A mysterious source of heat

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.

What do neutron stars look like inside?

Everything around us is constructed of atoms, which themselves consist of electrons and nucleons (i.e. protons and neutrons). This familiar structure of matter is, however, disrupted when matter is compressed to very high densities that reach beyond the density of an atom, called the nuclear density. It is one of the prime pursuits of modern physics to understand what happens to matter beyond this point. It is not possible to generate supra-nuclear densities in terrestrial laboratories on Earth. However, neutron stars are extreme objects in which matter is compressed to enormously high densities. These stellar bodies therefore serve as exciting, natural laboratories to further our understanding of the fundamental behavior of matter.

Neutron stars are the remnants of once massive stars that ended their life in a supernova explosion. A defining property of neutron stars is that these objects are very compact; while being roughly a factor of 1.5 more massive than our Sun, their radius is almost 100.000 times smaller. Due to their extreme compactness, neutron stars are the densest, directly observable stellar objects in our universe. These fascinating objects come in a wide range of manifestations, e.g. as single stars or as part of a binary, and can be detected at different wavelengths.

Unfortunately it is not possible to travel to a neutron star to conduct experiments of how their interiors look like. However, the macroscopic properties of neutron stars, such as their mass, radius and rotation rate, provide indirect yet powerful information about their interiors. The electromagnetic radiation coming directly from the surface of neutron stars, or from matter that revolves around them, can be used to measure these macroscopic properties. These observational constraints can then be used to infer for instance how high their central density is, what kind of particles are present, and what the superfluid properties of their interior are.

We recently reviewed how different types of electromagnetic observations can be employed to learn more about the interior of neutron stars. This included commonly used techniques of combining radio pulsar timing with optical spectroscopic studies to measure neutron star masses, as well as various techniques to measure neutron star radii from X-ray data. In addition, we touched upon various techniques that have not yielded strong constraints to date, but have great potential to be further developed in the future and can be particularly interesting when combined with other methods. Finally, we provided an outlook of the potential for neutron star research of the future generation of ground-based  observatories such as the Square Kilometer Array and the new class of 30-m telescopes, as well as new and upcoming X-ray facilities such as NICER, eXTP, Athena and X-ray polarimetry missions.

Degenaar & Suleimanov 2018, book chapter in The Physics and Astrophysics of Neutron Stars, Springer Astrophysics and Space Science Library: Testing the equation of state of neutron stars with electromagnetic observations

Paper link: ADS


Artist impression of the Square Kilometer Array (SKA), which is currently in the design phase. This radio facility is expected to be transformable in many areas of science, including measuring the masses (and spins) of neutron stars.

A very cool neutron star

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.

Accreting or cooling?

Some brave neutron stars are consuming gas from a big companion star that is about ten times as massive as the tiny neutron star itself. In these so-called Be X-ray binaries, the neutron star is typically in a very wide, eccentric orbit and only able to swallow gas from its companion when it’s making its closest approach. Usually this results in modest accretion outbursts. Occasionally, however, very bright and powerful “giant outbursts” are observed during which the neutron star has a much bigger banquet. X-ray binaries that harbor massive companion stars are younger than those with small companion stars (millions of years compared to billions of years). Furthermore, neutron stars accompanied by a massive star are more strongly magnetized (by a factor of 1000 or so) and rotate much slower (seconds versus milliseconds) than when they are fed by a small companion.

When neutron stars feed off a small companion, their 1-km thick crust is heated and cools on a timescale of years after a meal. This heating and cooling sequence provides very valuable information about the tantalizing interior of neutron stars, but there are many unanswered questions about these processes. For instance, it is not yet established how the spin rate and magnetic field strength of a neutron star affects its temperature changes. Given their widely different properties compared to neutron stars with small companions, searching for heating and cooling in Be X-ray binaries can potentially shed new light on these open questions. Giant outbursts should then provide the best opportunity for this quest, as we might expect a neutron star to become more severely heated (and hence more clearly cooling) when more matter is consumed.

Using the X-ray telescope on board of NASA’s Swift satellite, we followed the behavior two Be X-ray binaries, V0332+53 and 4U 0115+63, after their giant accretion outbursts. Interestingly, we discovered that the X-ray brightness of these neutron stars was higher in the months after they finished their meals than it was before they started eating. This could indeed be a sign of a heated crust! However, neutron stars with massive companions are generally more messy eaters than those with small donors; the quality of our data did not allow us to exclude the possibility that their X-ray emission was elevated because these neutron stars were still scraping for food after finishing their main course. Such behavior is in itself relatively unexplored and interesting to study. Our pilot project therefore warrants follow-up investigation to explore either of these exciting possibilities.

Wijnands & Degenaar 2016, MNRAS Letters 463, L46: Meta-stable low-level accretion rate states or neutron star crust cooling in the Be/X-ray transients V0332+53 and 4U 0115+63

Paper link: ADS


Artist impression of a Be X-ray binary; a neutron star in a wide, eccentric orbit around a massive companion. Image credit: Walt Feimer, NASA/Goddard Space Flight Center.


