**4.2 Direct detection**

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

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

*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].*

*pc*�<sup>3</sup> a. Further the authors in [14] compared this results

*<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>

*Progress in Relativity*

**Figure 5.**

**210**

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.

### **4.3 Others**

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

and momentum, so one could infer their existence from the amount of energy and momentum "missing" after a collision. The LHC also search for existence of supersymmetric particles which are one of the candidates for DM particle.

• *Searching for products of annihilation of its particles*—Indirect detection. This experiments search for the products of the self-annihilation or decay of DM particles in outer space. For example, in regions of high DM density (e.g., the center of our galaxy), two DM particles could annihilate to produce gamma rays or standard model particle–antiparticle pairs. Alternatively if the DM particle is unstable, it could decay into standard model (or other) particles. These processes could be detected indirectly through an excess of gamma rays, antiprotons, or positrons emanating from high-density regions in the galaxy or others.

#### **5. Milky way rotation curve**

DM manifests its existence through the shape of rotational curves of galaxies, in particular, through the rotational curve of our own galaxy, the Milky Way. This is what motivated us to take a glimpse on that topic and to compare results to those present in literature [23]. We have studied the rotational curve of Milky Way with radio telescope located in the Astronomical Observatory of the Jagiellonian University provided by EU-HOU project (EU-HOU project was founded with support from the European Commission, grant 510,308-LLP-1-2010-FR-COMENIUS-CMP. https://www.astro.uni-bonn.de/hisurvey/euhou/LABprofile/).

#### **5.1 The method**

This 3 m in diameter telescope runs observations on 1420 MHz frequency which is the emission line of neutral hydrogen. When the hydrogen atom undergoes a transition from the state of higher energy when the spins of the proton and the electron are parallel to the state of lower energy that is when the spins are antiparallel, emitted photon is equivalent to radiation roughly 21 cm wavelength in vacuum (see **Figure 6**). Even though such process occurs very rarely, given the abundance of the hydrogen in the Universe (i.e., 74% of its baryonic mass), it is a common phenomenon. Hence the hydrogen is also present in the interstellar space around the stars, and radio observations yield information on how the matter is distributed inside the galaxy, and knowing the Doppler shift of the observed radiation, one can calculate the velocity of the hydrogen cloud from which it comes from. This in turn gives us an idea how the hydrogen and the nearby matter move within the galaxy, i.e., orbit around its center. Knowing the velocities and distance of such hydrogen clouds, one can plot the rotational curve of the galaxy. This is called tangent point method. Thus using the data obtained from the telescope, the Doppler equation:

$$V\_r = \frac{f\_0 - f}{f\_0} \cdot c \tag{7}$$

The hydrogen atoms that we study are moving relatively to us so the signal coming from them is a subject to the same phenomenon as for the ambulance's siren applies. That is the change in frequency that enables us to calculate the radial velocity of such hydrogen cloud along the line of sight (which is defined by

To find the speed of the hydrogen cloud, a simple fact is used, that is the radial velocity results in difference between the projection of ours (Sun's) velocity on the line of sight and the hydrogen cloud's velocity on the line of sight (see **Figure 7**). The line of sight is determined along the galactic longitude (see **Figure 8**) on which

This results in the following equation for velocity of observed hydrogen cloud:

Among the objects observed along the given line of sight, the one with the smallest distance will have the biggest velocity. The smallest possible distance between us and the source is when it lies in the tangent point; hence simple

Eqs. (8) and (9) provide all required information to plot a rotational curve of the galaxy. This method works for objects in I and IV Quadrants of galactic longitude, that is for 0° <*l* <90°*and* 270°< *l*<360° and inside the galactocentric radius of the Sun.

*<sup>R</sup> sin l*ðÞ� *<sup>V</sup>*<sup>0</sup> *sin l*ð Þ (8)

*R* ¼ *R*<sup>0</sup> *sin l*ð Þ (9)

*V* ¼ *Vr* þ *V*<sup>0</sup> sin ð Þ*l :* (10)

*Vr* <sup>¼</sup> *<sup>V</sup> <sup>R</sup>*<sup>0</sup>

trigonometry allows us to determine the distance:

which simplifies Eq. (8) to

**213**

galactic longitude).

*Hydrogen 21-cm emission line.*

*Dark Matter within the Milky Way*

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

**Figure 6.**

we set the radio telescope.

one can calculate the source's velocity (speed) relative to us (*Vr*). *f* <sup>0</sup> is the frequency emitted by the hydrogen atom, f is the frequency the radio telescope receives, and *c* denotes the speed of light. The frequencies registered by the radio telescope are of course slightly different than 1420 MHz which is the frequency of emitted photon as measured at the lab and as emitted by the hydrogen atom.

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

and momentum, so one could infer their existence from the amount of energy and momentum "missing" after a collision. The LHC also search for existence of supersymmetric particles which are one of the candidates for DM particle.

