# Thread: Gravitational lenses and popular approximations

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## Gravitational lenses and popular approximations

http://www.extinctionshift.com/topic_05.htm

The author claims that the standard lens calculations are wrong.

Take an extreme case: the lens is next to the source (star), the situation of the galactic center, where the observed orbiting stars and estimated a central mass of about 4 million solar masses.

What should be the angle of deflection here: zero or 1/2 of the full deflection (in accordance with the formula GR)?

, this is the full deflection when the light goes from the source at a distance behind the lens d_s, to the observer at a distance from the lens: d_o, and both of these distances are large compared to the parameter b: d_s >> b, and d_o >> b;

After resetting one of these distances, we get half the deflection or zero?

The deflection for the Sun in the direction of 90 degrees, we have: d_o = 0, and: b = 1AU, the stars are far away: d_s >> b:

Apparently, measured 0.004'', or rather half, not zero.

Thus, reversing the situation: from a distant star should measure shift of the Earth's image by the same angle, because the path of light rays in both directions is exactly the same, right?

It is hard to imagine a zero deflection of the image source next to the Sun: d_s = 0 and b = R_s, because then the light would need to run in a straight line, which is impossible in the immediate vicinity of the Sun.
Sun itself should be greater for these 1.7'' (1/2 * 1.7'' around).

Thus, the author is probably right, and those orbits of stars near Sagittarius A* should actually be very deformed (according to GR), but they are not - why?

I think the standard approximations apply only to a particular case: a source is far behind the lens. Then they are applied to all possible cases, and so we have a zero deflection alleged to sources close to the lens, instead of half.

2. Given your previous ATM thread: http://www.bautforum.com/showthread....t-measurements , please be warned that this new thread you've started in the Q&A section needs to stay very much a Q&A thread. If you begin (continue) to push a view, you will be infracted for ATM outside of the ATM forum, directly back into suspension.

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## Einstein

Let me add one more interesting thing - Einstein ring:
http://en.wikipedia.org/wiki/Einstein_ring
220px-Einstein_Rings.jpg
Why these rings are always blue, unlike the central part?

4. Originally Posted by Hetman
Why these rings are always blue, unlike the central part?
I don't know why (or if) they are always blue. But why should there be any connection with "central part"? The light is from different objects.

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Originally Posted by Strange
I don't know why (or if) they are always blue. But why should there be any connection with "central part"? The light is from different objects.
Putting such an assumption, you will fall into his trap:
All distant galaxies must be blue, which is rather impossible and inconsistent with observations.

This leaves us with only one option: blue ring is a consequence of the presence of the lens.

6. Originally Posted by Hetman
... Why these rings are always blue, unlike the central part?
I'm not sure whether the colors we're seeing are natural... but the lensing galaxies we're seeing here are all old ellipticals, which tend to be not blue, for lack of star-forming regions... and the galaxies identified here are bright galaxies very actively doing star-forming, and probably showing Lyman-series UV red-shifted into the blue range... or perhaps they are closer than that, and are just blue because of the hot star-forming.

There may also be a bias that we wouldn't notice a blue arc around a blue galaxy.

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Originally Posted by Hetman
Let me add one more interesting thing - Einstein ring:
http://en.wikipedia.org/wiki/Einstein_ring
220px-Einstein_Rings.jpg
Why these rings are always blue, unlike the central part?
Not all of them are blue. Here is the lensing system RXS J1131-1231. Note the majority of the color is red, with a few blue areas. You can find the paper here. The reason the majority of them are blue is that even our most sensitive instruments cannot see normal galaxies beyond ~ z=1.2. The ones we do see are usually Seyfert or AGN type galaxies that emit in the ultraviolet. That emission is redshifted to the visible spectrum and appears as blue light. In the case of RXS J1131-1231, while the majority of the lensed galaxy is not blue, meaning it's not radiating in the ultraviolet, there are a few blue arcs that indicate very active star forming regions in the lensed galaxy, which are emitting in the ultraviolet.

