Spectral-Spatial Fluctuations (SSF) of CMBR

V.K. Dubrovich

¹ Special Astrophysical Observatory, Nizhnij Arkhyz, K.-Ch.R., 357147, Russia (dubr@sao.ru)
 

Abstract

The luminescence process for proto-objects moving with a peculiar velocity at high redshift is considered. It is shown that some primordial molecules could produce low-frequency photons (which correspond to the rotational lines) by decaying high-frequency rovibration photons from the CMBR. Due to the rather different numbers of these photons, a huge enhancement (relative to the pure reflection mechanism) of the emission line intensity from the proto-objects could occur at the appropriate wavelengths.

Key words: Radiation  cosmology: theory  molecular processes

1. Introduction

So, now we can try to investigate the next level of observational effects which are provided by proto-objects in the post recombination epoch. One of the most probable classes of such effects will be considered here. They are the so-called SSF - Spectral Spatial Fluctuations (Dubrovich, 1994). Actually, they are the proto-objects at high redshift - 10  z  300, which must contain some amount of molecules and which have a peculiar velocity  relative to the CMBR. There are necessary and sufficient conditions for the SSF to be produced. The theory of this process was discussed by Dubrovich (1977, 1983, 1994) and by Maoli et al. (1994). Some experiments were described by De Bernardis (1992) and some plans by Signore et al.(1993).

All this work is based on the simplest mechanism of the SSF formation - pure reflection of the CMBR photons due to the opacity of a proto-object in narrow spectral lines and the Doppler shift in frequency due to its peculiar velocity. In this paper another mechanism will be considered.
 

2. Luminescence of primordial molecules

Let us consider this process in detail. Taking into account only those chemical elements (the most abundant) which are predicted by the pure Big Bang model - H, He, D, ³ He, Li, and their ions, we can list the most probable molecules in the primordial matter at z = 100-200: H₂, H , HD, HD , HeH , LiH, LiH , H₂ D , ³ He⁴ He . All other molecules should be considered more critically, because their appearance is caused by some non-standard circumstances: non-equilibrium nuclear synthesis at the early times (z= ), or star formation at z = 200-300, etc. But, as was mentioned before, the pure model of the Universe is the most probable one. So, we won`t consider any other molecules here.

For obtaining the greatest interaction between molecules and photons, two values are important - the cross-section for scattering and the concentration (or relative abundance) of this molecule. The first parameter depends on the specific quantum structure of the molecule - its symmetry and charge. The second one depends on the abundance of the chemical elements of which it is composed and on the rate of the appropriate chemical reactions. According to these constraints, we should take into consideration only those molecules which have a large enough dipole moment and relatively high abundance. These are: HD , HeH , LiH, H₂ D , ³ He⁴ He . The molecules H₂ and H  have no dipole moment, while HD has a rather small dipole moment and the abundance of D is not high enough. LiH  has a very low potential of dissociation and so its abundance in a hot Universe is very small. So, we can expect only a small number of molecules to be visible from the early Universe: HD , HeH , LiH, H₂ D , ³ He⁴ He .
 
 

3. Consequences of CMBR fluctuations

here  is the component of the peculiar velocity along the line of sight and c is the speed of light. It should be pointed out, that if this fluctuation is caused by the interaction with a resonant system, it must occur only at the corresponding wavelength and, what is very important, there should be no influences from the one resonance to any other. In our case it means that this effect could be at the wavelength corresponding to the rotational and the rovibration transitions, but the amplitudes of the  from the separate transitions are fully independent. It is one of the fundamental properties of pure reflection.

On the contrary, the luminescence process causes the appearance of some photons at one wavelength due to the absorption of the appropriate photons at another wavelength. This new property of the process of interaction of matter and radiation leads us to new possibilities for SSF formation.

According to the previous investigations by Dubrovich (1977) and Maoli et al. (1994), and our new considerations, we obtain:

where  is the redshift of molecule's recombination by Saha,  is derived from this equation at , and .. The value of the optical depth (for rotovibrational transitions here) we will estimate on the base of the expressions obtained by Dubrovich (1994) for pure rotational transitions. The accuracy of such an estimation maybe not more than one order of magnitude.

where ,  are the total and the baryonic average densities of the matter relative to the critical one,  is the abundance of the molecule relative to the atomic hydrogen, z is the redshift of the proto-object, H is the Hubble constant, normalized to  = 75km/s/Mpc,  is the specific molecule constant, d is the dipole moment of the molecule,  and  are temperature of CMBR and the critical density at z = 0.
 