A mathematical tool to study X-ray bursts

Neutron stars can rip off gas from a nearby companion star and pull this material towards them; a process called accretion. The material that is accreted on to the neutron star undergoes nuclear reactions that can cause detonations generating more energy than an atomic bomb. Such thermonuclear bursts are observed as brief, bright flashes of X-ray emission that last for seconds to hours and repeat on a timescale of hours to months.

Not surprisingly, these violent explosions can be destructive to the surroundings of a neutron star. Indeed, evidence has been accumulating that X-ray bursts have a profound effect on the  accretion flow that transports material toward the neutron star. For example, the explosions can cool, blow away, or accelerate the in-falling flow of material. One way to investigate this is by studying how the X-ray energy spectrum of the accretion flow changes during an X-ray burst. This is not an easy task, however, because the X-ray burst emission typically outshines that of the accretion flow. Small changes in the weak accretion emission are therefore swamped by the bright burst emission.

Mathematical techniques that involve decomposing complex data into matrices (e.g., “non-negative matrix factorization”) have been previously applied to reveal subtle changes in the X-ray emission of super-massive and stellar-mass black holes. Motivated by those successes, we investigated the applicability of such techniques to study changes in the accretion emission induced by X-ray bursts.

For this purpose we used high-quality data obtained with the NuSTAR satellite of a well-known neutron star X-ray binary and thermonuclear burster 4U 1608-52. Our case study revealed that these mathematical techniques can be a very powerful tool to reveal changes in the accretion emission that remain hidden in conventional spectral analysis. Applying these techniques to NuSTAR data is particularly promising, as this instrument can provide valuable information on the  accretion geometry, that helps interpret the results from the X-ray burst analysis.

Degenaar, Koljonen, Chakrabarty, Kara, Altamirano, Miller, Fabian 2016, MNRAS 456, 4256: Probing the effects of a thermonuclear X-ray burst on the neutron star accretion flow with NuSTAR

Paper link: ADS


Artist impression of NASA’s NuSTAR mission (launched in 2012). Image credits: NASA.

Breaking model degeneracies

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.

Chemical processes in the crust of a neutron star

Neutron stars are one of the possible end products of the stellar life cycle. These objects are the compact remnants of once massive stars that burned all their fuel and consequently collapsed under their own gravity and exploded in a supernova. One can thus say that neutron stars are ‘dead stars’: they have no internal resources to replenish the energy that is lost via photons emitted from their surface and neutrinos escaping from their interior. When left alone, neutron stars would therefore slowly fade away over the course of millions of years. However, a neutron star can escape this fate when it is a member of a binary system: it can then regain energy by pulling off and accreting matter from its accompanying star (it can suck life out of its companion, so to say).

Accretion causes a complex network of nuclear reactions inside the neutron star, at a few hundred meters below its surface. These reactions serve as an effective energy supply. When the neutron star is done accreting, however, it will immediately start to loose energy again. Using sensitive X-ray telescopes and dedicated observing techniques, the signatures of these processes can be detected: the temperature of a neutron star rises during accretion episodes but then gradually decreases afterward. In particular, a detailed mapping of the ‘cooling curve’ of a neutron star can give unique insight into its tantalizing interior structure, one of the basic quests of neutron star research.

These cooling studies cannot be carried out for just any neutron star: in order to create detectable temperature differences, a neutron star must be very cold to start with, and/or accrete (i.e., be heated) for a long time. EXO 0748-676 is one of the few sources for which such a study could be carried out. This neutron star started accreting some time between 1980 and 1984 and happily continued to cannibalize its companion star until it suddenly stopped in 2008. We seized this rare opportunity to study a cooling neutron star and embarked on a monitoring campaign using the sensitive Chandra, XMM-Newton and Swift X-ray satellites.

Our X-ray observations revealed that EXO 0748-676 harbors a relatively hot neutron star, as expected given its long history of feasting on its companion. During the first year after it stopped accreting, its temperature was gradually decreasing indicating that the hot neutron star was cooling. However, between 2009 and 2011, we did not detect any significant temperature change any more. To verify that the neutron star had indeed stopped cooling, we obtained a new Chandra observation in 2013. Surprisingly, this new data point showed that the temperature had dropped again, indicating that cooling is ongoing. Excitingly, the apparent plateau of stalled cooling in 2009-2011 could be the result of a chemical process in which light and heavy atoms separate out in different layers.

If this process indeed occurs, it would suggest that the crust of neutron stars has a very ordered, strong structure. That has important implications for several observational properties of neutron stars, including the emission of gravitational waves from deformations in their structure. This result on EXO 0748-676 nicely illustrates how astronomical observations can be used to probe micro-physical processes occurring in the dense interior of neutron stars.

Degenaar, Medin, Cumming et al. 2014, ApJ 791, 47: Probing the Crust of the Neutron Star in EXO 0748-676

Paper link: ADS

 Schematic overview of the interior of a neutron star.  Credit: Chamel & Haensel 2008, LRR 11, 10

Schematic overview of the interior of a neutron star.
Credit: Chamel & Haensel 2008, LRR 11, 10