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Originally Posted by Tensor
Not all of them are blue. Here is the lensing system RXS J1131-1231. Note the majority of the color is red, with a few blue areas. You can find the paper here. The reason the majority of them are blue is that even our most sensitive instruments cannot see normal galaxies beyond ~ z=1.2. The ones we do see are usually Seyfert or AGN type galaxies that emit in the ultraviolet. That emission is redshifted to the visible spectrum and appears as blue light. In the case of RXS J1131-1231, while the majority of the lensed galaxy is not blue, meaning it's not radiating in the ultraviolet, there are a few blue arcs that indicate very active star forming regions in the lensed galaxy, which are emitting in the ultraviolet.
It is a blue relative to the center.
http://hyperphysics.phy-astr.gsu.edu...o/einring.html

Or maybe it was the opposite, namely:
later developed the hypothesis of young blue stars (in distant galaxies),
on the basis of the observed blue rings and arcs in the presence of gravitational lenses?

In the center of the Milky Way also noted a large blue stars around Sagittarius, which was a big surprise.

Or, simply, a red light bends more - too much, and never reaches the observer, so we see blue.
Similarly, the Moon is sometimes red during an eclipse - here blue bends too little, and red just right.
Last edited by Hetman; 2012-May-07 at 11:19 PM.

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Originally Posted by Hetman
It is a blue relative to the center.
http://hyperphysics.phy-astr.gsu.edu...o/einring.html
That is not the system I presented. I presented RXS J1131-1231. The background galaxy in the first picture is known as B1938+666. The background galaxy in the second is knows asSDSSJ1430. If you are going to argue data I presented, I would appreciate that you, at the very least, argue against my data. Especially since you quoted my data and the links to my data.

Originally Posted by Hetman
Or maybe it was the opposite, namely:
later developed the hypothesis of young blue stars (in distant galaxies),
on the basis of the observed blue rings and arcs in the presence of gravitational lenses?
NO, the spectrum and the line within would be different. I gave you the mainstream answer. If you think differently, by all mean, provide us with the spectra of the various systems that provide support for your contention.

Originally Posted by Hetman
In the center of the Milky Way also noted a large blue stars around Sagittarius, which was a big surprise.
And the spectra are different.

10. Originally Posted by Hetman
It is a blue relative to the center.
http://hyperphysics.phy-astr.gsu.edu...o/einring.html

Or maybe it was the opposite, namely:
later developed the hypothesis of young blue stars (in distant galaxies),
on the basis of the observed blue rings and arcs in the presence of gravitational lenses?

In the center of the Milky Way also noted a large blue stars around Sagittarius, which was a big surprise.

Or, simply, a red light bends more - too much, and never reaches the observer, so we see blue.
Similarly, the Moon is sometimes red during an eclipse - here blue bends too little, and red just right.
My bold. That is an atmospheric absorption effect, unrelated to gravitational lensing.

11. Originally Posted by Hetman
Or, simply, a red light bends more - too much, and never reaches the observer, so we see blue.
Similarly, the Moon is sometimes red during an eclipse - here blue bends too little, and red just right.
Isn't the atmospheric effect to bend the blue more, leaving the (relatively) unbent red?

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Originally Posted by Tensor
That is not the system I presented. I presented RXS J1131-1231. The background galaxy in the first picture is known as B1938+666. The background galaxy in the second is knows asSDSSJ1430. If you are going to argue data I presented, I would appreciate that you, at the very least, argue against my data. Especially since you quoted my data and the links to my data.
I'm sorry, but I do not see this picture of Einstein ring - there is probably a few objects that clutter the image.

Besides there have not applied the appropriate color mapping that is necessary to analyze wavelengths from distant sources - shades of red is not enough.

