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The Cosmic Microwave Background Radiation Temperature

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The Cosmic Microwave Background Radiation Temperature Astrophysics Homework Assignment The Cosmic Microwave Background Radiation Temp erature Work in groups of Due April Consult Fred Babb ott SB for observing assistance In this lab oratory exercise you will use the radio telescop e on the ro of of Science B to measure the intensity of the Cosmic Microwave Background Radiation CMBR The standard Big Bang mo del explains the CMBR as redshifted thermal radiation that decoupled from the matter in the Universe when temp eratures dropp ed far enough for hydrogen atoms to b ecome neutral For their discovery of the CMBR in Arno Penzias and Rob ert Wilson were awarded the Nob el Prize for Physics The CMBR is isotropic to a very high degree one part in At wavelengths in the cm range it is brighter than other forms of radiation when averaged over the sky At longer wavelengths the synchrotron radiation from the Galaxy dominates while at shorter wavelengths the Earths atmospheric emission is much stronger than the CMBR You will make your measurements in the middle of this window at a wavelength of cm Cloudy weather is no great concern for this exp eriment but nighttime observations are desirable to minimize solar interference The Radio Telescop e and Brightness Temp erature The radio telescop e consists of a meter parab olic reector and a receiver system tuned to cm wavelength radiation For a detailed description of the instrumental setup see the radio telescop e pro ject web page at wwwrasucalgarycaradiotel The telescop e resp onds to radiation within a b eam eld of view of ab out diameter centered on the p ointing direction of the antenna The receiver pro duces a voltage at the output that is prop ortional to the intensity of radiation within this b eam Radio astronomers often measure intensities in units of brightness temp erature If I is the radiation intensity the brightness temp erature is given by I T b k For an optically thick blackb o dy radiator with temp erature T it is easily shown that T T The b emergent intensity for an isothermal source is given by the solution of the radiative transfer equation I B e where B is the Planck Function and is the optical depth In the case where the Planck function can b e written in the form of the RayleighJeans approximation this equation b ecomes k T I e which from the denition of brightness temp erature can b e written T T e b It therefore follows that for an optically thick source T T Since for a xed wavelength b the brightness temp erature changes linearly with intensity the voltage output of the telescop e is prop ortional to the brightness temp erature of the source of radiation b eing observed You will use this fact to measure the brightness temp erature of the sky at cm The measurement will consist of two parts the calibration of the brightness temp erature resp onse of the antenna the measurement of the brightness temp erature of the sky The concept of this measurement is very simple The challenge is in taking careful measurements to minimize the error on the result Calibration The resp onse of the radio telescop e is read via a voltmeter attached to the output p ort of the detector system The calibration problem consists of relating the output voltage to the brightness temp erature of the source This is done by placing two optically thick sources of precisely known temp erature in the reception pattern of the receiver These sources consist of two buckets lled with microwave absorbing material one at ambient temp erature and one at liquid nitrogen temp erature Use these measurements to derive a relationship b etween the output voltage V V and the o brightness temp erature of the source You will nd that there is still a signicant output voltage even when the brightness temp erature of the source is K This residual output p ower arises from noise generated from the receiver electronics its temp erature equivalent is called the receiver temp erature T The output of the telescop e in temp erature units when lo oking at a source of r ec brightness temp erature T is thus T T T sour ce sy s r ec sour ce You should p erform the calibration twice once b efore and once after observing the sky to check for any drift in calibration and to assess the precision of the technique The Sky Temp erature The radio antenna acts as a mirror at cm reecting the radiation from a patch of the sky The output of the telescop e when p ointing at the sky will then b e T T T sy s r ec sk y The temp erature of the sky can in principle arise from two sources radiation from the atmosphere and radiation from outer space the CMBR The brightness of the sky will b e given by atm T T T e CMBR sk y atm In the case we can write T T T Assuming a planeparallel atmosphere atm sk y atm atm CMBR with secz where z is the zenith angle of the p ointing direction of the radio telescop e atm b eam we have T T secz T sk y atm CMBR Thus one should b e able to solve for and remove the atmospheric contribution by carefully measuring the telescop e resp onse as a function of zenith angle leaving only the CMBR brightness temp erature In practice this correction is dicult to achieve with the telescop e we have b ecause of contam ination from stray radiation entering the feed through sidelob es in the telescop es sensitivity pattern vs angle much as oaxis scattered light can contaminate optical telescop e photometry Stray radiation can come from the Sun the Milky Way the walls of the building or even your lab partners Exp eriments comparing the signal received with the full telescop e and that with the feed detached from the reector suggest the stray contribution from building walls may b e a few degrees K dep ending on p ointing direction By itself the feed acts as an antenna with a much broader b eam but with minimal sidelob es Signicant contamination from the Sun and the inner Milky Way near each other in the sky at this time of year is also present during daylight hours Celestial stray radiation can b e minimized by observing after sunset Take measurements at a variety of zenith angles and try tting the temp erature as a function of secz to nd the atmo spheric contribution Comment on whether you think terrestrial stray radiation contamination is still a problem The b est direction for measurements is toward the northwest which avoids most contamination from satellites an increasing problem in radio astronomy Even so building walls b ecome a serious issue for z Hand in your measurements calculations and the nal result with estimated error Comment on what you think are the main sources of uncertainty or contamination and how the exp eriment might b e improved .
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