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Hubble's law

2007 Schools Wikipedia Selection. Related subjects: Space (Astronomy)

          Physical cosmology

     * Age of the universe
     * Big Bang
     * Blueshift
     * Comoving distance
     * Cosmic microwave background
     * Dark energy
     * Dark matter
     * FLRW metric
     * Friedmann equations
     * Galaxy formation
     * Hubble's law
     * Inflation
     * Large-scale structure
     * Lambda-CDM model
     * Metric expansion of space
     * Nucleosynthesis
     * Observable universe
     * Redshift
     * Shape of the universe
     * Structure formation
     * Timeline of the Big Bang
     * Timeline of cosmology
     * Ultimate fate of the universe
     * Universe

            Related topics
     * Astrophysics
     * General relativity
     * Particle physics
     * Quantum gravity


   Hubble's law is the statement in physical cosmology that the redshift
   in light coming from distant galaxies is proportional to their
   distance. The law was first formulated by Edwin Hubble and Milton
   Humason in 1929 after nearly a decade of observations. It is considered
   the first observational basis for the expanding space paradigm and
   today serves as one of the most often cited pieces of evidence in
   support of the Big Bang. The most recent calculation of the constant,
   using the satellite WMAP began in 2003, yielding a value of 71 ± 4
   (km/s)/ Mpc. As of the 2006 data, that figure has been refined to 70
   ^+2.4[−3.2] (km/s)/Mpc.

Discovery

   In the decade before Hubble made his observations, a number of
   physicists and mathematicians had established a consistent theory of
   the relationship between space and time by using Einstein's field
   equation of general relativity. Applying the most general principles to
   the question of the nature of the universe yielded a dynamic solution
   that conflicted with the then prevailing notion of a static Universe.

   However, a few scientists continued to pursue the dynamical universe
   and discovered that it could be characterized by a metric that came to
   be known after its discoverers, namely Friedmann, Lemaître, Robertson,
   and Walker. When this metric was applied to the Einstein equations, the
   so-called Friedmann equations emerged which characterized the expansion
   of the universe based on a parameter known today as the scale factor
   which can be considered a scale invariant form of the proportionality
   constant of Hubble's Law. This idea of an expanding spacetime would
   eventually lead to the Big Bang and to the Steady State theories.

   Before the advent of modern cosmology, there was considerable talk as
   to what was the size and shape of the universe. In 1920 a famous debate
   took place between Harlow Shapley and Heber D. Curtis over this very
   issue with Shapley arguing for a small universe the size of our Milky
   Way galaxy and Curtis arguing that the universe was much larger. The
   issue would be resolved in the coming decade with Hubble's improved
   observations.
   Edwin Hubble.
   Enlarge
   Edwin Hubble.

   Edwin Hubble did most of his professional astronomical observing work
   at Mount Wilson observatory, at the time the world's most powerful
   telescope. His observations of Cepheid variable stars in spiral nebulae
   enabled him to calculate the distances to these objects. Surprisingly
   these objects were discovered to be at distances which placed them well
   outside the Milky Way. The nebulae were first described as "island
   universes" and it was only later that the moniker "galaxy" would be
   applied to them.

   Combining his measurements of galaxy distances with Vesto Slipher's
   measurements of the redshifts associated with the galaxies, Hubble
   discovered a rough proportionality of the objects' distances with their
   redshifts. Though there was considerable scatter (now known to be due
   to peculiar velocities), Hubble was able to plot a trend line from the
   46 galaxies he studied and obtained a value for the Hubble constant of
   500 km/ s/ Mpc, which is much higher than the currently accepted value
   due to errors in his distance calibrations. Such errors in determining
   distance continue to plague modern astronomers. (See the article on
   cosmic distance ladder for more details.)

   In 1958 the first good estimate of H[0], 75 km/s/Mpc, was published (by
   Allan Sandage). But it would be decades before a consensus was achieved
   (see 'Measuring the Hubble constant' below).

