# BETELGEUSE If Betelgeuse becomes a supernova what would we see?

Betelgeuse is one of the brightest stars that characterize the constellation of Orion. It is a red supergiant, at least 15 times more massive than the Sun, and with a radius that if positioned in place of the Sun would encompass all the internal planets. It is located relatively close to us, at about 640 light-years. Originally it was a blue giant that after exhausting the nuclear fuel in the nucleus underwent a drastic expansion phase until it became a red supergiant. According to mathematical models, this star is expected to become a supernova.

In recent days, even with the naked eye, there has been a sudden decrease in its brightness. This made many think that it is a prelude to the supernova phase. In reality it is in itself a variable star in brightness, caused by various expulsions of matter in semi-cyclical phases. It could be the last before his majestic death as a supernova, but although the stellar evolution models are extremely sophisticated, we do not have enough “temporal resolution”, precisely at the level of models, that allow us to accurately predict when it will explode. As part of this error bar Betelgeuse could explode from now to the next 100,000 years, and perhaps it may have already exploded since years or decades, but due to its distance and the finiteness of the speed of light the photons of this event have not yet been received.

These days I have been asked what would we see from here if Betelgeuse really entered the supernova phase. I had fun doing some simple calculations that provided me with the following.

We start from the formula:

m = M + 5 – 5 Log d

Where: m = apparent magnitude; M = absolute magnitude, and d = distance (in parsec, where 1 parsec = 3.26 light-years). Here the unknown is precisely m, which indicates what we would see from Earth at the distance at which Betelgeuse is located. The known terms are: m = 197 parsec and M = – 20 (known from a statistical study of the intrinsic brightness on average of supernovae).

In general, magnitude is an extremely practical way of representing the luminous flux of stars in logarithmic form, otherwise we would have to work with huge numbers. The more negative the magnitude, the brighter the star.

Doing the math, in the case of Betelgeuse it results:

m = – 13.5

What does this number mean? It means that if we saw the star in the supernova phase it would produce about 4 times more light than the full Moon (with m = – 12.0).

So the night sky would be illuminated by a “small sun” for at least two weeks. But it would be a “Sun” at least 5 orders of magnitude (1 followed by 5 zeros) less bright than the Sun (m = – 26.7), although 4 times brighter than the Moon.

What we would see would be an extremely bright point-like object. At 640 light years away we cannot see Betelgeuse as an extended object (like the Sun or the Moon). The brightness (on all frequencies) of a star, when not logarithmically expressed in magnitudes, is given by the formula:

L = 4 PI R ^ 2 S T ^ 4 (where R = radius, T = temperature, S = Boltzmann constant).

This means that here the decisive factor is given by the temperature, which in the case of a supernova can reach in the apical instants a value equal to 100 billion Kelvin degrees.

Obviously, apart from the night (and also daytime) spectacle of a supernova 10 times brighter than that seen in 1054 and which then gave rise to the well-known Crab Nebula, our planet would receive a powerful photon bath in all wavelenghts, neutrinos and cosmic rays (especially high energy protons), which would interact with the ionosphere giving rise to more or less striking effects (like aurora borealis) but which probably would not create any danger for us and for the ecosystem.

The Betelgeuse-supernova light would dim exponentially within a month. But in the meantime the shock front created by the supernova would travel at a speed of up to 30,000 Km/sec (equal to one tenth of the speed of light). It can easily be calculated that in 10 years the residue of this supernova would have a diameter of 1 light-year in continuous expansion. So what would we see from here 10 years after the detonation?

Knowing that the distance is d = 640 light-years and that the supernova remnant has reached a diameter D of 1 light year, using the simple formula:

A° = 2 arctan (D / 2d)

we obtain for A° the value of A° = 0.092°, expressed in degrees. Expressed in primes of arc, this corresponds to 5.52′. This is nothing but the angular measurement of the supernova-Betelgeuse remnant, seen from the distance from Earth. Compared to the angular diameter of the Moon which is 30′, we therefore expect that, 10 years after the explosion, the expanding supernova remnant is more than 5 times smaller than the Moon seen from here, and about 6 times larger than the planet Venus (66″). But it would still be an object no longer point-shaped but rather extended, characterized by a very soft brightness, albeit visible to the naked eye as a small weakly luminous ring.

100 years after the explosion, the diameter of the supernova remnant would be 10 light-years, which in angular dimensions for our great-grandchildren who will see the show from here is equivalent to a value of about one degree, or almost twice the angular dimensions of the Moon. It is presumable that at this stage the supernova remnant is much brighter than after only 10 years: the reason is due to the fact that, after a certain time, the supernova shock wave would have compressed the interstellar medium (a little ‘like a snowplow with snow) to the point of making it very dense (from 1 atom per cubic centimeter to one million atoms per cubic centimeter) and very hot, with a temperature of one million degrees well detectable in X-rays. At this stage we would receive a significant amount of high-energy particles and, this time for a long time, probably for 1000 years and beyond. It is unclear how the ionosphere of our planet would be affected (it could be problematic, perhaps).

In the ideal hypothesis that the shock wave does not encounter obstacles in its path (such as gas and interstellar dust swept and then compressed by the shock front), and assuming on the basis of statistical studies that this expanding supernova remnant reaches the maximum possible radius, after about 6500 years the remnant of the supernova-Betelgeuse would have a radius approximately equal to the distance at which Betelgeuse was before the explosion (600-700 light-years). In reality, considering that part of the kinetic energy is transformed into thermal and electromagnetic compression energy of the collected interstellar medium (which becomes a dense very bright envelope), the supernova should be subject to deceleration. Therefore the shock front might reach the solar system in no less than 20,000 years. At that point, provided that the radius reached by the shock front characterizes the upper limit (the lower limit is about 200 light years) detected by a statistical treatment of the observations of a large sample of supernova remnants, the shock front would envelop the solar system with effects that are not easily foreseeable, but certainly not very appealing: it is a dense and extremely hot gas in expansion. Let’s say that in 20,000 years or more the Earth could be engulfed with a “hot flash”, probably for a number of months.

Figure: Betelgeuse is the yellow star (up, left) in the Orion constellation.