Law of Hubble

Expansion of the universe and movements clean

It is an overall movement of the galaxies of the Univers. On this one superimposes the own movements acquired by the galaxies because of their nelles interactions Gravitation with their neighbors. For example, the Milky Way form a system gravitationally dependant with the Galaxie of Andromède which has both a very lengthened elliptic orbit which makes that currently, the galaxy of Andromède approaches us. In the same way, the Milky Way and the galaxy of Andromède approach little by little the Superamas of the Virgin. Nevertheless, beyond of a certain distance, the general movement of expansion overrides the movement clean, and all the remote galaxies move away from us.

Genesis of the law of Hubble

The law of Hubble draws its name from the American Astronome Edwin Hubble which published it in 1929. It was the first proof of the Expansion of the universe, a generic phenomenon predicted by the General relativity, and of the Big Bang, the cosmological Modèle which results from it most naturally. Hubble discovered this law by observing a Décalage towards the almost systematic red in the Galaxie S of which he had discovered before true nature using the observation of a certain type of variable stars, the Céphéide S. These stars are prone to variations of luminosity whose period is connected to the absolute luminosity according to a law established by the astronomer Henrietta Leavitt at the beginning of the 20th century. The observation of the period of variation of the céphéides in another galaxy thus made it possible to deduce their relative distance. The speed of escape of these same galaxies, it, was measured by the observation of a Décalage towards the red of their spectrum, effect interpreted as being due to their movement of escape (see Effect Doppler).

It is by comparing this shift with the distance from these galaxies, that it found a relation linear between the two, announced in 1929. For this reason, the paternity of the law of Hubble is allotted to Edwin Hubble, from where its name. However, two years earlier, Georges Lemaître had predicted the existence of this law by studying a type of model resulting from general relativity. In its article written in French and published in the Yearly of the scientific company of Brussels, it states clearly that this law, that it predicted is checked by the observations of which it lays out (for the majority works of Hubble and Gustaf Strömberg). Being published in French, and being translated into English by Arthur Eddington after the publication of the results of Hubble (in 1931), this result of Lemaître remained unperceived, the more so as the English translation of its article by Eddington is curiously cut down by the key sentence which states the relation.

Formulate law of Hubble

The speed of recession v of the galaxies being known by Doppler effect and its distance D measured by the céphéides (or any other method, to see Measurement of the distances in astronomy), the law of Hubble is written simply

v = H_0 D \;

where

H_0

is the Constante of Hubble, the letter H being of course used in the honor of Hubble. Index 0 is used to indicate that the value of the constant is measured today. This one is indeed not constant in time and was different in the past and certain theories suppose that it would increase since a few billion by years. However only its current value can be estimated directly.

One can replace if necessary speed v by his value deduced from the shift towards the red Z and the Speed of light C to obtain

c Z = H_0 D \;

These two laws are valid only for low values speed and/or relatively weak distances (smaller than the Rayon of Hubble, given by R_H = C / H ₀). At longer distance, the interpretation of the law of Hubble is more subtle and the formula which describes it is modified, to see physical Interprétation of the law of Hubble and Modifications with the law of Hubble below.

Physical interpretation of the law of Hubble

See also: Expansion of the universe

If one restricts oneself with the application of the law of Hubble in the local universe (a few hundreds of million years light), then it is completely possible to interpret the law of Hubble like a movement of the galaxies in space. Nevertheless, the law stating a speed of apparent recession proportional to the distance, its extrapolation results in concluding that sufficiently remote galaxies move away from us at a speed higher than the Speed of light, in apparent contradiction with the restricted Relativité. In fact, it is not within the framework of restricted relativity that one must apply the law of Hubble, but that of the General relativity. This one stipulates inter alia the concept relative speed between two objects (two distant galaxies, for example), is a purely local concept: one can measure the difference in speed between two objects only if their trajectories are “sufficiently close” one to the other. It is advisable of course to specify this last term, which in fact known as primarily that the concept relative speed has direction only in one area of the Espace-temps which can be correctly described by a Métrique of Minkowski. It is indeed possible to show (see Expansion of the universe) that the scale length beyond which one cannot locally describe any more a space expanding by metric of Minkowski is precisely the Rayon of Hubble, that is to say the distance beyond which the speed of recession apparent are precisely relativistic.

Interpretation in term of movement in space describes by restricted relativity thus becomes precisely invalid at the time when the paradox a speed of recession higher than speed of light emerges. This paradox is solved within the framework of the general relativity which makes it possible to not interpret the law of Hubble like a movement in space, but an expansion of space itself. Within this framework, the postulate of impossibility of going beyond speed of light frequently (and improperly) employed in restricted relativity reformulates in a more exact way while stating than no signal can move at an high speed with that of the light, the speeds being locally measured by observers in areas where space can be described by restricted relativity (either with small scales).

Value of the constant of Hubble

Modifications with the law of Hubble

As long as one considers galaxies of which the speed of recession is low, their distance to an observer varies little between the moment when they emit their light and the moment when this one is received by the observer. In the same way as long as the travel time of the light signal is small in front of time characteristic of the expansion, the Temps of Hubble the speed of recession and the growth rate vary little on this interval. Thus, there is no ambiguity in the definition of the quantity v , $H_0$ , and D . For long distance, it is advisable to specify what one understands by distance, and speed of recession. Moreover, nothing guarantees a priori that the linear relation mentioned above valid remainder. There exists in fact of the corrections to the law of Hubble. Those play a crucial role in cosmology because they make it possible in theory to directly reconstitute the recent history of the expansion.

If one calls D the distance which currently separates us from the galaxy observed, one can show that for shifts towards the red moderated, these two quantities are connected by the formula

z = \ frac {H_0 D} {C} + \ frac {1} {2} (1 + q_0) \ left (\ frac {H_0 D} {C} \ right) ^2

where the

q_0

quantity is the Paramètre of deceleration of the expansion, proportional to the derived second of the scale factor. This relation is important because it makes it possible to measure the parameter of deceleration and consequently to deduce the average pressure from the various matter shapes which compose the universe.

In practice, the quantity D is not measurable directly. What one measures, it is either the distance obtained by comparing the apparent luminosity of a star with its presumedly known intrinsic luminosity, $d_L$ (one speaks then about Distance of luminosity), or the distance obtained by measuring its apparent Diamètre, its real size in this case supposed being known, $d_A$ (one then speaks about angular distance). In this case, one generally expresses the distances according to the Redshift and not the opposite, and the formulas are written:

d_L = \ frac {C} {H_0} \ left (Z + \ frac {1} {2} (1 - q_0) z^2 \ right)

d_A = \ frac {C} {H_0} \ left (Z - \ frac {1} {2} (3 + q_0) z^2 \ right)

In practice for remote objects, one does not use the formulas above, which are valid only for small shifts towards the red. See the articles angular distance and Distance from luminosity for more details.

Other assumptions suggested

Reserves, initiated by Albert Einstein itself because of his preference for a static universe (see Universe of Einstein), were formulated with respect to the interpretation of the shift towards the red in term of flight of the galaxies or expansion of space. None the alternatives suggested is regarded as viable today, because of the lack of subjacent theoretical motivations (it primarily acts of phenomena ad hoc only called upon to reinterpret these results, like the tired Lumière) and which fail to propose a cosmological model giving an account of the whole of the observations from now on available (see the article Expansion of the universe). For example, the theory of the tired light fails to explain for the cosmological diffuse Fond has a spectrum black Corps.

References

Jean-Pierre Luminet, the invention of Big Bang , Threshold, coll “Points Sciences” (2004). In particular pages 102 and 108.

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