1 

A Role for Bose-Einstein Condensation in Astrophysics 

B. W. Ninham1,*, I. Brevik2,*, O. I. Malyi3,*, and M. Boström3,* 

 

1Department of Materials Physics, Research School of Physics, Australian National University, 

Canberra, Australia, 0200. 

2Department of Energy and Process Engineering, Norwegian University of Science and 

Technology, NO-7491 Trondheim, Norway 

3Centre of Excellence ENSEMBLE3 Sp. z o. o., Wolczynska Str. 133, 01-919, Warsaw, Poland. 

* E-mail addresses: Barry.Ninham@anu.edu.au; iver.h.brevik@gmail.com; 

oleksandr.malyi@ensemble3.eu; Mathias.Bostrom@ensemble3.eu 

 

Received: Mar 21, 2023 Revised: May 23, 2023 Just Accepted Online: Jun 06, 2023 Published: 

Xxx 

This article has been accepted for publication and undergone full peer review but has not been 

through the copyediting, typesetting, pagination and proofreading process, which may lead 

to differences between this version and the Version of Record. 

Please cite this article as: 

B. W. Ninham, I. Brevik, O. I. Malyi, and M. Boström, (2023) A Role for Bose-Einstein 

Condensation in Astrophysics. Substantia. Just Accepted. DOI: 10.36253/Substantia-2091 

 

Abstract 

We revive a 60-year-old idea that might explain a remarkable new observation of a periodic 

low-frequency radio emission from a source at galactic distances (GLEAM-X J162759.5-

mailto:Barry.Ninham@anu.edu.au
mailto:iver.h.brevik@gmail.com
mailto:oleksandr.malyi@ensemble3.eu


 

 

2 

523504.3). It derives from the observation that a high-density high-temperature charged 

boson plasma is a superconducting superfluid with a Meissner effect. 

 

Keywords: Bose-Einstein condensate, Charged Bose gas, Astrophysical Chemistry 

 

Introduction 

Sporadic forays over the years have explored the possibility that the physics of Bose-

Einstein condensation ought to play some role in Astrophysics, e.g. [1,2]. Many of the particles 

involved in stellar evolution are bosons, i.e. have zero or integer spin. Bose-Einstein 

condensation is a fundamental macroscopic manifestation of quantum physics. It would seem 

remiss of the Creator not to have employed the phenomenon somewhere in building the 

Universe. Especially is this so since Fermi-Dirac and Classical Statistical Mechanics do figure 

largely. A suggestion of a role for Bose-Einstein condensation was made 60 years ago when 

quasars were first observed [1], and forgotten. Later attempts failed because they considered 

superconductivity and Bose condensation as classical low-temperature phenomena like that 

which occurs for electrons in metals. But the phenomena are not limited and exist for very 

high-temperature high-density charged particles [1].  

We here revive that 60-year-old idea and suggest it might explain a recent extraordinary 

observation.  

 

 The Phenomenon   

Hurley-Walker et al. [3] recently reported an unusually slow periodic low-frequency radio 

emission from a source at galactic distances (GLEAM-X J162759.5-523504.3) with a pulse 



 

 

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period of 18.18 minutes. One clue to its origin is that high linear polarization has been shown 

to be characteristic of a source with strongly ordered magnetic fields [4-6]. The observations 

are unlike emissions characteristic of stars, white dwarfs, white binaries, or exoplanets. 

Furthermore, the 0.5-light-second upper limit on the object’s size and estimated brightness 

temperature of 1016 K led Hurley-Walker et al. [3] to propose that a radiation source is a 

compact object with a rotational origin.  

 

 

 

 

The Idea  

With that in mind, we give reasons to consider if Bose-Einstein condensation [1] might have 

something to do the phenomenon: 

 

(i) Stable nuclei in stellar interiors have zero or integer spin. Nuclei of higher and higher atomic 

numbers built up during the evolution of stars. They are charged bosons. 

(ii) A dense charged high-temperature boson plasma becomes nearly perfect as density 

increases (i.e., the Coulomb collective interactions become so weak that they can be ignored, 

and we can work with the perfect gas approximation). 