   After Hubble's discovery was published, Albert Einstein abandoned his
   work on the cosmological constant which he had designed to allow for a
   static solution to his equations. He would later term this work his
   "greatest blunder" since the belief in a static universe was what
   prevented him from predicting the expanding universe. Einstein would
   make a famous trip to Mount Wilson in 1931 to thank Hubble for
   providing the observational basis for modern cosmology.

Interpretation

   The discovery of the linear relationship between recessional velocity
   and distance yields a straightforward mathematical expression for
   Hubble's Law as follows:

          v = H[0]D

   where v is the recessional velocity due to redshift, typically
   expressed in km/s. H[0] is Hubble's constant and corresponds to the
   value of H (often termed the Hubble parameter which is a value that is
   time dependent) in the Friedmann equations taken at the time of
   observation denoted by the subscript 0. This value is the same
   throughout the universe for a given conformal time. D is the proper
   distance that the light had traveled from the galaxy in the rest frame
   of the observer, measured in mega parsecs: Mpc.

   For relatively nearby galaxies, the velocity v can be estimated from
   the galaxy's redshift z using the formula v = zc where c is the speed
   of light. For far away galaxies, v can be determined from the redshift
   z by using the relativistic Doppler effect. However, the best way to
   calculate the recessional velocity and its associated expansion rate of
   spacetime is by considering the conformal time associated with the
   photon traveling from the distant galaxy. In very distant objects, v
   can be larger than c. This is not a violation of the special relativity
   however because a metric expansion is not associated with any physical
   object's velocity.

   In using Hubble's law to determine distances, only the velocity due to
   the expansion of the universe can be used. Since gravitationally
   interacting galaxies move relative to each other independent of the
   expansion of the universe, these relative velocities, called peculiar
   velocities, need to be accounted when applying Hubble's law. The Finger
   of God effect is one result of this phenomenon discovered in 1938 by
   Benjamin Kenneally. Systems that are gravitationally bound, such as
   galaxies or our planetary system, are not subject to Hubble's law and
   do not expand.

   The mathematical derivation of an idealized Hubble's Law for a
   uniformly expanding universe is a fairly elementary theorem of geometry
   in 3-dimensional Cartesian/Newtonian coordinate space, which,
   considered as a metric space, is entirely homogeneous and isotropic
   (properties do not vary with location or direction). Simply stated the
   theorem is this:

          Any two points which are moving away from the origin, each along
          straight lines and with speed proportional to distance from the
          origin, will be moving away from each other with a speed
          proportional to their distance apart.

   The ultimate fate of the universe and the age of the universe can both
   be determined by measuring the Hubble constant today and extrapolating
   with the observed value of the deceleration parameter, uniquely
   characterized by values of density parameters (Ω). A so-called "closed
   universe" (Ω>1) comes to an end in a Big Crunch and is considerably
   younger than its Hubble age. An "open universe" (Ω≤1) expands forever
   and has an age that is closer its Hubble age. For the accelerating
   universe that we inhabit, the age of the universe is coincidentally
   very close to the Hubble age.
   Enlarge
   The ultimate fate of the universe and the age of the universe can both
   be determined by measuring the Hubble constant today and extrapolating
   with the observed value of the deceleration parameter, uniquely
   characterized by values of density parameters (Ω). A so-called "closed
   universe" (Ω>1) comes to an end in a Big Crunch and is considerably
   younger than its Hubble age. An "open universe" (Ω≤1) expands forever
   and has an age that is closer its Hubble age. For the accelerating
   universe that we inhabit, the age of the universe is coincidentally
   very close to the Hubble age.

   The value of Hubble parameter changes over time either increasing or
   decreasing depending on the sign of the so-called deceleration
   parameter q which is defined by:

          q = -H^{-2}\left( {{\; dH}\over {\; dt}} + H^2 \right)

   In a universe with a deceleration parameter equal to zero, it follows
   that H = 1/t, where t is the time since the Big Bang. A non-zero,
   time-dependent value of q simply requires integration of the Friedmann
   equations backwards from the present time to the time when the comoving
   horizon size was zero.

