Cosmic Microwave Background Radiation. Carl W. Akerlof April 7, 2013

Transcription

1 Cosmic Microwave Backgrond Radiation Carl W. Akerlof April 7, 013 Notes: Dry ice sblimation temperatre: Isopropyl alcohol freezing point: LNA operating voltage: K K 18.0 v he terrestrial coordinates for the Block M on the Diag are 4º N, 83º 44.9 W, 80 m altitde. he core of this experiment is a series of measrements of the black body emission of objects at varios temperatres at a freqency of 1 GHz. he Planck spectral distribtion fnction is given by: di df c e 3 h 1 h / k 1 Setting h k, a freqency of 1 GHz is eqivalent to a temperatre of K. his is n small relative to the three temperatres that are important for this experiment,.75 K, LN K and room K. hs, the spectral distribtion can be approximated as an expansion in x h / k : CNBR di df k 1 c x x For the temperatres of interest in this experiment, the terms in x can be ignored and the spectral intensity is simply proportion to. he temperatres of the two thermal reference loads are estimated in two different ways. For the room temperatre load, the temperatre can be directly determined by the yellow lollipop thermometer. For the liqid nitrogen load, the temperatre is a smoothly varying fnction of the ambient atmospheric pressre: log P/ P e o where P o is one atmosphere in whatever nits that are sed to measre P.

2 he voltage otpt of the 1 GHz LNA pls diode detector is proportional to the sm of two terms, a characteristic amplifier noise temperatre, amp, and the black body thermal radiation,. hs, c amp With calibration measrements, ( 1, 1 ), at room temperatre and (, ) at the liqid nitrogen boiling point, amp has the following vale: amp It follows that for additional measrements of a receiver otpt voltage,, the corresponding temperatre is given by: Assming ncorrelated measrement errors of 1 and for load temperatres and receiver voltages, the error in measred temperatre can be compted by standard error proportion techniqes: he critical measrements for this experiment involve observations of the sky from the roof of Angell Hall. he alti-az mont is designed for increments of 5 in zenith angle and 10 in azimth. he azimth setting ring shold be placed so that one position is de soth, aligned appropriately with the longitdinal axis of the bilding. Yo will need to make 1 measrements of receiver otpt for zenith angles from 0 to 55, repeated for azimth angles taken on 30 intervals. Repeated calibration with the room temperatre and liqid nitrogen thermal reference loads is reqired to remove systematic drifts. o redce the data, take each set of 1 measrements at fixed zenith angle. A robst measre of average in this case is the median of the 1 vales. A sefl estimate of the error can be obtained from the interqartile difference (see statistics notes). In this particlar case, an estimate of the standard deviation can be obtained from:

3 where the sky temperatres, i have been ordered by increasing vale. hese shold be compared with the error analysis described above. A plot of the sky temperatre vs. secant zenith shold sggest a straight line that can be extrapolated to zero. he intercept corresponding to zero path length in the atmospheric is yor estimate of the astrophysical contribtion, the CMBR. Estimate the error for this vale based on the errors of the vales that contribte to the comptation. wo other measrements can be obtained with this eqipment. here are two point sorces of 1 GHz radiation that can be sensed. One is the Sn and the second is a geosynchronos satellite de soth. A lens and screen has been attached to the receiver hosing to align the Sn with the receiver axis. he small holes in the frosted screen are drilled on a 5 grid. he geosynchronos satellite can be easily fond once yo estimate its zenith angle. hat can be estimated from the following parameters: G m 3 kg -1 s - M Earth kg R Earth 6371 km t sidereal s ϑ latitde UM 4.77 able 1. Orbital parameters A Slightly Better Analysis Procedre he data analysis method described above is slightly misleading becase it tends to confse temperatre with spectral intensity, the physical variable that is actally being directly measred. In particlar, when one points the receiver at the sky, the radiation intensity is comparable to a black body at 40 K. his, of corse, is not a real temperatre. he origin of this 1 Ghz radiation is the atmosphere with a scale height of 8 km. Its actal temperatre is of the order of 50 K bt it is highly transparent at these freqencies and therefore the intensity we observe is correspondingly lower. What we do observe is proportional to the path length throgh the medim and therefore proportional to sec zenith. We also wold like to avoid the nmerical x approximation that e 1 x if this is not absoltely necessary. he starting point of this analysis is to track a qantity that is directly related to intensity, not temperatre: e h / k 1 1 e n / 1 1 and can be compted from:

4 n log 11/ From a set of calibration measrements,,,, 1 1 and an observation,, one can obtain an estimate of : with a variance: (1 )( ) / (1 )( ) / n 1 1 hese intensity amplitdes shold be plotted as a fnction of sec and the intercept and error determined by the sal techniqes for linear regression. he CMBR temperatre can then be determined by the formla given above and its standard deviation is: zenith 1 1log 1 1. tea cart. two thermal reference loads 3. lollipop thermometer 4. two liqid nitrogen bckets 5. 1 GHz receiver assembly 6. receiver azimth ring 7. hex wrench for azimth ring 8. Agilent E363A DC power spply 9. Agilent 34401A mltimeter 10. two coax cables able. Eqipment for Angell Hall

5 A B C D able 3. Zenith angles for receiver mont. he oter and inner index plates are drilled on 15 and 0 centers, respectively able 4. Azimth angles for receiver mont, assming proper ring alignment. he pper and lower index plates are drilled on 30 and 40 centers, respectively.

6