Issue |
A&A
Volume 498, Number 2, May I 2009
|
|
---|---|---|
Page(s) | 357 - 359 | |
Section | Cosmology (including clusters of galaxies) | |
DOI | https://doi.org/10.1051/0004-6361/200810687 | |
Published online | 05 March 2009 |
Cosmic dark turbulence
(Research Note)
A. Nakamichi1 - M. Morikawa2
1 - Gunma Astronomical Observatory, 6860-86 Nakayama, Takayama Agatsuma, Gunma
377-0702, Japan
2 -
Department of Physics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo, Tokyo
112-8610, Japan
Received 27 July 2008 / Accepted 28 January 2009
Abstract
We aim for a consistent understanding of various scaling relations reported
for self-gravitating systems, based on the proposal that the collisionless
dark matter fluid turns into a turbulent state, i.e. dark turbulence, after
crossing the caustic surface in the non-linear stage. Kolmogorov scaling
laws with a constant energy flow per mass of
are suggested
from observations.
Key words: cosmology: theory - gravitation - turbulence - cosmology: dark matter - cosmology: observations - hydrodynamics
1 Introduction
We briefly report a possible origin of angular momentum as well as various scaling relations in self-gravitating systems (SGS) in the universe.
A typical mechanism of angular momentum acquisition for galaxies is tidal
torquing (see for example Schaefer 2008), in which a system of mass Macquires most of its angular momentum
(Sugerman et al. 2000) through tidal interaction before the turnaround time
.
On the other hand, we explore the fully nonlinear stage after the
shell-crossing time, just after
.
Although the amount of
angular momentum is mostly acquired before
,
a strongly
interacting nonlinear period after that should remove the previous
correlations. We assume that the collisionless dark matter (DM)
fluid turns into a turbulent state, i.e. cosmic dark turbulence (CDT), after
the shell-crossing time when multi-streaming initiates (Buchert 1999). The
shell crossing and the initiation of turbulence are actually redshift
dependent, which is quantitatively described in chapter 3 in Yoshisato
et al. (2003). The scale range of the turbulent region, identified as the scale
where shell crossing has already taken place at a given redshift, extends in
time and is about 10 Mpc and smaller at present.
Universal scaling relations associated with this turbulence may be relevant to explain several scaling relations such as the scaling relations in the velocity dispersion (Sanders & McGaugh 2002), in M/L ratio (Bahcall et al. 2000), in the power spectrum of density fluctuations (Sanchez & Cole 2007), in cosmic magnetic fields, as well as in angular momentum. The purpose of this study is to consider all of these scaling relations from a simple principle.
2 Fluid description for self-gravitating systems and the Kolmogorov law
A set of Jeans equations for SGS and the Poisson equation becomes
where


Where















We assume the energy flow is a constant d
,
which is essential to characterize turbulence. We then
have the scaling
in the inertial
regime, i.e. the viscosity term does not dominate as in the collisionless
stage under study. This scaling suggests that the time should scale as
for consistency. Since d
must
be a constant
,
we have
and
.
Then,
since
,
we
have
,
where f is a function of only the direction
.
Thus
represents an average velocity difference or the velocity dispersion
at the separation scale
.
Thus we obtain the relation, originally derived by Kolmogorov (1941),
which claims that the velocity dispersion increases with scale. A possible numerical factor of


or equivalently, the mass density at the scale r as



It should be emphasized that the viscosity term does not dominate in the present collisionless DM and even in this collisionless case, the virial relation holds as a consequence of dynamical relaxation (Iguchi et al. 2006).
3 Observational tests
3.1 Mass-angular momentum relation
We examine the angular momentum-mass relation, which has been the starting
point of the present study. By utilizing the rigid body approximation,
virial relation, and Eq. (4), we have the expression
with



3.2 The scale dependent magnetic field
Now we consider a possible relation between CDT and the large scale
distribution of cosmic magnetic fields. The magnetic field
and the
vorticity
actually satisfy very similar
equations of motion and a rough argument based on this fact is found in
Landau & Lifshits (1984), Sect. 74. Generation of the cosmic magnetic
field is studied in Gnedin et al. (2000), and further development of the
magnetic field is discussed in Schekochihin et al. (2005), for example.
Magnetic fields at higher redshift are discussed in Kronberg (2005) and
Kronberg et al. (2007).
However, a complete model and theory which systematically describe the
generation and development of the cosmic magnetic field on all scales have
not yet been established. Therefore we simply assume here the following
conditions as a tentative starting point for discussions. (a) The dynamo
mechanism is a general process to convert rotational energy into magnetic
fields in various cosmic scales with a constant conversion rate .
(b) Baryons should faithfully follow the motion of DM, at least at later
stages of the universe. The assumption (a) should be considered as a working
hypothesis at present motivated from the similarity in the equations for
and
.
The assumption (b) may sound strange if one
imagines a simple straight fall of baryons into a static potential well
formed by DM. However, since the DM is moving according to Eq. (3), we cannot suppose a static potential well. Furthermore, in the case of
galaxies, there is an empirical relation that DM has the same specific
angular momentum as baryons,which is widely supported and adopted in the
study of angular momentum of galaxies (Tonini & Salucci 2006). These facts
may support the idea that the baryons are dynamically coupled to turbulent
motions of DM.
Adopting the above assumptions, we consider that the portion of
of
the kinetic energy at scale r,
is supposed to turn
into the energy density of the magnetic field
.
This yields the relation
This result, expressed as the solid line in Fig. 2, is compared with observations (Vallee 1990, 1995). Guided by these data, we have chosen the value

