Neutrinos And Large Scale Structures

Dhungel, PR; Sharma, SK; Khanal, U.

doi:10.3126/sw.v6i6.2624

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“…In the majority of these works, Virial theorems / equations and their moments of various orders have been used. In this paper, Jeans masses have been calculated using Virial moments of these masses and are compared with those calculated in previous works 4 .…”

Section: Introductionmentioning

confidence: 99%

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Virial Moments of Large-Scale Neutrino Structures

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Abstract:In the course of studying the role of massive neutrinos and other particles in the large scale structures formation in the universe, Virial moments of the neutrino structures have been calculated. The Jeans masses calculated this way have been compared with the ones calculated earlier in our previous paper. VIRIAL THEOREM AND MOMENTS:In a system of N particles, gravitational forces tend to pull the system together and the stellar velocities tend to make it fly apart. It is possible to relate kinetic and potential energy of a system through the change of its moment of inertia. In a steady-state system, these tendencies are balanced, which is expressed quantitatively through the Virial Theorem. A system that is not in balance will tend to move towards its virialized state. The Scalar Virial Theorem tells us that the average kinetic and potential energy must be in balance. The tensor Virial Theorem tells us that the kinetic and potential energy must be in balance in each separate direction. The scalar Virial Theorem is useful for estimating global average properties, such as total mass, escape velocity and relaxation time, while the tensor Virial Theorem is useful for relating shapes of systems to their kinematics, e.g. the flatness of elliptical galaxies to their rotational speed.The Virial Equations of the various orders are, in fact, no more than the moments of the relevant hydrodynamical equations. The scalar Virial Equation for a system is given by VIRIAL MOMENTS OF JEANS MASS:As stated earlier, in the virial method, we take the moments of the equation of motion. These equations obviously involve the moments of the distribution of density, pressure, velocity, gravitational potential, etc. Here we are taking the spatial moments of various orders of Jeans mass given by eq. CONCLUSIONS:From the above analysis, it is seen that the large-scale structures of neutrinos of different mass and random velocity distribution can form at different neutrino temperatures, corresponding to different time. The earliest peak that occurs at x = 1.9 corresponds to the time when the neutrino temperature was 1220 K for the 0.2 eV neutrino. Similarly, the latest peak occurs at x = 9.58 corresponding to a temperature of 242 K. In between these two values, it is found that the Jeans mass peaks at a number of different x. Thus it can be interpreted to mean that a distribution of neutrino structures of different masses and of different ages should be in existence. Typical masses of these structures range from 6 x 10 19 to 4.5 x 10 20 solar mass . The distribution in size and age of such neutrino structures, and the effect of cold dark matter will be studied in future work. REFERENCES:

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Section: Introductionmentioning

confidence: 99%

“…where g is the number of spin degeneracy (six, for the three Integrating over y from 0 to ∞ gives the number density We had calculated the Jeans mass of neutrino structures by varying different parameters involved in it 4 . The Jeans mass, that is contained within Jeans radius (…”

Section: Introductionmentioning

confidence: 99%