• *Searching for products of annihilation of its particles*—Indirect detection. This experiments search for the products of the self-annihilation or decay of DM particles in outer space. For example, in regions of high DM density (e.g., the center of our galaxy), two DM particles could annihilate to produce gamma rays or standard model particle–antiparticle pairs. Alternatively if the DM particle is unstable, it could decay into standard model (or other) particles. These processes could be detected indirectly through an excess of gamma rays, antiprotons, or positrons emanating from high-density regions in the

DM manifests its existence through the shape of rotational curves of galaxies, in particular, through the rotational curve of our own galaxy, the Milky Way. This is what motivated us to take a glimpse on that topic and to compare results to those present in literature [23]. We have studied the rotational curve of Milky Way with radio telescope located in the Astronomical Observatory of the Jagiellonian University provided by EU-HOU project (EU-HOU project was founded with support from the European Commission, grant 510,308-LLP-1-2010-FR-COMENIUS-CMP.

This 3 m in diameter telescope runs observations on 1420 MHz frequency which

is the emission line of neutral hydrogen. When the hydrogen atom undergoes a transition from the state of higher energy when the spins of the proton and the electron are parallel to the state of lower energy that is when the spins are antiparallel, emitted photon is equivalent to radiation roughly 21 cm wavelength in vacuum (see **Figure 6**). Even though such process occurs very rarely, given the abundance of the hydrogen in the Universe (i.e., 74% of its baryonic mass), it is a common phenomenon. Hence the hydrogen is also present in the interstellar space around the stars, and radio observations yield information on how the matter is distributed inside the galaxy, and knowing the Doppler shift of the observed radiation, one can calculate the velocity of the hydrogen cloud from which it comes from. This in turn gives us an idea how the hydrogen and the nearby matter move within the galaxy, i.e., orbit around its center. Knowing the velocities and distance of such hydrogen clouds, one can plot the rotational curve of the galaxy. This is called tangent point method. Thus using the data obtained from the telescope, the Doppler equation:

> *Vr* <sup>¼</sup> *<sup>f</sup>* <sup>0</sup> � *<sup>f</sup> f* 0

one can calculate the source's velocity (speed) relative to us (*Vr*). *f* <sup>0</sup> is the frequency emitted by the hydrogen atom, f is the frequency the radio telescope receives, and *c* denotes the speed of light. The frequencies registered by the radio telescope are of course slightly different than 1420 MHz which is the frequency of emitted photon as measured at the lab and as emitted by the hydrogen atom.

� *c* (7)

https://www.astro.uni-bonn.de/hisurvey/euhou/LABprofile/).

galaxy or others.

*Progress in Relativity*

**5.1 The method**

**212**

**5. Milky way rotation curve**

**Figure 6.** *Hydrogen 21-cm emission line.*

The hydrogen atoms that we study are moving relatively to us so the signal coming from them is a subject to the same phenomenon as for the ambulance's siren applies. That is the change in frequency that enables us to calculate the radial velocity of such hydrogen cloud along the line of sight (which is defined by galactic longitude).

To find the speed of the hydrogen cloud, a simple fact is used, that is the radial velocity results in difference between the projection of ours (Sun's) velocity on the line of sight and the hydrogen cloud's velocity on the line of sight (see **Figure 7**). The line of sight is determined along the galactic longitude (see **Figure 8**) on which we set the radio telescope.

This results in the following equation for velocity of observed hydrogen cloud:

$$V\_r = V \frac{R\_0}{R} \sin\left(l\right) - V\_0 \sin\left(l\right) \tag{8}$$

Among the objects observed along the given line of sight, the one with the smallest distance will have the biggest velocity. The smallest possible distance between us and the source is when it lies in the tangent point; hence simple trigonometry allows us to determine the distance:

$$R = R\_0 \sin\left(l\right) \tag{9}$$

which simplifies Eq. (8) to

$$V = V\_r + V\_0 \sin\left(l\right). \tag{10}$$

Eqs. (8) and (9) provide all required information to plot a rotational curve of the galaxy. This method works for objects in I and IV Quadrants of galactic longitude, that is for 0° <*l* <90°*and* 270°< *l*<360° and inside the galactocentric radius of the Sun.

**Figure 7.** *Figure presenting two objects (A, B) along the line of sight. Hence object B lies in tangent point, i.e., its distance from the center of the galaxy is smaller, and its velocity is greater than the velocity of object A.*

#### **5.2 Results**

Twenty-nine objects with galactic longitude 0°<*l* <90° have been studied. Their positions on the map of the Milky Way are presented in **Figure 9**. Tangent point method applied to the data results in rotational curve presented in **Figure 10**.

