Activity

Measure the Age of Ancient Cosmic Explosions

In this project you will calculate the age of a supernova remnant using Las Cumbres Observatory and Hubble Space Telescope observations. You will compare the remnant's radius in images taken several years apart to determine the expansion velocity and use this to calculate how long ago the supernova explosion occurred.

Materials

Background Science 

Supernovae:

Supernovae are the violent explosions of stars occurring at the end of their lives. On average, one supernova goes off every 50 years or so in our Galaxy. Supernovae release more energy in a single instant than the Sun will produce in its whole lifetime! If the nearest massive star, Betelgeuse in the constellation Orion, were to go supernova it would (for a short time) be brighter than the full moon. 

There are two main types - Type Ia and II.  Type II are the explosions of very massive stars with mass greater than 8 times the mass of the Sun.  Type Ia are the explosions of stars similar in mass to the Sun, which have a binary companion and become unstable.

In order these images show an artist’s impression of a Type II supernova, a Type Ia supernova and the Spaghetti Nebula supernova remnant. Credit: ESO

Type II -These are caused by massive stars that 'live fast and die young', using up all of their hydrogen and helium fuel in only a few million years — thousands of times faster than the Sun burns its fuel. When the fuel supply is exhausted the star must burn heavier and heavier elements until, finally, when it can do no more to keep itself alive, the inner parts of the star collapse to form a neutron star or black hole, and the outer parts are flung off in an explosion we call a supernova

Type Ia - These happen when a star similar in mass to the Sun reaches the end of its life as a white dwarf star - a hot, dense core.  If this hot core has a binary companion star (two stars orbiting around a common centre of mass), the white dwarf will pull matter from the companion star onto its surface, until it becomes unstable and explodes as a supernova. Type Ia supernova can also be caused by two white dwarfs merging to the same end.

Read more about supernova exoplosions in SpaceBook.

Supernova Remnants:

No matter whether it is a Type Ia or Type II supernova, the enormous explosions from these stars ejects material into the surroundings at very high velocities, sweeping up the surrounding interstellar gas into a shell or a giant bubble.  This is known as a supernova remnant.  The ejected material and the swept-up compressed gas are very hot. The shell (or bubble) shines at different wavelengths, mainly in the X-ray, optical and radio. 

Supernova remnants are studied at many different wavelengths from optical light to X-rays.  Different things are happening in different wavelengths; when we observe in, say the X-ray, we are looking at the bits of the shell that are much hotter than the bits shining in the optical.   

In this activity we will concentrate on the optical emission that comes from the interaction between the outward moving shell and the interstellar material that surrounds the supernova. The material is compressed and heated to 10 thousand degrees Kelvin.  In the optical we can see the shocks caused by the expanding material as it sweeps outwards at high velocities. Using the H-alpha filter we will specifically see hydrogen gas.

During the initial collapse and rebound of the star's core when a supernova occurs, the outer layers of the star's material are ejected, yet most of the gas in a supernova remnant is not from the star but is collected afterward. As the remnant expands, it sweeps up the surrounding interstellar medium, material which builds up around the edge of the shockwave. The volume through which the remnant has expanded and the density of the interstellar medium can be used to calculate the mass of the remnant.

In the space between the stars, the density of material is very low - there isn’t much out there! In fact, the average density of the interstellar medium is about 1 x10-21 kg m-3

Cas A:

Cas A is a supernova remnant about 11,000 light years away. In optical light the remnant appears as a ghostly shell with bright filaments and dense clumps. As these clumps are largely composed of oxygen the OIII filter is best suited for observing this target.

Summary of terms:

symbol       description value
KE  kinetic energy of shell 1044 J
density density of surroundings 10-21 kg m-3
D distance to the supernova Find this value on the web

Preparation

To prepare for this activity, you will need to download the SAO DS9 software, the Ancient Cosmic Explosions spreadsheet and worksheet (ACE_spreadsheet.xls and ACE_worksheet.txt), and two observations of your chosen supernova remnant, taken at least 2-3 years apart (see list of materials).

The LCO science archive contains thousands of observations taken over the last four years, to find out how to search for observations of your chosen target see our online guide: How to search within the LCO Science Archive 

Remember you will need two observations of your chosen target taken several years apart in order to measure the expansion velocity.

If you plan to take your own observations with LCO, please note that supernova remnants are very faint and require long exposure times, some may even need to be observed in specific filters such as H-alpha or OIII. Information on how to observe with LCO can be found online at: https://lco.global/education/observing/

Instructions 

A. Measure the radius of the supernova remnant (ds9)

You will find that your LCO observations have been compressed as fpack or .fz files. fpack files can be opened directly in the SAO DS9 software (DS9), so don’t wrry about decompressing the files.

