# Discussion Questions

By

Dr Lim Zhi Han

,

Koh Zhi Yong

,

Gerald Kang Joon Kiat

●

Published 2022-09-10

1. Bats use echolation to determine distance. Can you think of a similar way to measure astronomical distances? Can we use this to find method the Astronomical Unit?

2. Read about Mira "the wonderful" star in the following articles

Article 1 Article 2

and answer the following questions.

(a) Assuming that Mira is 100 parsecs away from us, calculate the absolute magnitude of Mira when it is at its brightest and dimmest. In terms of luminosity, how much brighter or dimmer is Mira as compared to the Sun?

(b) "Mira is plunging through our part of the Milky Way with an unusually large space velocity, 130 kilometers per second." Is this velocity in the radial direction?

3. Refer to Figure 1 of Kaspi et al.¹ Compare the spectrums of PG 1351, PG 1354 and PG 1512 and discuss. From the spectrum of PG1512, what is the wavelength of the photons corresponding to the most prominent peak emitted from the quasar? (Obtain information on the redshift from Table 1 in the paper.)

4. Given the redshift of a particular quasar to be z=2.504, what is the observed wavelength of the Hydrogen Ly \alpha line?

5. In radio astronomy, spectral lines are usually displayed in a very different way. This is due to the unique way of data collection where the radio telescope/spectrometer scans a very narrow band of wavelegths at a time. Radio astronomers thus need to know exactly what they want to look for. This can be done by looking up the rest frame frequencies of their objects of interest. An example is as follows:

Note that the horizontal axis is given in terms of velocity. This velocity is the velocity of the source and this is related to Doppler redshifts.

(a) Using velocity as the horizontal axis may seem to be a strange choice. Can you think of a reason why this is useful in context of collecting a spectrum of a nebula (cloud of gas in between stars)?

Clue: this paper is on the "Astrophysical detection of the funny molecule \text{HeH}^+". So why is the CO spectrum doing there?

(b) Given that the spectral resolution of the \text{HeH}^+ spectrum is 3.6 km \text{s}^{-1}. Find the spectral resolution in terms of MHz.

Clue: Use the formulae related to Doppler redshift.

6. In Hubble's 1929 paper, he deduced the famous equation

v=H_{0}d

from the velocities and distance of several spiral galaxies. Perform a statistical analysis to determine the goodness-of-fit of his relation on his data (given below).