## The spectra of stars can be approximated by a Blackbody curve. But the real spectra include many absorption features that lead to something that looks like a very wiggly Blackbody curve.

### others

##### Description

Lab 4: The HR Diagram

The spectra of stars can be approximated by a Blackbody curve.  But the real spectra include many absorption features that lead to something that looks like a very wiggly Blackbody curve.  Despite the wiggliness, you can use Wein's Law to approximate the temperature of a star using the wavelength of peak emission in the star's spectrum.

λmax = (3x106 K nm) / T

Below are spectra for 5 different stars. Use Wein's law to calculate the approximate temperature of each one.  Note that the wavelengths for these spectra are given in Angstroms.  1 Angstrom = 10-10m, while 1 nm = 10-9m.

This is the spectrum of a spectral type F8 star. Using Wein's law, calculate its approximate temperature in K [do not write units in the answer boxes, just the value].

This is the spectrum of a spectral type K4 star. Using Wein's law, calculate its approximate temperature in K.

This is the spectrum of a spectral type M2 star. Using Wein's law, calculate its approximate temperature in K.

This is the spectrum of a spectral type A8 star. Using Wein's law, calculate its approximate temperature in K.

This is the spectrum of a spectral type O9 star. Using Wein's law, calculate its approximate temperature in K.

Stars are grouped into different spectral classes that actually tell us about their temperature, which our eye perceives as colour.

Temperature is one of the axes in the HR Diagram, which will be the subject of the remainder of this lab

Now we're going to talk about the Herzsprung-Russell Diagram, also called the HR Diagram, which is an extremely useful way to organize and display the properties of stars.  This lab will make use of an online simulator available

here: https://astro.unl.edu/mobile/HRdiagram/HRdiagramStable.html

Open the simulator and start exploring how to use it.  Note that you can either click on a portion of the diagram or click and drag the star with the "x" on it to different parts of the diagram.  The x-axis is temperature in Kelvin - in the centre of the x-axis you can see the exact temperature listed for the simulated star. The y-axis is luminosity in multiples of Lsun - the luminosity of the Sun.  The exact luminosity and radius values are given in the lower left corner of the diagram.   The size and the colour of your simulated star will change as you drag it around the diagram.

Use the simulator to fill in the table in the next question:

Drag and drop the colour that best matches the colour of your simulated star as you drag it to different place on the HR diagram to match the listed temperature and luminosity for each of the stars below.

Up in the upper right corner of the simulator is a drop-down menu under "Plots."  Select "Closest."  Now, all of the closest stars to the Sun are plotted.  Note that they are not randomly scattered around the plot, they all appear in a somewhat orderly pattern - very close to the faint green line labeled "Main Sequence."  (You can toggle off these stars after you take a look at roughly where they sit on the diagram by clicking on "None" under the "Plots" drop-down menu).

The Main Sequence is the part of the diagram where stars of many different masses will spent the majority of their lifetimes, while they are fusing hydrogen into helium, as our Sun is currently doing.  While on the Main Sequence, there is a specific relationship between stellar luminosity (L), stellar temperature (T), and stellar radius (R):

L is proportional to R2 T4

If you use units of LSun, TSun, and RSun, you can use this equation directly to explore the relationship between these values for different stars on the Main Sequence.

L = R2 T4

Use this relation to fill in the table in the next question.

Use the equation above to fill in the following table for the relationship between the radius, temperature, and luminosity of different stars on the Main Sequence.

