Conversion of Dark matter axions to photons in magnetospheres of neutron stars

M.S. Pshirkov1, S.B. Popov
PRAO of Astro Space Centre of the P.N.Lebedev Physics Institute
Sternberg Astronomical Institute

PACS numbers: 14.80. Mz, 95.35.+d, 97.60.Gb, 95.85.Bh

Abstract. We propose a new method to detect observational appearance of Dark Matter axions. The method utilizes observations of neutron stars (NSs) in radio. It is based on the conversion of axions to photons in strong magnetic fields of NSs (Primakoff effect). Whether the conversion takes place, the radio spectrum of the object would have a very distinctive feature – a narrow spike at a frequency corresponding to the rest mass of the axion. For example, if the coupling constant of the photon-axion interaction is GeV, the density of Dark Matter axions is , and the axion mass is , then a flux from a strongly magnetized ( G) NS at the distance 300 pc from the Sun is expected to be about few tenths of mJy at the frequency MHz in the bandwidth MHz. Close-by X-ray dim isolated neutron stars are proposed as good candidates to look for such radio emission.

1 Introduction

Most of the matter in the Universe is "dark", i.e. it can not be observed directly by astronomical observations, as the particles that form it are not baryons [1], [2]. A lot of types of new particles were suggested by the theorists to explain the Dark Matter (DM) problem. One of the best candidates with a strong theoretical background is axion – a light neutral pseudoscalar particle, which appears in spontaneous breaking of Peccei-Quinn symmetry [3] as a solution of the strong CP problem.

In fact, axions are not really dark. In external electromagnetic field they can couple to virtual photons and produce real photons (so-called Primakoff effect [4])


Several experiments that utilize the Primakoff effect are underway now. One direction of such studies is to look for an effect related to conversion of high energy axions from interiors of the Sun in strong magnetic fields in a laboratory [5], [6]. Also solar axions can be searched in X-ray observations because of conversion of these particles in the Earth magnetic field [7],[8]. All these experiments are searching for "hot" and "young" axions, not "cold" cosmological particles originated in the Early Universe. Here we propose an astronomical method to detect emission due to conversion of cosmological axions. Direct experimental searches for such axions are in progress now in laboratories, too [9].

The strongest magnetic fields known can be found in the surroundings of neutron stars (NS), so under certain conditions axions that constitute cosmological DM can experience the Primakoff effect in magnetospheres of NS. Possible use of such super-strong magnetic fields for searching light pseudo-scalar bosons in processes of photon conversion was previously discussed in several papers [10, 11]. In what follows, a possibility of detection of photons from such conversion is studied.

2 Theoretical model

The axion-photon coupling is given by the following term in a lagrangian:


where – the axion field strength, – tensor of the electromagnetic field strength and its dual tensor respectively, – the coupling constant.

The axion rest mass is assumed to be small due to cosmological and astrophysical constraints , the coupling constant is small either: GeV [12], [13].

The conversion probability in transverse magnetic field is [14] (we use Planck system of units where energy has inverse length dimensionality in eqns. (3), (10), (11)):


where is the axion-photon momentum difference:


is the plasma mass of a photon:


– the rest mass and the energy of the axion respectively.

We estimate the probability of the conversion of DM axions to photons in magnetosphere of a NS using several simplifying assumptions: 1) velocity of a NS relative to axions is perpendicular to its rotational axis (dispersion of axions velocities can be neglected due to its small value [9]) 2) -dependence for the magnetic field of a NS can be described by the following relationship , where – magnetic field strength on the surface of a NS, – radius of a NS.

Flux from the axion-photon conversion changes with a period equal to a half of the spin period of a NS because the dipole axis is perpendicular to the axion flow twice during one revolution.

If the plasma mass of photon is equal to zero the conversion is severely suppressed. However, density of charged particles in a NS magnetosphere is quite high and this makes the conversion possible. For our estimates we use the Goldreich-Julian density. There are claims that the plasma density in the region of closed field lines of highly magnetized stars – magnetars – can exceed the G-J density by several orders of magnitude [15]. This is related to the fact that magnetars have hard tails in their spectra, discovered thanks to observations aboard Integral satellite ([16] and references therein). On the other hand, X-ray Dim Isolated Neutrons Stars - also known as "The Magnificent seven", see below – which we discuss in this paper as prominent candidates do not have such hard tails, so we suppose that one can securely set the value of the plasma density in the case of the Magnificent seven equal to the G-J density. [17]:


– spin period of a NS (in seconds), – magnetic field (Gauss).