   We may define the "Hubble age" (also known as the "Hubble time" or
   "Hubble period") of the universe as 1/H, or 977793 million
   years/[H/(km/s/Mpc)]. The Hubble age comes to 13968 million years for
   H=70 km/s/Mpc, or 13772 million years for H=71 km/s/Mpc. The distance
   to a galaxy being approximately zc/H for small redshifts z, and
   expressing c as 1 light-year per year, this distance can be expressed
   simply as z times 13772 million light-years.

   It was long thought that q was positive, indicating that the expansion
   is slowing down due to gravitational attraction. This would imply an
   age of the universe less than 1/H (which is about 14,000 million
   years). For instance, a value for q of 1/2 (one theoretical
   possibility) would give the age of the universe as 2/(3H). The
   discovery in 1998 that q is apparently negative means that the universe
   could actually be older than 1/H. In fact, independent estimates of the
   age of the universe come out fairly close to 1/H

Olbers' paradox

   The expansion of space summarized by the Big Bang interpretation of
   Hubble's Law is relevant to the old conundrum known as Olbers' paradox:
   if the Universe were infinite, static, and filled with a uniform
   distribution of stars, then every line of sight in the sky would end on
   a star, and the sky would be as bright as the surface of a star.
   However, the night sky is largely dark. Since the 1600s, astronomers
   and other thinkers have proposed many possible ways to resolve this
   paradox, but the currently accepted resolution depends in part upon the
   Big Bang theory. In a universe that exists for a finite amount of time,
   only the light of finitely many stars has had a chance to reach us yet,
   and the paradox is resolved. Additionally, in an expanding universe
   distant objects recede from us which cause the light emanating from
   them to be redshifted and diminished in brightness, but this only
   partially resolves the paradox. According to the Big Bang theory, both
   effects contribute (the finite duration of the Universe's history being
   the more important of the two). The darkness of the night sky, then,
   provides a kind of confirmation for the Big Bang.

Measuring the Hubble constant

   For most of the second half of the 20th century the value of H[0] was
   estimated to be between 50 and 90 (km/s)/Mpc. The value of the Hubble
   constant was the topic of a long and rather bitter controversy between
   Gérard de Vaucouleurs who claimed the value was 80 and Allan Sandage
   who claimed the value was 40. In 1996, a debate moderated by John
   Bahcall between Gustav Tammann and Sidney van den Bergh was held in
   similar fashion to the earlier Shapley-Curtis debate over these two
   competing values. This difference was partially resolved with the
   introduction of the Lambda-CDM model of the Universe in the late 1990s.
   With this model observations of high-redshift clusters at X-ray and
   microwave wavelengths using the Sunyaev-Zel'dovich effect, measurements
   of anisotropies in the cosmic microwave background radiation, and
   optical surveys all gave a value of around 70 for the constant. In
   particular the Hubble Key Project (led by Dr. Wendy L. Freedman,
   Carnegie Observatories) gave the most accurate optical determination in
   May 2001 with its final estimate of 72±8 (km/s)/Mpc, consistent with a
   measurement of H[0] based upon Sunyaev-Zel'dovich effect observations
   of many galaxy clusters having a similar accuracy. The highest accuracy
   cosmic microwave background radiation determinations were 71±4
   (km/s)/Mpc, by WMAP in 2003, and 70 (km/s)/Mpc, +2.4/-3.2 for
   measurements up to 2006. With 1 parsec approximated to 3.086\times
   10^{16} meters, in the metric system H[0] is about 2.3\times 10^{-18}
   (m/s)/m (or Hertz). The consistency of the measurements from all three
   methods lends support to both the measured value of H[0] and the
   Lambda-CDM model.

   A value for q was measured from standard candle observations of Type Ia
   supernovae was determined in 1998 to be negative which implied, to the
   surprise of many astronomers, the expansion of the universe is
   currently "accelerating" (although the Hubble factor is still
   decreasing with time; see the articles on dark energy and the
   Lambda-CDM model).

   In August 2006, using NASA's Chandra X-ray Observatory, a team from
   NASA's Marshall Space Flight Centre (MSFC) found the Hubble constant to
   be 77 kilometers per second per megaparsec (a megaparsec is equal to
   3.26 million light years), with an uncertainty of about 15%
   Spaceflightnow - Chandra independently determines Hubble constant
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