Scientists know little about the interior of neutron stars, which contain about a Sun's worth of mass packed in a sphere the size of a large city. Now, a new study says that neutron stars behave like fillings of chocolates. A neutron star is the dense, collapsed core of a massive star that exploded as a supernova, and is the densest object astronomers can observe directly. Since the discovery of neutron stars more than 60 years ago, scientists have been trying to decipher their structure. Simulating the extreme conditions inside neutron stars has been difficult because they can hardly be recreated on Earth in the laboratory. 


Using equations of state, one can create models and describe properties such as density and temperature. An equation of state is an equation describing the state of matter and showing the relationship between physical conditions such as pressure, temperature, volume and internal energy. Scientists from Goethe University Frankfurt have used these equations to describe the structure of neutron stars from the stellar surface to the inner core.


The study describing the findings was recently published in The Astrophysical Journal Letters. 


Neutron stars behave like chocolate pralines


According to the study, neutron stars behave like chocolate pralines. A praline is a sweet substance made from nuts cooked in boiling water, and is used in desserts and as a filling for chocolates. A team of researchers, including physicists at Goethe University Frankfurt, and led by Professor Luciano Rezzolla at the Institute of Theoretical Physics, developed more than a million different equations of state. These equations satisfy the constraints set by data obtained from theoretical nuclear physics and astronomical observations, a statement released by Goethe University Frankfurt said.


Heavy and light neutron stars have cores and mantles of different types


The working group made a surprising discovery while evaluating the equations of state. They observed that light neutron stars, which are the neutron stars with masses smaller than about 1.7 solar masses, seem to have a soft mantle and a stiff core. On the other hand, heavy neutron stars, with masses larger than 1.7 solar masses, have a stiff mantle and a soft core. 


In the statement, Professor Luciano Rezzolla said the result is very interesting because it gives scientists a direct measure of how compressible the centre of neutron stars can be. 


Neutron stars can behave like hazelnut chocolates or those with a soft filling


Rezzolla explained that neutron stars apparently behave a bit like chocolate pralines. He said light stars resemble those chocolates that have a hazelnut in their centre, surrounded by soft chocolate, while heavy stars can be considered more like those chocolates where a hard layer contains a soft filling. 


Study used speed of sound to determine the structure of neutron stars


The speed of sound was crucial to this insight, because the quantity measure describes how fast sound waves propagate within an object, and depends on how stiff or soft matter is. On Earth, the speed of sound is used to explore the interior of the planet and discover oil deposits. 


The physicists modelled the equations of state and uncovered other previously unexplained properties of neutron stars. For instance, neutron stars probably have a radius of only 12 kilometres, regardless of their mass. Therefore, neutron stars are just as large in diameter as Goethe University's hometown Frankfurt, the statement says. 


Significance of the study


Dr Christian Ecker, one of the authors on the paper, said Goethe University's extensive numerical study not only allows researchers to make predictions for the radii and maximum masses of neutron stars. Researchers can also set limits on the deformability of neutron stars in binary systems, which refers to how strongly neutron stars distort each other through their gravitational fields. 


These insights are beneficial because they help pinpoint the unknown equation of state with future astronomical observations and detections of gravitational waves from merging stars, Dr Ecker said. 


Goethe University Frankfurt said that while the exact structure and composition of matter inside neutron stars continues to remain a mystery, the wait until its discovery can certainly be sweetened with a chocolate or two.