Name: Spectroscopy and Creating your Own H-R Diagram Spectroscopy Spectral lines (particularly absorption lines) are a key way for astronomers to measure the temperature of a star as well as determine more details about it including the atoms and molecules found in its atmosphere. We will explore what the general shape of a star's spectrum (i.e. the underlying blackbody spectrum) and spectral lines reveal these details about a star. Blackbodies Stars are considered blackbodies, which means that their spectrum is determined by their temperature. Each blackbody spectrum is a curve with one peak wavelength. 800 u(3) [kdm] D 8 'y o o 200 T=4000K T=3500K 0 500 1000 1500 2000 A Inm] 1) The image above contains the blackbody spectra of 5 stars of different temperatures. Use the image to answer the following questions: a) Fill in the table below to give the peak wavelength for each star. The peak wavelength is where the spectrum reaches its highest point. To find the peak wavelength simply find the highest point of the spectrum and go straight down to the x-axis to find the wavelength. Temperature of the Star (K Peak Wavelength (nm 3500K 4000 K 4500 K \\ | 5000 K \\ | 5500 K b) Which temperature star had the largest peak wavelength? ) Which temperature star had the shortest peak wavelength? 6000 5000 Temperature (K) 4000 3000 d) Plot your answers to a) above in the graph below: 500 600 700 800 900 Peak Wavelength (nm) e) According to the graph above, what happens to the peak wavelength of a star as the temperature of the star increases? f) Which temperature star should look the most blue? g) Which temperature star should look the most red? h) The exact peak wavelength of a blackbody spectrum can be determined by Wien's Law. 7 : . 2.9 x 10 According to Wien's Law: Apax(in nm) =75 1w Using Wien's Law, calculate the peak wavelength for our Sun (Temperature = 5780 K). 1) For the five stars where you measured their peak wavelengths on page 1, use Wien's law to calculate the true peak wavelength for each star. Calculate the accuracy of your measurement Calculated wavelength using Wien's Law Measured wavelength on page 1 using: Accuracy = % 100%. Calculated wavelength using Wien's Law Put your answers on table on the next page. Temperature | Calculated Wavelength | Measured Peak Wavelength Accuracy Using Wien's Law (Copy your numbers from table on Page 1 3500 K 4000 K 4500 K 5000 K 5500K Emission Lines Emission lines and absorption lines are created by the electrons in orbit around atoms and molecules. These electron cannot be at any distance they want from the nuclei instead they must be at fixed distances. Consider the diagram below: n=4 n=3 n=1 The electrons can only be found at set distances from the nucleus. In the diagram, n =1 is called the ground state and is the smallest distance the electron can be. This diagram only shows up to n = 4 but there are actually an infinite number of levels. The smaller the distance from the nucleus, the lower the energy of the electron. a) Which energy level in the diagram above has the LEAST energy? b) Which energy level in the diagram above has the MOST energy? c) If an electron falls from a higher energy level to a lower energy level (i.e. gets closer to the nucleus) does the energy of the electron increase or decrease? d) The energy that is lost when an electron falls to a lower energy level is emitted as a photon (or particle of light) with an energy exactly equal to the energy lost. Would an electron lose more energy if it went fromn=2ton=1orn=3ton=17? e) In the table below, the energies of the first four levels of a hydrogen atom are listed. Using this data, find the energy lost by an electron as it makes each possible transition to the n =1 and n = 2 energy level and the wavelength of the photon created. (6.626 x 10 ~3* x 3.0 x 1017) Change in Energy Hydrogen Electron -21.79 x 10-1 -5.447 x 101? 2421 x 10Y -1.362 x 101? Note that the energies are negative, so n = 1 is the smallest energy since it is the most negative. Transition n=2ton=1 n=3ton=1 n=4ton=1 Change in Energy (Be careful because you are dealing with two negative numbers) Wavelength of Photon Emitted (in nanometers) n=3ton=2 n=4ton=2 f) In the table above you should have found that the wavelengths for the transitionston =1 were much shorter than the transitions to the n = 2 level. Explain why that is true. Hint: Think about what short wavelength means for the energy of a photon. g) What type of electromagnetic radiation (x-ray, UV, visible, IR, etc.) are the transitions to n =1 found in? What type of radiation are the transitions to n = 2 found in? Hint: You may need to look online to see what wavelengths correspond to what types of radiation. Different elements have different emission lines, which helps us to tell whether an object has a specific element in it or not. Wavelength (nm) 400 430 460 490 520 550 580 610 640 670 700 Unknown gas ---I-IIII_ [N AR | K T T wo | R R h) Consider the spectra above of 5 elements plus an unknown element. Which element is the unknown element? Explain how you know. Absorption Lines If you examine the spectrum of a star, however, instead of seeing these emission lines, you will instead see dips in a blackbody spectrum. These dips are called absorption lines and are created by various elements and molecules in the atmosphere of a star. The electrons in the atmosphere of the stars absorb photons of just the right energy to move up to a higher energy level. These photons that they are stealing cause a dip in the blackbody spectrum at that energy or wavelength, creating the absorption lines. At the top of the