Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: David Cooper on 26/09/2018 01:43:08
-
I've heard various things about dark matter surrounding galaxies and its role in helping the outer material in a galaxy orbit the centre at a higher speed than is predicted for that material from the amount of visible mass in the galaxy alone.
What I don't understand about this is how an outer ring or halo of dark matter further out could speed up the rotation for the material in question rather than slowing it down. If you put more material round the outside (dark matter), that will reduce the inward force felt by the outer visible material, this force acting to try to pull it towards the centre of the galaxy, and this, according to the simulation I'm running in my head, should require it to orbit more slowly in order to maintain its distance from the centre. If you want it to orbit more quickly, I'd have thought you'd need to put the dark matter ring further in than the material that you want to orbit more quickly; not further out.
Where am I getting this wrong?
-
First off, the "halo" is not a ring. It is a spherical volume in which the galaxy is embedded. A ring shape is not what the word "halo" means in astronomy.
Also, within such a spherical volume, at any given point The only gravitational effect would be caused by that material closer to the center than that point (Newton's shell theorem).
The visible matter of the galaxy is mainly confined to the bulge and disk. Once you get away from the bulge and into the disk region, moving further out does not add much to the contribution that the visible matter contributes to to your orbital speed. The dark matter, however extends well above and below the visible matter disk and the thus the amount of DM closer to the center of the galaxy grows quite fast.
For example, the density of DM in the vicinity of the Solar system is so low that it would only adds up to the equivalent of a small asteroid within the entire volume of the Solar system. At that same density, the spherical volume of the region closer to the center of the galaxy than the solar system would hold a significant fraction of the entire visible galaxy's mass.
Thus extra mass, plus the mass of the visible matter closer to the center of the galaxy is what determines the orbital speed of the solar system ( and makes it higher than it would be is there just was the visible mass.)
-
Thanks for correcting my picture of it.
First off, the "halo" is not a ring. It is a spherical volume in which the galaxy is embedded. A ring shape is not what the word "halo" means in astronomy.
That fits with what I originally heard, but later mentions of it in documentaries led me to think it was more like a ring of this stuff further out, though perhaps this was just because of the use of the word "halo".
Also, within such a spherical volume, at any given point The only gravitational effect would be caused by that material closer to the center than that point (Newton's shell theorem).
So the net effect is always extra pull to the centre, but as you go closer to the centre, that extra pull can decline rather than going up (in the same way that the measured gravitational pull would go down as you approach the centre of a planet), with the result that material further out can stay in a circular orbit at a higher speed than expected. There's no 2D equivalent of Newton's shell theorem, and I presume that there's no way of generating the same end result from merely distributing dark matter carefully near the disc of the galaxy, but I'm now wondering now if anyone has any figures on how close to spherical this halo of dark matter needs to be. How much room might there be for it being squashed in towards the disc rather than being perfectly spherical? I'm trying to find out whether its distribution is affected by the distribution of visible matter at all to see if it might in some way be dependent on it or independent of it.
For example, the density of DM in the vicinity of the Solar system is so low that it would only adds up to the equivalent of a small asteroid within the entire volume of the Solar system. At that same density, the spherical volume of the region closer to the center of the galaxy than the solar system would hold a significant fraction of the entire visible galaxy's mass.
That improves my picture of it considerably, and it also relates to another thing I've been wondering. How much does the density of dark matter need to vary at different distances from the centre of the galaxy? The mention of Newton's shell theorem indicates that whatever it does, the density changes the same or a similar amount as you go out perpendicular to the disc as it does if you go out through the plane of the disc (from the centre), but I'd like to get some understanding of whether it's many times denser near the centre than it is where we are, or is the change over distance much more subtle? Is there a change in density of dark matter related to anything like the inverse square law as you go away from the centre?
-
Thanks for correcting my picture of it.
First off, the "halo" is not a ring. It is a spherical volume in which the galaxy is embedded. A ring shape is not what the word "halo" means in astronomy.
That fits with what I originally heard, but later mentions of it in documentaries led me to think it was more like a ring of this stuff further out, though perhaps this was just because of the use of the word "halo".
Also, within such a spherical volume, at any given point The only gravitational effect would be caused by that material closer to the center than that point (Newton's shell theorem).
So the net effect is always extra pull to the centre, but as you go closer to the centre, that extra pull can decline rather than going up (in the same way that the measured gravitational pull would go down as you approach the centre of a planet), with the result that material further out can stay in a circular orbit at a higher speed than expected. There's no 2D equivalent of Newton's shell theorem, and I presume that there's no way of generating the same end result from merely distributing dark matter carefully near the disc of the galaxy, but I'm now wondering now if anyone has any figures on how close to spherical this halo of dark matter needs to be. How much room might there be for it being squashed in towards the disc rather than being perfectly spherical? I'm trying to find out whether its distribution is affected by the distribution of visible matter at all to see if it might in some way be dependent on it or independent of it.
