Hubble's law

The Hubble constant H0, named after the American astronomer Edwin Hubble U.S., is one of the fundamental parameters of cosmology. It describes the rate of expansion of the universe at the present time. Meanwhile, the term Hubble parameter is also often used as the Hubble constant, strictly speaking, is not a constant but changes with time. The homogeneous process of expansion is called the Hubble flow.

The current value ( August 2012) for the Hubble constant was determined by the very precise calibration of the Cepheids as standard candles in the mid-infrared using the Spitzer Space Telescope and is

With Mpc for Megaparsec.

There are however, other measurement results using a variety of methods (see section measurements).

Definition

The expansion of the universe is described quantitatively by the scale factor a (t ), whose time evolution is given as a solution of the Friedmann equations of relativistic cosmology. The time-dependent Hubble parameter describes the expansion rate, and is defined by

Wherein the time derivative of the scale factor is.

The current value of the Hubble parameter is called the Hubble constant:

With the global age. The measured value of the Hubble constant provides the necessary initial condition for the solution of the Friedmann equations.

In the local universe ( over distances that are small compared to the radius of the observable universe ) is the Hubble constant, the proportionality of the ( approximately ) linear relationship between the distances D of galaxies and measured from its spectrum redshifts z:

Here c is the speed of light.

Frequently, the product is interpreted in terms of the Doppler effect as the recession velocity is then obtained

The exact relationship between frequency shift and cosmological distance is not linear and requires an integration over the time course of the scale factor A ( t).

First measurements gave a value of 2.3 × 10-18 s-1 for the Hubble constant H0 in SI units. In most cases, however, one chooses a traditional unit and then receives 72 km s-1 Mpc -1. This number is to be understood: we observe two galaxies A and B and measure their spectral lines. Do the wavelengths so that for the galaxy A higher by 72 km / s value than for B, the Galaxy A should be about 1 Mpc ( which is about three million light years) be further away than the galaxy as

Since galaxies do not only follow the cosmic expansion, but also show their own movements of typically a few hundred km / s, many galaxies must be studied over a sufficiently large distance range to separate both effects. The induced by cosmic expansion, " speed" and the cosmological redshift from a different source than an intrinsic speed and connected to it by the Doppler effect red or blue shift.

Hubble diagram

The plot of the redshift of astronomical objects against their distance from the earth is called Hubble diagram. A uniformly expanding universe means that the objects are located in this diagram along a straight line passing through the origin. The slope of this line is the Hubble constant.

The first Hubble diagram was published in 1929 by Edwin Hubble. In this publication, he reported a linear relationship between the distance of galaxies ( extragalactic nebula ) and its redshift. The determination of the distance of a distant astronomical object without recourse to the red shift takes place from the brightness of standard candles. The image of the object must be to so well resolved that no light other objects distort the measurement result. This is more difficult with increasing distance. The data used in the first Hubble diagram ranged up to a distance of about 2 Mpc. Nearly a century later measurements are possible up to about 700 Mpc. This gives a much more reliable indication of the Hubble constant is possible.

Measurements

Spitzer Space Telescope

Using data from the Spitzer Space Telescope, based on observations in the 3.6 -micron range ( near-infrared ) to recalibrate the Cepheid distance scale, the scientists at the Carnegie Hubble Program received new, highly accurate values ​​for the Hubble constant. Thus this could now be determined more accurately by a factor 3. It amounts to ( 74.3 ± 2.1 ) km / (s · Mpc ). Thus the Hubble constant has only an uncertainty of three percent. (As of August 16, 2012 )

Hubble Space Telescope

The Hubble Space Telescope is able to determine by means of a distance scale distances in the universe and hence the expansion rate of the universe. The indicators serve Cepheids ( pulsating stars with a relationship between period and maximum luminosity ) and supernovae of type Ia ( standard candles). Thus, for Z. accurate value for the Hubble constant has been determined:

