Growing
Faster than
the Speed of Light?
With Nino Panagia & Howard Bond
In January 2002 a dull star in an obscure
constellation suddenly became 600,000 times more luminous than our Sun,
temporarily making it the brightest star in our galaxy.
The star is called V838 Monocerotis (V 838 Mon) and is 20,000 light-years from Earth - about a fifth of the diameter of the Milky Way.
As well as getting a lot brighter, the star also illuminated surrounding shells of gas and dust. These are arranged around the star like a Russian doll, one inside another. Each shell has been thrown out into space at a different time over millions of years. They only become visible when the light from the brightening star reaches them.
As we knew how far away the star was, we were able to work out how far away the shells were from the star. But as we watched the object grow, we worked out that it appeared to be doing something impossible -
expa
Your challenge is to use mathematics to find out what was is really going on
First lets think about how the light got to us from V838 Mon.
Some of the light came straight towards us. Some of the light went away from us and was then reflected
back towards us by
the dust and gas behind the star. Some
of the light went at other angles and was reflected by the shells towards us.
Because the light took different routes to reach us, it arrived at different times. The light that came directly towards us
reached us first because it had taken the shortest route. This was followed by the light that had gone
in other directions.
The scale of V838 Mon is so huge that light that
went sideways reached us months after the direct light did.
Task
1: measuring the light routes:
If
we look at an image of V838 Mon 9 months after the star brightened, how much further will the light that has gone
sideways have traveled to get to us than the light that came directly and arrived 9 months before?
You’ll need to know that the speed of
light is
For help and the answer click
here.
What puzzled us was how how quickly the light echo increased in size.
Task 2 (Part a):
How
fast does V838 Mon appear to be expanding?
Use the images above and
our recommended
program 'ImageJ'
to measure the radius of the first light echo
(
Now, using the dates of the subsequent images
predict what the maximum size of each echo should have been. For example, if you find the first echo to have a radius of 3 light years, then the second echo, being 4 months later (May –
September), should have a radius no larger than 3⅓
light years.
Now measure the size of each subsequent
light echo and compare this to your predicted maximums. What do you find?
For help with this click
here.
To check your answers click
here.
We’ll begin by creating a model of what we think is happening as the light leaves V838 Mon. To make things easy we will make three simplifications.
1. There is just one layer of dust between the star and us and it is completely flat like a pane of glass. It its also perpendicular to the line directly between us and the V838 Mon
2. V838 Mon is a point source of light and only ‘erupted’ once
3. Hubble collected images regularly in equal time intervals
You’ll also need to use your knowledge of geometry & Pythagoras.
Let us talk you through visualising the geometry of the problem with this PowerPoint show
.
Geometrically the red lines must be bigger than
the blue lines because the blue lines are the shortest distance between each consecutive
circle and the red lines are not.
Mathematically, we can now find out how much
larger the red lines are than the blue lines by using Pythagoras’ Theorem.
(Click
here for a good
explanation of Pythagoras’ Theorem, or alternatively type “Pythagoras Theorem”
into Google to find your own explanations).
We’ll assume, for simplicity, that the images
were taken a month apart. This means
that the distance between consecutive circles is 1 “light-month”.
We’ll also assume that the base length, the time
it takes the direct light to reach the dust layer is 3 light-months.
To help illustrate things take a look at this PowerPoint Show.
Below are the images
from the Show
In images B – E the letter ‘x’ refers to the
unknown distance of the whole of the left hand side of the triangles and the letter
‘y’ refers to the unknown distance of each red line.
Click on them to enlarge and/or download.
A B C D E
In each image we’re finding the difference in
length between the red line and the blue line.
This means finding the length of the red line and then subtracting the
length of the blue line, which is always 1, from this.
For image A we can use simple Pythagoras.
For help with this click
here.
Images B – E are more complicated. To find the length of each red line,
labeled
y, find the height of the triangle, labeled x, and then subtract the height of
the previous triangle.
For
help with this click
here.
To check your answers click
here.
Will the apparent
expansion
of V838 Mon ever be
the same as the actual
expansion?
So, we’ve seen that V838
Mon did appear to expand
faster than the speed of light, we’ve also seen why this happened and we’ve even
created and analysed a mathematical model of the light echo phenomena.
WELL DONE!