Applying HR Diagrams: Spectroscopic Parallax & Stellar Sizes Version: 1.0 Author: Sean S
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Applying HR Diagrams: Spectroscopic Parallax & Stellar Sizes Version: 1.0 Author: Sean S. Lindsay History: Written October 2019; Last Modified: 28 October 2019 Goal of the Lab The goal of this lab is to extend our understanding of the properties of stars and how they relate to the HR diagram. In this lab, you will explore stellar luminosity classes, the luminosity-radius-temperature relationship, and the method of determining distances to stars called spectroscopic parallax. This will extend the usefulness of HR diagrams and further develop the connection between HR diagrams and understanding the evolutionary life cycles of stars. By the end of this lab, students are expected to know: 1. The Morgan-Keenan (MK) Luminosity Classes of stars 2. The distance determination method called Spectroscopic Parallax that is based on the HR diagram 3. The connection between stars luminosity, temperature, and radius via the luminosity-temperature-radius 4. Maybe Include: Main-sequence turn-off and stellar lifetimes. Tools used in this lab: ● An online table of Spectral Types temperatures: ● A ruler/straight-edge 1. Introduction: The Tale of Six Stars Fig. 1: A Hertzsprung-Russell Diagram. In this scatterplot of luminosity versus temperature, stars cluster into three primary regions: The giant region, the main sequence, and the white dwarf region In this lab, you will gain practical experience using the HR diagrams you explored in the previous lab. The goal is to learn how astronomers use HR diagram to connect properties of stars, and how we can use the HR diagram to determine the absolute magnitude of stars, which, in turn, can be used to calculate the distances to stars that are too far away for stellar parallax to be measured with our current technology. For the connecting properties of stars, you will see how the luminosity (the HR diagram y-axis) and temperature (the HR diagram x-axis) can be used to determine the radius of the star. As for using an HR diagram as a method to determine distances, we need to fill in a bit more background about stars (See Section 2). The ultimate goal of this lab is simple. Complete Table 1 on the student worksheet. That task, however, sounds rather dry, so let’s give it some meaning. In this lab, you are going to write the tale of six real stars. To accomplish this, you will: 1. Determine Observable Properties Using Stellarium: Use their observable properties found via Stellarium to determine their apparent, B – V color-index, and spectral class. 2. Determine the Temperature using Spectral Class: Instead of going through the University of Nebraska, Lincoln “Blackbody Curves and Filters Explorer,” to translate B – V to temperature, you will use a look-up table that connects the star’s classification to its temperature. 3. Determine the Absolute Magnitude & Luminosity from the HR diagram: You will then use that information to plot the stars on an HR diagram, and use the HR diagram to determine their absolute magnitudes, which is equivalent to the stars’ luminosities. ● There is a new trick here that we did not consider in the previous lab. Recall that on the HR diagram, we had the evolved stars in the “Giants” and “White Dwarfs” regions of the HR diagram. The spectra class of main-sequence stars and giant stars can be the same, but they are clearly different sizes and luminosities. So, if I know the spectral class of my star to an F5 star, is that star an F5 main sequence star, or is it an F5 giant? More so, are all giant stars the same type of giants, or can we further differentiate stars based on size? ● Being the dead cores of low-mass stars, white dwarfs don’t have the spectral lines that main-sequence and giant stars have, so how do we put those on the HR diagram? In this case, you will use the B – V color index, and I will give you the temperature. 4. Determine the Distance to the Star with the Distance Modulus: You now know each star’s apparent and absolute magnitude. You can use that information to calculate the distance modulus m – M, which can be used to calculate the distance to the star. ● This method of determining distance is used for stars that are too far away to have measurable stellar parallax ● This method is called spectroscopic parallax. This is a horrendous misnomer because it has nothing to do with the phenomenon known as parallax. 