Neutron stars are spherical bodies with typical radii of around 10.4 to 11.9 km, so very small by stellar standards. The masses of the neutron stars discovered so far are between about 1.2 and 2.0 solar masses , making them extremely compact . Their density increases from about 1 · 10 9 kg / m 3 on their crust with depth to about 6 · 10 17 to 8 · 10 17 kg / m 3 , which corresponds to about three times the density of an atomic nucleus . The mean density of a neutron star is around 3.7 to 5.9 · 10 17 kg / m 3 . This makes neutron stars the densest known objects without an event horizon . Typical stars of this type rotate very quickly and have a strong magnetic field .
The fastest rotating known neutron star is the PSR J1748-2446ad, discovered in 2004, with 716 revolutions per second. With an assumed diameter of ≤16 km, this means that the circumferential speed at its equator is around 70,000 km / s, which corresponds to almost a quarter of the speed of light . An even higher rotation frequency of 1122 Hz assumed for the neutron star XTE J1739-285 discovered in 1999 could not be confirmed in later investigations.
Neutron stars are of intense research interest, as details of their dynamic behavior and their composition are still unknown and extreme material properties can be investigated on them under conditions observable in nature.
As early as 1931, a year before Chadwick's discovery, Lev Dawidowitsch Landau theoretically proposed the existence of neutron nuclei, namely extremely dense core regions inside conventional stars. 1933 beat Walter Baade and Fritz Zwicky the modern version of neutrons sternen before: made of neutron star remains as a possible end product of stellar evolution. They had come to this interpretation while trying to explain the processes in the course of a supernova . Robert Oppenheimer and George Michael Volkoff calculated a theoretical model of a neutron star in 1939 and stated the maximum mass as 0.7 M ☉ (see also Tolman-Oppenheimer-Volkoff limit ).
In 1967, astronomers Jocelyn Bell , Antony Hewish and Martin Ryle discovered radio pulses from a pulsar that was later interpreted as an isolated, rotating neutron star. The energy source for these pulses is the rotation energy of the neutron star. Most of the neutron stars discovered so far are of this type.
In 1971 Riccardo Giacconi , Herbert Gursky, Ed Kellogg, R. Levinson, E. Schreier and Harvey Tananbaum observed impulses with a period of 4.8 seconds in an X-ray source in the constellation Centaurus , designated as Cen X-3 . They interpret this observation as a rotating, hot neutron star in orbit around another star. The energy for these impulses comes from the released gravitational energy , which comes from the gaseous matter of the star flowing into the neutron star.
In the early 21st century, almost 2,000 neutron stars were discovered, of which only a fraction allows detailed investigations due to unfavorable physical conditions. For the continuous detection of more of these stars, complex calculations are made with data obtained with systems such as the Effelsberg radio telescope , the Arecibo observatory or the Parkes observatory . To the necessary Hough transformations similar to solve computing power supercomputers, not only big are CPU - GPU - Cluster used, but in the context of Einstein @ home also distributed systems .
Neutron stars arise from massive stars in the main sequence at the end of their evolution. A distinction is made between two ways of developing into a neutron star.
- If the mass of the original main sequence star was between 8 and about 12 solar masses, the result is a neutron star with a mass of about 1.25 solar masses. The carbon burning creates an oxygen - neon - magnesium core. A process of degeneration follows. When the Roche limit is exceeded, the Roche -Lobe Overflow causes a loss of mass. After approaching the Chandrasekhar limit , it collapses into a neutron star. This moves at a similar speed as the original star through space. Stars that were part of an interacting double star can traverse this path , while single stars of this mass develop into AGB stars , then continue to lose mass and thus become white dwarfs .
- If the mass of the original main sequence star was greater than about 12 solar masses, a neutron star with a mass greater than 1.3 solar masses results. After an oxygen-neon-magnesium core has been created by burning carbon, the next development stages are oxygen burning and silicon burning , so that an iron core is created. As soon as this exceeds a critical mass , it collapses into a neutron star. A neutron star created in this way moves much faster through space than the original star and can reach 500 km / s. The cause is seen in the enormous movements of convection in the core during the last two phases of burning, which affects the homogeneity of the density of the star's mantle in such a way that neutrinos are ejected in an asymmetrical manner. Stars that were single stars or part of a non-interacting binary star can traverse this path.
