Astronomy | Astrophysics Answers

Problem C.1 : Earliest Galaxy Group (10 Points)

This problem requires you to read the following recently published scientific article:

Onset of Cosmic Reionization: Evidence of an Ionized Bubble Merely 680 Myr aer the Big Bang.

V. Tilvi et al 2020 ApJL 891 L10. Link: https://iopscience.iop.org/article/10.3847/2041-8213/ab75ec

Answer the following questions related to this article:

(a) What is the so called cosmic reionization process?

(b) What are Lyα lines and why did the researches want to observe them?

(c) What do the authors intend to point out with Figure 1 (see article)?

(d) How is confirmed that the peaks seen in Figure 3 are actually from Lyα emissions?

(e) How are the bubble sizes of the galaxies estimated?

(f) What is special about the findings in the article and what are the scientific implications?

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Space and time are interconnected according to special relativity. Because of that, coordinates

have four components (three position coordinates x, y, z, one time coordinate t ) and can be ex-

pressed as a vector with four rows as such:





ct

x

y

z





The spaceship from problem A.4 (Special Relativity - Part I) travels away from the Earth into the

deep space outside of our Milky Way. The Milky Way has a very circular shape and can be ex-

pressed as all vectors of the following form (for all 0 ≤ ϕ < 2π):





ct

sin ϕ

cos ϕ





(a) How does the shape of the Milky Way look like for the astronauts in the fast-moving space-

ship? To answer this question, apply the Lorentz transformation matrix (see A.4) on the circular

shape to get the vectors (ct0

, x0

, y0

, z0

) of the shape from the perspective of the moving spaceship.

(b) Draw the shape of the Milky Way for a spaceship with a velocity of 20%, 50%, and 90% of the

speed of light in the figure below (Note: The ring shape for a resting spaceship is already drawn.):

 Calculate the half-width of a spectral line of wavelength of λ= 550 nm when the 

temperature of the gas is 6 × 10⁵ K. Assume H atoms to be emitters.

The mass and radius of a neutron star is 2M and 15 km, respectively. Calculate the 

value of gravitational red shift for light of wavelength 6000 Å at a distance of 2 m 

from its surface.

Sketch the celestial equator, horizon, observer’s meridian and show the zenith and 

nadir on the celestial sphere for an observer at latitude 30°N.

Explain the need to postulate the existence of dark matter in the universe.

 Describe the nature of the central engine in an AGN.