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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).

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.