(iii) It can undergo Bose-Einstein condensation to a superfluid state. 

(iv) A conducting superfluid is a superconductor. A rotating superconducting superfluid has a 

Meissner effect. That is, it expels the magnetic field generated by rotation.  

(v) Such a magnetic field would be trapped in the lower-density surface region. This process 

continues as the star collapses and its rotation speeds up. 



 

 

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(vi) Massive synchrotron radiation follows that dissipates this increasing build-up of energy.  

 

The assumptions i-vi were originally made 60 years ago to explain the newly discovered 

quasars. Schafroth [8], Blatt [9], and Butler [10] had shown earlier that an ideal charged Bose 

gas below the critical point for superfluidity is a superconductor (see also Refs. [7,8-17]). These 

theories [7-17] call on electron pairing to generate charged bosons that then lead to Bose 

condensation and superconductivity at very low temperatures. Our situation is quite different. 

The stellar objects involve real boson nuclei of even spin. The high-density, high-temperature 

plasmas are close to ideal.  

 

We recall the process of nucleosynthesis in stellar interiors [18-21]. The theory explains how 

nuclear reactions convert lighter elements into heavier ones through the fusion of atomic 

nuclei. As the star evolves, the fuel elements involve successive steps, with H, He, C, O, Ne, Si, 

Fe, and U providing increasingly heavier energy sources that drive the stellar evolution to 

completion [18]. We need to estimate the critical temperatures and core densities for Bose 

condensation for stars with different fuel elements to check that they can have a Boson core 

region.  

  

Calculations  

Consider an assembly of ions of even spin, mass M and charge Ze, in a background electron 

gas. Under extreme high-density and high-temperature conditions, the system is expected to 

behave like a mixture of ideal gases. That can be achieved by ensuring that the average energy 

of Coulomb interactions between two ions is small compared to their kinetic energy. At 

densities approaching the critical value for Bose-Einstein condensation of ions, i.e., when their 



 

 

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chemical potential approaches zero, the mean energy, per particle of the ideal Bose gas is 

approximately equal to kT. The average distance between the particles is then [1] 

 

r ≈ 2 √3M/[4πρ]
3

≈  λ = ℎ/(𝑀𝑣) = ℎ/√2  M kT,    (1) 

 

where 𝜆 is the de Broglie wave length of an ion of mass M and kinetic energy ~𝑘𝑇 (taken in 

Eq (1) equal to Mv2/2). The condition that the actual gas be nearly ideal is [1] 

  

2𝑍2𝑒2

𝑟
≪ 𝑘𝑇.     (2) 

 

Hence, taking the requirement Eq. (2) with Eq. (1), the critical expressions for temperatures, 

density, and particle separation can be estimated to be of the order  

 

𝑇𝐶~
8𝑀𝑍4𝑒4

ℎ2𝑘
     (3) 

ρ𝐶~
384

𝜋

𝑀4𝑍6𝑒6

ℎ6
~

6

8𝜋

𝑀𝑘3

𝑍6𝑒6
𝑇𝐶
3,    (4) 

r𝐶~
ℎ2

4𝑀𝑍2𝑒2
~

2𝑍2𝑒2

𝑘𝑇𝐶
.    (5) 

 

The numerical values are summarized in Table 1. We expect that highly charged nuclei will be 

“dressed” by an inhomogeneous adsorbed relativistic electron cloud (mesons in another 

guise): just as for charged micelles or highly charged ions in electrolyte solutions. In that case, 

“bound” counterions are typically 80-90% of the bare charge. The effective charge is 10-20% 

of the actual charge. Without recognising such screening, estimated critical parameters for 

the separation of heavy ions become unphysical and ridiculous. In Table 1, we take two 



 

 

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extreme estimates to bound these uncertainties: the unscreened Z and Z=1. To illustrate our 

point, we present also the critical temperatures with 10% and 20% effective charges in Table 

2. For Uranium, from Table 2, the estimated critical temperatures are 1014 K<Tc<10
15 K. These 

bounds are similar in magnitude to the observed brightness temperature of 1016 K discussed 

by Hurley-Walker et al. [3]. 

