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