![]() |
Figure 1:
The relation between J/M2 and M for various objects; simple
points are from Muradian et al. (1999), and points with error bars are from
Brosche (1986); Brosche et al. (1989). The solid line represents our relation
Eq. (5) with
|
Open with DEXTER |
4 Summary
![]() |
Figure 2:
Cosmic magnetic fields in various scales. The deta are from Vallee
(1990), marked by stars; Vallee (1995), marked by squares and diamonds. The
solid line represents Eq. (6) with parameter
|
Open with DEXTER |

References
- Bahcall, N. A., Cen, R., Dav, R., Ostriker, J. P., & Yu, Q. 2000, ApJ, 541, 1 [NASA ADS] [CrossRef] (In the text)
- Brosche, P. 1986, Comments Asrophys., 11-5, 213 [NASA ADS] (In the text)
- Brosche, P., & Tassie, L. J. 1989, A&A, 219, 13 [NASA ADS] (In the text)
- Buchert, T. 1999 [arXiv:astro-ph/9901002v2] (In the text)
- Gnedin, N. Y., Ferrara, A., & Zweibel, E. G. 2000, ApJ, 539, 505 [NASA ADS] [CrossRef] (In the text)
- Iguchi, O., Sota, Y., Nakamichi, A., & Morikawa, M. 2006, Phys. Rev. E, 73, 046112 [NASA ADS] [CrossRef] (In the text)
- Kolmogorov, A. N. 1941, Dokl. Akad. Nauk SSSR, 30, 9 (In the text)
- Kronberg, P. P. 2005, Magnetic Fields in Galaxy Systems, Clusters and Beyond, Lect. Notes Phys., 664, 9 (In the text)
- Kronberg, P. P., Bernet, M. L., Miniati, et al. 2007, ApJ, in press [arXiv:0712.0435v1] (In the text)
- Landau, L. D., Lifshits, E. M., & Pitaevskii, L. P. 1984, Electrodynamics of Continuous Media Course of Theoretical Physics, 2nd edn. (Oxford: Butterworth-Heinemann) (In the text)
- Muradian, R., Carneiro, S., & Marques, R. 1999, Apeiron, 6, 186 (In the text)
- Nakamichi, A., & Morikawa, M. [arXiv:0805.0172]
- Sanchez, A. G., & Cole, S. 2007 [arXiv:0708.1517v2] (In the text)
- Sanders, R. H., & McGaugh, S. S. 2002, ARA&A, 40, 263 [NASA ADS] [CrossRef] (In the text)
- Schaefer, B. M. 2008 [arXiv:0808.0203v1] (In the text)
- Schekochihin, A. A., Cowley, S. C., Kulsrud, R. M., Hammett, G. W., & Sharma, P. 2005, ApJ, 629, 139 [NASA ADS] [CrossRef] (In the text)
- Sugerman, B., Summers, F. J., & Kamionkowski, M. 2000, MNRAS, 311, 762 [NASA ADS] [CrossRef] (In the text)
- Tonini, C., & Salucci, P. 2006, ApJ, 638, L13 [NASA ADS] [CrossRef] (In the text)
- Vallee, J. P. 1990, ApJ 360, 1 (In the text)
- Vallee, J. P. 1995, Ap&SS, 234, 1 [NASA ADS] [CrossRef] (In the text)
- Yoshisato, A., Morikawa, M., & Mouri, H. 2003, MNRAS, 343, 1038 [NASA ADS] [CrossRef] (In the text)
All Figures
![]() |
Figure 1:
The relation between J/M2 and M for various objects; simple
points are from Muradian et al. (1999), and points with error bars are from
Brosche (1986); Brosche et al. (1989). The solid line represents our relation
Eq. (5) with
|
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Cosmic magnetic fields in various scales. The deta are from Vallee
(1990), marked by stars; Vallee (1995), marked by squares and diamonds. The
solid line represents Eq. (6) with parameter
|
Open with DEXTER | |
In the text |
Copyright ESO 2009
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