Understanding Hubble's Law: Cosmic Expansion And Distant Galaxies

Edwin Hubble's 1929 paper, A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae, revealed that the universe is expanding and changed the course of science. Hubble's Law, also known as the Hubble-Lemaître Law, states that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the further away a galaxy is, the faster it is moving away from us. This is considered the first observational basis for the expansion of the universe and is one of the most important numbers in cosmology.

Hubble's Law can be expressed as v = H0D, where v is the recessional velocity, and D is the proper distance to a galaxy from the observer. The Hubble Constant, H0, represents the constant rate of cosmic expansion and has a value of about 70 km/s/Mpc. The inverse of the Hubble Constant is the Hubble Time, which is approximately 14.4 billion years and is related to the age of the universe.

Despite nearly a hundred years of astronomical measurements, scientists still debate the exact value of the Hubble Constant. The true value could provide valuable insights into our understanding of physics and the history of the universe.

Hubble's law

History

The discovery of Hubble's law is attributed to Edwin Hubble, who published his findings in 1929. However, Hubble's work built on the contributions of several scientists before him. In 1912, Vesto Slipher measured the first Doppler shift of a "spiral nebula" (the term used for spiral galaxies at the time) and discovered that almost all such nebulae were receding from Earth. In 1922, Alexander Friedmann derived a set of equations from Einstein's field equations, now known as the Friedmann equations, which showed that the universe might be expanding and presented the expansion speed if that were the case. Also in 1922, German astronomer Carl Wilhelm Wirtz deduced that more distant galaxies recede faster from the observer. In 1927, Georges Lemaître independently derived that the universe might be expanding and observed the proportionality between recessional velocity and distance to distant bodies.

Application

> v = H0D

Where:

• V is the recessional velocity, typically expressed in km/s
• H0 is Hubble's constant and corresponds to the value of H (often termed the Hubble parameter) in the Friedmann equations at the time of observation
• D is the proper distance from the galaxy to the observer, measured in megaparsecs (Mpc)

The Hubble constant can also be stated as a relative rate of expansion:

> H0 = 7%/Gyr

Meaning that at the current rate of expansion, it takes one billion years for an unbound structure to grow by 7%. The inverse of the Hubble constant, known as the Hubble time, is approximately 14.4 billion years. This can be used to estimate the age of the universe, which is currently estimated to be around 13.8 billion years.

Measurement

The Hubble constant can be measured in three main ways:

• Astronomical measurements: This involves measuring the distance to astronomical objects and their "recession velocity" or how fast they are moving away from the observer. The recession velocity can be determined using the Doppler effect, which causes the light from stars and galaxies moving away from Earth to increase in wavelength (a phenomenon known as redshift).
• Gravitational waves: Gravitational waves are ripples in spacetime produced during highly energetic events like neutron star collisions. By analysing the shape of these waves, astronomers can calculate how much energy was released during the collision and how much energy the signals are carrying when they reach Earth, which can then be used to calculate distance.
• Cosmic Microwave Background (CMB) modelling: The CMB is the radiation left over from the Big Bang. As the universe expanded, this radiation was redshifted, and the resulting clumpiness of matter and energy in the early universe was recorded in the CMB. By combining fundamental physics with estimates of the mass and energy contained within the universe, cosmologists can model the expansion of the universe and reproduce the observed clumpiness in the CMB.

Despite these methods, scientists still cannot agree on the exact value of the Hubble constant, and the true number remains a subject of active research.

The expansion of the universe

Hubble's Law can be expressed as v = H0D, where H0 is the Hubble constant, or the constant of proportionality between the "proper distance" D to a galaxy and its speed of separation v. The Hubble constant is often quoted in km/s/Mpc, which gives the speed of a galaxy 1 megaparsec away as 70 km/s. The Hubble constant can also be stated as a relative rate of expansion, which would be H0 = 7%/Gyr. This means that at the current rate of expansion, it would take one billion years for an unbound structure to grow by 7%.

The Hubble constant is considered one of the most important numbers in cosmology as it tells us how fast the universe is expanding, which can be used to determine the age of the universe and its history. The expansion of the universe is driven by all the mass, radiation, and energy contained within it. The Friedmann equation, derived from Einstein's famous equations for general relativity, can be used to predict how quickly the universe is expanding mathematically. These equations state that a denser universe expands more quickly, so the expansion was fastest when all the particles in the universe were packed closely together after the Big Bang.