Besides, I purposely omit quasars, because they are not subject to the laws of optics: a complete lack of arcs specific to the lenses.

lensed_quasar_2.jpg
http://dougintology.blogspot.com/200...l-lensing.html
Compare those cases: Einstein Cross with the other lenses.

NO, the spectrum and the line within would be different. I gave you the mainstream answer. If you think differently, by all mean, provide us with the spectra of the various systems that provide support for your contention.
No. The problem of the blue arcs has not yet been resolved, at all.

13. There are some strong observational factors in favor of detecting Einstein rings with red foreground galaxies and blue background ones. The galaxies with the greatest mass (both as determined for the stars alone, using luminosity and available population models, and for all matter, using velocity dispersions) are overwhelmingly elliptical galaxies, which are fairly red and look redder at greater redshift through the most common filter combinations. These are the galaxies for which the Einstein ring has the largest angular radius at a given redshift.

Trigonometry (well, its equivalent in the curved spacetime of an expanding Universe) means that more distant background objects give an Einstein-ring radius which is larger than closer background objects (it takes less deflection since there rays are not diverging as strongly). For high redshifts, the highest surface brightnesses in typical optical filters are usually star-forming galaxies which have flat spectra and are shown as blue. This isn't a requirement - if you look at galaxy clusters with lots of lensed arcs, especially in Hubble images which resolve the arcs well, you can find both red and blue ones.

Also, many of these lensed systems have been found by algorithms which take ground-based spectra and look for combinations of a low-redshift absorption spectrum and higher-redshift emission-line spectrum as an easy way to pick out likely lenses, a combination which works most effectively on this foreground-background color combination as well. (We've picked up interesting cases of backlit spirals by taking the "rejects" from that technique).

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Originally Posted by Hornblower
My bold. That is an atmospheric absorption effect, unrelated to gravitational lensing.
And what we have the gravitational deflection in the Galactic center?
This model is misinterpreted.

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Originally Posted by grapes
Isn't the atmospheric effect to bend the blue more, leaving the (relatively) unbent red?
Probably not. Without bending the moon would be black - the Earth is too big.

Or indeed the opposite is true: blue light bends stronger and bypasses the Moon.

16. I didn't mean that light would not be refracted at all, but the red not as much as the blue.

17. The refraction angle of sunlight into the umbra in a lunar eclipse is only about one degree, and I would estimate the dispersion as something on the order of an arcminute. Thus the red and blue light are still giving about the same coverage of the Moon's disk, but the blue is simply more weakened by greater absorption.

If I am not mistaken, there is no dispersion at all in gravitational refraction.

18. Originally Posted by Hetman
Thus, reversing the situation: from a distant star should measure shift of the Earth's image by the same angle, because the path of light rays in both directions is exactly the same, right?
No. The light would traverse the same path on both directions, and the local deflection angle would be the same, but the image deflection (angular image shift) would be very different because the two endpoints under consideration are at such different distances from the deflector. If you approximate the deflection as happening at a single point, the symmetry becomes that of a triangle - it is an isosceles triangle only in that case.

19. Originally Posted by Hetman
It is a blue relative to the center.
Or maybe it was the opposite, namely:
later developed the hypothesis of young blue stars (in distant galaxies),
on the basis of the observed blue rings and arcs in the presence of gravitational lenses?
Just as a matter of history, no. What we now know as lensed arcs were not initially identified as such, and settling on that as one of several explanations took years because their spectra really pushed observational technology in the mid-1980s. The blue colors of high-redshift galaxies were known statistically even before good spectroscopic redshifts were available, in the guise of what used to be called the faint blue galaxy excess. Later, with the advent of techniques to reliably identify candidate high-redshift galaxies for followup spectroscopy, such as Lyman break galaxies), the spectra made it unmistakeable that numerous high-redshift galaxies are rich in hot stars (although this emphatically by itself does not mean that all of them are; learning the mix of effective stellar ages requires complementary selection sensitive to cooler stars using infrared data).