Both paths have in common that a direct precursor star arises as a late development phase, the core mass of which, according to current models, must be between 1.4 solar masses (Chandrasekhar limit) and about 3 solar masses ( Tolman-Oppenheimer-Volkoff limit ) in order for a core collapse Supernova (types II, Ib, Ic) the neutron star is formed. If the mass is above it, a black hole is created instead ; if it is below it, there is no supernova explosion, but a white dwarf . However, astronomical observations show deviations from the exact limits of this model, because neutron stars with less than 1.4 solar masses have been found.
As soon as iron has accumulated in the core as a result of the silicon burning, no further energy generation via nuclear fusion is possible, since energy would have to be used for further fusion instead of being released due to the high binding energy per nucleon of the iron. Without this energy generation, the radiation pressure inside the star decreases, which counteracts the gravity inside the star. The star remains stable only as long as the opposing forces of radiation pressure and gravity are in equilibrium - the star becomes unstable and collapses due to the decrease in radiation pressure.
When the star collapses due to the decrease in radiation pressure, the core is strongly compressed by the collapsing masses of the star's envelope and by its own, now “overpowering” gravity. This increases the temperature to approx. 10 11 Kelvin. Radiation is emitted, of which X-rays make up the largest proportion. The energy released in this way causes a photo-disintegration of the iron atomic nuclei in neutrons and protons as well as the capture of electrons by the electrons from the protons, so that neutrons and electron neutrinos are created. Even after this process, the nucleus continues to shrink, until the neutrons build up what is known as degenerative pressure , which suddenly stops further contraction. When the star collapses, around 10% of its gravitational energy is released, mainly through the emission of neutrinos . In the core of the star, neutrinos arise in large numbers due to these processes and represent a hot Fermigas . These neutrinos now develop kinetic energy and strive outwards. On the other hand, matter from the outer layers of the collapsing star falls back onto its core. However, this is already extremely dense, so that the matter ricochets off. It forms a shell around the core and is subject to strong convection driven by entropy . As soon as enough energy has accumulated through the neutrinos and exceeds a limit value, the falling outer layers finally bounce off the interfaces and are strongly accelerated by the neutrinos, so that the compact star material is explosively distributed over a large space. This is one of the few known situations in which neutrinos interact significantly with normal matter. Thus, the thermal energy was converted into electromagnetic waves , which are released explosively within a few minutes and make the core collapse supernova visible from afar. Through this supernova, elements that are heavier than iron are also formed by nucleosynthesis .
In the case of very massive main sequence stars with more than approx. 40 solar masses, the energy of the neutrinos striving outwards cannot compensate for the gravitation of the falling material, so that a black hole is created instead of the explosion.
It is noteworthy that the formation of the neutron star initially takes place completely in the core of the star, while the star remains externally inconspicuous. The supernova only becomes visible to the outside after a few days . Thus, neutrino detectors detect a supernova earlier than optical telescopes.
Since the conversion of protons and electrons into neutrons is endothermic, this energy is ultimately fed by gravity during collapse.
There is also a side path in the evolution towards neutron stars, which applies to less than 1% of these stars. A white dwarf of an interacting double star crosses the Chandrasekhar limit by taking in material from the other star. It does not form a solid shell and therefore explodes.
Field and lens flare
The gravitational field on the surface of a typical neutron star is about 2 · 10 11 times as strong as that of the earth. The escape speed to which an object must be accelerated so that it can leave the neutron star is correspondingly high . It is in the order of 100,000 km / s, which is about a third of the speed of light . The strong gravitational field acts as a gravitational lens and deflects light emitted by the neutron star in such a way that parts of the back of the star come into view and more than half of its surface is visible.
According to the law of the equivalence of mass and energy , E = mc² , the gravitational binding energy of a neutron star of twice the solar mass is equivalent to a solar mass. That is the energy that is released in the supernova explosion.
Delivery of waves
A neutron star can emit gravitational waves . This is the case when it is not an ideal ball, for example because it has a bulge at one point that z. B. can arise through material absorption from the environment. Such a bump could also be a type of crystal made of ions trapped in a dense electron packing, such as can arise under cooling conditions. It is a special case that is counteracted by the gravitational field and the flattening effect of the high rotational speed . The ratio of the change in radius to the star's radius caused by the deformation is called ellipticity. It is approximately described with the larger the value, the stronger the emitted wave.
