Neutron stars have masses up to about 2.5 times the mass of our Sun, but their radii are nearly 50 thousand times smaller. This means that the matter that makes up neutron stars must be squeezed incredibly close together. In fact, neutron stars present the densest observable form of matter in the Universe. While in black holes matter is even more tightly packed, it is all hidden behind an event horizon and hence beyond our reach. For neutron stars, however, we can observe radiation from their surface and use that to infer what they look like on the inside. Neutron stars allow us to study how matter behaves when it is crushed to enormously high densities, conditions that we cannot replicate and study in laboratories on Earth.

Neutron stars are thought to have a 1-km thick solid crust, below which matter occurs in liquid form. It is generally thought that this liquid must be superfluid, meaning that it swirls around freely without experiencing any friction. On Earth, such fascinating, odd behavior is observed when liquid helium is cooled down to extremely low temperatures of about -270 degrees Celsius. There are, however, many uncertainties about how a superfluid works at the millions of degrees Celsius temperatures inside neutron stars. As a result, it is far from understood what the superfluid properties of neutron stars are exactly. This is very important to establish, as it likely has a profound effect on how various neutron star properties, such as their magnetic field strength, spin and interior temperature, evolve over their lifetime. Moreover, several observable phenomena of neutron stars, such as occasional distortions in their rotation called glitches or sudden cracking of their crust analogous to Earth quakes, likely depend on the detailed properties of their interior superfluid.

Since we cannot perform experiments on Earth that teach us how superfluids inside neutron stars may work, we need to reverse the problem. One promising way to do this is to track how a neutron star cools down after it has been heated up by gobbling up gas from a companion star. We call this cannibalistic action accretion and often this happens in spurts that we call  outbursts. The superfluid properties of its interior should influence both the extend to which the neutron star can be heated during accretion outbursts, and how its temperature then subsequently decreases when accretion stops and hence there is no more heat generation. One such neutron star that we previously established to be heated and subsequently cooling down is called HETE J1900.1-2455. In a previous study we tracked its temperature decrease and our modeling suggested that the neutron star would cool further. After having waited a few years, we took a new observation of the source with the Chandra X-ray satellite to verify this.

Chandra pointed towards our neutron star for over half a day and surprisingly saw almost nothing! HETE J1900.1-2455 turned out to have cooled so much that it was hardly generating any detectable X-ray emission, even for the very sensitive X-ray detector of Chandra. In the 16 hours that Chandra started at it, a mere 5 X-ray light particles were capture from the neutron star. In order words, only every 3 hours was the Chandra detector hit by an X-ray light particle from HETE J1900.1-2455. Perhaps somewhat counter-intuitive, the fact that we detected so little light from the source actually provides us with very interesting constraints on its interior properties. Performing a rigorous and conservative analysis (based on those 5 light particles!) we inferred the likely temperature of the neutron star and performed highly advanced simulations that take into account the physical properties of neutron stars, including their interior superfluid.

Our analysis revealed that the low temperature of HETE J1900.1-2455 must imply that it is able to cool its interior extremely rapidly. Two exciting possibilities that would allow for this is either that the neutron star is very massive or that a large fraction of its core is not superfluid. The latter option would contrast the general belief and would have profound implications for our understanding of many observable properties of neutron stars. The former option would be a very important finding because the most massive neutron stars put the strongest constraints on the behavior of ultra-dense matter.  Although both options are equally exciting, our current observations do not allow us to distinguish between the two. However, because of the significant science impact, Chandra will again point towards HETE J1900.1-2455 to allow us to obtain a new temperature measurement. This time, it will not stare at the neutron star for 16 hours, but for 6 full days!! If its temperature remained stable, we will then collect 50 X-ray light particles and be able to obtain a much more reliable temperature estimate. If it cooled further, however, we might not see any light at all. Ironically, the latter case would be the most exciting outcome. Part of the data has recently been taken and the remaining observations will come in soon. I can wait to find out what we will (not) see in those new Chandra observations!

