A galaxy's rotation curve is a measure of the orbital speed of stars as a function of distance from the galaxy's centre. The fact that rotation curves are primarily flat at large galactocen- tric distances (vrot(r) ~ constant) is the most common example of why astronomer's believe dark matter exists. Let's work out why! Assuming that each star in a given galaxy has a circular orbit, we know that the accelera- tion due to gravity felt by each star is due to the mass enclosed within its orbital radius r and equal to v/r. Here, ve is the circular orbit velocity of the star. (a) Show that the expected relationship between ve and r due to the stellar halo (p(r) x r-3.5) does not produce a flat rotation curve. (b) Show that a p(r) x r-² density profile successfully produces a flat ro- tation curve and must therefore be the general profile that dark matter follows in our galaxy.

A galaxy's rotation curve is a measure of the orbital speed of stars as a function of distance from the galaxy's centre. The fact that rotation curves are primarily flat at large galactocen- tric distances (vrot(r) ~ constant) is the most common example of why astronomer's believe dark matter exists. Let's work out why! Assuming that each star in a given galaxy has a circular orbit, we know that the accelera- tion due to gravity felt by each star is due to the mass enclosed within its orbital radius r and equal to v/r. Here, ve is the circular orbit velocity of the star. (a) Show that the expected relationship between ve and r due to the stellar halo (p(r) x r-3.5) does not produce a flat rotation curve. (b) Show that a p(r) x r-² density profile successfully produces a flat ro- tation curve and must therefore be the general profile that dark matter follows in our galaxy.

Similar questions

Globular clusters revolve around the Galaxy in highly elliptical orbits. Where would you expect the clusters to spend most of their time? (Think of Kepler’s laws.) At any given time, would you expect most globular clusters to be moving at high or low speeds with respect to the center of the Galaxy? Why? (If you would like to learn more about globular clusters, read Section 22.2 of the book, though it is not necessary to answer this question)
For a circular velocity profile of the type (r) = ar¹ ar1/9, where a is a constant and r is the radial distance from the centre of a spiral galaxy, find the ratio (r)/(r), where (r) is the epicyclic frequency and 2(r) is the angular velocity. Enter your answer to 2 decimal places.
Which of the following statements best describes our galaxy, the Milky Way? O A bulge dominated system, with little or no disk, approximately 27,000 light years across. A disk 100,000 lightyears across filled with gas and stars, with a bulge of older stars in the galaxy centre. A disk 27,000 light years across with a bulge of gas and newly formed stars in the galaxy centre. O A spherical (elliptical) galaxy, 100,000 lightyears across, with no gas and no new stars.
In the reading, you were told that there were roughly 10,000 galaxies in the image of the Hubble Ultra Deep Field alone. The image is roughly 10 square arcminutes and there are roughly 1.5*10^8 square arcminutes composing the entire sky. With that in mind and assuming that the Hubble Ultra Deep Field represents an average part of the sky, roughly how many galaxies may exist in the observable universe? (Please include commas for every factor of 1,000; for example 2,343,567,890)
The Milky Way grew through merging with many smaller galaxies. What are the observational signatures of this process? O The motion of old stars in the bulge and halo of our galaxy are randomly orientated, meaning they were formed from collisions of small, accreted, galaxies all on different paths. O The ordered motion of the bulge / halo stars means that they came from many objects. The random motions of stars in the disk means it was formed from collisions of small, accreted, galaxies. O The motion of young stars in the disk are all in the same direction, meaning they came in as seperate objects.
For the graph shown above, a) what quantity would you label the y-axis with if the distance is between galaxies and the Earth? Explain your answer. Think through what we know is happening, motion-wise, out there in the galaxy. b) Also explain why you think there are dots and a solid line, on the graph.
An observational survey of distant galaxies is undertaken that involves measuring their distances using cepheid variables and red-shifts using spectroscopy. Explain how cepheid variables can be used to measure the distances to galaxies. A spectral line is observed whose wavelength in the laboratory is de length of this spectral line observed in each galaxy, Xo, is listed in the table, along with the distance, d, to the galaxy. Determine the red-shift and the recession velocity of each galaxy and tabulate your results by making a copy of the table and filling in the blank spaces. Sketch a Hubble diagram using your results and determine the value of the Hubble constant Ho in units of km s-1 Mpc. 650 nm. The wave- Galaxy 1 652.69 Galaxy 2 Galaxy 3 Galaxy 4 Galaxy 5 653.01 do (nm) d (Mpc) 658.54 662.18 681.63 17 19 54 77 200 v (km s-1)
Please solve page 3 and 4 using the table below NGC NO. Galactic Longitude (deg) Galactic Latitude (deg) Distance from Sun (kpc) Distance (polar view) (kpc) NGC NO. Galactic Longitude (deg) Galactic Latitude (deg) Distance from Sun (kpc) Distance (polar view) (kpc) 1904 227 -30 13 1 1 6402 21 15 9 9 4590 300 36 10 8 6626 8 -6 6 6 5024 333 80 18 3 6637 2 -10 9 9 5272 42 79 10 2 6656 10 -8 3 3 5904 4 47 7 5 6681 3 -12 9 39 6093 353 20 10 9 6356 7 10 15 15 6121 351 16 2 2 6284 358 10 15 15 6171 3 23 6 5 6838 57 -5 4 4 6205 59 41 8 6 6864 20 -26 21 19 6218 16 26 5 5 6981 35 -33 17 14 6254 15 23 4 4 7078 65 -27 10 9 6266 354 7 7 7 7089 53 -36 12 10 6273 357 9 9 9 7099 27 -47 8 5…
Figure 2 shows the "rotation curve" of NGC 2742. It plots the “radial velocity (V)" (how fast material is moving either toward or away from us) that is measured for objects at different distances (R = radius") from the center of the galaxy. The center of the galaxy is at 0 kpc (kiloparsecs) with a speed of 9 km/sec away from us. (These velocities have been corrected for the observed tilt of the galaxy and represent true orbital velocities of the stars and gas.) 200 100 U4779 -100 As you can see, one side of the galaxy is moving with a negative velocity (spinning toward us), while the other side has a positive velocity (spinning away from us). Using Newton's gravity equation, we will be able to determine the gravitational mass of the entire galaxy and how the mass varies versus distance from the galaxy's center. -200 -8 8 -4 Radius (kpc) Read the following text carefully and follow the instructions: Select five radii spaced evenly from 0-10 kpc across the galaxy. Your selections should…