There is also a relationship between mass and luminosity for stars on the Main Sequence:

L is proportional to M3.5

If you use units of LSun and MSun, the formula becomes

L = M3.5

What is the luminosity of a 2 MSun star in units of LSun? [Do not write units in the box below, just the value]

Using the formula above, what is the mass of a star with a luminosity of 3,160 LSun in units of MSun?  [Do not write units in the box below, just the value]

Return to the HR diagram simulator to answer the following question.  Drag your test star around to fill in the blanks about the general trends in the diagram:

Hot stars are found at the: bottom, left, top, or right

Faint stars are found at the: bottom, left, top, or right

Luminous (bright) stars are found at the: bottom, left, top, or right

Cool stars are found at the: bottom, left, top, or right

Use the HR diagram simulator to select the best answer about the location of each type of star on the HR diagram:

Large blue stars are found at the: lower right, upper left, upper right, lower left

Small red stars are found at the: lower right, upper left, upper right, lower left

Small blue stars are found at the: lower right, upper left, upper right, lower left

Really large red stars are found at the: lower right, upper left, upper right, lower left

Notice as you drag your test star around the simulator that straight green lines appear and disappear.  These are "isoradius" lines - lines across the diagram where stars will have the same radius.  Use these lines to double check your answers to the previous question.

The equation below explains the relationship between luminosity (L), radius (R), and temperature (T) for any star in generic units:

L = 4π R2 σ T4

In the equation above, π and σ are constants.

Remember also Wein's Law λmax = (3x106 K nm) / T , which tells us the relationship between the wavelength of peak emission (which we perceive as colour in optical wavelengths) and temperature.

Use these two equations to explain the trends you just observed in colour, size, and luminosity on the HR diagram.

Select "Closest" from the "Plots" dropdown menu in the upper right to plot the locations of some of the closest stars to ⦁ the Sun on the HR Diagram.  Are most of these stars brighter or fainter than ⦁ the Sun?  Do you think this distribution is typical of stars in our Galaxy?

Move the cursor to the middle of the nearest star sample, where many of the stars are concentrated on the diagram. This region is close to ________________ (nothing - they are randomly distributed, or the dwarf stars, or the Main Sequence) on the diagram. The luminosities for these typical nearby stars are __________ smaller than, or the same as, or larger than that of ⦁ the Sun’s, their radii are ___________ smaller than, or larger than, or random compared to, the same as that of ⦁ the Sun’s, and their surface temperatures are  higher than, or lower than, or the same as that of ⦁ the Sun's.

Now we're going to look at a different population from stars.  From the "Plots" menu, select "Brightest."  How many of these stars are fainter than ⦁ the Sun?  Do these stars mostly fall on the main sequence or elsewhere on the diagram?  Describe their distribution.

This list of nearby stars is technically incomplete, because they left out a type of star called a "white dwarf."  One of these is the companion star to Sirius A, which we discussed earlier.  The white dwarf Sirius B has a luminosity of 0.027 LSun and a temperature of 25,000 K.  Drag the simulated star to that position and record the radius of Sirius B in units of RSun. [Do not write units in the box below, just the value]

Move the cursor to the star representing the hottest star in this sample. Its luminosity is approximately ___________ (180,000, 18,000, 150,000, 1,500) LSun, its radius is approximately____________ (10, 40, 1, 14) RSun, its and surface temperature is approximately ____________ (3200, 32, 32000, 320000) K. All of these values are ____________ (much larger than, or much smaller than, or both larger and smaller compared) to those properties for ⦁ the Sun.

Why do the brightest stars appear bright to us on Earth?  3 students debate:

Student A: “I think it’s because these stars must be very close to us. That would make them appear brighter to us in the sky.”

Student B: “I think it’s because these stars are very luminous. They are putting out a tremendous amount of energy.”

Student C: “I think it’s because these stars are very close and very luminous.”

Use the tools of the HR diagram simulator to support the views of one of the three students. Why are the stars we perceive as bright in the night sky really bright? (hint: You may find the drop-down options labeled "both the nearest and brightest stars" and "overlap" useful.)

Move the cursor to the star representing the largest star in this sample. Its luminosity is approximately __________ (5700, or 44000, or 440000) LSun, its radius is approximately __________ (5, or 50, or 510) RSun, and its surface temperature is approximately  __________

(3700, or 5700, or 7700) K. All of these values are __________ (both larger and smaller than, or much smaller than, or much larger than) those properties for the Sun.

Do you think that these brightest stars are very common or very rare in the galaxy?  Explain your reasoning.