New Physics: Sae Mulli,
Vol. 66, No. 8, August 2016, pp. 946∼949 http://dx.doi.org/10.3938/NPSM.66.946
Advent and Nature of Dark Matter - A Brief Summary
Hongsu Kim
∗Optical Astronomy Division, Korea Astronomy and Space Science Institute, Daejeon 34055, Korea (Received 13 July 2016 : revised 22 July 2016 : accepted 22 July 2016)
Thanks to the recent developments in observational technology, the study of cosmology today is often called precision cosmology. Nevertheless, present cosmology still involves a big mystery. That is, among the Universe’s energy budget, cosmologists have known for some time that dark matter occupies 23% of the Universe, dark energy occupies 73%, and the baryon occupies the remaining 4%. That is, 76% of the Universe still remains a complete mystery. In the present work, therefore, we would like to present our current understanding of dark matter, as well as the puzzle associated with its existence. That the nature of dark matter in the present Universe still remains a complete mystery or puzzle is fair to say. In the present work, however, we challenge a brief, albeit reliable, summary of up-to-date observational evidence for the existence of dark matter and introduce the theories underlying it.
PACS numbers: 95.36.+x, 95.35.+d, 04.50.Kd, 11.10.-z, 95.10.-a Keywords: Dark matter, Dark energy, Modification of gravity
I. SUMMARY OF THE UP-TO-DATE OBSERVATIONAL EVIDENCES
1. Galaxy Rotation Curve in the Dark Matter Halo
One obvious consensus among Astronomers is that most of the galaxies in the universe consist of the com- mon, stereotypical structure Bulge (where the lumi- nous stars are present) at the center, with the disk be- ing around it, and lastly the dark halo which extends from the disk all the way out till several hundred kilo parsec(pc) away from the center of each galaxy. And particularly, this halo in the outskirt of each galaxy is believed to be filled with dark matter and that is why it is dubbed, Dark halo!
Of course, this expectation is consistent with the only well-known nature of dark matter that Dark Matter clus- ters only on sub-M pc scale. Orbiting around galaxies like this M33 above in Fig. 1, its orbital velocity should go like :
V2(r) =G0M (r)
r .
∗E-mail: [email protected]
(Where G0 denote the Newton’s gravitational constant, M (r) is the total mass of a galaxy, r is the distance from the center of the galaxy [1]).
We also point out that the rotation velocity curve in- volving the Doppler shift of light emitted by the orbiting objects is given by, V2(r) = G0M (r)r +4πr2cG20P(with P being the radial pressure), where c is the speed of light [1].
Surprisingly, however, observations [1] reveal that this galaxy rotation curve turns out to be : V2(r) = G0×constant, that is, it is flat!
Such rather unexpected and hence puzzling result has been observed ever since the early stages of the Astro- nomical observation history, say, from 1900s [2,3]. And this flattened galaxy rotation curve has been the long- standing, solid observational evidence for the existence of dark matter spread out all over the space.
For instance, the rotation curve of the dwarf spiral galaxy M33 is shown above in Fig.1Rotation curves are observed usually via measurements of the Doppler shift of the 21 cm emission line from neutral hydrogen (HI) for distant galaxies and of the light emitted by stars of nearby galaxies.
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Advent and Nature of Dark Matter - A Brief Summary – Hongsu Kim 947
Fig. 1. (Color online) Flattened rotation curve in the dark halo of dwarf spiral galaxy M33 [1].
It is also interesting to note that this behavior of the rotation curve is independent of the mass of the host galaxy. Namely, this behavior of the rotation curve comes exclusively from the nature of the dark matter.
The well-known Tully-Fisher relation [1] between the total luminosity of a given galaxy and the outermost ro- tation velocity can be accounted for if both the luminous and the dark matter contributions are considered.
In order words, one can realize the great difference between theoretical and observational results like Fig.1.
Which is a evidence of the Dark Matter. Unless we adopt or employ the Dark Matter, it is obvious that the Ke- pler’s low breaks down which originate from the standard gravity theory like Einstein’s general relativity.
2. Mass to light ratio (M/L) puzzle
Here M/L denotes the so-called mass-to-light ratio given in the units of the solar mass-to-luminosity ratio and exhibits a large excess of dark matter over the lumi- nous matter.
Indeed, it is fair to say that, almost all types of bodies in the universe are luminous to some extent.
For instance:
(1) Star’s luminosity comes from the thermonuclear fu- sion, which is their engine.
