S.P.Spirydovich Abstract Estimation of the Cosmic Microwave Background Radiation The author discusses some aspects of experiment, which was built to measure temperature of cosmic microwave background (CMB) to verify result, which confirms predictions, based on Big Bang theory. The technique to measure background signal with presence of other noisy foregrounds was studied. Calculations for estimated data and two main graphs are presented and range of CMB temperature is identified. 1. Introduction One important part in our understanding of modern cosmology is the information gathered from measurements of the CMB radiation and based on Big Bang theory knowledge of density fluctuations in the early Universe, which was very hot due to the interchange of energy between matter and radiation. Then at the age of 300000 years (it means after Big Bang) the universe was cooled to a temperature of 4000 K. Now a blackbody temperature of Universe is 2.7 K and at this temperature there is a peak at the Planck spectrum at frequencies (~1-1000 GHz). The first to detect this radiation were A. A. Penzias and R. W. Wilson in 1965 [1]. In this paper our goal was to show one of the possible methods of the estimation of CMB with restrictions of ground-based lab. While analyzing CMB, the real problem was to distinguish features originating from the CMB from other sources of noise, due to atmosphere vapor, Galaxy, and stars as well as inner noise of equipment and those that originate from foregrounds. High sensitivity of experiment requires subtracting these foregrounds before we make any assumption of the source of radiation. To do this we use multi-temperature observations. It means we consider different sources of signal (atmosphere, stars, galaxy, ground or waveguide) to measure their power spectrum. Then we use approximation of blackbody nature of these sources to interpret their spectra as Planck spectra. In our case on the Earth we could not separate foregrounds of extraterrestrial sources, because there is no possibility to on the ground to recognize whether radiation is relic or it is from stars or galaxy. The experimental results of measurement of temperature of CMB [1] was expected to be 3.5 K which later was refined to be 2.7 K. In our experiment we have used radiometer with LNB converters to verify this results. 2. Apparatus The equipment to build a radiometer was chosen according to description of one in [3]. We have tried on one hand to verify the CMB temperature of 3.5K measured with output fluctuation of 1K in [1] for radiometer (fig.1), when gain variation is omitted. On
the other hand to change some parts of this radiometer to modern ones such as low noise blocks LNB (fig.2) in order to increase sensitivity of our experiment. The change of 3K in the output meter for a receiver in (fig. 1) was detected for intermediate frequency bandwidth of 10 7 cycles per second. An output response time was 1 second and with overall variations in the gain of.1 percent. It is important that the power of intermediate frequency amplifier is doubled if temperature of a resistor attached to a receiver increased by 300 K. (Initially resistor is at 300K). Output Antenna Modulating wheel Mixer Wideband amp. Second Detector Narrow amp. Oscillator D.C. amp Fugure 1. Block diagram to origial design of a Dick radiometer [3].
ANALYZER Horn TV- Receiver LNB 3-Way Splitter LNB Waveguide Liquid Nitrogen Cold Load Figure 2 The experimental system for measurement power spectrum of CMB.
In particular, instead of using modulating wheel (fig.1), which eliminates the gain variation noise, we used low noise block (LNB,, PMJ-LNB KU, 0.5 db, 650 MHz 1500 MHz range), which has noise in signal at 20K. Due to LNB there is a downshift of frequency of the incident radiation by about 10.7 GHz. After downshifting there is amplification of signal. The reason of downshifting is because 11 GHz signal travels with significant dissipation through coaxial cable, on the other hand 1 GHz signal travels well through the cable, that is why we use this frequency as an operational one. To provide 18 V D.C. bias we used a satellite receiver. For integration of the spectrum, so that to have value which is proportional, because of LNB downshift, to the detected signal power, we used spectrum analyzer (HP, model, E440713, 9KHz-26.5GHz range). Liquid helium temperature was used to average noise of 2500 K in Dicke radiometer (fig.1). In our case noise from LNB is at about 20K. To subtract noise it is necessary to compare signal from LNB with signal obtained from the source with known temperature. Such source of signal in our case was cold load (fig 2.) New apparatus had 2 new parts which were essential: Horn with LNB and wave guide with reference terminator (f ε (10,1.58*10 10 ) Hz). The wave guide with load served as the sample of black body radiation if load works properly it means absorbs almost all incident wave guide radiation. As reference pattern of radiation wave guide was connected with Horn and LNB. In this case we had anisotropy antenna- horn. Horn (antenna) and wave guide in the 11GHz frequency region has the highest sensitivity. 3. Analysis CMB frequency has approximate value of 11GHz, because first of all higher frequencies correspond to existence of atmospheric absorption due to water vapor (fig 5.). It means that for frequencies higher than 11GHz significant part of CMB would be absorbed in atmosphere and swamped by terrestrial sources, which finally leads to not reaching the Earth close to which the experiment was being performed. Secondly, at lower frequencies there is appreciable galactic and extragalactic emission.