5. Determine the Radius of the Star: The astronomer’s version of the Stefan-Boltzmann Law (a thermal radiation law explored a few labs ago), connects the star’s luminosity to the star’s size and temperature. This gives what is known as the luminosity-radius-temperature relationship. You will use each star’s temperature and luminosity to calculate the physical size of the star. The process above shows one of the examples of deep knowledge codified within the HR diagram. With just a few observable quantities, you can start accessing physical properties of the stars. This allows astronomers to understand the properties of stars and start making further connections between, say, the mass of stars and their temperature, or the luminosity of the star and the mass of the star, which can be used to determine how long stars will live on the main sequence. I hope you appreciate just how powerful of a tool you are playing with here. A little bit of light from the stars coupled with a good bit of know-how of how light and nature works allows you to unlock the essential nature of the stars themselves. 2. the Morgan-Kennan (MK) Luminosity Classes Before we can get to work, we need to resolve the problem of a single spectral class, e.g., F5 could be a low-luminosity main-sequence star or a high-luminosity giant star. For a single spectral class, there are multiple luminosity, or equivalently absolute magnitudes, that the star could truly have. Perhaps we should take a closer look at where stars fall on the HR diagram. 1 Figure 2 shows an HR diagram for 22,000 stars in the Hipparcos Catalog. Figure 2. The HR Diagram for 22,000 stars on the HR diagram. The large number of stars reveals that “giant” stars do not all fall in the same region. The majority of giant stars fall in the “Giants,” but the other large stars can be subdivided into three other regions: subgiants, bright giants, and supergiants. This is the basis of the Morgan-Keenan Luminosity Classification scheme. The large number of stars reveals that “giant” stars do not all fall in the same region. There are specific regions in the HR diagram where stars cluster. This provides the basis for the Morgan-Keenan (MK) Classification. Based on where stars cluster on the HR diagram, the MK Classification identifies FIVE separate luminosity classes (plus white dwarfs). Each of these 1 The Hipparcos satellite was launched by the European Space Agency (ESA) in 1989 and operated until 1993. It used stellar parallax to determine with distances to 118,200 stars with unprecedented accuracy. The ESA launched a follow-up mission called Gaian 2013, which is determining the parallax to approximately 1 billion stars. luminosity classes is designated with a Roman numeral. The main sequence stars are giving the luminosity class of V (“five”). The luminosity classes are: ● Luminosity Class, V - Main sequence stars ● Luminosity Class, IV – Subgiant stars ● Luminosity Class, III – Giant stars ● Luminosity Class, II – Bright Giant stars ● Luminosity Class, I – Supergiant stars o Luminosity Class I is further subdivided into: Ia – Luminous Supergiant stars Ib – Less Luminous Supergiant stars The luminosity classes extend the Harvard Spectral Classification (O B A F G K M) + (0 – 9) explored in the previous lab. Our Sun is a spectral class G2 star, but it is also a main-sequence star with luminosity class V. So, the full spectral classification for the Sun is G2 V. As the Sun ends its life on the main sequence, it will cool down and become a red giant star. It will become a K- or M-type star and first change to luminosity class IV star (subgiant on the subgiant branch of stellar evolution) and eventually become a luminosity class III star (giant on the red giant branch of stellar evolution). The spectral classes only account for the star’s spectral characteristics based on its temperature. The luminosity classes account for the star’s spectral characteristics based on its temperature, and the surface gravity effects on a star’s spectrum. The physics is a bit complicated, so the details are left out here, but as a star expands to become a giant or supergiant star, the surface gravity becomes smaller. The star is the same mass, but now the surface is much farther away, so the surface gravity is lower. The lower surface gravity manifests itself in the spectrum of a star in a few ways. Primarily, larger stars with lower surface gravity have: ● Narrower spectral lines due to decreased pressure broadening ● Subtle changes in the ratio of line strengths. Main-sequence stars have the highest surface gravity, and so will highest surface pressure and the most pressure broadening of lines. Main-sequence stars will have broad spectral lines. In general, supergiant stars have the lowest surface gravity, and hence the smallest surface pressure and the least pressure broadening of lines. Giant stars will have narrow spectral lines. You can see an example of the difference in spectral lines for G-type stars based on luminosity class in Fig.