Rotation curve

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The rotation curve of a galaxy describes the relationship between the orbital speed of its stars and their distance from the center of the galaxy. ${\displaystyle v(r)}$

Actual rotation curve of the spiral galaxy Messier 33 (yellow and blue dots with error bars) and one predicted based on the distribution of visible matter (gray line). The deviation between the two curves can be explained by a halo of dark matter surrounding the galaxy .

Observations

By observing the Doppler shift of spectral lines in the star spectra , it was found that galaxies rotate neither like a rigid body ( straight line through the origin as a rotation curve) nor like a Kepler system (rapid decrease in the rotation curve towards the outside), as it does in a gravitationally bound system would be expected. The American scientist Vera Rubin made the first research in the 1970s.

In reality, the rotation curves of many galaxies, including those of the Milky Way , show the following course: after a sharp rise in the inner areas, which corresponds to the rotation of a rigid body, they are approximately constant in the middle and outer areas of the galaxy ( flat rotation curve) or increase slightly.

The differential rotation of the Milky Way is described by Oort's rotation formulas .

Explanatory hypotheses

Play media file

Left: A simulated galaxy with a rotation curve that would be expected without dark matter.
Right: Galaxy with a flat rotation curve similar to the rotation curve of real observed galaxies

As an explanation, it can be assumed that there is far more matter in galaxies than can be seen. This led to the dark matter hypothesis .

Another explanatory hypothesis is to change the Newtonian laws , as it is assumed in the modified Newtonian dynamics .

Track speed

The gravitational force acts on an object of mass revolving around the center of a galaxy at a distance with the orbital speed ${\displaystyle r}$ ${\displaystyle v(r)}$ ${\displaystyle M}$

${\displaystyle F_{G}=G\cdot m(r)\cdot M\cdot {\frac {1}{r^{2}}}}$

as centripetal force

${\displaystyle F_{Z}=M\cdot v^{2}(r)\cdot {\frac {1}{r}}}$ ,

where is the mass enclosed in the sphere with radius around the center of the galaxy and is the gravitational constant . This results in the path speed in general ${\displaystyle m(r)}$ ${\displaystyle r}$ ${\displaystyle G}$

${\displaystyle v^{2}(r)=G\cdot m(r)\cdot {\frac {1}{r}}}$.

The visible matter of most galaxies is essentially concentrated in the center, in spiral galaxies in the so-called bulge . The matter in this area (radius , constant density ) (including stars) revolves around the center of this galaxy on circular paths. Therefore applies to ${\displaystyle s}$ ${\displaystyle \rho _{0}}$ ${\displaystyle r<s}$

${\displaystyle m(r)=\rho _{0}\cdot {\frac {4}{3}}\pi \ r^{3}}$

and thus for the path speed

${\displaystyle v(r)=r\cdot {\sqrt {G\cdot {\frac {4}{3}}\pi \rho _{0}}}}$.

The path speed is therefore proportional to in the central area ${\displaystyle v(r)}$ ${\displaystyle r}$

${\displaystyle v(r)\sim r}$.

With increasing distance from the center of the galaxy, the orbital velocity of matter increases until it reaches a maximum. The rotation behavior of the galaxy corresponds roughly to that of a rigid body. ${\displaystyle r}$ ${\displaystyle r<s}$

If, on the other hand , it would have to decrease again, as the density of the visible matter clearly decreases towards the outside and by far no longer grows linearly with it. From then on, the orbital velocity should be proportional to the reciprocal of the square root , as one would expect for an (ideal) Kepler system: ${\displaystyle r>s}$ ${\displaystyle v(r)}$ ${\displaystyle m(r)}$ ${\displaystyle r}$ ${\displaystyle r}$

${\displaystyle v(r)\sim {\sqrt {\frac {1}{r}}}}$

However, the observations show a very different picture. Outside the central area, i.e. H. after reaching the maximum, the path speed remains approximately constant. From the above general equation for one therefore necessarily obtains , i. H. a further increase in the enclosed galaxy mass that has not yet been observed . ${\displaystyle v(r)}$ ${\displaystyle m(r)\sim r}$ ${\displaystyle r}$

The reasons for this are still unknown, there are various (speculative) explanatory models. For example, it could be about invisible dark matter , which compensates for the decrease in the density of the visible matter outside the central area, or it could be a modified Newtonian dynamic .

Individual evidence

1. ^ E. Corbelli, P. Salucci: The extended rotation curve and the dark matter halo of M33 . In: Monthly Notices of the Royal Astronomical Society . 311, No. 2, 2000, pp. 441-447. arxiv : astro-ph / 9909252 . bibcode : 2000MNRAS.311..441C . doi : 10.1046 / j.1365-8711.2000.03075.x .
2. ↑ The explanation of the mass discrepancy in spiral galaxies by means of massive and extensive dark component was first put forward by A. Bosma in a PhD dissertation, see

   A. Bosma: The Distribution and Kinematics of Neutral Hydrogen in Spiral Galaxies of Various Morphological Types . Rijksuniversiteit Groningen . 1978. Retrieved December 30, 2016.

3. ↑ V. Rubin, N. Thonnard, WK Jr. Ford: Rotational Properties of 21 Sc Galaxies With a Large Range of Luminosities and radii from NGC 4605 (R = 4kpc) to UGC 2885 (R = 122kpc) . In: The Astrophysical Journal . 238, 1980, pp. 471-487. bibcode : 1980ApJ ... 238..471R . doi : 10.1086 / 158003 .
4. ↑ KG Begeman, AH Broeils, RH Sanders: Extended Rotation Curves of Spiral Galaxies: Dark haloes and Modified Dynamics . In: Monthly Notices of the Royal Astronomical Society . 249, No. 3, 1991, pp. 523-537. bibcode : 1991MNRAS.249..523B . doi : 10.1093 / mnras / 249.3.523 .
5. ^ V. Rubin, WK Jr. Ford: Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions . In: The Astrophysical Journal . 159, 1970, p. 379. bibcode : 1970ApJ ... 159..379R . doi : 10.1086 / 150317 .

Web links

• ASTROID: rotation curve of a spiral galaxy. (PDF, 101 KiB) Theory. In: Education Group. Education Group Gemeinnützige GmbH, October 25, 2008, archived from the original on September 16, 2019 (German).