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Originally Posted by Hetman
I'm sorry, but I do not see this picture of Einstein ring - there is probably a few objects that clutter the image.
Go back to post #7. I presented you with a image of a ring that was not blue. The image itself is all red. In the paper( the link is in the same post) the image has been cleaned up and you can see areas of blue, within the rings. I presented that system to refute your claim that all the lensed systems were blue.

Originally Posted by Hetman
Besides there have not applied the appropriate color mapping that is necessary to analyze wavelengths from distant sources - shades of red is not enough.
Which is why I presented the paper itself. I explains, in detail, exactly how they produced the image, how they applied the color mapping and how they analyzed the wavelengths. They analyzed the wavelengths to the point of being able to reconstruct the lensed galaxy. So, next time please read the presented paper, before stating what you think they didn't do.

Originally Posted by Hetman
Besides, I purposely omit quasars, because they are not subject to the laws of optics: a complete lack of arcs specific to the lenses.
Well, then, you have a problem dismissing this one. This is a Type 1 Seyfert spiral. Besides, your claim that quasars are not subject to the laws of optics, is not supported by mainstream optics.

Originally Posted by Hetman
No. The problem of the blue arcs has not yet been resolved, at all.
Yes it has. This paper provides the rest-frame ultra-violet spectra, at different wavelengths, along with the UV-blue Optical spectra of the "8 o'clock arc" lensed system. Besides this lensed system, the text mentions three other lensed Lyman Break Galaxies. If you don't think it has been resolved, please point out where in this paper they have made errors.

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Originally Posted by ngc3314
No. The light would traverse the same path on both directions, and the local deflection angle would be the same, but the image deflection (angular image shift) would be very different because the two endpoints under consideration are at such different distances from the deflector. If you approximate the deflection as happening at a single point, the symmetry becomes that of a triangle - it is an isosceles triangle only in that case.
This is the error of approximation.

for d_LS = 0 you get zero deflection, instead of the half: 2GM/c^2b > 0

And what if: d_LS < 0?
Impossible?
This is the case when the observer and the source are on the same side of the lens.

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Originally Posted by Tensor
Go back to post #7. I presented you with a image of a ring that was not blue. The image itself is all red. In the paper( the link is in the same post) the image has been cleaned up and you can see areas of blue, within the rings. I presented that system to refute your claim that all the lensed systems were blue.

Which is why I presented the paper itself. I explains, in detail, exactly how they produced the image, how they applied the color mapping and how they analyzed the wavelengths. They analyzed the wavelengths to the point of being able to reconstruct the lensed galaxy. So, next time please read the presented paper, before stating what you think they didn't do.

Well, then, you have a problem dismissing this one. This is a Type 1 Seyfert spiral. Besides, your claim that quasars are not subject to the laws of optics, is not supported by mainstream optics.

Yes it has. This paper provides the rest-frame ultra-violet spectra, at different wavelengths, along with the UV-blue Optical spectra of the "8 o'clock arc" lensed system. Besides this lensed system, the text mentions three other lensed Lyman Break Galaxies. If you don't think it has been resolved, please point out where in this paper they have made errors.

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Originally Posted by Hornblower
The refraction angle of sunlight into the umbra in a lunar eclipse is only about one degree, and I would estimate the dispersion as something on the order of an arcminute. Thus the red and blue light are still giving about the same coverage of the Moon's disk, but the blue is simply more weakened by greater absorption.

If I am not mistaken, there is no dispersion at all in gravitational refraction.
The diameter of the Moon is probably only 0.5 degree.

24. Originally Posted by Hetman
Please do not pretend you are a moderator and tell other people what they may and may not post. I am also starting to doubt that this is a simple Q&A thread, and starting to think it might be ATM.
Given your recent infraction record, you have used up your friendly reminders and will get an infraction for your attempt at moderation.

