A Machine Learning View of GW Supernovae

Title: Exploring supernova gravitational waves with machine learning

Authors: Ayan Mitra, Bekdaulet Shukirgaliyev, Y. Sultan Abylkairov, Ernazar Abdikamalov

Status: Submitted to MNRAS. [open access]

Institution of the first author: Department of Physics, Nazarbayev University, 53 Kabanbay Batyr Ave, 010000 Astana, Kazakhstan

How to measure the gravitational wave signal of a supernova if each event is unique? The authors of today’s paper use machine learning to rank the ancestors of more than 400 supernova waveforms and determine which qualities, if any, best predict the original mass of the supernova. dead star.

Beauty has been superficial

When a supernova (SN) occurs, the center of a dying star warps the very fabric of space and time around it, generating ripples that we measure as gravitational waves (GW). The death of massive stars can lead to the formation of black holes (BH) and neutron stars (NS), the giant corpses of our cosmos. Yet astronomers are unable to look directly at them as they form – the star’s innermost region is so dense it takes hours for photons to escape. During these few hours, the photons ricochet around inside the star, gaining and losing energy, so that they no longer carry information about the environment in which they were born.

Conversely, astronomers can immediately observe the formation of an NS or a BH thanks to gravitational waves, the imprint that their movements leave in space-time. Multimessenger observations of supernovae will be extremely valuable for this idea. However, compared to the familiar binary spirals of black holes, GW SNs are a bit more complicated, producing waveforms that are unique per event and difficult to interpret intuitively.

These obstacles currently prevent astronomers from learning the details of the deeper parts of a newborn corpse star, such as how the neutron star’s equation of state behaves or when it actually becomes a black hole. Surprisingly, astronomers also don’t know which stars (called “ancestors” by SN astronomers) become which stellar corpses when they die. Today’s authors sought to extract the progenitor mass of an SN by applying a machine learning algorithm to its gravitational wave signature and determine which moments of the gravitational wave signal best encode this information.

It’s what’s inside that counts

In its final hours, a star’s core fuses together all the elements of the periodic table, from hydrogen to iron. Meanwhile, the other layers of the star feel pulled towards the center by gravity. As these outer layers are pulled down, the base material acts as a hardened surface, rejecting the falling material and “bouncing” it back up (Figure 1).

Figure 1: Panel A: An illustration of the onion-shaped layers of a massive end-of-life star. The core stops fusing to the iron, but the force of gravity attracts the surrounding layers more. Panel B: Within milliseconds, the star’s inner layers collapse into a proto-neutron star, throwing off any further flow of matter with its neutron degenerating pressure. The material bounces off the surface and a shock wave (dotted line) is formed. If the shock is strong enough to survive the surface of the star, it will completely untie it and explode into a supernova.

The material bounces off the surface and a shock wave (dotted line) is formed. If the shock is strong enough to survive the surface of the star, it will completely untie it and explode into a supernova.

But there is another factor: how a star rotates. Some stars rotate slowly, and others so quickly that they flatten into an egg shape (like Achernar for example). The centrifugal force generated by strong rotation can also contribute greatly to the net direction of force and pressure inside a dying star. Thus, fast-rotating models avoid implosion via the magneto-rotational mechanism: the kinetic energy of their rotation is at the origin of the explosion. The proto-neutron star at the center of the explosion becomes slightly more egg-shaped as it spins, creating a visible disturbance with the GWs. The more massive or aspherical the object, the greater the stress GW (or “force”) to be measured on Earth.

In non-rotating or slowly rotating stars, the neutrinos emitted by the surface of the core (or proto-neutron star) cannot escape and cause a convection wave. There is a standoff between matter wanting to rain down and the pressure of neutrinos trying to escape, called “SASI” (Standing Accretion Shock Instability). When this external pressure prevails, the explosion occurs and prevents the star from falling completely on itself.

Therefore, the dynamics of the denser regions of the supernova strongly depend on the rotational force of the star, and in turn, gravitational waves as well. GW signatures of fast-spinning models are most affected by their flattening, while non-spinning models are considered to be most affected by core bouncing.

