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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 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 42 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 42 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.