 

In Table 1 we present the main information about the most probable and highly interacting primordial molecules and some estimate of the fundamental parameters that could be measured.

here:  is the dissociation potential of the molecule,  is the wavelength of the first rotational transition ( =c/2 ),  is the wavelength of the rovibration transition (),  refers to the highest wavelength where this molecule could now be seen,  is the limit to the molecule abundance which could be reached if we assume that  /c =  and that the observational limit which can be achieved is ,  is the lower limit which could be placed on the peculiar velocity if we assume  1 and an observational limit of the . The triatomic molecule H₂ D  is more complicated than the other molecules in Table 1

Now, we can write the expression for  in a more simple form:

In order to search for these molecules, the most auspicious wavelength regions (for the first rotational lines) can be found in Fig.2. The expected values of  are shown as a function of wavelength for each molecule and correspond to the value of . The red wings of these curves are actually due to the rate of recombination of each molecule, assuming Saha recombination rates. The blue wings are described by expression (8). The second rotational line of each molecule has a factor of two higher frequency and a value of K which is four times lower than the first one.

Fig. 2. The value of  for several molecules

Table 1.

Here are some comments to Table 1.

LiH: This is a very important molecule, because it consists of primordial Li. Its abundance is a good test for the epoch of nuclear synthesis in the early Universe. Its large dipole moment and relatively low frequency of the rotational and rovibration transitions lead to the high value of K. But unfortunately, its small abundance and some difficulties with the chemical processes of forming this molecule lead to a non-optimistic prediction for . Even so, this value of , eqn. 16 and the peak value of  from Fig. 2 lead to predicted values as high as about   =  for   = 0.1.

HD : This is also an important molecule, due to the presence of primordial deuterium, D. The abundance of D is about 5 orders of magnitude larger, than that of Li. But HD  has a dipole moment about 10 times less than LiH and a cross-section which is 100 times smaller. Another small factor is the abundance of H  at redshift z = 200, which might be about  relative to that of neutral hydrogen. Due to the relatively high frequency of the rotational and rovibration transitions, the resulting value of K is not very large. But, if high sensitivity were reached, this molecule might be seen.

HeH : This molecule does not have any low abundance constituents. There are only two small factors which lead to a low abundance: a high rate coefficient for destruction (by electron recombination and collisions with the neutral atoms of hydrogen) compared with the rate coefficient of formation, and a small abundance of H  at high redshift. But it might be the most likely molecule to be searched for.

H₂ D : This is the simplest triatomic molecule with a high dipole moment. It contains primordial deuterium. Due to the presence in its spectrum of very low frequency transitions, the value of K can be very high. In Table 1 the value K₀ corresponds to . It is very important that the redshift of the recombination H₂ D  be relatively high.

The expected abundances of these molecules in the early Universe are discussed by many authors (Lepp and Shull,1984, Puy et al, 1993, Palla et al, 1995, Maoli et al, 1996, Stancil et al, 1996a) and more recent results by Stancil et al.(1996b).

In order to observe SSF due to all these molecules, let us give some simple estimates of their main parameters. These are diffuse, extended objects, which will have only the narrow emission lines with the low brightness temperature in these lines. The width  of these lines depends on the object's size (linear - L or angular - ) (Dubrovich, 1982):

Here M is the mass of the proto-object,  is the mass of the Sun. At the redshift z = 100, if  then a protogalaxy with the mass  has

A proto-object with the mass of an ordinary cluster of galaxies, , will have an angular size:

The value of the peculiar velocity at the redshift z might be:

These parameters would be the most probable for the standard model of the Universe.
 

4. Observational aspects

where  is a noise temperature . The IRAM observation (de Bernardis at al.,1993) has the  =1000 K. At  =13cm one can has  =100 K. Taking into account 100 times' less  here one could see that absolute value of  measured in both cases are equal. But the  which is predicted at  =13 cm is about three order of magnitude more than at  = 1.3 mm. There is another problem for observations at low frequency - it is that we need to have a full aperture radiotelescope with an appropriate angular resolution. For proto-objects with  size it must be about 600 m diameter. For this case  MHz and  from (24) is

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