So, the photon plasma mass depends on radius as follows:

Here . The conversion takes place when the photon plasma mass coincides with the rest mass of the axion,

The critical radius and the critical magnetic field can be derived from the following condition:

and therefore:


For cold axions (, [9]) the certain relation holds:


The difference between the photon plasma mass and the axion mass depends on the length of axion’s path near the critical point (the conversion radius) before conversion takes place:

On the other hand, that length can be determined from the condition of maximum probability (3):


As a result we have:


After rewriting the expression for the probability of conversion with (7), (8), (10), we obtain:


where coefficient is needed to adjust eq. (3) written in Planck system of units to system that is used in conclusive calculations. The full flux of photons also depends linearly on the critical radius because the amount of axions that propagate through the region of active conversion increases linearly with growth of the critical radius. So, finally we can write down our estimate for the amount of energy that comes from the conversion in one second, :


It is clear that the probability rises sharply with growth of the NS spin period and the rest mass of axion. However, there are limitations on 222Soft Gamma Repeaters (SGRs) are neutron stars with the strongest known magnetic fields, G. Fields of the most magnetized pulsars do not exceed few G. There is no evidence of existence of NS with fields stronger then G (although the physical limit of field strength is about  G). and (it can not be less than radius of NS ), so we should specify our candidates for observations for future estimates.

3 Possibility of observation

For subsequent estimates we assume the range of axion rest masses .

Using (6) and (5) we can obtain the following relation:


After substitution of typical values of axion rest mass and NS parameters into the equation for conversion probability (12) it can be seen that relevant conversion takes place only for magnetic fields G – so we need a NS with strong magnetic field. Also it is favorable to have a NS situated close to the Solar system with a spin period as large as possible.

In our opinion, the best candidates to produce observable signal due to axions conversion are X-ray dim isolated NSs. Seven objects of this type are known (they are dubbed the Magnificent Seven (M7), and we use this term below), see a review on isolated NSs in [18]. They possess very strong magnetic fields (up to G) and they are located not far from the Solar system ( 300 pc[19] 333The closest object RX J1856.5-3754 is located at pc[20]). Their present evolutionary state is not known, yet: we do not know whether the M7 sources are similar to normal pulsars or whether they have already passed this evolutionary stage, and so do not produce radio pulsar-like emission. We use the Goldreich-Julian density of charged particles in magnetosphere for our estimates. If the density is significantly higher than the Goldreich-Julian value (about such possibility see, for example, [21]), the conversion would be greatly depressed, see eq. (12) because it would take place in area with low magnetic field strength and therefore the probability of conversion would be tiny.

So, let the magnetic field on the surface of NS be equal to G, spin period is equal to 10 s and the distance from the Earth is equal to 300 pc.

For :

It is essential to estimate total mass of axions that fly through the zone of active conversion () per unit time to obtain estimates for the energy of electromagnetic waves from the conversion [22].


where –axion density, – NS velocity relative to DM, – NS mass. Density of the DM, (and therefore the density of axions) is set equal to [9] (the density may be smaller as such large values can appear only if a source is in a caustic, but as the flux depends on it linearly, it can be easily recalculated with any value of the axion density), velocity was set equal to and we use mass and radius . Total mass of axions propagating through the "active" region per second is:

The energy that comes from the conversion every second can be estimated as:

The electromagnetic flux at from a source might be . Radio waves would have frequencies near central frequency corresponding to the rest mass of axion , MHz in the bandwidth  MHz. The density of that flux might be equal to 0.2 mJy.

