**2. The dark matter problem**

The term "dark matter" (DM) was introduced due to the contribution by Fritz Zwicky as early as in 1930s of the twentieth century. Studying the Coma cluster (of galaxies) located 320 million light-years away, Zwicky estimated [1] masses of the galaxies that make up this cluster based on the amount of light they emit. It turned out that such an amount of (*luminous*) matter wasn't large enough to explain the trajectories and velocities of those galaxies. Zwicky claimed then that the gravitational attraction exerted by the luminous matter was not enough to hold the cluster together and if there wasn't some kind of additional, nonluminous matter that provide extra gravity force, the galaxies would fly apart. These findings seemingly intriguing by themselves had not been taken seriously by scientific community. And only findings of Vera Rubin [2], some 40 years later, led to the formulation of the fundamental and still unresolved problem. Rubin studied rotational curves of galaxies. Rotational curve of a galaxy is a plot presenting how the orbital velocity of objects in this galaxy changes with increasing distance from the galaxy's center (see **Figure 1**). It turned out that the shapes of the curves did not comply with the theoretical predictions based on the mount of matter estimated due to the emitted light.

**Figure 1** illustrates this discrepancy. When being close to the center of the galaxy, the plot agrees with what one would expect: the rotational curve increases

#### **Figure 1.**

*Figure schematically representing discrepancy between observed (B) and predicted (A) rotational curves of galaxies that indicates presence of dark matter in halos of such galaxies. Credit: PhilHibbs, Wikipedia, https:// pl.wikipedia.org/wiki/Krzywa\_rotacji\_galaktyki#/media/Plik:GalacticRotation2.svg, Creative Commons Attribution-Share Alike 3.0 Unported license.*

#### *Dark Matter within the Milky Way DOI: http://dx.doi.org/10.5772/intechopen.90267*

galaxies without invoking hidden matter at all. Yet such an approach seems to be in tension with recent findings of van Dokkum et al. about the ultra-diffuse galaxies. There appear to exist galaxies devoided of dark matter—then what about MOND predictions? This contribution is completed with the rotational curve of the Milky Way determined with 3 m in diameter radio telescope in the Astronomical Observatory of the Jagiellonian University. Obtained rotational curve is flat which

The term "dark matter" (DM) was introduced due to the contribution by Fritz Zwicky as early as in 1930s of the twentieth century. Studying the Coma cluster (of galaxies) located 320 million light-years away, Zwicky estimated [1] masses of the galaxies that make up this cluster based on the amount of light they emit. It turned out that such an amount of (*luminous*) matter wasn't large enough to explain the trajectories and velocities of those galaxies. Zwicky claimed then that the gravitational attraction exerted by the luminous matter was not enough to hold the cluster together and if there wasn't some kind of additional, nonluminous matter that provide extra gravity force, the galaxies would fly apart. These findings seemingly intriguing by themselves had not been taken seriously by scientific community. And only findings of Vera Rubin [2], some 40 years later, led to the formulation of the fundamental and still unresolved problem. Rubin studied rotational curves of galaxies. Rotational curve of a galaxy is a plot presenting how the orbital velocity of objects in this galaxy changes with increasing distance from the galaxy's center (see **Figure 1**). It turned out that the shapes of the curves did not comply with the theoretical predictions based on the mount of matter estimated due to the

**Figure 1** illustrates this discrepancy. When being close to the center of the galaxy, the plot agrees with what one would expect: the rotational curve increases

*Figure schematically representing discrepancy between observed (B) and predicted (A) rotational curves of galaxies that indicates presence of dark matter in halos of such galaxies. Credit: PhilHibbs, Wikipedia, https:// pl.wikipedia.org/wiki/Krzywa\_rotacji\_galaktyki#/media/Plik:GalacticRotation2.svg, Creative Commons*

indicates the presence of dark matter in the halo of our galaxy.

**2. The dark matter problem**

*Progress in Relativity*

emitted light.

**Figure 1.**

**204**

*Attribution-Share Alike 3.0 Unported license.*

rapidly that reflects an obvious fact that the velocity of a test object (a "star") increases as the effective gravitational force is growing (at a given radius, only the mass enclosed within a sphere of that radius is relevant in terms of excreting gravitational force—Newton's Shell Theorem). Past a certain distance though (when increasing a distance from the massive center of galaxy does not enclose adequately bigger amounts of mass), the effective force of gravity should decline (as R2 will increase faster than the mass enclosed in a sphere of a radius being that distance from the center so the force of gravity will decline) which should result in lower orbital velocities.