For example, the density of DM in the vicinity of the Solar system is so low that it would only adds up to the equivalent of a small asteroid within the entire volume of the Solar system. At that same density, the spherical volume of the region closer to the center of the galaxy than the solar system would hold a significant fraction of the entire visible galaxy's mass.
That improves my picture of it considerably, and it also relates to another thing I've been wondering. How much does the density of dark matter need to vary at different distances from the centre of the galaxy? The mention of Newton's shell theorem indicates that whatever it does, the density changes the same or a similar amount as you go out perpendicular to the disc as it does if you go out through the plane of the disc (from the centre), but I'd like to get some understanding of whether it's many times denser near the centre than it is where we are, or is the change over distance much more subtle? Is there a change in density of dark matter related to anything like the inverse square law as you go away from the centre?
One estimate would put the DM density at just 1%-2% higher than the density in the region of the Solar system, so it is a not a steep increase. But a lot of factors for which we don't have a complete picture of goes into that estimate. How far does the halo extend?. Is it spherical or more squashed to an oblate spheroid?, What exactly is the rotation curve for our galaxy? (Ironically, it is easier to measure the rotation curves of other galaxies rather than our own)
As far as the use of the word "halo" goes. The ring shape you sometimes see representing the halo of a religious figure is more or less a stylized version.
For example is many works of religious art, you get something like this for halos
(https://steemitimages.com/0x0/https://upload.wikimedia.org/wikipedia/commons/7/7d/Simon_ushakov_last_supper_1685.jpg)
Here the halos are more full circles, which to me suggests that the artist was trying to depict an overall glow or aura surrounding the head rather than a disk or ring structure.
Sometimes such a glow can be associated with a visible ring like this.
(https://edc2.healthtap.com/ht-staging/user_answer/reference_image/14726/large/Halos_around_lights.jpeg?1386670234)
Which is an optical effect caused by the medium between the viewer and light source and not actually a physical structure.
This has morphed over time to the stylized halo most people are familiar with like seen here.
(https://www.shareicon.net/data/512x512/2016/05/13/764358_angel_512x512.png)
The astronomical use of halo is much closer to the original usage than the torus shape most lay people associate the word with.
-
One estimate would put the DM density at just 1%-2% higher than the density in the region of the Solar system, so it is a not a steep increase.
Do you mean 1 to 2% higher at the centre of the galaxy? If the density goes down that slowly, that suggests it goes out a very long way, but the further out expanse of it would have a more uniform effect on things, leading to no net pull from it and making it hard to detect. Even if you can record the speeds of dwarf galaxies nearby, in the same plane or far above or below it, you probably can't know what their orbits are without watching them for thousands of years, so I doubt there's adequate data.
What exactly is the rotation curve for our galaxy? (Ironically, it is easier to measure the rotation curves of other galaxies rather than our own)
I didn't think I could be reading rotation curve graphs correctly before, but it's now clear that the outer material in galaxies really can be moving at a higher orbital speed than material further in (still taking longer to go round though, which helps to hide the effect in animations: http://ircamera.as.arizona.edu/NatSci102/NatSci/lectures/darkmatter.htm (http://ircamera.as.arizona.edu/NatSci102/NatSci/lectures/darkmatter.htm)). I see what is meant now by the curves being flat - no reduction in orbital speed as you look further out.
I've been thinking for a while about writing a program to attempt to simulate this and to try out different ways of getting the same end result, so your help here is very much appreciated. I now have a much better idea of what I need to do and how to go about it. I want to write a program that enables the user to edit the amount of matter (visible and dark) in different locations and to see the resulting orbital speeds for visible matter at different distances from the centre. The simplest way to do this might be to have an array of 26x26 data cells (with names from aa to zz, aa being the centre of the galaxy, az being the outer edge of the visible disc, and za being a point above the centre of the galaxy as far away from it as the outer edge of the visible disc). The user will then type mass values into each of these cells. The program will then produce from that data for the mass in different places all round the galaxy, and duplicate below whatever's above the disc. 26 speeds will then be produced from that data by calculating the gravitational pull towards the centre on each point along the radius of the disc. This will let anyone who wants to to try experimenting with different dark matter distributions, and maybe some new alternatives will emerge from that which generate the right kinds of rotation curve, for example, by doing such things as putting more dark matter up and down the axis.
If anyone wants to help design the program feel free to make suggestions. At the moment, I'm thinking it might be easiest to construct a grid for the gravity data of 51x51x51 cells, then use the 26x26 cell data to calculate the mass content of the 132651 cells. 25 lots of calculations would then need to be done to calculate the orbital speeds, each lot involving 132651 acceleration forces being calculated and then averaged.
The astronomical use of halo is much closer to the original usage than the torus shape most lay people associate the word with.
Maybe they should have gone for "orb".