Discovering a pattern

1st January 1925 was the day when we discovered the Universe. It was when Edwin Hubble’s work showed that the Milky Way is not the only galaxy in the cosmos. This discovery set the stage for the expanding Universe and an initial Big Bang. But while observing the distant galaxies, Hubble discovered a pattern. He noted that a galaxy’s recessional velocity v (the velocity with which it appears to move away from us) is proportional to its distance d.

This means that the farther a galaxy is, the faster it moves away from us. This is called Hubble’s law (or the Hubble–Lemaître law). Although the relation appears simple, it contains one of the Universe’s biggest mysteries. It’s the number that equates the two sides, the Hubble constant.

Over the years, researchers have tried to limit the value of the Hubble constant. Still, the results added more to the confusion every time rather than clearing things up, leading to a cosmology crisis. But before moving to this crisis, let’s try to understand what the Hubble constant portrays in the physical sense.

The meaning of the Hubble constant

The Hubble constant establishes a direct relationship between a galaxy’s recessional velocity and the distance to that particular galaxy. If we measure this recessional velocity in terms of km/s and take the distance between us and the galaxy in Megaparsecs (Mpc), it would clearly state the Hubble constant has units of km/s/Mpc. A parsec is a unit of cosmic distance that equals 3.26 light years. You can learn more about cosmic distances in our Basics of Astrophysics series.

So, if the value of the Hubble constant is 70 Km/s/Mpc, it would mean that for every megaparsec of its distance, a galaxy will acquire an extra recessional velocity of 70km/s.

Represented by H_o, the Hubble constant is a significant number in cosmology. It can help have an end-to-end test of our understanding of the Universe, from the Big Bang to its final fate. The physical representation of H_o seems easy to comprehend. But if it is so easy, why is it so difficult to obtain a precise value of the Hubble constant? Why is it considered a notoriously tricky entity to calculate? The answer lies in the parameters involved to evaluate the same.

Determining the Hubble constant

To calculate the value of the Hubble constant observationally, we need two quantities: the recessional velocity of a galaxy v and its distance d from us. The recessional velocity can be measured by observing the wavelength shifts of spectral lines emitted by the object, known as the object’s cosmological redshift. However, the second parameter, the distance, is comparatively problematic.

Cepheid variables

One of the standard ways to measure the distance to a galaxy is by observing the cepheid variables in it. Like all other variable stars, Cepheids progress through a complete cycle from maximum brightness to a minimum and then back to maximum again. A Cepheid’s variability period is directly related to its luminosity. The longer the variability period, the more luminous the Cepheid is.

Astronomers observe the Cepheids and compare their apparent brightness with their intrinsic brightness. Then, by measuring the difference between the observed and actual brightness, one can estimate their distance using the distance modulus equation. In this way, Cepheid variables act like standard candles, and Edwin Hubble used these variable stars to measure the distance in the first place.

However, before making calculations, the period-luminosity relationship has to be calibrated with nearby Cepheid variables, whose distance can be measured using the parallax method. This stepwise measurement of cosmic distances is called the cosmic distance ladder, and the problem is that the uncertainty compounds with each step.

Edwin Hubble was able to plot the variation between the distance and recessional velocity for 46 galaxies, thereby obtaining a value for the Hubble constant of 500 km/s/Mpc or about seven times what astronomers think it is today. But Cepheids can only be used to measure distances from about a kiloparsec to 50 Megaparsecs. So what about distances greater than this range? We cannot fix a constant’s value just by observing the behavior of galaxies up to 50 Mpc. We need to peer further for precise estimates, and that’s where the type Ia supernovae come into the picture.

Type Ia supernovae

A type Ia supernova occurs when a white dwarf feeding upon its companion undergoes a runaway fusion, eventually exploding into a supernova. Such explosions are exceptionally bright, making them excellent standard candles to calculate longer distances.

The Hubble SH0ES program, which stands for Supernova, H0, for the Equation of State of Dark Energy, has significantly contributed to calculating the Universe’s expansion rate using these supernovae. In 2019, the SH0ES team reported a value of Hubble constant around 74 km/s/Mpc. The SH0ES project considers the galaxies lying within 2 billion light-years away, which means that it measures the present expansion rate of the Universe. But when cosmologists compared it with theoretical predictions, a crisis broke in front of them.

Theory vs. Observation

After the Big Bang, we know that the superheating of all the matter in the Universe released enormous amounts of energy. As the Universe expanded, the radiation got more and more redshifted. The cosmic microwave background, or CMB, is extremely helpful in estimating how much the radiation has redshifted. The CMB is the remnant electromagnetic radiation from an early stage of the Universe, which is not uniform. Instead, it’s made up of hotter and colder patches that signify the clumpiness of matter and energy in the very early Universe.

Researchers combined fundamental physics with estimates of the amount of mass and energy contained within the Universe to model its expansion from its initial state to the present day. Consequently, with the precision obtained in different methods, the best measurements appeared to converge on a value between 67-68 km/s/Mpc. That’s clearly different from what the observational values say. The mathematical predictions expect the Universe to expand slower than that calculated from Hubble’s data. And this has been one of the biggest crises in cosmology so far.

Researchers have been trying to achieve greater accuracy in their observational values, and recently, they have reached a new milestone in this domain. The SH0ES team reviewed all the data taking into account over 1,000 Hubble orbits, and analyzed 42 supernovae milepost markers that are exploding at a rate of about one per year. This almost marks a complete analysis of all the supernovae accessible to the Hubble Space telescope so far.

Finally, they converged on a Hubble constant estimate of 73 ± 1 km/s/Mpc. This value is again higher than the theoretical predictions of 67.5 ± 0.5 km/s/Mpc. But, the measurement is about eight times more precise than Hubble’s expected capability. And given the large Hubble sample size this time, there is only a one-in-a-million chance of the new estimate being wrong.

Although the cause of the discrepancy between the predicted and observed values of the Hubble constant remains uncertain, the new results are expected to open the door to discovering new physics. Astronomers are also looking for new phenomena and objects to measure the distances in the Universe. They include neutron star mergers and red giant stars. Also, with NASA’s Webb Space Telescope, we can expect to have sharper resolutions and even more precise results in the future.

Learn Astrophysics at Home

Did you always want to learn how the universe works? Read our 30-article Basics of Astrophysics series absolutely free of cost. From the popular topics such as stars, galaxies, and black holes to the detailed concepts of the subject like the concept of magnitude, the Hertzsprung Russell diagram, redshift, etc., there is something for everyone in this series. All the articles are given here. Happy reading!