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Cosmology: Hubble Constant (Hubble Parameter)

In 1929, Hubble made a rather surprising observation that would significantly change our perceptions of the universe. He published this observation in a paper he wrote under the title “the relationship between distance and perpendicular velocity between extragalactic nebulae”. In simpler words, he studied the connection between the distances of celestial bodies and the speeds of their distance. The results he found were incredible. The further away a galaxy was from us, the faster it was moving away in proportion to that. How far, how fast … today we call this state the Hubble constant, or more accurately the Hubble parameter.

This should have been a physical interpretation of the situation, because if in the universe the bodies are somehow moving away from each other, it should be in a random way. So a galaxy that is too far away should be able to get close to us, or the one that is too close should be able to get away. But that wasn’t the case. Obviously, as the distance increased, so did the speed of distance. This means that there is a repulsive factor in between. With this observation, Hubble revealed the first observational results of the expanding universe model. Today, we know that the reason distant galaxies are moving further away from us is because of the expansion of the universe in between.

You can think of the expansion of the universe as the swelling of a bubble. The points (galaxies) located on the balloon will move away from each other as the balloon swells.

Hubble Constant (Hubble Parameter)

This distance-distance rate relationship, which Hubble studied, not only gave an interpretation of the universe, but also gave recognition to a new parameter: the Hubble constant (or Hubble parameter). When Hubble charted this relationship, he saw that it could be represented by a truth.

In Hubble’s 1929 article, distance – distance-radial velocity is the graph itself.

This means that mathematically it has a correct equation. In this way, if we can measure the speed at which an object moves away from us, we can find its distance to us; even if we know its distance to us, we can find the speed at which it moves away from us. But this gives us only the speed due to the expansion of the universe, not the speed of the body in space. In a real case, it is not as simple as о to make a healthy measurement, as the velocity of the object will also be included in the velocity we measure. If the distance speed of an object is v and its distance is D, there is a relationship between them as follows.

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v = H0 x d

Here H0 is the parameter that we call the Hubble Constant today. The constant expression here does not mean that it is constant over time, but that it is constant enough that it does not change during our daily life, its current value. In fact, the word” parameter “rather than” constant ” is more appropriate, but as a general usage, we prefer to call the Hubble constant when we talk about its current value, the Hubble parameter when we talk about its change over time. If it is not fixed, we will not address it here, as it is a slightly more complex issue. For now, we just need to know that we can accept this as a constant in short periods of time.

The Value Of The Hubble Constant

Because of calibration errors that Hubble made in its measurements, it measured the value of the Hubble constant quite differently than the value we know today. The value he found was 500 kilometers per second, for 1 Mpc (1 megaparsec about 3.2 million light years). 500 km S-1 Mpc-1 as physical representation. After that, Allan Sandage managed to draw this value to 75 km S-1 Mpc-1, which is also approximately correct today, in 1958, 29 years after Hubble’s conclusion, in his article titled “Current Problems on the extragalactic distance scale”. We would like to point out that Sandage was a valuable scientist who made a very serious contribution to cosmology, and his achievement is absolutely admirable.

Today, especially with the satellites we have launched in recent years, we have started to minimize errors thanks to developing technology. Remember, each measurement contains a margin of error. Although we do not specify error ranges here, as we do not want them to make eye crowds, these accounts all have a certain plus-minus range. Currently, this ratio has been significantly reduced.

Current Value Of Hubble Constant

Hubble constant with contributions from Chandra satellite in 2006 77.6+14.9-12.5 km s-1 was measured as Mpc-1. Note the plus-minus expression here. This means that when we take into account the margin of error in our measurements, the Hubble Constant can vary from 92.5 to 65.1. This is a very serious error range. But in a very short time, we closed this gap. With the launch of WMAP and Planck satellites after Chandra, this value, along with Planck’s results in 2015, 70.4+1.3-1.4 km s-1 was announced as Mpc -1. Thus, although we are still not fully satisfied, we have reduced the error range to a fairly minimum.

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Redshift

The relationship in Hubble’s publication was between distance and perpendicular speed (distance speed). But when the distances are too large, we no longer use the concept of perpendicular speed. An object moving away shows us an event that we call a redshift in its spectrum (electromagnetic spectrum). All absorption and release lines that we see in the spectrum of the object shift in the complete red direction on the spectrum. This amount of slip directly gives us the speed at which the object moves away. Since it is more practical to express it in this way, today we prefer to use the Redshift parameter (denoted by z).

Shift to red and blue on the spectrum

In the figure above, we see how the Redshift event was detected. In the laboratory, when we take the spectrum of an object, absorption lines appear on the spectrum, as in the middle. These lines are specific to the elements, which is a kind of fingerprint of the elements. We also see the same lines in celestial bodies, and these lines must always be at the same points (wavelengths). But depending on the distance and proximity of the object, these lines can shift (shift) to red or blue. If it is a blue shift, the object is approaching, and if it is shifting to red, it is moving away.

In physics, we express the Z parameter in terms of the wavelength λ0 of the line in the spectrum observed in the laboratory and the wavelength λg in which the same line is measured in the celestial body as follows. z=λg/λ0-1

In this case, λg becomes greater than λ0, since the wavelength of a body sliding to Red will grow, and the parameter z gets a positive value. If the observed wavelength and laboratory wavelength are the same, the object does not show any Redshift, i.e. z=0.

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Galaxies Sliding Blue

We talked about distant galaxies moving away faster than we do, because it’s caused by the expansion of the universe… but at the same time, bodies have their own speeds that aren’t caused by the expansion of the universe. So even if the universe between them wasn’t expanding, they would somehow either get closer to us or get away. The speed that we measure actually contains the sum of these two speeds.

Naturally, there are galaxies that both shift to blue (converge) and shift to Red (move away). But as the distance increases, the Redshift will also increase significantly, the body’s own speed now remains small enough to disappear in it. So we don’t see a galaxy that’s too far away and slides blue. The blue ones appear in the cluster of galaxies in which we are located, in galaxies that are gravity-bound to us. The most famous of these is the Andromeda galaxy, which will come very close to us in a few billion years and merge with us

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