Our rotational curve plot, **Figure 10**, is comparable to the plot obtained from data from LAB survey [24] and consistent with the ones that can be found in literature [23, 25]. We follow [25] in their choice of function to fit the data, namely

$$\frac{V}{V\_0} = a \left(\frac{R}{R\_0}\right)^b + c \tag{11}$$

**Figure 8.**

*Dark Matter within the Milky Way*

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

**Figure 9.**

**215**

*Figure presenting galactic longitude. L = 0° is direction from the solar system to the center of galaxy.* Credit*: File:*

*Artist's\_impression\_of\_the\_Milky\_Way.Jpg: NASA/JPL-Caltech/ESO/R.hurt.*

*Map of the hydrogen clouds used to determine the rotational curve of the Milky Way.*

where we put *<sup>V</sup>*<sup>0</sup> <sup>¼</sup> <sup>220</sup> *km <sup>s</sup>* and *R*<sup>0</sup> ¼ 8*:*5 kpc and find the coefficients to be *a* ¼ �5*:*495*e* � 06, *b* ¼ �21*:*28, and *c* ¼ 0*:*9808.

We conclude that the rotational curve reveals the existence of dark matter within the Milky Way. Taking (nonrelativistic) law of gravity, that is, the force of gravity is proportional to inverse squared distance, one would expect that the farther away the hydrogen clouds (constituting the distribution of matter) are from the massive center of the galaxy, the lower their velocities will be. As one see from the rotational curve, **Figure 10**, this is not the case; the velocities seem to be constant over a distance of roughly 3 kpc. Which means there is nonluminous matter distributed in such a way just to "keep up" with the increasing distance from

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

#### **Figure 8.**

**5.2 Results**

**214**

**Figure 7.**

*Progress in Relativity*

where we put *<sup>V</sup>*<sup>0</sup> <sup>¼</sup> <sup>220</sup> *km*

*a* ¼ �5*:*495*e* � 06, *b* ¼ �21*:*28, and *c* ¼ 0*:*9808.

Twenty-nine objects with galactic longitude 0°<*l* <90° have been studied. Their positions on the map of the Milky Way are presented in **Figure 9**. Tangent point method applied to the data results in rotational curve presented in **Figure 10**. Our rotational curve plot, **Figure 10**, is comparable to the plot obtained from data from LAB survey [24] and consistent with the ones that can be found in literature [23, 25]. We follow [25] in their choice of function to fit the data, namely

*Figure presenting two objects (A, B) along the line of sight. Hence object B lies in tangent point, i.e., its distance*

*from the center of the galaxy is smaller, and its velocity is greater than the velocity of object A.*

*R R*0 *<sup>b</sup>*

We conclude that the rotational curve reveals the existence of dark matter within the Milky Way. Taking (nonrelativistic) law of gravity, that is, the force of gravity is proportional to inverse squared distance, one would expect that the farther away the hydrogen clouds (constituting the distribution of matter) are from the massive center of the galaxy, the lower their velocities will be. As one see from the rotational curve, **Figure 10**, this is not the case; the velocities seem to be constant over a distance of roughly 3 kpc. Which means there is nonluminous matter distributed in such a way just to "keep up" with the increasing distance from

*<sup>s</sup>* and *R*<sup>0</sup> ¼ 8*:*5 kpc and find the coefficients to be

þ *c* (11)

*V V*<sup>0</sup> ¼ *a*

*Figure presenting galactic longitude. L = 0° is direction from the solar system to the center of galaxy.* Credit*: File: Artist's\_impression\_of\_the\_Milky\_Way.Jpg: NASA/JPL-Caltech/ESO/R.hurt.*

**Figure 9.** *Map of the hydrogen clouds used to determine the rotational curve of the Milky Way.*

#### **Figure 10.**

*Rotational curve obtained from 21-cm line observations of the Milky Way. Note that the velocity of the studied objects appears to be constant over roughly 3 kpc distance.*

the center of galaxy and make it so that the velocities of hydrogen atoms are almost constant as the distance increases.

#### **6. Conclusions**

The problem of missing matter discovered by Fritz Zwicky in 1933 appears to be still an open question. The most important premise of existence of the dark matter is the shape of rotational curves of galaxies, introduced as a tool for studying galaxy rotation by Vera Rubin. With our current understanding of the Universe, the dark matter, still a mysterious substance, makes up 86% of all the matter in the Universe. Throughout the years various attempts have been made to explain its nature. Some of the ideas have been proven unlikely (MACHOs). Some of them contradict each other (DAMA/LIBRA, the COSINE-100 collaboration). Yet even simple Milky Way's observations as presented in Section 5 lead to the conclusion that the dark matter is present in the halo of our galaxy.

**Author details**

**217**

Aleksander Kaczmarek<sup>1</sup>

*Dark Matter within the Milky Way*

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

and Technology, Wroclaw, Poland

provided the original work is properly cited.

Technology, Wroclaw, Poland

\* and Andrzej Radosz<sup>2</sup>

\*Address all correspondence to: a.kaczmarek12@wp.pl

1 Faculty of Fundamental Problems of Technology, Wroclaw University of Science

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

2 Department of Quantum Engineering, Wroclaw University of Science and

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