Inhomogeneity of dark matter and luminous objects induced by open cosmic string

Vistas in Astronomy, Vol. 37, pp. 515-518, 1993 Printed in Great Britain. All rights reserved.

OO83-6656/93 $24.OO © 1993 P~gamon PtcffisLtd

INHOMOGENEIq OF DARK MA'ITER AND LUMINOUS OBJECTS INDUCED BY OPEN COSMIC STRING* Tetsuya Hara, t Petri M~'a6nen~ and Shigeru M i y o s h i t tDepartment of Physics, Kyoto Sangyo University, Kyoto 603, Japan :~Department of Astrophysics, University of Oxford, Oxford, U.K. and Department of Theoretical Physics, Oulu University, Ouh, Finland

Cosmic string model is one of the most viable theory for the formation of galaxies and large scale structure of the universe (Vilenkin 1985). Here, we investigate the inhomogenity of dark matter and luminous objects induced by open cosmic string (Stebbins et al. 1987: Hara and Miyoshi 1987: Rees 1986). To treat such problem realistically, we have to calculate the relativistic motions of cosmic strings (Albrecht and Turok 1989; Bouchet and Bennett 1990) and the induced velocity field of dark matter by such cosmic strings within and over the horizon (Vachaspati and Vilenkin 1991). But it seems to have too much parameters to do so, then we have made some simple assumptions, such as the simple open cosmic' string model where one open cosmic string pass through the horizon at each stage and Newton approximation that Newton gravity could be applied as far as it is considered within a horizon. We do not consider the effect of loop cosmic string. Under such approximation for open cosmic string model, we investigate the characteristic features of the inhomogenity of dark matter and luminous objects. At first, we adopt the fiat Friedmann universe (f~ = 1) with cold dark matter for simplicity and investigate the motion of cold dark matter from the radiation dominant to matter dominant stages. We assume that the cosmic string passes through the horizon scale at redshift zi simultaneously and the effects of open cosmic string could be treated as one dimensional motion of particles, representing the dark matter, to the plane swept by open cosmic string. We have calculated the deviation length ~x(z i, z) of particles which is the deviated length at z from the homogeneous expansion due to the wake created at zi by open cosmic string (Stebbins et al. 1987; Hara and Miyoshi 1987). Next we consider the ratio R(zi, z) of this deviation length ~ x(zi, z) to a half of the horizon length l(zi, z) at z which is the horizon at zi and elongated due to expansion till the redshift z. Here we assume that open cosmic string pass through about the center *) Here only the abstract is described, see the detailes in the papper (Hara et al. 1992)

516

T. Hara et al.

of the horizon region, so R(zi, z) is expressed as R(zi, z)= ~x(zi, z)/(/(zi, z)/2). This ratio is almost the same value for the vast range of zi, increases with time and become almost unity at around 1+z=30(G/~/~)43.10 -e) for 1-bzi~1024 (corresponding to the comoving horizon size 10-2°Mpc), where/~, and p are the line density, the velocity of cosmic string and ), = (1 -/~2)- Ir2. If we define the critical size/e(z) as the size where the value R becomes unity at 1 + z, the size/©(z) increases almost ~ 1020 order during the stage from 1 + z= 30(G/,/~),/3.10s) till the p r e s e n t as shown in F i g u r e 1. At 1 + z - 8 ( G / ~ y / 3 . 1 0 -e) a n d 1+z-~l(Gp/~),/3.10-6), the size l(z) are about ~10-4Mpc and ~4Mpc in comoving scale, respectively. The inhomogenity of dark matter increase rapidly during this stage. The meaning of R is that fraction R of dark matter within the horizon /(zi, z) contracts into the wake created by the cosmic string at zi and inhomogenity within this horizon scale is very large if R becomes of order of unity. The situation of R = 1 also means that the inhomogenity of the scale smaller than/¢(z) is almost erased at stage 1 + z, because the region of dark matter smaller than le(z) are contracting or clustering into the wake of size le(z) at around z. After R(zi, z) becomes unity, as almost all the dark matter within the region l(z i, z) has accumulated to the wake, the dark matter has not fallen into the wake anymore. We designate such wake as completed wake and size of it as /c(z). In later, the completed wake will be accumulated to the other larger wake. The thickness ~ h of the wake is generally A h - 0 . 1 5 × le(z), so the number of dark matter fragments within the completed wake is of the order one ( or ~4), if the wake is considered to be unstable for the wavelength of ~ A h (Narita et al. 1988). It is probable that the distribution and clustering of dark matter fragments at 1 + z-- 1~4 is related to the Lyman r~clouds which is shown in Figure 2. We have calculated one dimensional contraction of dark matter numerically and estimated the thickness of the wake which indicates the mass scale of the gravitational inhomogenity within the wake. Generally the density inhomogenity within the wake is expected because the inhomogeneous dark matter is falling into the wake as discussed above and the disk is unstable for the fragmentation. The mass scale of the inhomogenity (or fragments) within the wake is the key to understand the formation of luminous objects. Then, considering the simple thermal process for baryonic matter, we derive the J e a n s mass in each stage which is the next key to derive the inhomogeneous distribution of luminous objects. Because the dark matter is the dominant component of the universe, baryon gas cloud could only contract within the well of dark matter potential. For such contraction of baryon gas cloud, the mass scale of the inhomogenity of the dark matter should be greater than the Jeans mass of baryon gas cloud. Using this constraint, we derived the condition in which wake the luminous objects are formed. The mass scale of the fragments in the wake is Mr--- 7pbcdAh(rrAh)Z ~--10 l~(Ax/4.5Mpc)3hso - XM,~

