Nearby and Distant Galaxies: A Brief Note

 

Nearby and Distant Galaxies: A Brief Note

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,

University of Niš, pavleipremovic@yahoo.com, Niš, Serbia

In our previous communications, we defined nearby galaxies as those whose cosmological redshift (or just simply redshift), z_G, is from 0.001 to 0.1 (or 0.001 ≤ z_G ≤ 0.1) and distant galaxies with z_G > 0.1 [1-3], emphasizing that there is no sharp boundary between them. This definition needs some further explanation. 

The redshift of nearby galaxies is approximately defined (in wavelength) by the following equation

z_G = (λ_G – λ)/λ    … (1)

where λ is the wavelength of light emitted by nearby galaxies and λ_G is its wavelength measured by an Earth’s observer.

If the recessional speed of nearby galaxies υ is much smaller than the speed of light c (≈ 3×10⁸ m sec^-1)[1] then this speed is defined based on the non-relativistic Doppler effect by the following equation

υ = cz_G    … (2)

In this case, recessional speed is the product of redshift, z_G, multiplied by the speed of light c. 

The starting point of numerous papers related to the recessional speed of nearby galaxies is Hubble’s law equation based on the assumption that υ = cz_G << c. This equation states that

υ = cz_G = H₀D_G … (3)[1]

H₀ is Hubble’s constant and D_G is the proper distance (hereinafter distance). This equation is based on two assumptions: (a) speed is the only cause of redshift of nearby galaxies (see https://www.loop-doctor.nl/hubble-and-humason-measured-redshift) and (b) their peculiar motion is negligible and this is highly likely for most of these galaxies.

A good approximation for υ = cz_G << c is υ = cz_G ≤ 0.1c or briefly z_G ≤ 0.1 [1]. Let us now find the distance range of “megamaser” galaxies. Plugging z_G ≤ 0.1 into eqn. (3) and after a bit of algebra we have

D_G ≤ 0.1c/H₀    … (4).

We know that c/H₀ is Hubble’s distance equal to about 13.8 Gly. Hence, nearby galaxies are those on distance D_G ≤ 1.38 Gly and distant galaxies are with D_G > 1.38 Gly. Taking into account the above-defined low limit for z_G (≥ 0.001), we propose the following distance range for nearby galaxies: 0.0138 Gly ≤ D_G ≤ 1.38 Gly.

The upper limit for nearby galaxies[1], z_G ≤ 0.1, defined above is based on eqn. (4). On the other hand, their lower limit is arbitrarily defined on the basis that the maximum peculiar speed[2] of about 300 km sec^-1 or 0.001c. (See the definition given above).

A problem that has received little attention despite its importance is the fact that we do not know the recessional/peculiar speeds of any of nearby galaxies at all (for example, see https://www.loop-doctor.nl/hubble-and-humason-measured-redshift/). Moreover, we do not even knoaes from 23.7 Mly[3] to 447 Mly [1, and references therein]. Therefore, all of them are nearby galaxies.

References

[1] P. I. Premović, Distant galaxies in the non-expanding (Euclidean) Universe: the light speed redshift. The General Science Journal, December 2021.

[2] P. I. Premović, The redshift of light emitted by nearby and distant galaxies in the observable Universe. The General Science Journal, December 2021.

[3] P. I. Premović, The photon quantum of energy of the observable Universe. The General Science Journal, December 2021.

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[1] I. e., υ = z_Gc << c.

[2] Of course, the equations (1) - (3) can only be used when the recessional speed υ << c (in particular, when υ ≤ 0.1 c) at higher υ, equations must be derived based on the Special theory of relativity.

[3] Or the lower limit for distant galaxies.

[4] In general, peculiar speed = υ - D_GH₀/c.

[5] The peculiar motion is not negligible only for this galaxy [1].