The inverse of the Hubble constant is the Hubble time, which is approximately 14.4 billion years and is related to the age of the universe. The current best estimate for the age of the universe is 13.8 billion years. However, there is a slight complication as the speeds of the farthest stars and galaxies that we can observe don't match what the Hubble constant predicts. This is because the Hubble constant is not actually a constant and changes over time.

The age of the universe

The Hubble constant is denoted by the symbol H0, where the subscript denotes that the value is measured at the present time. It is named after Edwin Hubble, who first calculated the constant in 1929. Hubble's original value for H0 was 500 km per second per megaparsec, but modern estimates place the value at about 67 km per second per megaparsec. The reciprocal of the Hubble constant lies between 13 billion and 14 billion years, and this cosmic timescale serves as an approximate measure of the age of the universe.

The Hubble constant is calculated by measuring the "recession velocity" of an astronomical object (i.e., how fast it is moving away from the observer) and its distance from Earth. The recession velocity can be determined by measuring the redshift of an object—the shift in the light it emits toward the red end of the visible light spectrum. The farther away an object is, the faster it is moving away, and thus, the greater its redshift.

The history of the universe

The Ancient View: Before the development of modern science, humans had various beliefs about the size and shape of the universe. Some ancient cultures envisioned the universe as a vast, infinite expanse, while others proposed more limited conceptions.

The Great Debate: In the early 20th century, a significant debate took place between astronomers Harlow Shapley and Heber Curtis. Shapley argued for a small universe confined to the Milky Way galaxy, while Curtis proposed a much larger universe, indicating the existence of galaxies beyond the Milky Way.

Edwin Hubble's Discovery: In 1929, astronomer Edwin Hubble published groundbreaking research that revolutionized our understanding of the cosmos. Hubble's Law, also known as the Hubble-Lemaître law, revealed that galaxies are moving away from Earth at speeds proportional to their distance. This observation provided strong evidence for an expanding universe and became a foundational concept in physical cosmology.

Improving Measurements: Over the following decades, astronomers refined their techniques and utilized more advanced technology to study the universe. They employed methods such as measuring redshift, using "standard candles" to determine distances, and analyzing the cosmic microwave background radiation. These efforts led to more precise measurements and a deeper understanding of cosmic expansion.

The Hubble Space Telescope: Named after Edwin Hubble, the Hubble Space Telescope played a crucial role in advancing our knowledge of the universe. It provided detailed observations of distant celestial objects, such as supernovae and Cepheid variable stars, allowing for improved calculations of distances and a better understanding of cosmic expansion.

Dark Energy and Dark Matter: In the late 20th and early 21st centuries, astronomers made intriguing discoveries about the composition of the universe. They found that it consists of not only ordinary matter (baryons) but also exotic forms of matter and energy, such as dark matter and dark energy. Dark energy, in particular, was proposed to explain the accelerating expansion of the universe.

Ongoing Research: Today, astronomers and cosmologists continue to refine their measurements and models of the universe. The quest to determine the precise value of the Hubble constant remains a challenging puzzle, with different methods yielding slightly different results. This discrepancy has led to new hypotheses, such as the possible existence of dark radiation or new forms of dark energy.

The history of our understanding of the universe is a fascinating journey from ancient speculation to modern scientific exploration. Each discovery has deepened our appreciation of the vastness and complexity of the cosmos, and ongoing research continues to unveil new mysteries and insights.

The discovery of Hubble's law

Edwin Hubble is credited with the discovery of Hubble's Law, which he published in 1929. However, Hubble's work built on the research of others, and the Belgian priest, astronomer and academic Georges Lemaître had derived the same principle two years earlier, in 1927. Hubble's work was also supported by the observations of Vesto Slipher, who had been studying the movement of spiral nebulae (now known to be spiral galaxies) since 1912.

Hubble's Law states that the universe is expanding, and that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the further away a galaxy is, the faster it is moving away from us. This is now considered the first observational basis for the expansion of the universe and is often cited in support of the Big Bang model.

Hubble's discovery was made using observations of distant galaxies. He measured the distance of these galaxies from Earth and calculated their recession velocity, finding a rough proportionality between the two. This was possible thanks to Henrietta Leavitt's period-luminosity scale, which allowed him to calculate the distance of variable stars from Earth.

Hubble's original estimate for the Hubble constant, the ratio of distance to redshift, was 170 kilometres per second per light year of distance. This has since been refined, and the current value is around 70 kilometres per second per megaparsec.

Hubble's discovery has been described as one of the most important events in the history of astronomy, and it has had a profound impact on our understanding of the universe.

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