THE UNIVERSITY
of LIVERPOOL





SUMMER 1999 EXAMINATIONS

Bachelor of Science: Year 1

Bachelor of Science: Year 2

Master of Physics: Year 1

Master of Physics: Year 2

ASTRONOMY FUNDAMENTALS

 

 

TIME ALLOWED: 1 hour 15 minutes


INSTRUCTION TO CANDIDATES

Answer both questions.

The questions carry equal marks.


The marks allocated to each part of a question are indicated in square brackets.

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


1 AU = 1.5 x 1011 m

1.

Answer all parts of this question.

(a)
Use the Rayleigh criterion to calculate the diffraction-limited resolution in arcseconds of the human eye (assume the pupil has diameter 5mm and we observe at wavelengths of 550nm). Potentially how much better is the resolution of the 10m diameter Keck telescope at the same wavelength? What limits the resolution attainable in practice by this telescope? [5]

(b)
The new wide-field optical fibre-fed spectrometer 2dF (`two-degree field') is mounted at the prime focus of the Anglo-Australian Telescope (AAT). If the focal length of the AAT at the spectrometer is 12.7 metres calculate the diameter (in metres) of the area over which 2dF can position its light-collecting fibres. [5]

(c)
A galaxy has right ascension 7$^{\rm h}$ 30$^{\rm m}$ and declination -10$^{\circ}$. If it is to be observed from Hawaii (latitude 19$^{\circ}$), at what time of year does the galaxy transit the meridian at local midnight and at what altitude does it transit? [5]

(d)
A binary system contains stars which are separated by 0.3 arcsec. It is observed with the Hubble Space Telescope and the stars are found to have apparent magnitudes 11 and 8. If, when observed with a ground-based telescope, the binary is unresolved, what is its integrated magnitude? [5]

(e)
Define the cosmological density parameter $\Omega_0$ and briefly describe how the determination of its value is of importance to astronomy. [5]




2.

Answer either (a) or (b).

(a)
Explain how astronomers measure distances using Cepheid variable stars. Make clear reference to how the technique is calibrated. [12]

A nova underwent an outburst during which it brightened, reaching a peak apparent magnitude of mV=-1.1. Spectra showed that an absorption line which had a rest wavelength of 6563 ${\rm\AA}$ had been Doppler-shifted by 37 ${\rm\AA}$ (assume the systemic velocity is zero i.e. the central system is not moving with respect to the observer). If this absorption occurs in material ejected during the outburst, calculate the velocity of ejection. [3]

Eight years after outburst, photographs showed the expanding material in the form of a faint shell with a radius of 16 arcsec surrounding the nova. Show that the distance to the nova is about 180 parsecs. What was its absolute visual magnitude at outburst and what physical effect unrelated to the nova itself may cause this to be an underestimate of the brightness? [10]

(b)

Describe the evolution of a star of the same mass as the Sun following the onset of hydrogen burning in the core. Illustrate your answer with a labelled sketch of its path on an HR diagram, clearly explaining the various phases indicated on the path. [12]

Consider a gas cloud orbiting a spiral galaxy at a radius R. Show that the rotational velocity of the cloud V is given by $V\,=\,\sqrt{GM/R}\ ,$ where M is the mass of the galaxy within radius R. State the assumptions necessary in deriving this simple law.

[4]

A schematic of the observed rotation curve of a spiral galaxy is shown below.

galaxy rotation curve,

From the equation above show that in region A (the bulge of the galaxy), where $V\propto R$, the density must be approximately constant. Describe clearly and with reference to the equation derived above how the flat part of the rotation curve, region B, provides evidence for the existence of `dark matter'. [9]