Gravitational lensing

A comparatively new method makes use of the gravitational lens effect is used. This brightness variations are evaluated by a gravitational lens. The light from a source galaxy is deflected by a galaxy in front of it, which results in multiple images of the source. If going the brightness of the source galaxy, then this becomes apparent at different times in the different images. From the time difference, the absolute distance can then be calculated. From the determined distance and redshift as a measure of the speed at which objects move away from us, can the expansion rate of the universe determined. The analysis of Hubble images after the gravitational lensing method gives:

WMAP

The space probe WMAP uses the temperature distribution of the electromagnetic radiation in the microwave range. A part of this microwave radiation provides the cosmic background radiation, which is attributed to the Big Bang. You measure extremely small temperature fluctuations ( anisotropies ) caused by scattering of the radiation at the first protogalaxies and their patterns are preserved. For five years, measurements with WMAP ( WMAP5 called ) gives:

Space Telescope Chandra

Measurements with the Chandra Space Telescope revealed:

Supernovae and Cepheids

A distance and speed measurement of 261 Type Ia supernovae and 600 Cepheids found:

Planck Space Telescope

Measurements of the Planck Space Telescope ESA were as follows:

Hubble time

The reciprocal of the Hubble constant 1/H0 is called Hubble time. In uniform expansion in an empty universe it would be like the world age, ie the time elapsed since the Big Bang time.

Depending on the content of the universe to normal ( baryonic ) matter, dark matter and dark energy, the expansion can also be delayed or accelerated, so that the world the age of the Hubble time is different:

By a correction term F

Inter alia depend on the density of the parameters

• The total matter (normal baryonic and dark matter, see Lambda - CDM model ) and
• Of dark energy (see also cosmological constant ).

For example, the world age would be less than the Hubble time (see figure) for a long time discussed cosmological models with flat geometry () and without dark energy ():

With today's measurements of the satellite WMAP ( WMAP5 ) and the 2dFGRS ( 2 ​​degree Field Galaxy Redshift Survey) in combination with the measurements of independent missions

Results in a Hubble time of

A correction factor of

And thus a world age of

The comparison of world ages or Hubble time with independent age determinations of celestial objects such as stars and globular clusters was again important in the critical evaluation of measurements of the Hubble constant and other cosmological parameters: the resulting world age must be greater than that of the individual objects, otherwise arise the measured values ​​does not make sense.

History

The first considerations for Hubble constant believed to originate from the Belgian priest Georges Lemaître and physicist, who in the " Annales de la Société Scientifique de Bruxelles " wrote an essay in 1927 and identified the constant to

After further references, among others, by Carl Wilhelm Wirtz it was a work of Edwin Hubble in 1929 that a powerful case a linear relationship between redshift and distance of galaxies. Hubble determined for the proportionality constant has a value of

The correspondingly small world aged only about two billion years ago was soon seen as problematic compared to age determinations of rocks.

To a first significant correction down it came in the 1950s after the discovery of different stellar populations by Walter Baade. Unaware of this fact, Hubble had assumed in his earlier work on low luminosities for the Cepheids, which he used for distance determination.

Further improvements soon gave values ​​of

The complex multi-step measurement procedure led to a long and intense debate from the 1970s to the 1990s to determine the precise value of the Hubble constant. A group led by Allan Sandage and Gustav Tammann suggested values ​​before by 50 km s -1 Mpc -1, while astronomer Gerard de Vaucouleurs and as Sidney van den Bergh higher values ​​preferred by 100 km s -1 Mpc -1. During this time, it came into use, the Hubble constant as

To describe and illustrate the dependence of further cosmological calculations of the exact value of the Hubble constant by explicit indication of its dependence on the factor h.

This controversy is now largely completed. After the final results of the " H0 Key Project " with the Hubble Space Telescope, the Hubble constant was found to be from the combination of four different methods:

For three years, measurements with the space probe WMAP ( WMAP3 ) and the 2dFGRS data resulted as the value: