**3.2 MACHOs**

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

#### **3.3 MOND**

stars (and us) are made of is just a tiny part of the mass-energy content of the

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

Hypothetical particles that constitute the dark matter are called WIMPs which stands for weakly interacting massive particles. All the matter that we know (and us) is made of baryonic matter, i.e., the matter is made of baryons. WIMPS would be a new type of particles beyond the standard model. Those should be massive, subject to the gravitational force, and possibly other forces that are comparable to the weak force. One such candidate for WIMP could be a stable supersymmetric particle. Supersymmetric model has a particle of this property which was even called a "Wimp Miracle," but we have not yet observed any trace of supersymmetry, moreover, Wimp Miracle in any of the particle colliders. WIMPs also should not interact via electromagnetism; hence the DM is not visible in any wavelength. We only can "see" the DM due to its gravitational interactions, which are strong enough

This phenomenon is observed when the light rays passing near a very massive object are deflected (due to the curvature of space–time produced by this object) in

**3. Possible solutions and even more problems**

to cause a phenomenon known as gravitational lensing.

Universe (see **Figure 2**).

an almost perfect Universe.

*Progress in Relativity*

*3.1.1 Gravitational lensing*

**206**

**3.1 Wimps**

**Figure 2.**

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

#### **Figure 3.**

*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/.*

modified rather than an invisible matter to be found. Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian dynamics at low accelerations, suggested as an alternative to dark matter concept [8, 9]. In Ref. [8] Milgrom considered the possibility that Newton's second law does not describe the motion of objects under the conditions which prevail in galaxies and systems of galaxies. Newton's laws have been tested in high-acceleration environment like the Earth or the solar system. The stars in the outer parts of the galaxies move in the circumstances of extremely low accelerations compared to what we know from everyday life. To illustrate how small such accelerations might be, let us calculate the acceleration of average star (the Sun) located on the suburbs of average galaxy (the Milky Way):

$$a = \frac{V^2}{R} = \frac{\left(220 \frac{km}{s}\right)^2}{8.5 \, kpc} \approx 1.845 \times 10^{-10} \frac{m}{s^2} \tag{4}$$

Milgrom proposed then a generalized form of Newton's second principle, claiming the inertia term not to be simply proportional to the acceleration of an object but being rather a more general function of it:

$$
\mu \cdot \mu (a/a\_0) \overrightarrow{a} = \overrightarrow{\mathbf{F}}.\tag{5}
$$

In expression (5) *m* is gravitational mass, *a* is acceleration, *a0* is some acceleration constant, and *μ* is a nonlinear function with the following properties:

$$
\mu(\mathfrak{x}\gg\mathbf{1})\approx\mathbf{1}, \mu(\mathfrak{x}\ll\mathbf{1})\approx\mathfrak{x}\tag{6}
$$

present, the Milky Way contains big amount of the dark matter. The velocity dispersion of our galaxy is 75 km/s [13]. The NGC1052-DF2 is about 100 times lighter than the Milky Way; however, the velocity dispersion of NGC1052-DF2 was found to be only roughly 8.5 km/s [10]. If the galaxies can be formed and exist without the dark matter, i.e., the dark matter is not present in all existing galaxies, then the attempts to explain their dynamics by applying MOND might be at risk.

*Constraints on the intrinsic velocity dispersion of NGC1052-DF2. The result found in [8] (red dot star) is consistent with two other studies mentioned by authors and shows that such velocity dispersion indicates lack of*

In 2012 Moni Bidin et al. [14] published a paper in which they estimated surface mass density in the solar neighborhood. Results obtained match the expectations of visible matter alone without the need of adding the dark matter component. The difference between the measured mass of matter (derived in this study) and the mass of visible matter (i.e., mass of matter that is estimated in the independent way based on the amount of emitted) provides an estimate of the amount of DM in the volume under analysis, and constraints on the shape of the DM halo can be derived. The fundamental basis for this measurement is the application of the Poisson– Boltzmann and Jeans equations to a virialized system in steady state. This allows to estimate either the local density at the solar position or the surface density (mass

**4. Detection of dark matter**

**Figure 4.**

**209**

*the dark matter.* Credit*: [10].*

*Dark Matter within the Milky Way*

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

**4.1 Gravitational interaction with ordinary matter**

The acceleration constant is found to be *<sup>a</sup>*<sup>0</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>2</sup> � <sup>0</sup>*:*<sup>2</sup> � <sup>10</sup>�<sup>10</sup> *<sup>m</sup> <sup>s</sup>*<sup>2</sup> [8]. Phenomenological success of MOND is that applying it produces flat rotation curves of galaxies as observed and that this simple law is sufficient to make predictions for a broad range of galactic phenomena.

#### **3.4 Ultra-diffuse galaxies**

Recent studies of van Dokkum et al. [10, 11] have uncovered new class of object referred to as *ultra-diffuse galaxies*. NGC1052-DF2 and NGC1052-DF4 are large, faint galaxies with an excess of luminous globular clusters, and they have a very low-velocity dispersion. Velocity dispersion is the dispersion of radial velocities about the mean velocity for a group of objects. Low-velocity dispersion indicates that the galaxy has little or no dark matter. NGC1052-DF2 was studied with the Keck Cosmic Web Imager (KCWI), a new instrument on the Keck II telescope that was optimized for precision sky-limited spectroscopy of low surface brightness phenomena at relatively high spectral resolution. The spectroscopy data was used to describe kinematics of the galaxy. This result was based on the radial velocities of globular clusters that were assumed to be associated with the galaxies. It was claimed in Ref. [10] that taking observational uncertainties into account, the determined intrinsic velocity dispersion is consistent with the expected value found for the stars alone and lower than expected from DM halo (see **Figure 4**). The dynamical mass of NGC1052-DF2 determined in [10] was 1*:*<sup>3</sup> � <sup>0</sup>*:*<sup>8</sup> � <sup>10</sup><sup>8</sup>*Mʘ*, and the stellar mass, i.e., luminous matter, was found to be 1 � <sup>0</sup>*:*<sup>2</sup> � <sup>10</sup>8Mʘ.

To give a reader some intuition and place this in some context, it is worth to notice that the stellar mass of the Milky Way found in [12] was 6*:*08 � 1*:*14 � 10<sup>10</sup>*Mʘ*. It is broadly accepted in literature, and as will the following section

#### **Figure 4.**

modified rather than an invisible matter to be found. Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian dynamics at low accelerations, suggested as an alternative to dark matter concept [8, 9]. In Ref. [8] Milgrom considered the possibility that Newton's second law does not describe the motion of objects under the conditions which prevail in galaxies and systems of galaxies. Newton's laws have been tested in high-acceleration environment like the Earth or the solar system. The stars in the outer parts of the galaxies move in the circumstances of extremely low accelerations compared to what we know from everyday life. To illustrate how small such accelerations might be, let us calculate the acceleration of average star (the Sun) located on the suburbs of average galaxy

(the Milky Way):

*Progress in Relativity*

*<sup>a</sup>* <sup>¼</sup> *<sup>V</sup>*<sup>2</sup>

object but being rather a more general function of it:

broad range of galactic phenomena.

**3.4 Ultra-diffuse galaxies**

**208**

*<sup>R</sup>* <sup>¼</sup> <sup>220</sup> *km*

*s* <sup>2</sup>

Milgrom proposed then a generalized form of Newton's second principle, claiming the inertia term not to be simply proportional to the acceleration of an

*m* � *μ*ð Þ *a=a*<sup>0</sup> *a*

tion constant, and *μ* is a nonlinear function with the following properties:

The acceleration constant is found to be *<sup>a</sup>*<sup>0</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>2</sup> � <sup>0</sup>*:*<sup>2</sup> � <sup>10</sup>�<sup>10</sup> *<sup>m</sup>*

stellar mass, i.e., luminous matter, was found to be 1 � <sup>0</sup>*:*<sup>2</sup> � <sup>10</sup>8Mʘ.

To give a reader some intuition and place this in some context, it is worth to notice that the stellar mass of the Milky Way found in [12] was 6*:*08 � 1*:*14 � 10<sup>10</sup>*Mʘ*. It is broadly accepted in literature, and as will the following section

nological success of MOND is that applying it produces flat rotation curves of galaxies as observed and that this simple law is sufficient to make predictions for a

In expression (5) *m* is gravitational mass, *a* is acceleration, *a0* is some accelera-

Recent studies of van Dokkum et al. [10, 11] have uncovered new class of object referred to as *ultra-diffuse galaxies*. NGC1052-DF2 and NGC1052-DF4 are large, faint galaxies with an excess of luminous globular clusters, and they have a very low-velocity dispersion. Velocity dispersion is the dispersion of radial velocities about the mean velocity for a group of objects. Low-velocity dispersion indicates that the galaxy has little or no dark matter. NGC1052-DF2 was studied with the Keck Cosmic Web Imager (KCWI), a new instrument on the Keck II telescope that was optimized for precision sky-limited spectroscopy of low surface brightness phenomena at relatively high spectral resolution. The spectroscopy data was used to describe kinematics of the galaxy. This result was based on the radial velocities of globular clusters that were assumed to be associated with the galaxies. It was claimed in Ref. [10] that taking observational uncertainties into account, the determined intrinsic velocity dispersion is consistent with the expected value found for the stars alone and lower than expected from DM halo (see **Figure 4**). The dynamical mass of NGC1052-DF2 determined in [10] was 1*:*<sup>3</sup> � <sup>0</sup>*:*<sup>8</sup> � <sup>10</sup><sup>8</sup>*Mʘ*, and the

<sup>8</sup>*:*<sup>5</sup> *kpc* <sup>≈</sup>1*:*<sup>845</sup> � <sup>10</sup>�<sup>10</sup> *<sup>m</sup>*

! <sup>¼</sup> *<sup>F</sup>* !

*μ*ð Þ *x* ≫ 1 ≈1, *μ*ð Þ *x* ≪ 1 ≈*x* (6)

*<sup>s</sup>*<sup>2</sup> (4)

*<sup>s</sup>*<sup>2</sup> [8]. Phenome-

*:* (5)

*Constraints on the intrinsic velocity dispersion of NGC1052-DF2. The result found in [8] (red dot star) is consistent with two other studies mentioned by authors and shows that such velocity dispersion indicates lack of the dark matter.* Credit*: [10].*

present, the Milky Way contains big amount of the dark matter. The velocity dispersion of our galaxy is 75 km/s [13]. The NGC1052-DF2 is about 100 times lighter than the Milky Way; however, the velocity dispersion of NGC1052-DF2 was found to be only roughly 8.5 km/s [10]. If the galaxies can be formed and exist without the dark matter, i.e., the dark matter is not present in all existing galaxies, then the attempts to explain their dynamics by applying MOND might be at risk.

### **4. Detection of dark matter**

#### **4.1 Gravitational interaction with ordinary matter**

In 2012 Moni Bidin et al. [14] published a paper in which they estimated surface mass density in the solar neighborhood. Results obtained match the expectations of visible matter alone without the need of adding the dark matter component. The difference between the measured mass of matter (derived in this study) and the mass of visible matter (i.e., mass of matter that is estimated in the independent way based on the amount of emitted) provides an estimate of the amount of DM in the volume under analysis, and constraints on the shape of the DM halo can be derived. The fundamental basis for this measurement is the application of the Poisson– Boltzmann and Jeans equations to a virialized system in steady state. This allows to estimate either the local density at the solar position or the surface density (mass

per unit area) of the mass within a given volume. Authors in Ref. [14] derive analytical expression for surface density as a function of distance from the galactic disk plane Σ(Z) to estimate the surface mass density between 1.5 and 4.5 kpc distance from the galactic disk plane using data from of the kinematics studies of about 400 red giants kinematics. The authors in [14] claimed that the estimate of the surface mass density matches the expectation of visible mass alone and the degree of overlap between the two curves is striking. There is no need for any dark component to account for the results: the measured Σ(Z) implies a local DM density *<sup>ρ</sup>*ʘ*DM* <sup>¼</sup> <sup>0</sup> � <sup>1</sup> *<sup>M</sup>*<sup>ʘ</sup> � <sup>10</sup>�<sup>3</sup> *pc*�<sup>3</sup> a. Further the authors in [14] compared this results with models of DM disk present in literature such as Ref. [15] hereafter OM; Ref. [16] hereafter SMH, which is standard DM halo model; or Ref. [17]—the model with minimal local DM density—hereafter MIN. Comparison of these findings is presented in **Figure 5**. Authors in Ref. [14] claim that the OM model is excluded at 8 sigma confidence level, SHM at 6 sigma, and even MIN model at 4.1 sigma. (Sigma confidence level says how many values lie within the number of standard deviation of the mean. For example, in particle physics there is a convention of a five-sigma effect being required to qualify as a discovery, that is to say that 99.99994% of the values must lay within 5 standard deviations of the mean; 8 sigma is even higher confidence level). Authors conclude that the measurement of the mass surface density at the solar galactocentric position between 1.5 and 4 kpc from the galactic plane accounts for the visible mass only. The DM density in the solar neighborhood, extrapolated from the observed curve of Σ(Z), is at variance with the general

consensus that it must be in the range 5 <sup>13</sup> *<sup>M</sup>*<sup>ʘ</sup> <sup>10</sup><sup>3</sup>

Sun in a circular orbit at a speed of 220 km s<sup>1</sup>

way have a little chance of success.

