Light echo and geometry of Ellipsoid!!!

( The expansion of light echo of V838 Monocerotis Red variable star as seen by Hubble Space Telescope as taken between May 2002- Feb 2004)

Introduction-

Echo -( In acoustics ) echo is the reflection of sound waves when incident sound wave is reflected by an object. In echo, this reflected waves reach the observer sometime after main sound is heard.

Light echo- A phenomena in Astronomy when reflected light reaches observer so

metime after main light ray reaches.

Ellipsoid- A quadratic surface having Cartesian co-ordinates are

Light echo-

During a sudden burst of light or flash of light as seen during novae and supernova explosions, some part of light rays are reflected due to the interstellar dust which are found in many galaxies. For an observer situated at a distance from the source, initial direct light rays will reach first and then the reflected rays will reach giving it an echo form.

Interestingly, expansion of these light echos might appear to be at Super luminal speed ( Faster than speed of light).

Unlike sound echo which is a short lived phenomena, light echo can last for many yea

rs and is easily seen through images.

Interestingly, the image of V838 Monocerotis red variable star which is 20,000 ly from the sun shows a Light echo. In 2002,Jan 6 a sudden outburst happened in the Monocerotis constellation.

Astronomers observing the light curve of this explosion discovered light curve was similar to nova. v838 after reaching maximum Visual magnitude in February started dimming. But in March, v838 regained the luminosity and was brightening more and more reaching million times Solar luminosity ( Luminosity of sun). It was discovered that this brightening was due to the expanding layers. The expansion continued with increased speed.

After some period, the color of this outer layer turned red as Expanding gases cool down after some period.

Conclusion- It was concluded that the later light intensity was due to the light echo produced by the first explosion which was a nova. Light echo expanded 4-7 light years in just few month.

This means rate of expansion was faster than speed of light.

REASON FOR LIGHT ECHO AND THE SUPER LUMINAL VELOCITY DURING ITS EXPANSION.

When there is sudden burst of light, some light rays get reflected many times due to

In this image at right, a star shape at center can be considered as a Nova or Supernova explosion. The tiny blue sphere at bottom is the earth. The hazy material around Nova is Intergalactic dust which causes reflection of light rays.the interstellar dust present. ( I found an image on internet during studying light echo concept which I want to share)

The part of ray of light is without any reflection in case of A path. For B and C path, light rays are reflected

somewhere in the dust. For path A, observer at earth will receive the light first and directly. Light rays from B will reach next and then from C.

For anyone on the earth, all three location points ( A,B,C) appear in the sky to be at the same place.

So for observer light rays from B and C will appear to come from same location but the distance of B point is less from earth than C. So the expansion ( relative) of the Light echo will appear to be Super Luminal AS THE SPEED OF LIGHT IS CONSTANT AND SAME EVERYWHERE. SO DISTANCE TRAVELLED BY LIGHT RAYS IN A,B,C SCENARIO IS SAME.

Relation with Ellipsoid

On surface of an ellipsoid, consider any two focal points. Like in this figure, consider earth at the end of the blue line and the nova at the end of red line. The boundary of ellipse is the region of intergalactic dust. In this case, total length of blue and red line is around 10 units.If we move these pair of lines at any position on the ellipsoid, the total length of lines remain constant.

Considering the earth and the nova on this ellipsoid

light rays from the nova will have to travel same distance to reach the earth regardless their path. So after considering an ellipsoid it is clear why expanding light echo appears to be faster than speed of light.