Supernovae, neutron stars and black holes (A-level only)

What you'll learn:

• How supernovae produce as much energy in a few days as the Sun will in its entire lifetime.
• Why Type 1a supernovae act as "standard candles" and how they led to the discovery of dark energy.
• The extreme composition and density of neutron stars.
• How to define a black hole and calculate its event horizon (the Schwarzschild radius).

When stars reach the end of their lives, the delicate balance between gravity pulling inwards and radiation pressure pushing outwards is broken. For massive stars, this battle ends in catastrophic collapse, giving birth to some of the most extreme objects in the universe.

Supernovae

A supernova is the explosive death of a star. The defining property of a supernova is a rapid and massive increase in its absolute magnitude. Over just a few days, a dying star can become billions of times brighter, often briefly outshining its entire host galaxy!

To understand just how powerful these explosions are, AQA wants you to compare a supernova's energy output to that of our Sun.

• Over its 10-billion-year main sequence lifetime, the Sun will output roughly $10^{44}J$ of energy.
• A typical supernova releases this exact same amount of energy—$10^{44}J$—in a matter of weeks.

Type 1a Supernovae and Standard Candles

There are several types of supernovae, but Type 1a supernovae are exceptionally important to astrophysicists. A Type 1a supernova occurs in a binary star system when a white dwarf accretes (steals) mass from its companion star. Once the white dwarf's mass reaches a critical threshold (the Chandrasekhar limit, about $1.4$ times the mass of the Sun), it becomes unstable and detonates.

Because they all explode at the exact same critical mass, every Type 1a supernova produces exactly the same peak power output.

Since all Type 1a supernovae have a known peak absolute magnitude ($M\approx -19.3$), they are perfect standard candles for measuring distances to incredibly distant galaxies.

The Type 1a Light Curve

A light curve is simply a graph showing how an object's brightness changes over time. You must be familiar with the shape of the Type 1a light curve.

Notice two key features:

1. A very steep, rapid rise to a sharp peak (occurring around 20 days after the initial explosion).
2. A much slower, gradual exponential decay in brightness over several months. (Remember that the magnitude scale is inverted: a more negative number means a brighter object!)

Dark Energy and the Accelerating Universe

In the late 1990s, astronomers used Type 1a supernovae to measure the distances to very faraway galaxies. They expected to find that the universe's expansion was slowing down due to gravity.

Instead, they found that distant supernovae were noticeably dimmer than expected. If they were dimmer, they must be further away than the standard expansion models predicted. This controversial discovery led to the conclusion that the expansion of the Universe is actually accelerating.

To explain this acceleration, physicists proposed the existence of dark energy—a mysterious repulsive force that permeates all space. Because dark energy is poorly understood and we cannot yet detect it directly, it remains one of the biggest controversies and open questions in modern cosmology.

Neutron Stars

When a giant star (between about $8$ and $20$ solar masses) goes supernova, its core collapses inwards. Gravity squeezes the core so tightly that electrons are forced into protons, combining to form neutrons. The remnant left behind is a neutron star.

Gamma Ray Bursts

When supergiant stars finally collapse to form either a neutron star or a black hole, the violent implosion can fire out twin jets of highly energetic radiation from the poles. We observe these across the universe as gamma ray bursts (GRBs). These bursts are fleeting but represent some of the most luminous electromagnetic events in the universe.

Black Holes

If the dying star's core is incredibly massive (greater than about $3$ solar masses), not even the outward pressure of tightly packed neutrons can halt the gravitational collapse. The core collapses indefinitely to a single point of infinite density, called a singularity. This creates a black hole.

Because nothing can travel faster than the speed of light, absolutely nothing—not even photons of light—can escape the gravitational pull once it passes a certain boundary.

Supermassive Black Holes

While standard "stellar-mass" black holes form from dying stars, there is another terrifyingly large class of black holes. Supermassive black holes contain the mass of millions or even billions of Suns. Astronomers now believe that a supermassive black hole resides at the centre of almost every major galaxy, including our own Milky Way (which hosts a black hole called Sagittarius A*).

The Schwarzschild Radius

The boundary around a black hole where the escape velocity becomes exactly equal to the speed of light ($c$) is called the event horizon. The distance from the singularity to the event horizon is known as the Schwarzschild radius ($R_s$).

You can calculate this radius using the formula:

$$R_s\approx \frac{2GM}{c^2}$$

Where:

• $R_s$ is the Schwarzschild radius in metres ($m$)
• $G$ is the gravitational constant ($6.67\times 10^{-11}{N\; m}^2{kg}^{-2}$)
• $M$ is the mass of the black hole in kilograms ($kg$)
• $c$ is the speed of light in a vacuum ($3.00\times 10^8{m\; s}^{-1}$)

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