208”
Mimosa
ß-Crus 
0.00761”
Sol
Sun
2 X 105
Distance (lightyears)
Distance (A.U.)
HSC Physics E3: Astrophysics Activity 4: Limits of Stellar Parallax
Aim: To gather and process information to determine the relative limits to trigonometric parallax distance
determinations using recent ground-based and space-based telescopes.
Write a 400 word report on this issue, including relevant diagrams.
A bibliography must be included and in-text referencing used.
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
HSC Physics E3: Astrophysics Activity 5: Spectra
Aim: To process information to examine a variety of spectra produced by discharge tubes, reflected sunlight,
incandescent filaments
Method
On the disk supplied is the spectra produced by discharge tubes, sunlight and incandescent filaments. (in jpg
format).
For each image:
1. List the features that can be found in the spectra.
2. List any elements that can be identified in the spectra.
3. Note any unusual characteristics of the spectra.
HSC Physics E3: Astrophysics Activity 6: Stellar Surface Temperature
Aim: To analyse information to calculate the surface temperature of a star from its intensity/wavelength graph
Method
Attached is the intensity / wavelength graph of several spectral classes.
Calculate the surface temperature of each star from this data.
HSC Physics E3: Astrophysics Activity 7: Stellar Distances
IA
d
 100(M B  M A ) / 5
)
I
B
10
Aim: To solve problems and analyse information using:
and
to calculate
the absolute or apparent magnitude of stars using data and a reference star
M  m  5log(
Method
1. Do Humphrey’s Set 74
2. Analyse the two images given for this activity:
(a) calculate the magnitude of the star from the data.
(b) Use the information about its spectral class to calculate its average brightness and hence absolute
magnitude.
(c) Calculate the distance to the star in parsecs and light-years.
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
HSC Physics E3: Astrophysics Experiment 8: Photometry
Aim: To perform an investigation to demonstrate why it is important to use filters for photometry
Method
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
HSC Physics E3: Astrophysics Activity 9: Measurement Technologies
Aim: To identify data sources, gather, process and present information to assess the impact of improvements in
measurement technologies on understanding of the celestial objects
Write a 400 word report on this issue, including relevant diagrams.
A bibliography must be included and in-text referencing used.
HSC Physics E3: Astrophysics Experiment 10: Light Curves
Aim: To perform an investigation to model the light curves of eclipsing binaries using computer simulation
A free program is available at www.isc.tamu.edu/~astro/ebstar/ebstar.html (Mac platform)
A free program is available at http://www.lsw.uni-heidelberg.de/~rwichman/Nightfall.html (Unix, Linux platform)
A free program is available at http://www.physics.sfasu.edu/astro/software/EBS1A2.ZIP (Windows platform)
In any of the above programs, use the simulation to create light curves for the following situations:
1. A binary where both bodies are of equal size and luminosity.
2. A binary where one body is ten times larger than the other but at the same luminosity.
3. A binary where both bodies are of equal size but one is ten times the luminosity of the other.
HSC Physics E3: Astrophysics Activity 11: Kepler’s Third Law
Aim: To solve problems and analyse information by applying Kepler’s Third Law:
the mass of a star system
1. Do Humphrey’s Set 72
m1  m2 
42 r 3
GT to calculate
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
HSC Physics E3: Astrophysics Activity 12: HR Diagrams
Aim: To present information by plotting Hertzsprung-Russell diagrams for: nearby or brightest stars; stars in a
young open cluster; stars in a globular cluster
The following activity is an extract from http://geocities.com/CapeCanaveral/Hall/4180/astro/H-R_Lab.html
During the late 19th and early 20th centuries, astronomers obtained spectra and parallax distances for many stars, a
powerful tool was discovered for classifying and understanding stars. Around 1911-13, Enjar Hertzsprung and
Henry Norris Russell independently found that stars could be divided into three groups in a diagram plotting stellar
luminosity and surface temperature. Most stars, including our Sun, lie on the main sequence. Rare but very
luminous cool stars are called red giants while low luminosity hot stars are called white dwarfs. Later in the
twentieth century, a full theory for the evolution of stars was developed. A star traces a complex path in the
Hertzsprung-Russell diagram (H-R diagram) as its burns different nuclear fuels and evolves.
In this activity, you will construct a H-R diagram using MS Excel.
