BOX 24.6 Write a one paragraph summary explaining the evidence for Dark Matter.
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Question
BOX 24.6
Write a one paragraph summary explaining the evidence for Dark Matter.
Many thanks in advance.
X24.6 The Evidence for Dark Mater vivid evidence for dark matter comes from galaxy rotation curves. Since ists have been able to measure the Doppler shifts of both stel- t and the 21-cm radio emissions irom hydrogen gas with enough accuracy 150 70, a lig me measure data,1 lar the rotational speed of spiral galaxies. Figure 24.13 shows data from 100 halo f of the spiral galaxy NGC 2403. We also can also calculate what we his rotational speed should be using Newtonian physics (since the here, this should be fine). If the galaxy were spherically symmetric disk fit from Gauss's law that the mass M(G) within a given radius r attracts re located at the center and the mass outside has no effect. Therefore, the for a star of mass m in a circular orbit at a given radius r is given by Gauss's would know orbital speed 15 radius (kpc) (24.8) FIG, 24.13 This diagram shows that a large halo of dark matter is Now, a spiral galaxy is not spherically symmetric, so the actual prediction will required to match the rotation curve he somewhat more complicated, but it can easily be done numerically in a way of the spiral galaxy NGC 2403 that actually fits the distribution of stars in the galaxy disk. The "disk fit curve in Credit: Chris Mihos (adapted) feure 24.13 represents such a prediction. You can see that for radii beyond about Skoc (16 kly), the velocity curve begins to fall off as something like r 12, because virtually all of the galaxy's visible mass is within this radius. Of course, there rm be mass in the galaxy in the form of dust, gas, dim stars, giant planets, etc, that can't see, but if it is distributed in the same way as the stars are, the curve's shape will not change, only its amplitude. (The "disk fit" curve shown actually assumes that there is twice as much matter in the spiral disk as can be seen.) However, you can see that this nowhere near fits the actual data for NGC 2403. The stars in the disk of this galaxy orbit much more rapidly than expected. More- over, no adjustment of the "disk fit" curve amplitude will make it fit, because the velocity data are actually flat for large radii, not decreasing as r The only way to fit these data is to assume that in addition to the visible matter in the disk (and any unseen matter distributed in the same way) the galaxy is surrounded by a huge halo of dark matter. It is hard to estimate the total amount of matter in the halo (because the amount continues to increase beyond radii for which we can see any thing), but the total galactic mass implied by these data is at least 10 times as much as that in the form of stars. (See problem P24.7 for more discussion of these data.) The statistical analysis of velocities of galaxies in clusters can also be used to estimate a cluster's total gravitational mass. Specifically, the virial theorem of Girl /r), where?v) is the averaged squared speed of galaxies in the cluster, M is the cluster's total mass, and l/r is the average inverse galactic separation. Since v2 and a r? can be estimated compute the cluster's mass M. The result is typically mechanics (see problem P24.8) implies that from observations, we can y 50 to 80 times the mass one would estimate from the stars in the galaxies. Other evidence comes from gravitational lensing: the degree of lensing ob served in photographs such as figure 13.5 implies masses for the foreground galaxy much larger than associated with the visible stars. The evidence that puts the constraints on the total dark-matter density at present comes from examin e tiny fluctuations in the cosmic microwave background. We will discuss this tightest ing th in more detail in a later chapter on the early universe (chapter 28) relativ Collectively, these observations imply that the total density of cold (non- stic) dark matter comprises about 27% of the total energy density of the nerse. However, considerations regarding nucleosynthesis in the early universeExplanation / Answer
Key points for evidence of dark matter:
1) Galaxy cluster and Galactic roatation curves: The rotation velocity of a galaxy can be measured from Doppler shifts of its spectral lines. With the distance of the galaxy known, we can use Keppler or Newton laws to compute the mass of the galaxy in fact we can map the mass as a function of the distance from the center of the galaxy. Then using the virial theorem the gravitational mass we get is not equal to the mass due to luminous matter.
2)The Cosmic Microwave Background: It is the earliest photo of our universe. The existence of dark matter leaves characteristic imprint on the CMB. The Wilkinson Microwave Anisotropy Probe was the first instrument to measure CMB power spectrum hence giving us the evidence of dark matter.
3)Gravitational lensing:As the light leaves its source, the huge gravity of the cluster bends that light, creating multiple images which is called strong gravitational lensing.By using the details of the image distortion, we can get a rough map of the distribution of dark matter in the galaxy cluster.
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