Also, asteroseismic gravitational waves are triggered by the fact that the models predict compact star oscillates and is in an unstable situation, such as when he is disturbed by external influence. In this case, depending on the direction of rotation and the viscosity of the star , the gravitational wave can even trigger additional waves due to the associated loss of energy.
Worldwide research efforts are being made to find such an asymmetrical star because the expected signal to be detected with a gravitational wave detector occurs continuously, which u. a. an exact position determination allowed. In a systematic search in 2016, no neutron star with a bulge of more than 1 cm was found within 100 parsecs of the earth.
When the core zone of the forerunner star collapses, its diameter is reduced to less than one hundred thousandth of its original value. Due to the associated pirouette effect , a neutron star initially rotates at around a hundred to a thousand revolutions per second. The highest rotational frequency measured so far is 716 Hz (Pulsar PSR J1748-2446ad ). It is not too far below the stability limit of a pure neutron star of around 1 kHz due to the centrifugal force .
Various effects can change the frequency of rotation of a neutron star over time. If there is a binary star system in which there is a flow of material from a main sequence star to the neutron star, an angular momentum is transmitted that accelerates the rotation of the neutron star. Values in the range of 1 kHz can be set. The magnetic field emitted by the neutron star is one of the slowing effects that can increase its period of rotation to several seconds or even minutes.
The known properties of the particles involved result in the following shell structure for a typical neutron star with a diameter of 20 km:
There is zero pressure on the surface. Since free neutrons are unstable in this environment, there are only iron atomic nuclei and electrons there. These atomic nuclei form a crystal lattice . Due to the enormous force of gravity, however, the highest elevations on the surface are a few millimeters high. A possible atmosphere of hot plasma would have a maximum thickness of a few centimeters.
The zone of crystalline iron atomic nuclei continues to a depth of about 10 m. The mean density of the crystal lattice increases to about a thousandth of the density of atomic nuclei. Furthermore, the proportion of neutrons in the atomic nucleus increases. Neutron-rich iron isotopes are formed that are only stable under the extreme pressure conditions there.
From a depth of 10 m, the pressure is so high that free neutrons also exist. This is where the so-called inner crust begins : a transitional layer that is 1 to 2 km thick. In it there are areas of crystalline iron atomic nuclei in addition to those of neutron liquid, with the proportion of iron decreasing from 100% to 0% with increasing depth, while the proportion of neutrons increases accordingly. Furthermore, the mean density increases to that of atomic nuclei and beyond. A nuclear pasta may form at the bottom of the inner crust .
Following the inner crust, the star consists predominantly of neutrons, which are in thermodynamic equilibrium with a small proportion of protons and electrons . If the temperatures are sufficiently low, the neutrons there behave superfluid and the protons superconductive . For a typical neutron star, the associated critical temperature is around 10 11 Kelvin; Neutron stars become superfluid very shortly after their formation.
It is not known which forms of matter exist from a depth at which the density increases to five to ten times that of atomic nuclei, since such densities have so far not been generated even when atomic nuclei collide in terrestrial particle accelerators and thus cannot be studied.
A core zone with pions or kaons may already begin below this . Since these particles are bosons and are not subject to the Pauli principle, some of them could adopt the same basic energetic state and thus form a so-called Bose-Einstein condensate . They could do little to counter the enormous external pressure, so that a second collapse into a black hole would be possible. Another possibility would be the presence of free quarks . Being next up- and down quarks and strange quarks vorkämen, to such an object as a strange star (Engl. Referred strange = strange) or quark star . Such a form of matter would be stabilized by the strong interaction and could therefore also exist without the gravitational external pressure. Since quark stars are denser and therefore smaller, they should be able to rotate faster than pure neutron stars. A pulsar with a rotation period of less than 0.5 ms would already be an indication of the existence of this form of matter.
A sudden, tiny increase in the rotational frequency was observed several times in four pulsars, followed by a relaxation phase lasting several days . It could be a kind of earthquake , in which an exchange of angular momentum takes place between the crystalline iron crust and the vortices of superfluid neutron fluid that rotate further inside without friction.