 

 

 

 

 

 

Fuel element 

[A,Z] 

𝑻𝑪 (Z=1) 

[K] 

𝝆𝑪 (Z=1) 

[g/cm3] 

𝑻𝑪 (Z) 

[K] 

𝛒𝑪 (Z) 

[g/cm3] 

He [4,2] 4.7 × 108 3.5 × 1010 8 × 109 2 × 1012 

C [12,6] 1.4 × 109 2.9 × 1012 2 × 1012 1 × 1017 

O [16,8] 1.8 × 109 9.0 × 1012 8 × 1012 2 × 1018 

Ne [20,10] 2.3 × 109 2.2 × 1013 2 × 1013 2 × 1019 

Si [28,14] 3.2 × 109 8.5 × 1013 1 × 1014 6 × 1020 

Fe [56,26] 6.6 × 109 1.3 × 1015 3 × 1015 4 × 1023 

U [238,92] 2.8 × 1010 4.4 × 1017 2 × 1018 3 × 1029 

 

Table 1. The critical temperatures and mass densities for different fuel elements in the core 

of a Boson star are derived from Equations (3)-(5). Since we did not include screening we 

present two different estimates (a) based on setting Z=1 (columns 2 and 3) and (b) using Z 



 

 

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from column 1 (columns 4 and 5). Here ℎ = 6.626 × 10−27erg s, 𝑘 = 1.381 × 10−16erg/K, 

𝑒 = 4.803 × 10−10esu, and we estimate the mass as 𝑀 = 𝐴 × 1.66 × 10−24g (Atomic 

number x proton mass). 

 

 

 

 

 

 

Fuel element 

[A,Z] 

𝑻𝑪  

(𝒁 → 𝒁 ×0.1) 

[K] 

𝑻𝑪  

(𝒁 → 𝒁 × 𝟎.𝟐) 

[K] 

He [4,2] 8 × 105 1 × 107 

C [12,6] 2 × 108 3 × 109 

O [16,8] 8 × 108 1 × 1010 

Ne [20,10] 2 × 109 4 × 1010 

Si [28,14] 1 × 1010 2 × 1011 

Fe [56,26] 3 × 1011 5 × 1012 

U [238,92] 2 × 1014 3 × 1015 

Table 2. The critical temperatures for different fuel elements in the core of a Boson star are 

derived from Equations (3)-(5). Estimates (a) based on setting 𝑍 → 𝑍 ×0.1 (column 2) and 𝑍 →

𝑍 ×0.2 (column 3). Constants used are same as in Table 1. 

 



 

 

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With even the lowest densities N(He), the accompanying electron gas is highly relativistic and 

degenerate. We intend to go beyond these simple estimates using a screened intervening 

plasma including both magnetic and dielectric susceptibilities. Notably, the core temperatures 

for the seven ages of a 20Mo star discussed by Trimble are T=1.9 × 10
8K for a star with Helium 

as fuel element and T=3.7 × 109K for a star with Silicon as fuel element [18]. These numbers 

are in surprisingly good agreement with our estimates based on using Z=1 in Table 1.  

 

Figure 1. Number density (𝑁) of stable nuclei vs. temperature phase diagram for the charged 

Bose gas. The condensation line shown use Eq. (4) and the data from Table 1. Adapted from 

Figure 1 in Ref. [1]. The data points from the unscreened model (Z from Table 1) are shown as 

red symbols while the results corresponding to Z=1 model are shown as blue symbols. We 

indicate schematically a region relevant for white dwarfs (large black circle) (from Figure 1 in 

Ref. [1]). 

 

In region I, near the condensation line, 𝜌~
6

8𝜋

𝑀𝑘3

𝑍6𝑒6
𝑇3, the system is nearly an ideal Bose gas. 

Above the condensation line in region II (high density, high temperature), a rotating gas should 

become superconducting, Region III corresponds to the classical Debye-Hückel (high 

temperature, low density) region, and in region IV conditions are favourable for the formation 



 

 

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of a lattice (low temperature, low densities). Region V (low temperature, high density), 

exhibits an energy gap (c.f. eq. (7)), where the quasi-particle elementary excitation energy has 

the form [1,12,13] 

 

ε(𝑝) = √(
𝑝2

2𝑚
)
2

+ (ℏω𝑝)
2

,   (7) 

 

where 𝜔𝑝 is the classical plasma frequency. 