25. Originally Posted by Hornblower
The refraction angle of sunlight into the umbra in a lunar eclipse is only about one degree, and I would estimate the dispersion as something on the order of an arcminute. Thus the red and blue light are still giving about the same coverage of the Moon's disk, but the blue is simply more weakened by greater absorption.
And it's full-spectrum white light, not a handful of discrete bands. You'd see it smeared out in a rainbow streak if dispersion was significant.

Even if sunlight was a handful of narrow bands and dispersion was strong enough to spread them out like that, you wouldn't see a reddened moon, you'd see multiple (possibly overlapping) instances of moon images, each with completely saturated colors. Same goes for gravity lensing.

26. To illustrate, this is what wavelength-dependent refraction looks like: http://theketelsens.blogspot.com/201...ing-light.html

The images of gravitational lensing clearly aren't showing this effect. Neither do images of stars being gravitationally deflected by the sun, for that matter. It certainly doesn't explain anything about the appearance of the moon.

A simple explanation's already been given for the rings tending to be blue. Lensing is likely to be seen when a bright galaxy is behind a dim but massive one. A dim and massive galaxy is probably one without much new star formation, consisting of small red stars, and a bright galaxy with lots of new star formation will have a lot of young, hot giant stars...so a bias is quite expected.

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I checked the equation of the curve for the ray of light, and it resolved the problem.

The deflection of light from a source close to the lens is obviously 2GM / c ^ 2 b, but the image magnification remains virtually nil.

http://www.extinctionshift.com/topic_07.htm
These proposals are entirely wrong.
I don't understand why the author spent a lot of days to create the drawings and descriptions, and not bothered to calculate the path of light to see these angles accurately and unambiguously.

Originally Posted by cjameshuff
To illustrate, this is what wavelength-dependent refraction looks like: http://theketelsens.blogspot.com/201...ing-light.html

The images of gravitational lensing clearly aren't showing this effect. Neither do images of stars being gravitationally deflected by the sun, for that matter. It certainly doesn't explain anything about the appearance of the moon.

A simple explanation's already been given for the rings tending to be blue. Lensing is likely to be seen when a bright galaxy is behind a dim but massive one. A dim and massive galaxy is probably one without much new star formation, consisting of small red stars, and a bright galaxy with lots of new star formation will have a lot of young, hot giant stars...so a bias is quite expected.
Thank you for the idea to solve the problem of blue and bright rings, but I'm not able to accept such an interpretation.
Ideas of blue galaxies whose brightness increases with distance, seem to me to be extremely unrealistic, to put it mildly.
http://www.universetoday.com/93285/h...ed-galaxy-arc/
http://arstechnica.com/science/2012/...rliest-galaxy/

28. Originally Posted by Hetman
Ideas of blue galaxies whose brightness increases with distance, seem to me to be extremely unrealistic, to put it mildly.
You are the only person to mention anything of the sort. We are simply more likely to see lensing with a bright galaxy containing young stars behind a dim but massive galaxy containing old stars. Dim foreground galaxies with young stars are going to be low mass, bright foreground galaxies with lots of star formation going on will tend to obscure their lensed backgrounds.

29. Would the massive gravity of the lens attracting the relatively close (to it) lensed galaxy, cause the lensed to accelerate towards the lens and thus to us?
I assume the math would show not, but thought it worthwhile to be clarified.

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Originally Posted by cjameshuff
You are the only person to mention anything of the sort. We are simply more likely to see lensing with a bright galaxy containing young stars behind a dim but massive galaxy containing old stars. Dim foreground galaxies with young stars are going to be low mass, bright foreground galaxies with lots of star formation going on will tend to obscure their lensed backgrounds.
I do not think it was crucial.

Ring is always on the outside - all around, so we should also observe the reverse colors: red ring around the blue galaxies.
And in fact this should be the rule, because of the redshift.

Blue rings must be related to the lensing phenomenon, or even directly to the mechanism of gravity.

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