1. In DS9 click file > open and select your first image.  Repeat this step to open your second image and select Frame > Tile to see the images side-by-side. 

2. The first thing you’ll need to do is adjust the visibility of your object by adjusting the fit, brightness and contrast of your images.

Do this by selecting Zoom > Fit and he click Scale > Log. Hold the right mouse button and drag your cursor across the image to change the brightness and contrast. You can also alter the colour of your observation to optimise visibility of your remnant. To do this select the Color button on your task bar.

You should see the ring of the remnant clearly in each of the images. The first measurement will determine and compare the radius of this ring in each image. Do this by outlining the ring of your supernova remnant in both images with a circle.

3. Go to Edit > Region and then Region > Shape > Circle

4. Draw a circle over the supernova, marking out the shape of the shell, making sure that the circle is as big as the supernova remnant. The circle on both of your images must encompass the same region of the supernova remnant as in the image below.

5. Starting with your first image, go to Region > Get Information. A box will appear showing the centre co-ordinates of the circle. (Tip: In DS9, look for the blue line around your observation to check which image you are analysing).

6. Next, click on the box marked physical next to the Radius values. Select WCS and choose the type of units you want, we will use arcmin and radians.  (The example below shows the radius in arcmin = 1.73454).

7. Open the ACE_spreadsheet and ACE_worksheet and note down your radius value in arcmin and radians where indicated.

8. Repeat these steps to determine the radius for your second image and note down these values.

B. Find the distance to your supernova remnant (Simbad)

9. The next step is to find the distance to your supernova remnant. There are several online astronomical catalogues that can provide this information, such as Simbad.

To find the distance using Simbad, visit http://simbad.u-strasbg.fr. Click basic search and enter the name of your supernova remnant. Scroll down to Collections of Measurements and click display all measurements. You will need the distance in light years (ly)

For Cas A the distance is 10,200 ly.

10. Note down the distance on your spreadsheet and the  worksheet.

At this point, you are able to find the age of your supernova remnant using our automated spreadsheet. The final piece of information needed is the time difference between your two images. With this value we can calculate the remnants expansion velocity and use this to calculate the age. When you have entered the time difference between your two observations where indicated on the spreadsheet, you will find the age of your supernova remnant where indicated on your spreadsheet! Congratulations!

If you'd like to calculate the age manually, continue following the steps of this activity.

C. Calculate the size of your supernova remnant

10. The next step is to work out the diameter of the supernova remnant. This can be done using the equation below:

d = D tan (θ)
 
  • d = diameter of remnant in metres 
  • D = distance to remnant in metres 
  • θ is the angle on the sky in degrees   

11. Begin by calculate the distance to your supernova remnant in metres and note your result on your worksheet: 1 light year = 9.5 × 1015 m.

12. θ is your radius in radians, as noted on your worksheet.

14. With these values you can use the equation above to calculate the diameter of your remnant, note this down on your worksheet.

12. Finally, calculate the radius of your supernova remnant in metres and note down your result on your worksheet: 0.5 x radius

D. Calculate the volume of your supernova remnant

13. Now that you have the physical radius, use the equation below to work out the volume of your supernova remnant and note down the result on your worksheet.

V = (4/3) π R

  • V is volume
  • R is the radius in metres, found on your worksheet 

D. Calculate the mass of your supernova remnant

The volume through which the remnant has expanded and the density of the interstellar medium can be used to calculate the mass of the remnant in kg. Remember that density is a measure of how much mass is in a given volume. 

15. With a value for both density and volume you can calculate the mass of your supernova remnant:

M = D x V
  • M is the mass of your supernova remnant
  • V is the volume through which your remnant as expanded (find this value on your worksheet)
  • D is average density of the interstellar medium: 1 x10-21 kg m-3

E. Calculate the expansion velocity of your supernova remnant

16. The next step is to calculate the velocity of the material in your supernova remnant. A typical supernova explosion will eject about 1044 Joules of energy into the surroundings. This is the value you will use for kinetic energy (K.E.). Use the following equation, where M is mass. Note the result on your worksheet.

V = (2 K.E. /M)1/2

 

F. Calculate the age of your supernova remnant

17. Calculate the age of your supernova using the distance to your supernova remnant and its expansion velocity. Note: this assumes that the exploding material has been travelling outwards at a constant speed, and that the mass has been constant. Note down the result on your worksheet.

Time = distance / velocity

  • time is the age of your remnant in seconds
  • distance here is actually the size of the remnant (i.e. the distance the shell has travelled since the explosion)
  • velocity is the expansion velocity (see your worksheet)

18. Convert time to years and write down your result below: 1 sec. = 3.1709791983765⋅10-8 year

Age of your supernova remnant _______________________ years

Congratulations, you just calculated the age of an ancient cosmic explosion!