The wisdom of machine learning

The authors of today’s article applied a machine learning (ML) technique called “random forest” to digitally generate supernova gravitational waves. A random forest works much like the logic of a flowchart, representing a large number of decision trees (explained in this AstroBite!). The authors generated the waveforms from a multitude of different starting conditions (Figure 2).

Figure 2: Distortion of gravitational waves as time progresses in supernova explosion. Each panel represents a different spin rate (top: slow; middle: moderate, bottom: fast) for each of the four ZAMS masses, indicated by the number following the “s” in the figure legend. Note that the most drastic characteristic appears around 0 ms: it is the “bounce”. At >6 ms, convection occurs within the supernova, creating features that appear more chaotic and unpredictable. Figure 3 in the article, with text added by the AstroBites author.)

The following features were sampled by the authors when generating their SN waveforms:

  • 100 different rotation profiles, ranging from slow to fast.
  • Deletonization: how much of the mass of the nucleus is radiated into leptons – electrons and neutrinos. (This affects power budget and core mass by +/- 10%)
  • 4 different Zero Age Main Sequence (ZAMS) progenitor masses: 12, 15, 27 and 40 solar masses. (These are sizes commonly used in the literature.)

Using each of these combinations, the authors found a total of 402 SN models that successfully exploded (instead of collapsing on their own). The next step was to train a fraction of their waveform bank on the ML algorithm to see if it could correctly identify the ZAMS mass of the remaining untested population.

Beauty in the eye of the classifier

The authors find that there are very few physically discernible differences between ZAMS masses when examining GW strains of this duration (Figure 3). This may imply that the information provided by gravitational waves, such as the strength of the bounce, was not sufficient to represent the iron core at the time of star death. (The mass of the iron core is a quantity related to the mass of ZAMS, Figure 1.)

Figure 3: A confusion matrix, or the performance of the ML algorithm. Here it is tested on 10% of the authors catalog of 402 waveforms to predict the mass of the supernova ancestor at a GW strength of SNR=100. The success of the algorithm is determined by identifying how many times the ML was correct (diagonal boxes) for each progenitor size (x and y axes). Each time the ML classifier was incorrect is recorded in the off-diagonal boxes. (Figure 6 in today’s article.)

Additionally, they find that the ML algorithm was best able to classify more accurately using waveform information that spans -2 to 6 milliseconds (Figure 2). To convince yourself of this, revisit Figure 2 and ask yourself which areas were most reproducible between SNe, and which parts of the wave are unique to an individual explosion. The latter is difficult to anticipate with each new explosion created by nature.

The biggest difference of all the waveforms, in the eyes of the ML, is around 2.5ms. Physically, this area of ​​the waveform is called “ringdown”, i.e. when the formed cadaver relaxes into its static rotation (Figure 2). The fact that this moment is important for the ML classifier means that the difference in initial masses (one of the knobs the authors turned) influences the properties of the proto-neutron star, giving the algorithm a defining feature for differentiate GW strains from one another and classify the ancestor.

Figure 4: A measure of model accuracy for (gravitational) SNRs of 1, 10, 25, 50, 70, and 100. Accuracy is the number of labels the model guesses correctly out of the total number of predictions. Even at its best, at an SNR of 100, there is a 70% chance of correctly classifying the progenitor mass. (Figure 5 in today’s article.)

After training and testing their random forest classifier on over 400 variable GW signal strength (or SNR) waveforms, the authors conclude that there was still not enough information to say for sure with what mass of ZAMS each of the waveforms started. Although they tested their algorithm on strong signals of SNR up to 100, they were unable to use this part of the waveform to identify with more than 70% accuracy (Figure 4). They conclude that this means that the bounce and early ringing alone are not enough information to determine the mass of the star’s iron core at the end of its life (related to the mass of the ancestor) and may instead require multimessenger neutrino observation or more GW information such as a longer signal.

Astrobite edited by Katya Gozman, Lili Alderson, and Mark Popinchalk

Featured image credit: Edited from NASA, ESA, by J. Hester and A. Loll (Arizona State University) – HubbleSite: gallery, version.

About Lindsay De Marchi

Lindsay DeMarchi is currently a graduate student at Northwestern University. She is obsessed with gravity and uses multi-messenger methods to analyze the final moments of stellar collapse.

Sherry J. Basler