Dark Matter and Luminous Objects

101a(1 + z)-S(Gyfl),/3.10-S)Shso- 1M@ and the Jeans mass is Mj ~ (5 ~kT/(GmHp)3/~P- I/2

517

( for the wake of 1 + zi = 104),

which are shown as a function of the epoch 1 +z in Figure3. The formation of luminous objects are satisfied as the condition M r > Mj ( or Mf > 10xMw ). The prominent wakes of dark matter are formed after the trace of cosmic string which has passed around 1 + z ~ 104 when the comoving horizon size is ~40Mpc. In such wakes, the luminous objects of ~I06M@ (First objects or globular clusters ) and ~I01°~11M@ (sub-galaxies and galaxies) are formed at l + z ~ 1 0 ~ and I + z = 8 ~ f l , respectively, therefore the large scale structure of the luminous objects could be explained. The main subject of this work is to point out the inhomogenity of dark matter and luminous objects induced by open cosmic string. It is expected that there are many types of wakes of which surface density and size are different. On such inhomogenity, baryon matter falls in and some of the wakes could be the seeds for luminous objects and others are not. After the stage 1 + z ~ 30(G/~/~)43,10-6), the inhomogenity of dark matter begins to cluster and inhomogeneous objects merge violently which we call "Violent clustering stage" and the large scale inhomogenity erases the small scale inhomogenity which may occur even in the prominent wake. It is the characteristic feature pointed by so called " bottom up " scenario discussed in the last few decades (Kaiser et al. 1991 ). These phenomena could be observed by the clustering and merging of the Lyman alpha clouds as shown in Figure 2. On the other hand, luminous objects are formed within the wake where baryons are accumulated. It is the characteristic feature pointed out by so called" pancake " o r " top down " scenario (Zeldovich et al. 1982). So the both features of the formation theory could be understood under open cosmic string model. This model presents the unified view of the both theory" top down "and "bottom up ". Although we have used an idealized simple model of open cosmic string and there are many problems left in the model, it seems to us that such simple model could explain some of the characteristic features of the observations; i) Formation of the large-scale structure of the universe, ii) Formation of sub galaxies (faint blue galaxies?) and galaxies, iii) Formation of globular clusters, iv) Gravitational potential for Lyman alpha clouds, v) The mass and size of the Local Group of galaxies, vi) Formation of dwarf galaxies, vii) Formation of clusters of galaxies (Hara and Miyoshi 1991, preprint) viii) Large-scale peculiar velocities of galaxies (Hara, MiihSnen and Miyoshi 1992, preprint))

518

T. Hara et al. I,

•

The above vi), vii) and viii) are not treated in this paper. From the comparison with the observations, the parameter G/~/~),1 ~ 3.10- s is recommendable and the number of the open cosmic string per horizon is expected 1 ~ 3 . I"ls ,,-|*

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

_--

.

.

.

_A

Fi 8. I

/

.

I!

104 /

.

*-t.L,

A

(l+Z) -~

lois

. °..o''"

tO )

lo xs /

~/

|0 |

lo s

4.~ ,~

*

i

i

ao'I

I

i

t

i

I

1 10-4

Fig. 2

10")

~O'S

I+Z

LO "1

(I+Z)- I Fig. 3

Fig. 1 lc(z)versus (l+zi)-l The horizon sclaes lc(z)where R becomes 0.5 and unity at z are plotted against the 1 +z by dashed and solid line, respectively. The increase lc(z)means that the clustering has occurred violently. Fig. 2. dN/dz ofLyman a clouds versus l+z. The expected value ofdN/dz are shown for the case R=0.5 and R = I by solid and long dashed curves., respectively. The observed values are also added by triangles with Iv errors with vertical bars. It could be explained that the decrease of the Lyman a clouds in the universe is due to the merging of the dark matter. Fig. 3 Mass versus (1 +z) -! The fragmented mass ofdark matter within the wake of 1 +zi= 10 4, l0 s and 10s are plotted by sold, dashed and dotted lines, respecrively. The Jeans mass of baryonic matter under appropriate assumptions are also shown by dotted line. Bouchet, F., and Bennett, D. 1990, Phys. Rev., D4I, 720 Hara, T., and Miyoshi, S. 1987, Prog. Theor. Phys., 77, 1152 Kaiser, N.,et al. 1991, M. N. R. A. S., 252, 1 Narita, S.,et al. 1988, Prog. Theor. Phys. Suppl. 96, 69 Stebbins, A.,et al. 1987, Ap. J., 322, 1 Vachaspati, T. and Vilenkin, A. 1991,Phys. Rev. Letters, 67, 1057 Vilenkin, A. 1985, Phys. Rep., 121,263 Zeldovich, Ya. B., Einasto, J. and Shandarin, S. F. 1982, Nature, 300,407