*Dark Matter within the Milky Way*

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

**4.2 Direct detection**

**4.3 Others**

**211**

DM is observed by using measurements of the thick disk kinematics and is independent of the choice of data, because very similar results were obtained by means of other kinematical results in the literature. It is clear that the local surface density as measured in Ref. [14], extrapolated to the rest of the galaxy, cannot retain the

therefore confirmed by this study, and this finding tells us that indirect attempts to detect the dark matter by investigating its interactions with ordinary matter in that

The experiments that aim at the direct detection due to scattering do not agree with each other yielding different constraints on the mass of the DM particles. The DAMA/LIBRA experiment [20] is the only one to claim positive result of detection which however has not been yet confirmed by the other groups (detectors). The aim of this experiment is detecting low-energy recoil photons from the scintillator crystals of thallium-doped sodium iodide NaI(Tl) placed in the detectors under the ground. Such photons would be emitted when the DM particle collides with one of the scintillators. If what we know about the DM is right, then since the Earth orbits the Sun, the DM particles should pass through the planet and hence have a chance to collide with those of the detectors. The idea of the experiment is that if one takes into account the revolution of the Earth around the Sun and the revolution of the Sun around the center of our galaxy, then the signals coming from the collisions should be modulated as in June the relative velocity of the Earth and the DM flux is the biggest hence yielding the biggest number of collisions. The data collected from the phase II of the experiment have all traits required to claim the presence of the DM in our part of the galaxy. The annual modulation is present only in the events concerning the photons with energies exactly within the energetic range theoretically predicted for the DM particles. Yet the DAMA/LIBRA is a singular case. Several groups have been working to develop experiments aiming at reproducing DAMA/LIBRA's results using the same target medium. To determine whether there is evidence for an excess of events above the expected background in sodium iodide and to look for evidence of an annual modulation, the COSINE-100 experiment [21] uses the same target medium to carry out a model-independent test of DAMA/ LIBRA's claim. Their results from the initial operation of the COSINE-100 experiment were published in [21], and no excess of signal-like events above the expected background in the first 59.5 days of data from COSINE-100 has been observed. Assuming the so-called standard DM halo model, this result rules out spinindependent WIMP–nucleon interactions as the cause of the annual modulation observed by the DAMA/LIBRA collaboration. Another such experiment is the XENON100 experiment that searches for electronic recoil event rate modulation by measuring the scintillation light from a particle interacting in the liquid xenon. The results of this experiment published in [22] also exclude the DAMA/LIBRA results.

We will present here very briefly the other two methods of detection of DM:

• *Production of DM particles in colliders*—If the DM particles were created, for instance, in LHC, they would escape through the detectors unnoticed (due to their non-electromagnetic nature). However, they would carry away energy

*pc*<sup>3</sup> (e.g., [18, 19]). Lack of

. A deep missing mass problem is

#### **Figure 5.**

*Observational results for the surface mass density, as a function of distance from the galactic plane (black curve), compared to the expectations of the models discussed in the text (thick gray curves). The dotted and dashed lines indicate the observational 1σ and 3σ strip, respectively. Expectations for the known visible mass are indicated by the thick gray curve labeled as VIS.* Credit*: [14].*

consensus that it must be in the range 5 <sup>13</sup> *<sup>M</sup>*<sup>ʘ</sup> <sup>10</sup><sup>3</sup> *pc*<sup>3</sup> (e.g., [18, 19]). Lack of DM is observed by using measurements of the thick disk kinematics and is independent of the choice of data, because very similar results were obtained by means of other kinematical results in the literature. It is clear that the local surface density as measured in Ref. [14], extrapolated to the rest of the galaxy, cannot retain the Sun in a circular orbit at a speed of 220 km s<sup>1</sup> . A deep missing mass problem is therefore confirmed by this study, and this finding tells us that indirect attempts to detect the dark matter by investigating its interactions with ordinary matter in that way have a little chance of success.
