Gravitational Deflection of Light from the Stars Orbiting the

[Thomas Smid]

In the last few years, it has become a well established fact that at
the center of our galaxy there is a supermassive object with a mass of
about 4 million solar masses. This is clearly proven by the orbits of
stars very close to the galactic center( see for instance
http://www.mpe.mpg.de/www-ir/GC/ ).

I just wonder how the deflection of light by the gravitational field
of Sagittarius A* affects the apparent position of these stars. The
point is that with a mass of 4*10^6 solar masses and a distance of
about 10 light days (which corresponds to a distance of 2.6*10^11 km
or 3.7*10^5 solar radii) the usual deflection formula would result in
a deflection 4*10^6/ 3.7*10^5 /2 = 5 times larger than the
gravitational deflection near the sun's limb, i.e. about
9" (arcseconds) (I added the additional factor 1/2 in the ratio
because of the fact that the light is produced within the
gravitational field and does not come from outside like for the solar
case). Since 10 light days at a distance of 26,000 light years
corresponds to an angle of 0.2" (see also
http://www.astrophysicsspectator.com/tables/MilkyWayCentralStars.html
), this means that, according to GR, we should see the stars actually
at a distance 45 times further from the galactic centre than they
appear to be.

Does anybody have an explanation for the absence of any gravitational
deflection of this magnitude here?

Thomas

[Ulf Torkelsson]

Thomas Smid skrev:

> In the last few years, it has become a well established fact that at
> the center of our galaxy there is a supermassive object with a mass of
> about 4 million solar masses. This is clearly proven by the orbits of
> stars very close to the galactic center( see for instance
> http://www.mpe.mpg.de/www-ir/GC/ ).
>
> I just wonder how the deflection of light by the gravitational field
> of Sagittarius A* affects the apparent position of these stars.

This is addressed briefly in a recent paper:

Gillessen, S., Eisenhauer, F., Trippe, S., Alexander, T., Genzel, R.,
Martins, F., Ott, T., 2009,
Monitoring Stellar Orbits Around the Massive Black Hole in the Galactic
Center
ApJ, 692, 1075

http://cdsads.u-strasbg.fr/abs/2009ApJ...692.1075G

The effect is only important when the stars are behind the black hole
and our line-of-sight passes close to the black hole.

Ulf Torkelsson

[Phillip Helbig---remove CLOTHES to reply]

In article <mt2.0-7533...@hercules.herts.ac.uk>, Thomas Smid
<thoma...@gmail.com> writes:

> we should see the stars actually
> at a distance 45 times further from the galactic centre than they
> appear to be.

Can you clarify the question? How should we SEE stars other than where
they APPEAR to be? (As someone once remarked, Wagner's music is better
than it sounds.)

Note two differences with respect to the deflection during a solar
eclipse: a) in the eclipse case the background stars are essentially at
infinity and b) we know the real positions since we can observe them
when the sun is far away.

[Thomas Smid]

On 10 June, 13:10, hel...@astro.multiCLOTHESvax.de (Phillip Helbig---
remove CLOTHES to reply) wrote:
> In article <mt2.0-7533-1244541...@hercules.herts.ac.uk>, Thomas Smid

>
> <thomas.s...@gmail.com> writes:
> > we should see the stars actually
> > at a distance 45 times further from the galactic centre than they
> > appear to be.
>

> Can you clarify the question? =A0How should we SEE stars other than where
> they APPEAR to be? =A0(As someone once remarked, Wagner's music is better
> than it sounds.)

It wasn't a question. I merely noted that according to my calculation
of the deflection, we should see the stars in a substantially
different position than they are. And I was looking for an explanation
of this (be it that may calculation was incorrect).

>
> Note two differences with respect to the deflection during a solar
> eclipse: a) in the eclipse case the background stars are essentially at
> infinity and b) we know the real positions since we can observe them
> when the sun is far away.

What has the distance of the star got to do with it? A light ray comes
from the star, goes through a perihelion close to the sun, and goes
symmetrically out again towards earth. It wouldn't make any difference
for the apparent position if the light ray would be for instance
emitted from the perihelion in the first place. The only difference
would be that the deflection would be a factor 1/2 smaller (as the in-
going deflection which occcurs for the infinity case is missing).

Thomas