Black Hole, Why Don’t You Come Over? White Dwarf Supernova!

Title: White Dwarfs in Dwarf Spheroidal Galaxies: A New Class of Compact-Dark-Matter Detectors

Authors: Juri Smirnov, Ariel Goobar, Tim Linden, and Edvard Mörtsell

First Author’s Institution: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom

Status: Published in PRL [open access]

Over the past decade, surveys have unveiled the existence of a mysterious new class of faint supernovae known as Calcium-rich (Ca-rich) transients. These supernovae are distinguished from their peers not only by their relative faintness, but by the odd places they are being found: rather than appearing in the parts of galaxies with the highest density of stars like other types of supernova, they’re often found lurking in the farther-out and more diffuse edges of their home galaxies. 

Unsuprisingly, astronomers and astrophysicists would love to find a simple, plausible model for the formation of Ca-rich gap transients that can explain all of these oddities at once. Better yet, many astronomers and astrophysicists would be very excited to learn that these events are related to another great astrophysics mystery: dark matter. In today’s paper, the authors suggest such an astronomical two-for-one with a model which explains Ca-rich transients as being the result of very small but massive dark matter objects impacting low-mass white dwarfs and causing them to explode as supernovae. 

Figure 1: The cumulative event rates for Type Ia supernovae (solid black line) are compared against those of Ca-rich transients (dashed red line) at different distances from their presumed host galaxies’ centers. Type Ia supernovae tend to occur at galactocentric distances where there are the most stars (dashed black line), whereas Ca-rich transients tend to occur at much further distances. The authors of today’s paper create a model in which these events are caused by interactions between white dwarfs and dark matter. This model’s resulting Ca-transient event rate prediction (solid red line) is shown to closely match the observed event rates. (Figure 1 in today’s paper)

White Dwarfs: “Nuclear Bombs in Space”

To understand the potential interplay between white dwarf (WD) stars, Ca-rich supernovae, and dark matter suggested in this paper, we should briefly revisit the more well-established connection between WDs and Type Ia supernovae. Type Ia supernovae are known to peak at very similar luminosities after their initial explosion and occur in a wide variety of stellar environments. These features suggest a common formation process which isn’t related to a particular galactic environment like a star-forming region. These observations, along with many others over the past several decades, led astronomers to a strong consensus about their formation, namely the idea that such supernovae are the result of exploding WDs.

Why white dwarfs specifically, you might ask? WDs, unlike most other stars, are not supported by their own internal gas pressure or by the energy given off from nuclear fusion in their cores (WDs are mostly carbon, which is unable to fuse at typical WD temperatures). Instead, these dense objects leftover after the death of some main sequence stars, are supported almost entirely by a quantum mechanical effect known as electron degeneracy pressure. Very roughly put, the inability for electrons to share the same quantum state prevents the electrons in the WD from getting squeezed too close together, even under immense external pressure. 

This principle of electron degeneracy pressure cannot support arbitrarily high masses, however. Eventually, if enough mass is packed onto a WD, the interior temperature will rise and initiate the fusion of carbon into even heavier elements, suddenly unleashing huge amounts of energy in the form of a Type Ia supernova. In today’s paper, the authors therefore refer to WD as “essentially nuclear bombs in space…” Because this process tends to occur close to a specific limiting mass (known as the Chandrasekhar limit), most supernovae formed via this process will involve similar amounts of material undergoing the same explosive chain of events, leading to consistent astronomical features. And because such an explosion requires that WDs gain mass over time, it is commonly accepted that such events can only occur when a WD is in a binary system with another star, whose mass is slowly accreted onto the WD via tidal forces. This model also provides a natural explanation as to why Type Ia supernova event rates are correlated with the density of stars in a galaxy, and are not specific to particular environments like star-forming regions: WDs form from older populations of stars, so they or their progenitors have had long periods of time to disperse throughout a given galaxy.

Ca-rich transients, named for their large Calcium emission-line features, have much dimmer peak luminosities than Type Ia supernovae and are often found far-out from the centers of galaxies, with event rates that don’t follow stellar populations. Their relative faintness indicates that whatever exploded was likely significantly less massive than WDs at the Chandrasekhar-limit, but studies of these events have found that a WD progenitor is still the most likely case. This is in part due to the fact that such events feature low amounts of ejected mass compared to what is expected from the supernovae of main-sequence stars, or from Type Ia supernovae. Additionally, their preferential occurrence in early-type galaxies suggests their progenitors are from older stellar populations, where WDs are more common. But what could be causing these WDs to explode if they’re not approaching the Chandrasekhar limit?

Primordial Black Hole Pin-Pricks

As we mentioned, WDs go supernova as a result of the ignition of carbon fusion in their cores, and this typically comes about through the increased pressure and heating associated with these stars accreting mass over time. However, if some other process were able to suddenly deposit large amounts of energy into the WD, this runaway thermonuclear explosion could occur in WDs at any mass, not just in those near the Chandrasekhar limit. 

This is where dark matter comes in! As we’ve covered before, dark matter refers to the idea that our astronomical observations on large distance scales seem to imply the presence of a huge amount of mass which we don’t directly see. Whether the mass is made up of new particles, tiny black holes, or isn’t there at all is still very much an open question.