next page you see the spectra of 4 different stars; Each of these star spectra is a blackbody spectrum with absorption lines. Star A Star B Relative Flux Approximate "peak" Star C Star D 40 500 600 700 800 900 Wavelength (run) a) The diagram above shows the spectra of 4 different stars. For each star, draw a smooth curve over the top of the spectrum that shows the blackbody spectrum of the star that we would see if there were no absorption lines. Star D has been done for you as an example. b) Each curve you drew should have a peak to it. Measure the peak of each star's spectrum and use Wien's law to calculate the temperature of the star. Star Peak Wavelength (nm) Temperature A B C D c) Place the four stars in order from hottest to coldest based on their calculated temperature. Does this match what you see in their spectra with the peaks of the wavelengths (i.e. are the hotter stars peaking more at shorter wavelengths?) 6Solar Spectrum Emission Spectrum of lron d) In the image above you see a spectrum of the Sun and the emission line spectrum of iron. The dark strips in the solar spectrum are the absorption lines. --- Based on what you see above, is there evidence that the Sun has iron in its atmosphere? Explain ---- Based on what you see above, is there evidence of other elements in the Sun's atmosphere as well besides iron? Explain. Creating Your Own H-R Diagram In this lab we are going to measure the luminosity and temperature for 12 stars and use these results to create a Hertzsprung-Russell Diagram! Apparent and Absolute Magnitude - We use apparent magnitude to describe how bright a star looks in the sky. The smaller the number the brighter the star looks. - We use absolute magnitude to describe the luminosity of a star. The smaller the number, the higher the star's luminosity. a) Two stars are seen in the sky. Star A has an apparent magnitude of -2. Star B has an apparent magnitude of +3. Which star looks brighter in the sky? b) Consider the same two stars from the previous question. Which one has the highest luminosity? Explain your answer. ) Look at the data table on the next page that contains the information on all 12 stars in our sample. What star is the brightest in the sky? d) What star in the sample is the faintest in the sky? e) Can you tell from the data which star has the highest luminosity? If not, what additional information do you need along with the apparent magnitude in order to find the star's luminosity? Distance a) The stellar parallax for each star in our sample is also listed in the table. Which star is located closest to us? Explain how you know. b) Which star is located farthest from us? How do you know? c) Calculate the distance to each star using the following equation and record your answers in the Table: Distance (in light years) = 3260 / Parallax (in milliarcseconds) Table/Chart of Measured Stellar Properties Star Name Apparent Parallax Distance Distance Absolute Spectral Magnitude (milliarcsecs) Modulus Magnitude Type HD 8.83 5.14 124320 HD 37767 8.93 1.66 HD 24189 6.57 10.08 HD .22 13.61 107399 HD 17647 8.70 15.95 BD +63 9.47 66.46 137 HD 66171 7.56 21.15 Feige 40 8.03 0.73 HD 9.02 0.47 221741 HD 5351 9.13 41.45 HD 27685 7.4 26.96 HD 21619 7.32 3.97 9Changing From Apparent to Absolute Magnitude a) Absolute magnitudes are another way of measuring the luminosity of a star. The same rules apply as for apparent magnitude the smaller the number the higher the luminosity. Apparent Magnitude Absolute Magnitude Geddy +7 0 | Alex | +5 | +6 \\ | Neil | +10 | -5 | In the chart above, which of these 3 imaginary stars has the highest luminosity? b) Which star in the chart above looks the brightest in the sky? ) Which star would you think is the closest to us? Explain. d) Which star would you think is the farthest from us? Explain. e) Using the distance for each star in the table we are going to change the apparent magnitudes that you recorded into absolute magnitudes. Calculate the distance modulus for each star in the sample and record it in the table. Distance Modulus = 5 x log(Distance) 7.57 f) The distance modulus you entered is how much smaller a star's absolute magnitude is compared with its apparent magnitude. As you increase the distance to a star, what happens to the size of the distance modulus? g) Calculate the absolute magnitude for each star using: Absolute magnitude = Apparent magnitude Distance Modulus h) Which star has the largest luminosity? Explain your answer. i) Which star has the smallest luminosity? Explain your answer. 10 ) Find the distance to Alphecca using the following equation to convert distance modulus to distance: Distance Modulus + 5 Distance (in parsecs) = 10 5 d) Convert your answer from c) into light years. 1 parsec = 3.26 light years e) The true distance to Alphecca is 75 light years. Calculate the accuracy of your estimate. Actual Distance Estimated Distance Actual Distance Accuracy (in percent) = 100 X f) Finally, we have another star called Haul. Haul is a G2V star with an apparent magnitude of -26.8. Repeat the steps you used for Alphecca to calculate: 1) Estimated absolute magnitude of Haul from your H-R diagram: 2) Distance Modulus of Haul 3) Distance to Haul in parsecs 4) Distance to Haul in light years g) Haul is not the real name of the star (it is actually its name in Welsh in case you are interested). Based on the data from question f) take your best guess as to the real name of Haul. Explain. h) To check your accuracy, convert the distance of \"Haul\" from light years to AU. 1 ly = 63,240 AU. i) Calculate the accuracy of your distance measurement to \"Haul\". 14