We made estimates for the values of axion rest mass between 0.1 and 10 . Probability of the conversion rises swiftly with increase of axion rest mass and reach its saturation value at (fig.1). The predicted observable flux has a sharp peak at that value of axion rest mass and then steeply decreases (fig. 2). The bandwidth of the signal from the conversion smoothly increases with increasing axion rest mass (fig. 3)

The estimates above are only upper limits. We do not take into account the dipole structure of the magnetic field:


where – the unit vector along the radius vector , – the vector of the magnetic dipole. Accurate estimates with an exact configuration of the magnetic field, can slightly reduce our predictions for the flux. Also, the flux might be smaller because of the reverse conversion, but these questions require a detailed study of individual cases, and so we do not discuss them in this note.

It is necessary to mention the possibility of photons absorption due to their propagation in high-density plasma near a NS surface. Indeed, the EM waves of a certain frequency can not propagate through regions where plasma frequency exceeds the EM wave frequency. In the case of a NS that moves through an axion flow away from the Earth, converted photons will be reflected by the magnetosphere so the sought signal will be weakened. In the opposite case, dense plasma will act as a mirror, sending converted photons to the Earth, thus boosting the signal (it might be confined in a solid angle less than ).

Probability of conversion could be further decreased by the effect of vacuum polarization [11]. However, the strength of magnetic field in a region of active conversion is well below the critical value . The variability of the signal depends on the angles and between the spin and magnetic axis and between the spin axis and the velocity vector of a NS.

In general, the flux variability with time is very complicated and should be studied numerically. The figure 4 represents the dependence of the amplitude of the flux variability on the angle when the relative velocity of NS to axions is perpendicular to its axis of rotation.

It is easy to see that the variability will be significant for the angles close to ( if ) and usually it will not exceed 0.1. The period of variation might be twice shorter than the spin period of the NS.

At the moment the most stringent upper limits on the radio emission from the M7 are given by [23]. At the frequency 820 MHz they are about 10 mJy. At lower frequencies the situation is less clear. The group from Pushchino [24] announced detection of pulsed emission from two NSs belonging to the M7. On the other hand, recent observations with GMRT (Joshi et al., poster at COSPAR-2008 and work in progress) do not confirm it. In the near future LOFAR observations [25] can be used to put better limits or to detect the signal due to axion-photon conversion. The signal from the conversion will be strongly depolarized because direction of magnetic field is different in various parts of active conversion region.

4 Conclusions

We suggest to use radio observations of close-by X-ray dim cooling isolated NSs to search for observational appearances of DM axions. Whether the axion-photon conversion in NS’s magnetic field takes place, the radio spectrum of the object might have a very distinct feature – a narrow spike at a frequency corresponding to the rest mass of axion. If the coupling constant of the photon-axion interaction is GeV, the density of DM axions is and a NS with  G is located at the distance of 300 pc from the Solar system, then the flux density of signal for axions with rest mass of is as large as several tenths of mJy at the frequencies MHz in the bandwidth MHz.

Acknowledgements. M.P. wishes to thank Dr. Mikhail Sazhin for useful comments. S.P. thanks Alexander Gvozdev and Igor Ognev for discussions. The work of S.P. was supported by INTAS and by the RFBR grant 07-02-00961.


Probability of conversion vs. the axion rest mass.
The probability,
Figure 1: Probability of conversion vs. the axion rest mass. The probability, , increases with the mass increase. There is a saturation at because of the process of reverse axion-photon conversion that effectively suppresses further growth of . Here and in the figures thereinafter, the magnetic field on the surface of NS is equal to G, spin period is equal to 10 s and the distance from the Earth is set to 300 pc.
Flux density of the signal that comes from the conversion of axions of
a certain rest mass.
Figure 2: Flux density of the signal that comes from the conversion of axions of a certain rest mass.
Bandwidth of the possible signal from the conversion vs. the frequency of observation (axion rest mass).
The bandwidth is defined by the magnitude of axion-photon momentum
Figure 3: Bandwidth of the possible signal from the conversion vs. the frequency of observation (axion rest mass). The bandwidth is defined by the magnitude of axion-photon momentum difference from the eqs. ((9),(10)),
Dependence of the variability of the flux on the angle
Figure 4: Dependence of the variability of the flux on the angle between the axis of rotation and the magnetic dipole axis.



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