Degenaar, Page, van den Eijnden, Beznogov, Renolds, Wijnands 2021, MNRAS 508, 882: Constraining the properties of dense neutron star cores: the case of the low-mass X-ray binary HETE J1900.1-2455

Paper link: ADS

Understanding how neutron stars look like on the inside, i.e. what their structure is and what they are made of, is one of the main challenges of modern astrophysics. There are several different ways through which we try to unravel this. One avenue is to measure how the temperature of neutron stars evolve after they have been eating.

Humans gain energy by eating and so do neutron stars. The meal of a neutron star consists of gas that is supplied by a companion star. By consuming this gas, the outer layers of a neutron star get heated up. Once they stop eating, this gained energy is  radiated away and therefore the neutron star cools down again. How hot neutron stars become during their dinners, and how quickly they cool afterwards, depends strongly on their interior properties.

We use sensitive X-ray telescopes to measure how the temperature of neutron stars evolve after they have been consuming gas from their companion. Such studies have revealed that many neutron stars are much more strongly heated during their dinners than is predicted by theoretical models. This is referred to as the shallow heating problem, because the heat appears to be generated just below the surface of the neutron star. It has puzzled us for over a decade now where this shallow heat comes from.

In a previous study, we proposed that the well-known neutron star X-1 in the constellation Aquila, aka Aql X-1, could provide the key to unravel the mysterious source of shallow heat. This neutron star feasts off its companion about once a year and its heating and cooling can thus be studied and compared after multiple dinners.

Using the Chandra and Swift satellites, we studied Aql X-1 after three meals (in 2011, 2013 and 2016) that were very similar. Since the neutron star consumed approximately the same amount of gas during these three episodes, we expected that it would have been heated to similar extend and hence cool in the same way. However, we found that the temperature of the neutron star was strikingly different after its 2016 dinner than after the other two. Within our current understanding of heating and cooling of neutron stars, it is very difficult to understand why its temperature should be so different.

Instead of unraveling the mysterious source of shallow heat, our dedicated study of Aql X-1 seems to have further complicated the picture. We thus have to go back to the drawing board to think of a new experiment to find out what causes the shallow heat inside of neutron stars.

Degenaar, Ootes, Page et al. 2019, MNRAS in press: Crust cooling of the neutron star in Aql X-1: Different depth and magnitude of shallow heating during similar accretion outbursts

Paper link: ADS

The observed temperature of the neutron star in Aql X-1 after three different outbursts. Although the outbursts were very similar and we thus expected the neutron star to heat up and cool down in the same way, the temperature evolution after the 2016 outburst (black stars) was very different from that seen after the 2011 (red circles) and 2013 (blue squares) outbursts.

HETE J1900.1-2455 is a neutron star that swallows material from a small companion star that a mass of only about 10% of our Sun. It was discovered in 2006 with NASA’s Rossi X-ray Timing Explorer and exhibits some exceptional properties.

Firstly, HETE J1900.1-2455 showed pulses of X-rays every 2.65 millisecond. This shows that the magnetic field of the neutron star is channeling plasma to its magnetic poles which are then heated and lighting up in X-rays. As the neutron star rotates around its own axis a dazzling 377 times per second, this bundle of X-rays sweeps across our line of sight like a light house. Approximately 10% of all neutron stars with low-mass companions show such X-ray pulsations. Secondly, unlike most neutron stars that are eating for only a few weeks at a time, HETE J1900.1-2455 continued to be active for over a decade. Until 2015…

In 2015 November, HETE J1900.1-2455 suddenly dropped off the radar of the Japanese X-ray detector MAXI, which is mounted on the International Space Station and continuously scans the X-ray sky. The sudden drop of X-ray emission indicated that this neutron star had finally stopped eating. To test this, we observed this neutron star with two X-ray satellites that are more sensitive than MAXI and can thus detected much fainter X-ray light, Chandra and Swift. Our observations were carried out a few months after it had disappeared from the daily MAXI scans.

We found that the neutron star had indeed peacefully gone back to sleep. The X-rays observed during quiescent episodes are usually due to heat that radiated by the neutron star. Somewhat surprisingly, we found that HETE J1900.1-2455 was much colder, about 600 000 degrees Celsius, than we typically see for neutron stars after they have been active for many years (>1 million degrees Celsius). The reason that neutron stars are so hot after long meals is because consuming gas generates energy that heats their interior.