The idea that dark matter consists of a huge number of tiny black holes is the focus of today’s paper, although the idea of other heavy dark matter candidates interacting with WDs has been explored in existing scientific literature as well. These black holes could have been formed from fluctuations in the very dense early universe, and are therefore referred to as primordial black holes (PBHs). These tiny objects could range from atomic size to the size of planets, and could have masses ranging from sub-kilogram to several hundred solar masses, although some PBH masses have been found to be inconsistent with certain astrophysical observations. 

Given a population of PBHs which constitute the universe’s dark matter, one can calculate an expected rate of events in which a PBH enters the interior of a WD. During such an encounter, the friction caused by the PBH moving around inside the WD can heat the star’s interior, potentially igniting carbon fusion and setting off a supernova explosion with lower intensity than a typical Type Ia.

Figure 2: The relative event rate of PBH-white dwarf ignition events in Milky Way-like galaxies compared to dwarf spheroidal galaxies (dSphs) at various distances from the center of the host galaxy. The authors of today’s paper find that dSphs may actually have a higher relative rate of these events due to their high fraction of dark matter contents, low dark matter velocities, and old stellar populations. This could potentially explain the observed galactocentric distribution of Ca-rich transient events. (Figure 2 in today’s paper)

An Astronomical Two-For-One

With the basic physics of PBH-induced detonation of WDs fairly well understood, the next question that the authors of today’s paper had to contend with was whether such a scenario could indeed explain the observed characteristics, spatial distribution, and event rate of Ca-rich transients. To do this, the authors created a model of the WD population in Milky Way-like galaxies as a function of galactocentric distance as well as a model of WD populations in dwarf spheroidal galaxies (dSphs), small galaxies which orbit larger ones like the Milky Way and may be the host of many Ca-rich transient events. These population models are combined with models of each environment’s dark matter density profiles. Because the amount of heating caused by a PBH-WD encounter is dependent on the PBH’s mass as well as the velocity they enter the WD with, the authors also had to consider the average velocity of dark matter particles expected in different galactic environments and explore a range of possible PBH masses. 

Intriguingly, the authors found that under the assumptions of their model, Ca-rich transient events would be more likely to occur at farther distances from their host galaxies’ centers. They explain this via a confluence of three factors: 1) dSphs have a higher ratio of dark matter to visible matter than Milky Way-like galaxies, 2) dark matter particle velocities in dSphs are expected to be low, yielding greater chances for PBH-WD interactions, and 3) dSphs tend to be made up of older stellar populations, theoretically increasing the fraction of WDs within them. The relative occurrence rate of PBH-WD encounters in both Milky Way-like galaxies and in dSphs predicted by their model can be seen in Figure 2.

The various assumptions that go into these models generate fairly large uncertainties on the final event rate, so they are intended mostly to show that such a model could reproduce the observed event rates, given the right underlying parameters. For example, the authors find that the ratio between the WD ignition rates within a Milky Way-like galaxy and a dSph galaxy is expected to be between 1 and 4 in their models, with observations of Ca-rich transient event rates fitting best to an event rate ratio of 3. Figure 1, displayed above, shows that a cumulative event rate at various galactocentric distances of PBH-WD ignition predicted by this model does closely match the observed rates of Ca-rich transients. While many other models have been put forward to explain these mysterious Ca-rich transients that don’t involve black holes or dark matter at all, the ability to reproduce many of their oddities with a single model is likely to be tantalizing to some researchers.

Figure 3: The 95% credible region for what fraction of dark matter can be made up of PBHs at a particular mass under the assumption that PBHs are causing Ca-rich transients. In order for PBHs to make up 100% of the dark matter and be consistent with the Ca-rich transient event rate, they would have to have masses around 1024-1025 grams, but this conflicts with microlensing surveys done by the Hyper Suprime-Cam on the Subaru Telescope. At lower PBH masses, PBHs can only make up some small fraction of the overall dark matter to be consistent with the Ca-rich transient event rate. (Figure 3 in today’s paper)

Does it Matter if it’s Not Dark Matter?

Even if it doesn’t turn out to be the case that this class of not-quite-“super”-novae are triggered by sudden interactions with nanometer-scale black holes formed in the early universe, the idea itself is interesting because it allows us to put constraints on the abundance of these compact dark matter candidates. Given that the existence of PBHs at various masses would be expected to occasionally cause WD detonations, setting limits on how frequently such events actually occur can help to rule out certain parts of PBH parameter space. Even as it stands now, if all Ca-rich transients were found to be caused by PBH interactions, the model the authors put forward in this paper puts limits on the percentage of DM that those PBHs could explain. Figure 3 shows explicitly what these limits look like for PBHs of various masses.

Regardless of whether Ca-rich transients turn out to be the result of exotic phenomena like PBH interactions or something more mundane, this paper is a good example of the many fun ways in which extreme astrophysical environments can be repurposed as testing-grounds for all sorts of strange and intriguing theoretical phenomena. And if you’re concerned about being pin-pricked by a wandering PBH anytime soon, don’t fret! You (probably) have nothing to worry about.

Astrobite edited by Katherine Lee

Featured image credit: Modified by the author from NASA and H. Richer (University of British Columbia) and NASA

About Lucas Brown

I'm a current master's student at Tufts University interested in cosmology, relativity, and gravitational physics. I am currently doing research on the stochastic gravitational wave background and pulsar timing arrays. Outside of physics I love playing piano, climbing, and spending time with my dog.

1 Comment

  1. I don’t know what I love more, the title of this summary (I see what you did there. Well done.) or the fun paper itself!

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