A star consisting primarily of neutrons is stabilized by forces that are a consequence of the Pauli principle . According to this, a maximum of two neutrons of the star can be in the same energetic state, whereby they differ in the orientation of their spin . As a result of quantum mechanics , the possible energy states form an energy ladder whose rung spacing increases as the star's volume decreases. Since the states from the lower end of the ladder are all occupied, energy must be supplied to the neutrons at the upper end of the ladder during compression. This phenomenon leads to a counter pressure, the so-called Fermi pressure , which can withstand gravitational pressure. Since the pressure in this situation hardly depends on the temperature, but almost exclusively on the distribution of the quantum mechanically permitted energy states, this state of matter is called degenerate matter . If the mass of the immediate precursor star is greater than the Tolman-Oppenheimer-Volkoff limit of about three solar masses (according to a paper published in January 2018, about 2.16 solar masses for non-rotating neutron stars and up to about 20% higher for rotating ones), then there is no equilibrium possible, and the star continues to collapse to the black hole according to the current state of knowledge .
It is noteworthy that the typical diameter of a neutron star in the context of this model is directly related to the neutron mass, i.e. an astronomical quantity is a direct function of a microcosmic natural constant, apart from factors that result from the as yet unknown equation of state. Incidentally, the stability of a white dwarf is based in an identical way on the Pauli principle, which in this case applies to electrons instead of neutrons.
Temperature and more
- The temperature inside a neutron star is initially 100 billion Kelvin . The emission of neutrinos, however, removes so much thermal energy that it drops to around one billion Kelvin within a day. Within approx. 100 years the temperature drops to approx. 300,000 Kelvin. Only after about 100,000 years do emitted photons contribute more than neutrinos to the temperature drop. After a million years, the temperature drops below 10,000 Kelvin.
- When the neutron star is a pulsar , it gives off electromagnetic radiation . This can also manifest itself as a gamma-ray flash . About 1% of the massive stars end up like this.
- The equation of state for a neutron star is still unknown. It is believed to be significantly different from that of a white dwarf. The equation of state of a white dwarf is that of a degenerate gas , which can be described to a good approximation with the special theory of relativity. With a neutron star, however, the effects of general relativity are no longer negligible. This also results in the observed deviations from the predicted limits of the masses for a neutron star.
Neutron stars have an extremely strong magnetic field , which is important both for their further development and for astronomical observation. As a result of the laws of electrodynamics , the product of the star's cross-section and the magnetic field remains constant when the precursor star collapses. For a typical neutron star, this results in an increase in the magnetic field by a factor of 10 10 to values in the range of 10 8 Tesla (10 12 Gauss ). The mass density that can be assigned to such a magnetic field via its energy density in combination with the equivalence of mass and energy according to E = mc 2 is in the range of a few dozen g / cm³. These magnetic fields are so strong that atoms in their area of influence would assume an elongated cigar shape, as the interaction of the electrons with the magnetic field dominates over those with the nucleus. Due to the rotation of the neutron star, a Hall voltage of the order of 10 18 V is established between the center and the equator . This corresponds to an electric field strength of several 1000 V per atomic diameter.
Types and examples
If the axis of the magnetic field is inclined to the axis of rotation , radiation ( radio waves , X-rays ) in the direction of the magnetic poles with typically 100,000 times the total radiation power of the sun is emitted due to the interaction with the surrounding plasma . If the observer is in a suitable position, periodic radiation is observed. Such radiation sources are known in astronomy as pulsars or radio pulsars. The energy required for this is taken from the rotational energy , which is largely consumed within a few million years. A similar time course is to be expected with regard to the magnetic field and the temperature.
If there are ionized gases ( plasma ) in the vicinity of the pulsar , the electrons are carried along by the magnetic field at the poles and at the same time move outwards along the axis of the magnetic field. At the latest at the point where the axis rotates at the speed of light, they can no longer follow it and stay behind. They emit part of their kinetic energy as X-rays and gamma rays in the direction of this axis. Such objects are called X-ray pulsars .
Typical systems of this type are X-ray binary stars consisting of a star that is currently expanding into a red giant and a neutron star, with material flowing to the neutron star, forming an accretion disk around it and finally crashing onto its surface. X-ray powers are emitted that are in the range of 10,000 times the solar power.
A special class are neutron stars, which are formed with an initial rotation period of less than 10 ms. In this case, a special dynamo effect also converts the energy of convection currents inside the star into magnetic energy. The flux density of the magnetic field can rise to values of over 10 11 Tesla within a few seconds after the collapse . The associated energy density would correspond to a mass density in the range of many kg / cm³. Such objects are called magnetars . Due to the larger magnetic field, they are slowed down much more so that their rotation frequency drops below 1 Hz after around 1000 years. During this initial phase, they occasionally experience gigantic X-ray bursts. Around a dozen candidates for such X-ray-active magnetars are known in the Milky Way.
