PH104 Lab 5 Stellar Classification Pre-Lab

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1 Name: Lab Time: 1 PH104 Lab 5 Stellar Classification Pre-Lab 5.1 Goals This is a series of labs designed to help is in understanding the nature and lives of stars. There are 3 total labs in this sequence. Two of these have to do with the HR diagram model of stars, the third is a stellar corpse lab. Once students have finished this lab sequence, they will understand: The ranges on the properties of stars. Those properties include: Temperature Mass Luminosity Radius The life stages for high and low mass stars The possible stellar corpses left behind How to find black holes and neutron stars. How to use stars to find the distances to galaxies and other objects. 5.2 Stellar Model We are going to jump right in with the model of stellar properties. This model is built exactly like we have built models in the past. We look for real physical properties of stars that will in the end help us to understand the lives of the stars Temperature What if we were to go out and look at the Sun with every type of telescope possible. We could see how the Sun looks in every possible wavelength of light, starting with x-rays all the way to radio. If we look at the brightness (or intensity) of each wavelength of light coming from the Sun we would see something amazing. Each wavelength of light the Sun emits has a different brightness. If we were to make a plot of those wavelengths we would see a plot similar to the one in figure 5.1. This is called the Thermal Spectrum.

2 2 PH104 LAB 5. STELLAR CLASSIFICATION PRE-LAB The Sun is acting like a blackbody. Many objects act as blackbodies, since blackbodies absorb all wavelengths of radiation falling in on them, and remit radiation at all wavelengths. Figure 5.1: Sample Thermal Spectrum of the Sun. Figure 5.2: Plot of λ max vs. Temp.. On thing we notice with a thermal spectrum is that there is one wavelength emitted by the blackbody that is brighter than all of the other wavelengths emitted. This is known as the maximum wavelength or λ max. If we look at stars we notice that hotter stars have a thermal spectrum where λ max is toward higher energy shorter wavelengths, and that the opposite is true for cooler

3 5.2. STELLAR MODEL 3 stars. If we make a plot of λ max versus Temperature (Fig 5.2), we see that there is a relationship between the maximum wavelength of light a star emits and the temperature of the star. This relationship is... T star (K) = λ star max(m) (5.1) Where λ max is given in m. T star (k) is given in Kelvin. The temperature given here is called the effective temperature. The effective temperature of a star is a physical property that we need for our model. In order to find the temperature of a star we need to find λ max. Question#1: Given that for the Sun m, calculate the effective temperature of the Sun Luminosity The luminosity of a star is a measure of the total power output of a star. It is usually measured in Watts, but we will use a unit based on the Sun (L Sun ), where the Sun is 1 L Sun, and all other stars will be some number of Solar Lumens (L Sun ). Magnitudes When we look at the stars we see that they are all different brightness. We could go outside and classify those stars by their brightness by giving the brightest stars the number 1, and the next brightest the number 2, and so on, until we could not see any more stars. This would be called a magnitude scale. Since all of the stars are different distances from us, this magnitude that we have given them is only how bright they appear from Earth. We call this apparent magnitude (m). Question#2: In table order the stars from brightest to dimmest as seen from Earth. Hint: Remember that the smaller the number the brighter the star. Star Name Apparent Magnitude Brightness Ranking Sun Vega 0 Pollux 1.15 Spica 0.96 The apparent magnitude of a star depends on the distance to that star, so going out in our backyard an loooking at a star we can only infer the temperature from

4 4 PH104 LAB 5. STELLAR CLASSIFICATION PRE-LAB the color of the star. Any other property is going to take some work. What if we were to place all of the stars at a distance of 10 parsecs, and we look at their relative brightness again. This means that the brightness we see has to do with their absolute property luminosity. This is called absolute magnitude (M). You will notice that most stars will have a different apparent magnitude and absolute magnitude Question#3: In table order the stars from brightest to dimmest as seen from Earth. Hint: Remember that the smaller the number the brighter the star. The absolute magnitude is something that we can use to find the luminosity. Star Name Absolute Magnitude Brightness Ranking Sun 4.77 Vega 0.55 Pollux 1.08 Spica The relation between absolute magnitude and luminosity is L star = M L Sun (5.2) where M = M Sun M star and L Sun is the luminosity of the Sun. We can make our calculations easier by doing everything in units of L Sun. This means that the Sun would be 1 L Sun and Pollux would be 30 L Sun according to table??. Question#4: What is the luminosity of Vega in Solar units? The Radius of Stars We can calculate the luminosity of a star is we know its radius through the following relationship: where L is the luminosity of the star π is the constant π = 3.14 σ is a constant equal to watts/(m 2 Kelvin 4 ) L = 4πr 2 σt 4 (5.3) Knowing the radius and effective temperature of a star, we can find the luminosity. However using equation 5.2 and converting the luminosity to Watts, and knowing

5 5.3. THE MODEL 5 the temperature of the star in Kelvins, we can also figure out the radius of the star in km. This is just a matter of some algebra. However, why don t we just find the radius of a star in Solar Units (R Sun ). R star (R Sun ) = where L star is the luminosity of the star in Solar Luminosities. T Sun is the effective temperature of the Sun, 5,800 Kelvin. T star is the effective temperature of the star given in Kelvins. TSun 4 Tstar 4 L star (5.4) Question#5: Given that the effective temperature of Vega is 8913 K, calculate Vega s radius. Us the temperature for the Sun that you found previously. 5.3 The Model The model of stars that we have put together will help us to explain the model of stellar evolution. The model in this case is a set of properties that we can apply all stars with the express idea that this will help us to understand the evolution of stars. WE will talk about the evolution of stars. 5.4 Conclusion We can plot the properties of stars into an effective diagram. This diagram known as the Hertzsprung-Russell diagram will allow us to talk about most of the life stages of stars. This will be done in the lab.

A1101, Lab 5: The Hertzsprung- Russell Diagram Laboratory Worksheet

Student Name: Lab TA Name: A1101, Lab 5: The Hertzsprung- Russell Diagram Laboratory Worksheet One of the most basic physical properties of a star is its luminosity, the rate at which it radiates energy