Activity

Calculate the Age of Ancient Cosmic Explosions

In this project you will study LCO observations of supernova remnants to measure how fast they are expanding and 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.

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 

In this project you will choose a supernova remnant to study, with the final goal of using observational data to calculate its expansion velocity and age.

You can either use observations from the LCO data archive or make your own observations. If you plan to use data from the LCO archive, a selection of supernovae remnants has been provided below. Click on a supernova remnant to find an observation taken using a red (R-band) or H-alpha filter. Once you have clicked on an image the filter will be listed on the right-hand menu.  

Just go to the webpage and type in the name of the supernova remnant you want, click on the relevant thumbnail and select ‘FITS” from the right-hand options bar.  Be aware that the red filter may be listed as ‘Bessell-R’. 

If you are taking you own observations, please note that these objects are very faint and require long exposure times. The table below provides information on the exposure time needed for each object and which filters to use. 

A full guide to observing with LCOGT can be found online at: 

http://lcogt.net/files/OnSkyGuide.compressed.pdf  

 

Instructions 

1. Start ds9 and open the supernova remnant FITS file you have chosen to work with.

2. Your image may appear black to begin with, try out different options in the toolbars. You are looking for an image that shows as much detail as possible of the supernova remnant.

This image of Cas A is shown demonstrating the following DS9 settings: 

 You will now determine the radius of the remnant by placing a circle over the shell.  This will tell you the angular size of the remnant.

3. Go to Region > Shape > Circle

4. Draw a circle over the supernova, marking out the shape of the shell. Aim to be as exact as possible.

5. Go to Region > Get Information 

6. A box will appear showing the centre co-ordinates of the circle.

7. 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 degrees.  The example below shows the radius in degrees = 0.0301 degrees

8. Note down your radius value below and use this to work out your diameter in degrees.

Radius in degrees =

 

___________________________________________________

Diameter in degrees =

 

___________________________________________________

Now that you know the diameter of your supernova remnant, you will calculate the age of the supernova remnant and find out when the source star exploded. To do this you will need to calculate the distance to your supernova remnant in metres.

9. Calculate the distance to your supernova in metres and note your result in the table below. Remember that 1 light year = 9.5 × 1015 m.

Name

Distance (light years)    

 

Distance (metres)         

Cas A             

       10,200

                          

E102-72

              190,000

 

 

10. The next step is to work out the size of the shell. Do this using the equation below:

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

11. Begin by calculating θ for your supernova. This will be your radius from step 8, but you will need to convert your radius from degrees into a unit called radians (rad): 360 deg = 2π rad or 1 deg = 0.0174 rad. Note your result on the table below.

12. Next calculate the diameter of your supernova remnant using the equation above and use this value to calculate the radius: 0.5 x diameter. Note down your results in the table below.

Name                    

 degrees                  

Diameter (m)               Radius (m)                

Cas A

 

                               

                                   

                                  

E102-72     

 

     

 

13. Now that you have the physical radius, you can work out the volume of your supernova remnant, a figure that will allow you to work out its mass.  Where V is volume and the R is the radius in metres, use the equation:

V = (4/3) π R
 

14. Enter your result into the table below. 

In this table you will also find a value for density. Remember that density is a measure of how much mass is in a given volume. For example, the density of water is 1000 kg m-3, whereas the same volume of iron or lead will be much heavier.  Lead is 10 times denser than water. 

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! This is the density value we will be using in the calculations below.

 

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

Mass = density x volume

 

Enter your result into the table below.

Name

Volume (M3)

 

Density (kg-3)

Mass (kg)

Cas A

                                     

               1 x10-21 kg m-3

                                   

E102-72                      

 

                1 x10-21 kg m-3 

 

 

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.

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

 

Velocity =___________________________________

17. The final step is to calculate the age of your supernova. You can do this using the distance to your supernova remnant and its expansion velocity:

 

Time = distance / velocity

 

The distance here is actually the size of the remnant (i.e. the distance the shell has travelled since the explosion) and time is actually the age of the remnant. Your result will be in seconds, convert it to years and note down your result below.

Note: this assumes that the exploding material has been travelling outwards at a constant speed, and that the mass has been constant.

Age of your supernova remnant =________________________________ years

 

Congratulations, you just calculated the age of a real supernova remnant!