1. Getting the Data into Excel.
To enter an item in a cell, simply click at the cell and type. Use arrows to move between cells. Set up the headings
as show below. You will see that the range of luminosities is so great that the diagram looks silly
Nearest Stars
Name
Sun
Proxima Centauri
Alpha Centauri A
Alpha Centauri B
Barnard’s Star
Wolf 359
BD +36 2147
L 726-8A
UV Ceti
Sirius A
Sirius B
Ross 154
Ross 248
Epsilon Eri
Temperature (K)
5860
3240
5860
5250
3240
2640
3580
3050
3050
9230
9000
3240
3050
4900
Luminosity
1.0
0.00006
1.6
0.45
0.00045
0.00002
0.0055
0.00006
0.00004
23.5
0.003
0.00048
0.00011
0.30
Log(Luminosity)
Radius
To obtain logs of the luminosities, go the cell next a luminosity, type =log10(C2) and the log of the luminosity
(which is zero for the Sun) should then appear in the cell. To repeat this for other stars, drag the dot at the lower
right corner of the cell down to the other rows. These operations can also be done in other ways eg. using the
function wizard (fx icon) and Fill Down in the Edit menu.
Repeat these steps for the tables on the next page.
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
Brightest Stars
Name
Sun
Sirius A
Canopus
Alpha Centauri A
Arcturus
Vega
Capella
Rigel
Procyon
Betelgeuse
Achernar
Beta Centauri
Altair
Alpha Crucis
Alderbaran
Temperature (K)
5860
9230
7700
5860
4420
9520
5200
11200
6440
3450
15400
24000
7850
25400
15400
Luminosity
1.0
23.5
1400
1.6
110
50
150
42000
7.2
12600
200
3500
10
3200
95
Log(Luminosity)
Radius
Luminosity
Log(Luminosity)
Radius
Luminosity
Log(Luminosity)
Radius
Stars in a Young Open Cluster
Name
Temperature (K)
Stars in a Globular Cluster
Name
Temperature (K)
2. Plotting the H-R Diagram
To plot a diagram, highlight the cells to be plotted, including the labels. Open the Chart Wizard; select XY scatter
plot (format 1 or 3) and the plot should appear. Follow the remaining steps and instructions to complete the graph.
Astronomers historically plot the H-R diagram with temperature decreasing to the right. To do this, click on the
labelled X-axis, enter the axis scale page, and reverse the order of the X-axis.
Print your H-R diagrams for the Nearest and Brightest stars. This is done by double clicking on the chart, entering
the File menu, Print Preview and (if you like it) Print. On your printed chart, identify the main sequence stars, red
giants and white dwarfs. Label a horizontal axis with the spectral type classifications used by astronomers. O
(52000-33000 K), B (30000-11000 K), A (9500-7600 K), F (7200-6200), G (6000-5600 K), K (5200-4100 K), M
(3900-2600 K)
Save your data. This will be required for the next activity.
On a separate sheet discuss the differences between the nearest and brightest stars in the H-R diagram. Can you
deduce which kinds of stars are most common in the galaxy and which kinds are rare? Are the bright stars we see at
night that make up the constellations mainly the common or rare types?
Domremy – HSC Physics Module 9.7 Astrophysics: Student Notes
HSC Physics E3: Astrophysics Activity 13: Stellar Evolution on HR Diagrams
Aim: To analyse information from a H-R diagram and use available evidence to determine the characteristics of a
star and its evolutionary stage
You will require your data from the previous activity.
1. Stellar populations and radii
Stellar surfaces are approximately “black body” emitters which obey the Stefan-Boltzmann law:
Luminosity = Area X Temperature4. The shapes of stars are spheres with Area=Xradius2. We can combine these
formulae to deduce the size (radii) of stars in different portions of the H-R diagram:
Radius  luminosity½ X Temperature2.
Using the Sun’s radius as a unit, estimate the radius of a selected red giant star (upper right in the H-R diagram) and
a white dwarf (lower left).
2. Stellar Evolution.
Use a new part of the spreadsheet to input data showing the stages of evolution for the Sun. The table below gives
the calculated solar properties during the T-Tauri (pre-main sequence), main sequence and red giant phases. The
current age of the Sun is 4.6 billion years.
Evolution of the Sun
Age (years)
106
107
108
4.6 X 109
1010
1.002 X 1010
1.1 X 1010
Temperature (K)
4800
4800
5800
5800
5800
4800
3400
Luminosity
3
0.3
0.8
1.0
1.8
3.0
350
Log(Luminosity)
Radius
1. Print out an H-R diagram showing the Sun’s evolution. Use a format that connects the dots.
2. What is the Sun’s radius at its most luminous point as a red giant?
3. Comment on the fate of the planets when the Sun becomes a red giant (1 A.U.  200 solar radii)
HSC Physics E3: Astrophysics Activity 13: Stellar Evolution on HR Diagrams
Aim: To present information by plotting on a H-R diagram the pathways of stars of 1, 5 and 10 solar masses during
their life cycle.
On the same plot of an HR diagram, present the evolution of a 1, 5 and 10 solar mass star, fully labelling each stage
and stating a nominal length of time at each stage.