 

A Diversion. With Bose Einstein condensation in stellar systems, further unanticipated 

complications may occur. As they contract under the influence of gravitational forces, their 

core densities and temperatures will increase, leading to charged Boson core regions with 

increasingly heavy fuel elements. Available nuclear mass models show that not all numbers of 

proton-neutron combinations would be stable. For each state there is a minimum and a 

maximum number of neutrons and protons that are stable: a phenomenon known as the 

neutron and proton drip line [22]. The nuclear mass models demonstrated that certain 

ensembles of protons and neutrons are inherently unstable. That is, the ground-state 

configurations of such species are energetically unstable to the emission of a constituent 

nucleon [22]. The matter is still open. 

Even the established sign of nucleon-nucleon interactions which can be used for plausible 

models of Bose condensation with neutron pairing [2] has been questioned. The data dating 

back to Seaborg’s work from which that conclusion was reached has never been questioned. 

See references in [23,24]. Be that as it may, the possibility that Bose condensation and 

consequent magnetic events of even quarks and other exotic objects in the cores of neutron 



 

 

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stars has seriously been broached [25]. Returning to our main theme, Hurley-Walker et al. [3] 

speculated that their observations might be due to a compact rotating magnetar. However 

magnetars are made of neutrons, that is fermions. Our considerations apply to bosons. Our 

propositions might then be appropriate rather to the early stages of the collapse of one of a 

pair of rotating massive binary stars. This would be consistent with the very low frequency of 

the pulses. 

 

Conclusions  

Quantum coherent Bose-Einstein condensation is a general property of matter with particles 

of even spin. Therefore, it might reasonably be expected to play a role in astrophysics one way 

or another, just as Fermi-Dirac statistics does in the theory of white dwarf and neutron stars. 

Attempts to invoke Bose condensation and superconductivity are few [1-2]. The present 

proposal is unlike the original low temperature theories of superconductivity [10-11, 14-17]. 

It is concerned with a phenomenon that occurs with charge bosons at high temperature and 

high density [1]. The charged ideal Bose gas is superfluid below its critical point [1,12]. And a 

rotating superfluid has a Meissner effect [8-10] with consequent, expulsion and buildup of 

large magnetic effects. The observed linearly polarized ultra-long period low-frequency radio 

emission is known to be related to magnetic fields [5-7]. The Bose-Einstein condensation could 

be the origin of the magnetic fields and the phenomenon, not previously observed, might be 

of wider occurrence, as anticipated in [25] A. Mann, “The strange hearts of neutron stars”, 

Nature 579, 20-22 (2020). 

 

Acknowledgments: The authors thank the "ENSEMBLE3 - Centre of Excellence for 

nanophotonics, advanced materials and novel crystal growth-based technologies" project (GA 



 

 

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No. MAB/2020/14) carried out within the International Research Agendas programme of the 

Foundation for Polish Science co-financed by the European Union under the European 

Regional Development Fund and the European Union's Horizon 2020 research and innovation 

programme Teaming for Excellence (GA. No. 857543) for support of this work. The authors 

are grateful to Professor Nikolai Bunkin for drawing our attention to the work of Hurley-

Walker and colleagues. 

 

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	Sporadic forays over the years have explored the possibility that the physics of Bose-Einstein condensation ought to play some role in Astrophysics, e.g. [1,2]. Many of the particles involved in stellar evolution are bosons, i.e. have zero or integer ...
	We here revive that 60-year-old idea and suggest it might explain a recent extraordinary observation.
	[10] M.R. Schafroth, S.T. Butler, and J.M. Blatt, “Quasichemical equilibrium approach to superconductivity”, Helv. Phys. Acta 30, 93 (1957) .
	[16] J. Bardeen, L.N. Cooper, and J.R. Schrieffer, “Theory of Superconductivity”, Phys. Rev. 108, 1175 (1957).