(2) Galaxies’ luminosity comes from their bulge region which is just the collection of luminous stars.
(3) Planet’s luminosity comes from the reflection of light from their nearby star off the planet’s surface.
Nevertheless, even if we count all types of sources of luminosity like above, the luminous mass or the apparent mass sum is always M /L >> 1, namely, the total mass is much greater than the luminous mass consisting of, say, (1),(2) and (3) above !
To conclude, therefore, one comes to the conclusion that in the universe, the non-luminous dark matter dom- inates over the luminous mass (or matter).
In a sense, therefore, this mass-to-light ratio (M/L) puzzle is a more general and solid observational evidence for the existence of dark matter spread out all over the space.
3. Weak gravitational lensing
The most successful techniques to investigate the as- trophysics of Dark Matter is the gravitational lensing which consist of strong, weak, and micro lensings. In the present work, therefore, we particularly focus on weak gravitational-lensing as it demonstrates the distribution of the Dark Matter around galaxies or galaxy clusters.
In the flowing, therefore, we provide a brief introduc- tion of this gravitational lensing. Observasionwise gravi- tational lensing represent the distortion of the lens image as the light signal which originate from the back of the lens as it travels the vicinity of the lens. More precisely the deflection of the trajectory of the light beam gener- ates the distortion of the lens image when viewed from a large distance. This distortion of lens image is given in the Fig. 1 in the reference [4].
In the figure, the linear blue scale on top shows the gravitational lensing magnification, which is propor- tional to the projected mass along the line of sight [4].
From the nature of weak gravitational lensing one can expect that weak lensing spectrum may involve the effect of the Dark Matter. Such expectation is indeed the case and it has been studied in [5–10].
II. INTRODUCTION OF UNDERLYING THEORIES
1. Particle Physics Approach
As far as the Dark Matter and the Dark Energy is con- cerned there is a consensus in the community. Whatever
948 New Physics: Sae Mulli, Vol. 66, No. 8, August 2016
their nature is, one thing is obvious and that is, it is non-baryonic.
To be more specific, they are not quark composites.
That is, their nature is not governed by standard model for strong interaction, namely QCD
Therefore any successful model theory for Dark Matter and Dark Energy has to depart from Weinberg-Glashow- Salam standard model.
2. Field Theory Approach
In terms of the Lagrangian for the underlying theory of the Dark Matter and Dark Energy, there is another consensus in the community.
That is, the Lagrangian for any successful model the- ory of the Dark Matter and the Dark Energy should have either non-canonical form of potential term, which is coined, “quintessence” model or non-canonical form of kinetic term, which is coined, “k-essence” model.
Canonical form of the action(Lagrangian) in a quan- tum field theory
S =
∫ d4x√
gL
=
∫ d4x√
g[−1
2gµν∇µϕ∇νϕ− {−1
2m2ϕ2+ λ 4!ϕ4}]
To summarize, therefore, in the canonical form of the action the kinetic(energy)term is given by the quadratic term of the derivative of the field and the poten- tial(energy) term is given by the (renormalizable) power law in the field. Obviously the first term is the kinetic term whereas the second term is the the potential term.
1) Quintessence Model
In this approach, the potential term in the Lagrangian should be given by a non-canonical form, that is, the potential terms usually is given by power series in the field but for the Quintessence model it is given by a highly non linear term for example, a highly non-linear term in Dark Matter and Dark Energy field.
<potential term of the action>→ non-canonical V =
∫
d4x√g[+eαϕ2] (e.g., scalar soliton field)
2) k-essence Model
In this approach, the kinetic term in the Lagrangian should be given by a non-canonical form, that is, the kinetic term is usually given by the quadratic terms in the field derivative but for the k-essence model it is a highly non-linear term in the derivative of Dark Matter and Dark Energy field.
<kinetic term of the action>→ non-canonical K =
∫ d4x√
g[−gµν∇µΦ∇νΦ
Φ ]
(e.g. Brans-Dicke theory of gravity [5])
III. CONCLUDING REMARKS
For the Dark Matter, despite its overwhelming mys- tery, there is one obvious consensus in the community:
That is, as long as one maintains either the standard model for gravity, namely, Einstein’s general theory of relativity, or the standard model for particle physics, namely, Weinberg-Glashow-Salam standard model, or both, one never accomplishes satisfying understanding of the phenomena associated with it. In the present work, therefore, we employed the strategy where alternative theories of particle physics have been introduced.
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