For our given frequency 11GHz according to [1] radiation averaged over all directions should not exceed 3x10-3 K due to the Galaxy as well as the extragalactic sources and 10-9 K due to stars. The multi-temperature technique has been applied to calculate temperature of CMB (T cmb or T sky ). We use subscript index (sky) since the signal has not subtracted from different sources of radiation. Power spectrum of sky was measured at different orientations to observe anisotropy, spectrum of blackbody radiation of ground and spectrum of partly cooled waveguide in nitrogen (T=77 K). Effective temperature of wavegiude T guide =195K can be assumed if only a fifth (approximately 20cm) of the length of waveguide had been cooled at 77K. Other four fifths of the length of waveguide were kept at room temperature T room =300K. The fact that there is significant change of temperature in the region of waveguide close to nitrogen was neglected. It was also assumed that spectrum for waveguide was the same as if T guide had a constant temperature along the waveguide. To calculate T sky we integrated 3 spectra S sky -(fig.3), S warm and S cold -(fig.4) over the LNB operation frequency range and used T ground and T guide. According to technical characteristics LNB operation frequency range was from.95ghz to 1.5 GHz. There was not detected any appreciable signal at 11GHz, because there was a shift to LNB operation frequency region. The ratios of power spectra gave S cold =0.79*S warm, S sky =0.92*S warm.. This yields a temperature for the sky of 325 K.. Using Roll and Wilkinson s assumption of linearity we have a similar result. If a 200 K shift corresponded to an 8% decrease, a 21% decrease would correspond to a temperature shift of 525 K. This would indicate a temperature of 225 K, which is not correct. An expected temperature for the sky is around 7± 1 K, a 3.5± 1 K contribution from the atmosphere and a 2.7±.5 K contribution from the background radiation [1]. Finally if the effective temperature of the load was to be assumed 195 K under the conditions mentioned above, the calculated temperature of the sky would be approximately 10 K. Particular description of calculation method can be found in the Appendix. 4. Conclusion The specific equipment was assembled and measurement of CMB was performed. The CMB temperature at 11 GHz was estimated to be not higher than 10K, which close to other experimental data obtained with more precise tools. Temperature of cold waveguide can be measured more precisely to avoid using any model of temperature distribution along waveguide. Results from additional experiments could solve the problem of effective temperature measurement of cold waveguide. Nevertheless effective temperature of waveguide T guide =195 K showed result of Tsky=10K, that pointed out the good assumption was made pretty good.
Two main results could be underlined as following. First of all we measured signal with parameters (temperature and frequency), which agree with predictions of Big Bang theory. Secondly further developments of the system together with advanced methods of noise measurement could show more precise value for CMB temperature. Other research projects, related with distinguishing signal from different backgrounds, such as air or space navigation, could become real world applications. Acknowledgments I would like to thank Professor S. Durbin, A. Soliman, and S. Nowling for their discussions and patience. References 1 A. A. Penzias and R. W. Wilson, Astrophys. J. 142, 419 (1965). 2 R. H. Dicke, Rev. Sci. Instr. 17, 268 (1946). 3. P. G. Roll and D. T. Wilkinson, Annls of Phys. 44, 289 (1967). Appendix 4h u( f) 4 2 c f = fkt ( bar πhbar e 1) - Plank s formula for black body radiation density. Then we define f IT = df *( u( f, T) )= const * T f b a Frequencies fa and fb are the corresponding frequencies over which the LNB is supposed to be sensitive and they are much smaller than frequency f the spectrum peak. Since we observe only LNB downshifted frequencies (fa and fb), then I300 is approximately equal to that for the ground (assuming blackbody radiation from the ground). Isky is the integral corresponding to the sky. Then I195 is approximately equal to that for the cold load. Now the area under our graphs is A, B, and C for ground, sky, and cold load respectively.
The area under our graphs (from fa to fb) should be proportional to that of u(f,t) provided that we shift our graphs up or down correctly. Assuming that either the machine or we have shifted our graphs to a uniform offset I 300 b [ A ( f f )] a = κ ζ b [ B ( f f )] a I = κ ζ? I = b 195 κ C ζ f f Therefore: a [ ( )] [ ] B A I A C I I I? = ( ) [ ] After integration we have 300 195 300 [ B A] [ A C] = 3. 091 Then we calculated I sky correspond I 10 or T sky =10K.
ROOF (single shot) -35 0 2000000000 4000000000 6000000000 8000000000 1E+10 1.2E+10-40 -45-50 I (arb. units) -55-60 Sky Ground -65-70 -75-80 Freq (Hz) Figure 3. Power spectra for sky and ground.
Difference between Cold Guide and Warm 10 0-10 0 2000000000 4000000000 6000000000 8000000000 1000000000 1200000000 0 0 Amp (Ref. level 1mV) -20-30 -40-50 Cold Guid Warm LNB Differenc -60-70 -80 freq Figure 4. Difference in amplitudes for power spectra for cold and warm reference load.
Figure 5. Contribution the spectra of atmospheric vapor and galaxy at wavelength of 1-100 cm.