Check your feedback from part 2 to ensure that your spectral types are correct. If they are not correct, refer back to that procedure to verify the types.
Note: as you follow these instructions, fill in your answers on this spreadsheet (Excel, Google Docs).
Copy the star names and spectral types from the previous assignment in the table.
Go to the following website to determine the mass of the stars. You will find a column of values. The first column is the spectral type and the second column is the mass in solar masses. For example, the first line of the table says that an O0Ia0 star has a mass of 160.0 solar masses. For luminosity class I stars, use the "Ia" or "Ib" value from the chart, not the "Ia0" value. Save some time looking for your spectral type by using Ctrl-F or Command-F for Macs.
Is your spectral type a middle value? Take an average! For example, F9.5V is halfway between F9V and G0V. G6II-III is halfway between G6II and G6III. A5Iab is halfway between A5Ia and A5Ib. Find each of those masses and calculate the average between the two.
It is time to review some of the principles of stellar evolution. If we consider how long it takes the star's light to reach us, it is possible that one or more of the stars may have died and would not be part of the constellation any more. In this part of the project, you will be determining the order in which the stars will die.
Unfortunately, there isn't an easy algorithm for determining how old a star is. The metallicity (proportion of elements more massive than H or He) is used to divide stars into Population I and Population II, but we can expect that different parts of the galaxy are going to have different rates of change of the metallicity with time. As such, we won't be able to determine the current ages of the stars and we'll have to do something a bit dangerous — we will assume that each star in the cluster just reached that stage of its life (a main sequence star was just born, a giant star just became a giant star, etc.)
The luminosity class tells you what kind of star you have, whether it is a main sequence, giant, or supergiant star. We can calculate the main sequence lifetime based on the mass of the star that you looked up. For main sequence stars (luminosity class V), the main sequence (MS) lifetime is given by the following equation, where M is the mass of the star in solar masses.
For each of the stars (whether they are main sequence stars or not), calculate the main sequence lifetime. Fill in the appropriate column in the table below. Round your answers to three significant digits. For example, 456,789,123 would be rounded to 457,000,000.
The stages of stellar evolution proceed more quickly as the star approaches death. We'll approximate the lifetime of a giant star as roughly 1/10 of the main sequence lifetime. We'll also assume that the lifetime of a supergiant star is 1/100 of the main sequence lifetime. Giants and supergiants have already completed their main sequence lifetimes.
Use this information to find the completed and remaining lifetimes of each of your stars. Remember that all stars will go through a giant stage, so if you have a main sequence star, add the giant stage lifetime to the main sequence lifetime. For stars with more than eight solar masses, there will be a supergiant stage as well. Be sure to add this in to your remaining lifetime value.
If you have a luminosity class II star, we will find the lifetime in the same manner as the lifetime of a class I (or Ia or Ib) star. If you have a luminosity class IV star, we will find the lifetime in the same manner as the lifetime of a class III star.
If you have a star with two luminosity classes listed, such as II-III or IV/V, use the first class to determine the lifetimes. For example, use II for II-III or IV for IV/V.
Here are the guides to follow:
| Situation | Past Life Stages | Completed Lifetime Calculation |
|---|---|---|
| Main Sequence Star (V) | None | None |
| Giant (III) or Subgiant Star (IV) | main sequence | 1 × MS lifetime |
| Supergiant Star (Ia or Ib) or Bright Giant Star (II) | main sequence, giant | 1.1 × MS lifetime |
| Situation | Future Life Stages | Remaining Lifetime Calculation |
|---|---|---|
| Main Sequence Star (V), < 8 solar masses | main sequence, giant | 1.1 × MS lifetime |
| Main Sequence Star (V), > 8 solar masses | main sequence, giant, supergiant | 1.11 × MS lifetime |
| Giant (III) or Subgiant Star (IV), < 8 solar masses | giant | 0.1 × MS lifetime |
| Giant (III) or Subgiant Star (IV), > 8 solar masses | giant, supergiant | 0.11 × MS lifetime |
| Supergiant Star (Ia or Ib) or Bright Giant Star (II) | supergiant | 0.01 × MS lifetime |
|
Examples: 1) A 1 solar mass main sequence star will live for (10,000,000,000 years) ÷ 12 = 10,000,000,000 (10 billion) years on the main sequence. It will live as a giant star for 0.1 × 10,000,000,000 years = 1,000,000,000 (1 billion) years. Its remaining lifetime will be 10,000,000,000 + 1,000,000,000 = 11,000,000,000 (11 billion) years. This is the same as 1.1 × 10,000,000,000 years = 11,000,000,000 years. 2) A 10 solar mass giant star had a main sequence lifetime of (10,000,000,000 years) ÷ 102 = 100,000,000 (100 million) years. Its giant lifetime is 0.1 × 100,000,000 = 10,000,000 (10 million) years. It will also become a supergiant which will live for 0.01 × 100,000,000 years = 1,000,000 (1 million) years. The remaining lifetime of this star is 10,000,000 + 1,000,000 = 11,000,000 (11 million) years. This is the same as 0.11 × 100,000,000 years = 11,000,000 years. |
Once you have finished assigning remaining lifetimes to each of the stars, number them by the order in which they will die. Give a number "1" to the first star that will die, a number "2" to the next one to die, and so on. If two stars die at the same time first, they are both "1," and the next star is "3."
We know also that the end fate of a star is dependent on the mass of the star. For each of the stars, record what the end fate of the stellar core will be; whether it will produce a white dwarf, a neutron star, or a black hole. If it is less than eight solar masses, it will end as a white dwarf. If it is between eight and 25 solar masses, it will end as a neutron star. If it is larger than 25 solar masses, it will end as a black hole. Record your answers in the chart on the spreadsheet (Excel).
You can see a fully worked example here.