ASPH 611 Term Project
A University of Calgary Department of Physics and Astronomy
Graduate Course in Radio Astronomy
Julie Grant, December 12, 2005
Properties of the Telescope
Figure 2: The receiver chain used in the detection of the 21cm line.
Figure 3: The feed horn with the radio wave absorber attached.
Figure 4: The 1.42 GHz radio telescope block diagram, courtesy of Fred Babott.
The noise temperature of the receiver can be calculated when the power gains of the receiver chain are known, Figure 4. The noise temperature of the receiver is given by
where TR is the receiver noise temperature, and Tn are the noise temperatures of the components in the chain, and Gn-1 are the gains of the components in the chain. The gains are measured in dB and need to be converted using the power conversion
Once TR is calculated, the receiver noise in dB can then be calculated by the Nose-Temperature-Noise-Figure-Chart (Kraus)
where T is the noise temperature (K), To is 290 K, and F is the noise figure (dimensionless). The noise figure in dB can the be calculated by
The noise values for our system are: a system noise temperature of 27K and a noise figure of 0.39 dB.
Neutral atomic hydrogen, HI, makes up nearly the entire interstellar medium, and allows for 21-cm radio wavelength investigation of the entire Galaxy (with the exception of a few directions). The 21-cm line of atomic hydrogen is due to the hyperfine transition in the ground state of the atom corresponding to a frequency of 1420.406 MHz.
Figure 5: Idealized Hydrogen-line profiles. Part (a) displays the line profile for a stationary cloud of gas, (b) displays the line profile for a cloud of gas moving away, (c) displays the line profile for a stationary cloud of gas with internal turbulence and (d) displays the line profile of a typical galactic cloud of gas. (Kraus, Radio Astronomy 2nd Ed. Page 8-90.)
In order to fully understand the galactic kinematics and differential galactic rotation, one must observe the HI throughout our Galaxy. When detecting the 21-cm line, one gets a line profile, or spectrum, giving the intensity as a function of frequency. This frequency measures the Doppler shift from the rest frequency of 1420.406 MHz. Doppler shifts are measured as relative motion between the telescope receiver and the radiation source. If a stationary region of neutral hydrogen is scanned, the line will be centered at 1420.406 MHz, see Figure 5. However, the majority of HI in the Galaxy is moving relative to the Earth, thus the profile will be shifted based on whether the region is moving towards or away from the observation. The frequency shift is related to the velocity of recession V by
where V is the velocity of approach or recession, c is the velocity of light, delta v is the frequency shift, and v is the rest frequency. A 1 km s-1 shift corresponds to a 4.74 kHz frequency shift. These velocities are expressed relative to the local standard of rest, thus allowing for the peculiar motion of the Sun with respect to the nearby stars, with negative velocities corresponding to regions moving towards the observer and positive velocities are regions moving away from us. The natural width of the 21-cm emission line is 10-16 km s-1 however, the widths measured by radio telescopes are much broader. Profiles observed within 10o of the galactic equator are around 100 km s-1, while measurements in directions near the galactic centre have total widths of 500 km s-1 (Butler Burton, W. 1988).
The broadening of the line is due to both thermal and turbulent motions of the atoms within a region of gas and can broaden a line by 5 km s-1. These broadening methods are not enough to account for the broadening that is seen by radio telescopes, but they do give us insight into the structure of a profile. The majority of the broadening is due to rotation characteristics of the Galaxy (Butler Burton, W. 1988).
The temperature sensitivity is given by
where Tsys is the system temperature (~70o), delta v is the bandwidth and t is the integrations time. Since we are dealing with a spectrometer, the above equation gives a per channel temperature sensitivity when used with the channel bandwidth (~3.6kHz/channel). This size of bandwidth will account for all the shifting of the line that was mentioned above and it will allow for enough channels to contribute to the removal of the continuum emission during the data processing phase.
Nyquist sampling theory states that in order to fully sample an incoming signal, equally spaced samples should be taken at the minimum frequency of twice the highest frequency. Our band is centred at 3.6 MHz and our bandwidth is 3MHz, so according to Nyquist we should sample at twice the highest frequency (3.6 + 1.5 MHz) of 4.8 MHz. However, our bandshape covers a full 8 MHz so we will introduce aliasing in our final spectra. Thus we will need to sample at twice the highest frequency of our band, 16 MHz.
Last modified: 10:22 am July 17, 2014