- In addition to the neutron matter, a nucleus of a quark-gluon plasma could also be present in the center of a neutron star . Such a hypothetical structure is called a quark star .
- X-ray Dim Isolated Neutron Stars
List of examples
- RX J1856-3754 : Nearest neutron star, no microwave radiation detectable
- PSR 1913 + 16 : neutron double star
- PSR B1257 + 12 : pulsar with planets
- PSR B1620-26c : Planet orbiting the pulsar PSR B1620-26
- PSR B1919 + 21 : First pulsar discovered
- PSR J1748-2446ad : Pulsar with the smallest known rotation time
- Scorpius X-1 : Brightest X-ray source in the sky
- Swift J1818.0-1607 : The youngest known magnetar to date
- Thorsten Dambeck: The lighthouses of radio astronomers . In: Astronomie heute , June 2004, pp. 18-23,
- Jerome Novak: Neutron stars: ultra-dense exotic species . In: Spektrum der Wissenschaft , March 2004, pp. 34-39,
- Chryssa Kouveliotou , RC Duncan, C. Thompson: Magnetare . In: Spektrum der Wissenschaft , May 2003, pp. 56-63,
- George Greenstein: The Frozen Star - Pulsars, Black Holes, and the Fate of Space . dtv, 1988, ISBN 3-423-10868-1 (popular scientific presentation of the topic, including history of discovery)
- Joachim Herrmann: The great lexicon of astronomy . Orbis, 2001, ISBN 3-572-01286-4
- Gently instead of with a big bang. On: Wissenschaft.de of February 10, 2005. Neutron stars could not only arise from supernovae, but also directly from white dwarfs.
- Out of step - astrophysicists discover a neutron star that pulsates irregularly in an unusual way : Telepolis
- scinexx .de: Neutron star: bizarre liquid in the core February 28, 2011
- scinexx.de: How heavy can a neutron star get? January 12, 2018
- astronews.com: The birth of a neutron star June 28, 2013
- astronews.com: Mass limit for neutron stars April 12, 2016
- astronews.com: How big are neutron stars? 5th December 2017
- astronews.com: The maximum mass of a neutron star January 16, 2018
- D. Meschede: Gerthsen Physik. 22nd edition, 2004, p. 630.
- Neutron stars. In: umd.edu. www.astro.umd.edu, accessed January 12, 2017 .
- The value 3.7 · 10 17 kg / m 3 results from the mass 2.68 · 10 30 kg and the star radius 12 km; the value 5.9 · 10 17 kg / m 3 results from the mass 4.2 · 10 30 kg and the star radius 11.9 km
- P. Kaaret et al .: Evidence of 1122 Hz X-Ray Burst Oscillations from the Neutron Star X-Ray Transient XTE J1739-285 . In: The Astrophysical Journal . 657: L97-L100, 2007 (English, iop.org [accessed February 18, 2020]).
- Deepto Chakrabarty et al .: The spin distribution of millisecond X-ray pulsars . In: American Institute of Physics Conference Series . No. 1068 , 2008, p. 67 , doi : 10.1063 / 1.3031208 , arxiv : 0809.4031 , bibcode : 2008AIPC.1068 ... 67C (English).