Vera Rubin and Kent Ford published their first rotational curve in paper [2]. They presented there the rotation of Andromeda based on spectroscopic survey of emission regions applying neutral hydrogen, Hα, and [NII] λ6583 emission lines. Further works, see, e.g., [3], revealed that most of the galaxies have rather flat rotational curves like the one in **Figure 1**. The fact that more distant stars have almost constant velocity attracted the attention of scientists. The circular velocities of the stars are due to gravity which plays the role of centripetal force. Combining Newton's law of gravity with an expression for centripetal force yields the following relation:

$$\frac{GM}{R^2} = \frac{V^2}{R},\tag{1}$$

where *G* is universal gravitational constant, *M* is mass exerting a gravitational force, *V* denotes velocity of a (test) object orbiting mass *M*, and *R* is the distance between them. One obtains from Eq. (1)

$$M = G V^2 R.\tag{2}$$

Since *G* is constant and *V* appears to be constant as we can see in rotational curves (see **Figure 1**), it would mean that the mass of a galaxy increases linearly with the distance from its center:

$$M(R) \sim R.\tag{3}$$

As we know most of galaxies including the Milky Way have a bright massive center, a *bulge*, with majority of stars placed in that range and possibly a supermassive black hole in the middle. The farther away from the center, the fainter the regions are, i.e., less stars hence less matter is present, and linear dependence (3) is almost impossible to be obeyed. Computer simulations show that the galaxies move in a way we can observe them only if there is another than ordinary, luminous, form of matter, namely, dark matter. The amount of dark matter should be as large as almost five times more than the amount of ordinary matter. This is in agreement with calculations made within lambda-cold dark matter model (Λ-CDM) and the data from Wilkinson Microwave Anisotropy Probe (WMAP) [4] as well as Planck mission [5]. Λ-CDM model is a parametrization of the Big Bang cosmological model in which the Universe contains three major components: first, a cosmological constant denoted by lambda (Greek Λ) and associated with *dark energy*; second, the postulated *cold dark matter* (abbreviated CDM); and third, *ordinary matter*. It is often referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good description of the content of the Universe. WAMP was a satellite designed to map the cosmic microwave background (CMB) radiation over the entire sky in five frequency bands. The agreement between Λ-CDM model and the data from WAMP is good enough, which supports the validity of this model [4, 5]. The Λ-CDM model indicates that the matter the

such a way that a distant observer observes it lensed. **Figure 3** illustrates gravitational lensing: the stretched structures are distant galaxies, whose light was bent by the DM between them and the observer. This allows to calculate the mass required to cause such phenomenon [6]. Large aggregations of massive DM particles are able

Massive astrophysical compact halo objects (MACHOs) was another hypothesis invoked to explain the presence of large amount of nonluminous matter in galactic halos. Those, contrary to the WIMPS, would have been regular astrophysical objects emitting little or no radiation such as black holes, neutron stars, as well as brown dwarfs and unassociated planets, which drift unseen through interstellar space providing extra gravity. Thorough investigations have shown that this concept rather fails to explain the expected amount of the DM. One way to detect MACHOS' influence, as described in [7], is to look for events of microlensing caused by them. Such microlensing would cause observable apparent amplification of star's flux. In [7] it was shown that the number of such events is far too less that would have been expected. That rules out MACHOS as the candidates for DM. Moreover, the studies of abundance of baryons created in the Big Bang show that baryon density is consistent with the mean cosmic density of matter visible optically and in X-rays. It implies that most of the baryons in the Universe are visible but not dark and that

In the former sections, we have discussed the attempts of solving or explaining the problem of the missing matter. That is to find or to claim existence of unknown, invisible substance. Yet there is another idea based on a different assumption. In 1983 Milgrom [8] proposed an idea that maybe it is the theory that needs to be

*An image of gravitational lensing obtained with Hubble space telescope showing a distant image of galaxies which had been stretched due to the warping of space–time caused by a massive object between them and the*

*observer.* Credit*: ESA/Hubble https://www.spacetelescope.org/images/potw1506a/.*

to produce such image letting us to know it's out there*.*

most of the matter in the Universe consists of nonbaryonic DM [7].

**3.2 MACHOs**

*Dark Matter within the Milky Way*

*DOI: http://dx.doi.org/10.5772/intechopen.90267*

**3.3 MOND**

**Figure 3.**

**207**

#### **Figure 2.**

*Estimated distribution of matter and energy in the universe based on Planck data. Credit*: ESA, Planck reveals an almost perfect Universe.

stars (and us) are made of is just a tiny part of the mass-energy content of the Universe (see **Figure 2**).
