Advanced Observational Astronomy

THE UNIVERSITY
of LIVERPOOL

MAY 2001 EXAMINATIONS

Degree of Master of Physics : Year 3
Degree of Bachelor of Science : Year 3

ADVANCED OBSERVATIONAL ASTRONOMY

TIME ALLOWED : Three Hours

In the event of a student answering both parts of an either/or question and not clearly crossing out one answer, only the answer to part (a) of the question will be marked.

$\begin{displaymath} B_{\nu}(T) = \frac{2 h \nu^3}{c^2} \frac{1}{\left(e^{h \nu /k T} - 1\right)} \end{displaymath}$

$\begin{displaymath} \kappa_{\nu} = 1.73 \times 10^{-13}\left[1 + 0.130 \log_{10}... ...} \right) \right] \frac{n_e^2}{T_e^{3/2} \nu^2} \;\;\; m^{-1} \end{displaymath}$

THE UNIVERSITY
of LIVERPOOL
Section A

(a) An optical telescope with focal length f = 343cm is equipped with a CCD detector which has pixels of physical size 24 $\mu m$ . What is the pixel size in arcseconds of the images produced? [4]

(b) The CCD in Part (a) is replaced by another with pixels half the size but with the same read noise per pixel. What is the resulting change in signal-to-noise ratio achieved in both the read-noise-limited and background-noise-limited cases when observing (i) a point source (assuming all the flux falls on a single pixel) and (ii) an extended source (assuming constant surface brightness)? Justify your answers. [6]

(c) Write down the formula for the theoretical resolution of a telescope of aperture D at a given wavelength $\lambda$ . Discuss if ground-based telescopes of arbitrarily large dimensions can achieve an arbitrarily large resolution. [4]

(d) Show how the theoretical spatial resolution limit of a single telescope can be increased by a factor of nearly 2.5 by masking the aperture. What is the principal drawback of this masking method in practice? [6]

(e) What is the Point Spread Function (PSF)? What are the factors determining the shape of the PSF? [4]

(f) What is the physical process producing the X-ray continuum associated with large clusters of galaxies? By considering the gravitational potential of a typical cluster show that it should not be surprising to find this continuum emission to be bright at X-ray wavelengths and the intracluster gas to be very hot. [5]

(g) Explain what is meant by ``brightness" ( $B_{\nu}$ ) and ``flux density" emitted by an astronomical object at radio frequencies. If two extended objects (e.g. HII regions) are intrinsically identical, but one is viewed at twice the distance of other, what are the relative radio flux densities and brightnesses measured in the two objects? Briefly explain your answers. [6]

(h) Describe briefly (in two or three sentences) the physical mechanism responsible for synchrotron radiation and two types of astronomical object that are sources of such radiation. [5]

THE UNIVERSITY
of LIVERPOOL
Section B

(a)

(i) List and discuss the three main physical processes responsible for the absorption of starlight in the Earth's atmosphere and the wavelengths affected in each case. [12]

(ii) Explain what is meant by `seeing' and `scintillation'. [4]

(iii) Consider optical CCD observations of the core of a Galactic globular cluster. Explain what is the best method (aperture photometry or profile fitting) to extract photometric information from the images taken. [2]

(iv) Discuss the procedure to follow in order to derive instrumental magnitudes through the profile fitting method from a CCD image. Suppose that the image has been already Dark- and Bias-subtracted and Flat-Fielded.

[12]

(i) Write brief notes on the physical processes and astronomical sources of line and continuum emission that can be observed in the X-ray, near-infrared (1 to 3 $\mu$ m) and millimetre/sub-mm wavebands. [12]

(ii) The CO molecule has a dipole moment of 0.11 Debye while the value for CS is 1.97 Debye. Which molecule's rotational transitions would you choose to observe in order to detect the densest gas in a Galactic star-forming region? Explain your answer in terms of the excitation properties of these two molecules. If the observed ratio of the strengths of the $J=1 \rightarrow 0$ transitions of ¹²CO and its rare isotope ¹³CO is 10, find the optical depth of the ¹²CO line (assume the isotopic abundance ratio is 90). [9]

(iii) Give three basic requirements for a good array detector for use in the 10 $\mu$ m and 20 $\mu$ m wavebands and the reasons for them. Explain why a chopping secondary mirror is necessary for observations at these wavelengths and why a combination of chopping and nodding the telescope is often used.

[9]

(i) A compact, spherical HII region, radius 0.8pc at a distance of 700pc from the Sun, produces the radio-frequency spectrum shown below.

radio spectrum

1) Name and describe briefly the process likely to be dominating the radio-frequency emission from this object. Justify your answer in terms of the conditions in this type of object or in terms of the shape of the spectrum. [4]
2) Use the spectrum to estimate the electron temperature and electron number density in the emitting gas. [9]

(ii) Explain the need for and principle of heterodyne receiver systems for use at radio and millimetre-wave frequencies. Include in your answer a short discussion of signal sidebands. [8]

(iii) A two-element radio interferometer with steerable antennae located at the equator, is separated along the east-west line. It observes two point sources of equal brightness, separated by a small angle $\beta$ in RA. Show that the difference $\Delta P$ between the signal path differences in the interferometer for the two sources is greatest as they transit the meridian and negligible on the horizon. If $\Delta P$ is exactly half a wavelength at the meridian, sketch the resulting fringe pattern as the interferometer tracks the sources from rising to setting and explain its main features.

[9]

(i) Discuss the physical reasons for the natural broadening and Doppler broadening of spectral lines. [7]

(ii) Consider a $\rm Fe^{56}$ absorption line located at wavelength $\lambda$ =4000 Angstrom in the solar spectrum (T=6000 K). Determine the half width of the line due to Doppler broadening and compare this value with the natural half-width of the line ( $\sim$ 0.00012 Angstrom). [5]

(iii) Describe the effect of a magnetic field on a given spectral line emitted by a gas, when the light is observed:

a) in an arbitrary direction with respect to the direction of the magnetic field (neither perpendicular, nor parallel);

b) in the direction perpendicular to the direction of the magnetic field;

c) in the direction parallel to the direction of the magnetic field.

What type of stars shows the greatest measured stellar magnetic field strength? [9]

(iv) Write down the condition of constructive interference for grating spectrometers. Derive the expression of the corresponding angular dispersion and point out the main difference with respect to the case of a prism spectrometer. [5]

(v) What is the main disadvantage of a grating as a dispersing element? How can it be overcome ? [4]