- Werner Becker: X-Ray Emission from Pulsars and Neutron Stars, in: Werner Becker (Hrsg.): Neutron Stars and Pulsars, 2009, p. 95
- James Chadwick: On the possible existence of a neutron . In: Nature . Volume 129, p. 312. (Written February 17, 1932, published February 27, 1932)
- Lew Dawidowitsch Landau: On the theory of stars . In: Physical Journal of the Soviet Union . Volume 1, No. 2, 1932, pp. 285–288, (written in February 1931, received on January 7, 1932, published in February 1932, also in: Dirk TerHaar (Ed.): Collected papers of LD Landau . Pergamon Press, Oxford [ua] 1965, pp. 60-62): “ All stars heavier than 1.5 certainly regions in which the laws of quantum mechanics (and therefore possess of quantum statistics) are violated. [...] We expect that this must occur when the density of matter becomes so great that atomic nuclei come in close contact, forming one gigantic nucleus. ”
- Walter Baade and Fritz Zwicky: Remarks on Supernovae and Cosmic Rays . Physical Review . Volume 46, 1934, pp. 76-77
- Julius Robert Oppenheimer and George Michael Volkoff: On massive neutron cores. In: Physical Review . Volume 55, 1939, pp. 374-381
- Panel Reports: New Worlds, New Horizons in Astronomy and Astrophysics, 2011, p. 233
- B. Knispel et al .: Pulsar Discovery by Global Volunteer Computing, in: Science 329, 5997, (2010) p. 1305
- Roman Wyrzykowski: Parallel Processing and Applied Mathematics, Part I, 2010, p. 487
- Ed van den Heuvel : Formation and evolution of neutron stars in binary systems , in: Altan Baykal, Sinan K. Yerli, Sitki C. Inam, Sergei Grebenev (eds.): The Electromagnetic Spectrum of Neutron Stars , 2006, p. 197
- Ed van den Heuvel: Compact stars and the evolution of binary systems , in: DJ Saikia, Virginia Trimble (Ed.): Fluid Flows to Black Holes - A Tribute to S Chandrasekhar on His Birth Centenary , 2011, p. 68
- John Antoniadis: Multi-Wavelength Studies of Pulsars and Their Companions, 2015, p. 4
- Chris L. Fryer, Aimee Hungerford: Neutron Star Formation, in: Altan Baykal, Sinan K. Yerli, Sitki C. Inam, Sergei Grebenev (eds.): The Electromagnetic Spectrum of Neutron Stars, 2006, p. 4
- Chris L. Fryer, Aimee Hungerford: Neutron Star Formation, in: Altan Baykal, Sinan K. Yerli, Sitki C. Inam, Sergei Grebenev (eds.): The Electromagnetic Spectrum of Neutron Stars, 2006, p. 6
- Wolfgang Demtröder: Experimentalphysik 4 - Nuclear, Particle and Astrophysics . 3. Edition. Springer-Verlag, Dordrecht Heidelberg London New York 2010, ISBN 978-3-642-01597-7 , 11th Birth, Life and Death of Stars, Section 11.9 .
- Chris L. Fryer, Aimee Hungerford: Neutron Star Formation, in: Altan Baykal, Sinan K. Yerli, Sitki C. Inam, Sergei Grebenev (eds.): The Electromagnetic Spectrum of Neutron Stars, 2006, p. 6
- Searching For Continuous Gravitational Wave Signals With The Hough Transform
- Einstein's Gravitational Waves May Set Speed Limit For Pulsar Spin
- DA Baiko, AA Kozhberov. Phonons in a magnetized Coulomb crystal of ions with a polarizable electron background. Physics of Plasmas, 2017; 24 (11): 112704
- S. Bonazzola, E. Gourgoulhon: Gravitational waves from neutron stars, in: Jean-Alain Marck, Jean-Pierre Lasota (ed.): Relativistic Gravitation and Gravitational Radiation, 1997, p 156
- The LIGO Scientific Collaboration, The Virgo Collaboration: Results of the deepest all-sky survey for continuous gravitational waves on LIGO S6 data running on the Einstein @ Home volunteer distributed computing project (2016) online
- ME Caplan, CJ Horowitz (2017) Rev. Mod. Phys. 89, 041002
- Gordon Baym: Ultrarelativistic heavy ion collisions: the first trillion seconds, p.7, arxiv : 1701.03972
- Edward Shuryak: Heavy Ion Collisions: Achievements and Challenges, p. 52, arxiv : 1412.8393v2
- Luciano Rezzolla, Elias R. Most, Lukas R. Weih: Using Gravitational-wave Observations and Quasi-universal Relations to Constrain the Maximum Mass of Neutron Stars. (PDF) In: The Astrophysical Journal Letters, Volume 852, Number January 3, 2018, accessed January 13, 2018 . doi: 10.3847 / 2041-8213 / aaa401 , arxiv : 1711.00314v2
- How heavy can a neutron star get? - Astronomers calculate upper mass limit for exotic star remnants. scinexx , January 12, 2018, accessed January 13, 2018 .
- Werner Becker: X-Ray Emission from Pulsars and Neutron Stars, in: Werner Becker (Hrsg.): Neutron Stars and Pulsars, 2009, p. 101
- Panel Reports: New Worlds, New Horizons in Astronomy and Astrophysics, 2011, p. 231