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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

Electromagnetic

Radiation Spectra

Telescopes

Resolution

Sensitivity

Adaptive Optics

Interferometry

Astrometry

Parallax

parsec

Light

year Satellites

Black

Body

Radiation

Emission

Spectra

Absorption

Spectra

Astronomical

Objects

Stellar

Spectra

surface temperature,

rotational and

translational velocity,

density and chemical

composition of stars

Magnitude

Colour

Index

HR Diagram


Astrophysics Module Plan

Module Length: 7 weeks

Focus Area Time Concept Text Summary Practical

1. Our understanding

of celestial objects

depends upon

observations made

from Earth or from

space near the Earth

½ 1. discuss Galileo’s

utlisation of the

telescope to identify

features of the Moon.

½ 2. discuss why some

wavebands can be more

easily detected from

space

1 3. define the terms

resolution and sensitivity

of telescopes.

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

1 4. discuss the problems

associated with ground-

based astronomy in terms

of resolution and

absorption of radiation

and atmospheric

distortion.

1 5. outline methods by

which the resolution

and/or sensitivity of

ground-based systems

can be improved,

including:

– adaptive optics

– interferometry

- active optics.

2. (Act 2) gather, process and present

information on new generation optical

telescopes

2. Careful

measurement of a

celestial object’s

position, in the sky,

(astrometry) may be

used to determine its

distance

1 1. define the terms

parallax, parsec, light

year

1 2. explain how

trigonometric parallax

can be used to determine

the distance to stars

1. (Act 3) solve problems and analyse

information to calculate the distance to a star

given its trigonometric parallax using d = 1/p

1 3. discuss the limitations

of trigonometric parallax

measurements

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.



3. Spectroscopy is a

vital tool for

astronomers and

provides a wealth of

information

1 1. account for the

production of emission

and absorption spectra

and compare these with a

continuous blackbody

spectrum

1. (Act 5) perform a first-hand investigation to

examine a variety of spectra produced by

discharge tubes, reflected sunlight, incandescent

filaments

1 2. describe the

technology needed to

measure astronomical

spectra

1 3. identify the general

types of spectra produced

by stars, emission

nebulae, galaxies and

quasars

1 4. describe the key

features of stellar spectra

and describe how this is

used to classify stars

1 5. describe how spectra

can provide information

on surface temperature,

rotational and

translational velocity,

density and chemical

composition of stars

3. (Act 6) analyse information to predict the

surface temperature of a star from its

intensity/wavelength graph

4. Photometric

measurements can be

used for determining

distance and

comparing objects

1 1. define absolute and

apparent magnitude

2 2. explain how the

concept of magnitude can

be used to determine the

distance to a celestial

object


information using:

M m 5log(d

10)

and

IA

IB100(MB MA) / 5

to calculate the absolute or apparent magnitude

of stars using data and a reference star

1 3. outline spectroscopic

parallax

1 4. explain how two-

colour values (ie colour

index, B-V) are obtained

and why they are useful

2. (Exp 8) perform an investigation to

demonstrate the use of filters for photometric

measurements.

1 5. describe the

advantages of

photoelectrictechnologies

over photographic

methods for photometry

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



5. The study of binary

and variable stars

reveals vital

information about

stars

1 1. describe binary stars in

terms of the means of

their detection: visual,

eclipsing, spectroscopic

and astrometric

1. (Exp 10) perform an investigation to model

the light curves of eclipsing binaries using

computer simulation

2 2. explain the importance

of binary stars in

determining stellar

masses


information by applying Kepler’s Third Law:

m1 m2 42r 3

GT to calculate the mass of a star system

1 3. classify variable stars

as either intrinsic or

extrinsic and periodic or

non-periodic

1 4. explain the importance

of the period-luminosity

relationship for

determining the distance

of Cepheids

6. Stars evolve and

eventually ‘die’

2 1. describe the processes

involved in stellar

formation

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 2. outline the key stages

in a star’s life in terms of

the physical processes

involved

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

1 3. describe the types of

nuclear reactions

involved in main-

sequence and post-main

sequence stars

1 4. discuss the synthesis

of elements in stars by

fusion.

2 5. explain how the age of

a globular cluster can be

determined from its zero-

age main sequence plot

for a HR diagram

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.

2 6. explain the concept of

star death in relation

to:

– planetary nebula

– supernovae

– white dwarfs

– neutron stars/pulsars

– black holes


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.


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


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 Parallax Angle Distance

(parsecs)

Distance (light-

years)

Distance (A.U.)

Sirius -Canis Major 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

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.




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

Aim: To solve problems and analyse information using: M m 5log(

d

10) and

IA

IB100(MB MA) / 5

to calculate

the absolute or apparent magnitude of stars using data and a reference star

Method


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.


HSC Physics E3: Astrophysics Experiment 8: Photometry

Aim: To perform an investigation to demonstrate why it is important to use filters for photometry

Method


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



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: m1 m2

42r 3

GT to calculate

the mass of a star system


http://www.isc.tamu.edu/~astro/ebstar/ebstar.html


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 Temperature (K) Luminosity Log(Luminosity) Radius

Sun 5860 1.0

Proxima Centauri 3240 0.00006

Alpha Centauri A 5860 1.6

Alpha Centauri B 5250 0.45

Barnard’s Star 3240 0.00045

Wolf 359 2640 0.00002

BD +36 2147 3580 0.0055

L 726-8A 3050 0.00006

UV Ceti 3050 0.00004

Sirius A 9230 23.5

Sirius B 9000 0.003

Ross 154 3240 0.00048

Ross 248 3050 0.00011

Epsilon Eri 4900 0.30

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.


Brightest Stars Name Temperature (K) Luminosity Log(Luminosity) Radius

Sun 5860 1.0

Sirius A 9230 23.5

Canopus 7700 1400

Alpha Centauri A 5860 1.6

Arcturus 4420 110

Vega 9520 50

Capella 5200 150

Rigel 11200 42000

Procyon 6440 7.2

Betelgeuse 3450 12600

Achernar 15400 200

Beta Centauri 24000 3500

Altair 7850 10

Alpha Crucis 25400 3200

Alderbaran 15400 95

Stars in a Young Open Cluster Name Temperature (K) Luminosity Log(Luminosity) Radius

Stars in a Globular Cluster Name Temperature (K) Luminosity Log(Luminosity) Radius

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?


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=Xradius

2. We can combine these

formulae to deduce the size (radii) of stars in different portions of the H-R diagram:

Radius luminosity½ X Temperature

2.

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) Temperature (K) Luminosity Log(Luminosity) Radius

106 4800 3

107 4800 0.3

108 5800 0.8

4.6 X 109 5800 1.0

1010

5800 1.8

1.002 X 1010

4800 3.0

1.1 X 1010

3400 350

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.

Documents

HSC Physics Module 9 - members.optushome.com.aumembers.optushome.com.au/galenneubronner/Physics/97phys/97phyn… · Domremy – HSC Physics Module 9.7 Astrophysics: ... 1 4. discuss