Exam (elaborations)
21-22 Exam for Introduction to Astrophysics
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- The University Of Sheffield (TUOS)
Exam for Introduction to Astrophysics
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PHY104PHY472
Data Provided:
Formula sheet and physical constants
Data Provided:
A formula sheet and table of physical constants is attached to this paper.
DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010
ASTRONOMY
DEPARTMENT OF PHYSICS AND ASTRONOMY
ADVANCED QUANTUM MECHANICS 2 hours
Spring 2022
AnswerIntroduction to Astrophysics
question ONE (Compulsory) and TWO other questions, one each from3 hours
section A and section B.
Instructions:
All questions are
Answer all marked
FOUR out offrom
questions ten.Section
The breakdown on the
A and any TWO right-hand
questions from side of B.
Section the
paper is meant as a guide to the marks that can be obtained from each part.
Answering the exam questions should take no more than TWO hours, but you will have THREE
hours in a 24-hour window to complete the exam and upload your answers to Crowdmark.
Make sure you retain time stamped photos/scans of your work in case you experience any
problems with uploading files.
Section A is worth 40 marks in total and all questions in section B are worth 30 marks each.
The breakdown on the right-hand side of the paper is meant as a guide to the marks that can
be obtained from each part.
Cross through any work that you do not wish to be examined.
PHY104 TURN OVER
1
PHY472 TURN OVER
, PHY104
SECTION A
1. A binary system has an apparent V-band magnitude of 9.4 mag.
(a) If the system has a parallax of 3.2 milli-arcsec, and the primary is 1.1 magni-
tudes brighter than the secondary in the V-band, what are the absolute V-band
magnitudes of the two components? [8]
(b) Estimate the spectral types of the components if B-V = +0.1 for the primary and
B-V = +0.3 for the secondary. Justify your answer. [2]
2. (a) Define the terms monochromatic flux and bolometric flux. [2]
(b) A cloud of hot, ionised gas has a monochromatic surface flux Fν [W m−2 Hz−1 ]
given by
2
kν
for ν ≤ 1010 Hz ,
Fν = 2 × 10−26 for 1010 < ν ≤ 5 × 1011 Hz ,
0 for ν > 5 × 1011 Hz,
where k is a constant. Calculate the bolometric surface flux. [8]
3. A compact star cluster consists of 200 identical stars and lies at a distance of 3 kpc.
(a) What would be the apparent visual magnitude of the cluster if each star has an
absolute visual magnitude of 0.5 mag, and dust extinction is neglected? [7]
(b) If an interstellar visual extinction of 1.5 mag per kpc applies, how much fainter
would the cluster appear due to the presence of dust? [3]
4. Spectroscopic observations reveal that the 656.28 nm nebular emission line of hydrogen
is observed at a wavelength of 672.03 nm in a distant galaxy.
(a) What is the recession velocity (in km s−1 ) of the galaxy? [3]
(b) If the present value of the Hubble constant is 70 km s−1 Mpc−1 , what is the dis-
tance to this galaxy in Mpc? [2]
(c) If its physical radius is 5 kpc what is the galaxy’s angular diameter (in arcsec)? [3]
(d) How bright would a Type Ia supernova in the galaxy appear if its absolute visual
magnitude is –19.5 mag? (interstellar extinction may be neglected). [2]
PHY104 CONTINUED
2
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