The fact that our temperature measurement of HETE J1900.1-2455 was so low, despite 10 years of activity, places exciting constraints on its interior properties. In particular, it requires that the central, liquid part of the neutron star is strongly superfluid. A superfluid is very peculiar liquid that has zero viscosity and freely moves without experiencing any friction. In laboratory experiments on Earth, liquid helium can be made superfluid when it is cooled down to nearly zero temperature. It is quite amazing that in neutron stars superfluidity can be achieved at temperatures of nearly a million degrees Celsius.

The constraints on the intriguing interior properties of HETE J1900.1-2455 will become even stronger if the neutron star cools further down now that it has stopped eating. We therefore plan further temperature measurements of this neutron star in the future.

Degenaar, Ootes, Renolds, Wijnands, Page 2017, MNRAS Letters 465, L10: A cold neutron star in the transient low-mass X-ray binary HETE J1900.1-2455 after 10 yr of active accretion

Paper link: ADS

Schematic representation of the structure of a neutron star.

Neutron stars are sometimes referred to as “dead stars”, because they cannot burn nuclear fuel in their interior as other stars do. Nevertheless, neutron stars can generate energy by accreting gas from a companion star in an X-ray binary.

When a neutron star accretes material, its ~1 km thick crust is compressed. This compression induces nuclear reactions such as atomic nuclei capturing electrons and nuclear fusion reactions. Theoretical calculations and accelerator experiments (e.g., such as done at the nuclear superconducting cyclotron laboratory at Michigan State University), provide a handle on how much heat should be generated inside neutron stars as a result of accretion. These results can then be compared with astrophysical observations.

Neutron stars often feast on their companion only for a few weeks/months (in exceptional cases years), after which they typically sag for years/decades before becoming active again. It is during these periods of quiescence that heat radiation from the neutron star (which have a temperature of millions of degrees Celsius) can be detected with sensitive X-ray satellites such as Chandra, XMM-Newton, or Swift. Since neutron stars do not generate energy when they are not accreting, they will gradually cool as they radiate their heat away as X-rays. Excitingly, dedicated efforts have allowed to detect the cooling trajectories of 7 neutron stars by now.

In this area of research there is thus a direct interplay between astrophysical observations of neutron stars, theoretical calculations about their interior, and nuclear accelerator experiments that mimic the nuclear reactions that take place in their outer layers. Interestingly, our X-ray observations seem to suggest that neutron stars are heated to a larger extend than is currently accounted for by nuclear heating models. It appears that there is a puzzling source of extra energy generation in the outermost layers of the neutron star, referred to as a “shallow heat source“, the origin of which remains to be established.

So far, it appears that the amount of extra heating differs between sources. It is not clear, however, if this is due to their different outburst properties (e.g., length, duration, total accreted mass, accretion geometry), or relates to different neutron star parameters (e.g., rotation period, age, mass, radius). A powerful way to break these degeneracies would be to observe cooling curves for one particular source after different types of outbursts. If the shallow heating is different for each outburst, it is likely related to the accretion properties — else we need to seek its origin in the properties of the neutron star itself.

We took up this challenge by studying the prolific neutron star X-ray binary Aql X-1, which is active approximately once every year and exhibits a wide range of outburst properties. In particular, we exploited the unique flexibility and good sensitivity of the Swift satellite to study the temperature evolution of the neutron star after different outbursts. The first test was to prove whether cooling is actually observable for this particular neutron star, which definitely appears to be the case. Future observations of Aql X-1 aiming to study the cooling trajectories after different outbursts are therefore a very promising avenue to elucidate the origin of the shallow heat generation in neutron star crusts that puzzles astrophysical observers, physicists and nuclear experimentalists.

Waterhouse, Degenaar, Wijnands, Brown, Miller, Altamirano, Linares 2016, MNRAS 456, 4001: Constraining the properties of neutron star crusts with the transient low-mass X-ray binary Aql X-1

Paper link: ADS

Long-term activity of Aql X-1 as seen through daily monitoring observations with Swift/BAT (launched in 2005) and MAXI (launched in 2009). This illustrates the frequent activity of this neutron star X-ray binary. Figure from Waterhouse et al. 2016.