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radone
2008-Jan-15, 12:28 AM
Can we tell the mass of an object based on gravitational lensing ie if some bright object A were behind this object B, can we infer the mass of B based on the amount of lensing that occurs to A's light?

DaveC426913
2008-Jan-15, 02:56 AM
In theory, yes.

I think there are difficulties with accuracy of estimates though.

StupendousMan
2008-Jan-15, 02:20 PM
Can we tell the mass of an object based on gravitational lensing ie if some bright object A were behind this object B, can we infer the mass of B based on the amount of lensing that occurs to A's light?

In theory, if you know

- the distance to object A
- the distance to object B
- the intrinsic shape of object A
- the mass of the object B
- (for more precision) the distribution of mass of object B

and if you have measurements of high enough quality, then you can figure out the mass of object B.

ngc3314
2008-Jan-15, 07:15 PM
In theory, if you know

- the distance to object A
- the distance to object B
- the intrinsic shape of object A
- the mass of the object B
- (for more precision) the distribution of mass of object B

and if you have measurements of high enough quality, then you can figure out the mass of object B.

Oops, gotta be a typo there. You need to know the two distances - that plus the ring radius for a symmetric lens tells you the mass enclosed within a (nearly cylindrical) piece of object B, which can be extrapolated to the total mass if you know the mass distribution law of B. For multiple-object lenses, you sample the enclosed mass within two regions (one for each image), and the same extrapolation issue applies. This is why folks have worked so hard to get stellar velocity dispersions for elliptical lens galaxies - that scales well with total dynamical mass for ellipticals as a group, so you could turn the problem around and ask what distances you need (that is, find H0 in a way independent of the traditional distance ladder). To do that properly (or as properly as the unknown 3D shape of the galaxy will allow), you need an additional scaling quantity, which you can get from the time delay of beams along each image path. For lensed and variable quasars, this has been measured in a few cases, with results for H0 that are usually lower than the favorite 72 or so but not wildly so when asymmetric error distributions are factored in. (I think StupendousMan was also including the weak-lensing case in which the shape of the lensed object matters more).

radone
2008-Jan-15, 07:20 PM
In theory, if you know

- the distance to object A
- the distance to object B
- the intrinsic shape of object A
- the mass of the object B
- (for more precision) the distribution of mass of object B

and if you have measurements of high enough quality, then you can figure out the mass of object B.

I'm confused. In your known variables, you included "the mass of object B". But, that's the unknown variable. Was that supposed to be "the mass of object A"? And do you make a rough calculation of the mass of object A based on its shape? Could you not also make a rough calculation of the mass of object B based on its shape, also?

Following from that, if you can learn the mass of object B based on those known variables, does dark matter throw the calculated mass of object B based on gravitational lensing out the window since it too should cause lensing of the light from object A?

ngc3314
2008-Jan-15, 09:01 PM
I'm confused. In your known variables, you included "the mass of object B". But, that's the unknown variable. Was that supposed to be "the mass of object A"? And do you make a rough calculation of the mass of object A based on its shape? Could you not also make a rough calculation of the mass of object B based on its shape, also?

Following from that, if you can learn the mass of object B based on those known variables, does dark matter throw the calculated mass of object B based on gravitational lensing out the window since it too should cause lensing of the light from object A?

(Typo in object B mass twice noted above...)

Dark matter, light matter, massive particles of magic pixie dust, everything - all contribute to gravitational lensing, which is what makes the technique so powerful for galaxies. The mass you get is the total.

radone
2008-Jan-15, 09:40 PM
(Typo in object B mass twice noted above...)

Dark matter, light matter, massive particles of magic pixie dust, everything - all contribute to gravitational lensing, which is what makes the technique so powerful for galaxies. The mass you get is the total.

Thanks for that. Just a few more questions. The mass you get is the total of what? Is it the mass of the obect causing the lensing or the mass needed to cause the amount of lensing seen?
If it is the mass needed to cause the amount of lensing that is seen, did we at one time sorta discount much of the interstellar 'debris' that's in the way because the mass of such debris is miniscule compared to the mass of a galaxy? But, with dark matter being 95% of the universe, does this not through off our previous mass calculations of that same galaxy?

ngc3314
2008-Jan-15, 11:00 PM
TThe mass you get is the total of what? Is it the mass of the obect causing the lensing or the mass needed to cause the amount of lensing seen?

If you're measuring the mass via lensing, those would have to be the same, modulo the fraction of mass enclosed by the lensing region. (It took me a while to grok the fact that spherical shells don't cancel in lensing like they do for Newtonian gravity in their interior; lensing angle works more like 1/r than 1/r^2 so a cylindrical approximation is the starting place for small angles). It is an important issue in assessing various solutions to the dark-matter question that lensing gives roughly the same masses as do the virial theorem, galaxy rotation curves, and X-ray profiles of galaxy clusters. This is a big deal because the physics involved is completely different. (The virial theorem and X-ray profiles for clusters of galaxies use the same physics, with electrons replacing galaxies as the test particles for the X-ray technique).