FRB 121102 Casts New Light on the Photon Mass

TL;DR

This paper uses precise measurements of the repeating FRB 121102's dispersion measure and known redshift to set new upper limits on the photon mass, improving previous constraints and highlighting the potential of future FRB observations.

Contribution

It provides a novel constraint on the photon mass using FRB 121102 data with high-precision redshift and dispersion measure measurements.

Findings

Photon mass constrained to less than 2.2 x 10^{-14} eV/c^2

Redshift measurements enable improved photon mass limits

Future FRB observations could further tighten constraints

Abstract

The photon mass, $m_\gamma$, can in principle be constrained using measurements of the dispersion measures (DMs) of fast radio bursts (FRBs), once the FRB redshifts are known. The DM of the repeating FRB 121102 is known to $< 1$\%, a host galaxy has now been identified with high confidence,and its redshift, $z$, has now been determined with high accuracy: $z = 0.19273(8)$. Taking into account the plasma contributions to the DM from the Intergalactic medium (IGM) and the Milky Way, we use the data on FRB 121102 to derive the constraint $m_\gamma \lesssim 2.2 \times 10^{-14}$ eV c$^{-2}$ ($3.9 \times 10^{-50}$ kg). Since the plasma and photon mass contributions to DMs have different redshift dependences, they could in principle be distinguished by measurements of more FRB redshifts, enabling the sensitivity to $m_\gamma$ to be improved.

Equations

$$\Delta t_{\mathrm{DM}}=415{\left(\frac{\nu }{1\mathrm{GHz}}\right)}^{-2}\frac{\mathrm{DM}}{10^5\mathrm{pc}\mathrm{c}{\mathrm{m}}^{-3}}\mathrm{s}.$$

$$\Delta t_{\mathrm{DM}}=\int \frac{dl}{c}\frac{{\nu }_p^2}{2{\nu }^2},$$

$$\mathrm{D}{\mathrm{M}}_{\mathrm{IGM}}=\frac{3c{H}_0{\Omega }_{\mathrm{IGM}}}{8\pi G{m}_p}{H}_e(z),$$

$$H_e(z)\equiv {\int }_0^z\frac{(1+z^{\prime })d{z}^{\prime }}{\sqrt{{\Omega }_{\Lambda }+(1+z^{\prime }{)}^3{\Omega }_m}},$$

$$\Delta t_{m_{\gamma }}=\frac{m_{\gamma }^2}{2H_0}\cdot \left(\frac{1}{E_1^2}-\frac{1}{E_2^2}\right)\cdot H_{\gamma }(z),$$

$$H_{\gamma }(z)\equiv {\int }_0^z\frac{d{z}^{\prime }}{(1+z^{\prime }{)}^2\sqrt{{\Omega }_{\Lambda }+(1+z^{\prime }{)}^3{\Omega }_m}}.$$

Full text

KCL-PH-TH/2017-01, CERN-TH/2017-007

FRB 121102 Casts New Light on the Photon Mass

Luca Bonettia,b,c, John Ellisd,e, Nikolaos E. Mavromatosd,e,

Alexander S. Sakharovf,g,h, Edward K. Sarkisyan-Grinbaumh,i,

Alessandro D.A.M. Spalliccia,b,c

*aObservatoire des Sciences de l’Univers en région Centre, UMS 3116, Université d’Orléans

1A rue de la Férollerie, 45071 Orléans, France

bPôle de Physique, Collegium Sciences et Techniques, Université d’Orléans

Rue de Chartres, 45100 Orléans, France

cLaboratoire de Physique et Chimie de l’Environnement et de l’Espace, UMR 7328

Centre Nationale de la Recherche Scientifique

LPC2E, Campus CNRS, 3A Avenue de la Recherche Scientifique, 45071 Orléans, France

dTheoretical Particle Physics and Cosmology Group, Physics Department

King’s College London, Strand, London WC2R 2LS, United Kingdom

eTheoretical Physics Department, CERN, CH-1211 Genève 23, Switzerland

fDepartment of Physics, New York University

4 Washington Place, New York, NY 10003, United States of America

gPhysics Department, Manhattan College

4513 Manhattan College Parkway, Riverdale, NY 10471, United States of America

hExperimental Physics Department, CERN, CH-1211 Genève 23, Switzerland

iDepartment of Physics, The University of Texas at Arlington

502 Yates Street, Box 19059, Arlington, TX 76019, United States of America

Abstract

The photon mass, $m_{\gamma}$, can in principle be constrained using measurements of the dispersion measures (DMs) of fast radio bursts (FRBs), once the FRB redshifts are known. The DM of the repeating FRB 121102 is known to $<1$%, a host galaxy has now been identified with high confidence, and its redshift, $z$, has now been determined with high accuracy: $z=0.19273(8)$. Taking into account the plasma contributions to the DM from the Intergalactic medium (IGM) and the Milky Way, we use the data on FRB 121102 to derive the constraint $m_{\gamma}\lesssim 2.2\times 10^{-14}$ eV c*-2* ($3.9\times 10^{-50}$ kg). Since the plasma and photon mass contributions to DMs have different redshift dependences, they could in principle be distinguished by measurements of more FRB redshifts, enabling the sensitivity to $m_{\gamma}$ to be improved.

The photon is generally expected to be massless, but a number of theorists have challenged this assumption, starting from de Broglie and nowadays considering models with massive photons for dark energy and dark matter. Examples of mechanisms for providing mass include Standard Model Extensions with supersymmetry and Lorentz invariance breaking [1] and Higgs mechanisms [2]. In view of these possibilities and its fundamental importance, it is important to constrain the magnitude of the photon mass as robustly as possible. The most robust limits available are those from laboratory experiments [3] - see [4, 5] for reviews - but these are much weaker than those derived from astrophysical observations. The Particle Data Group (PDG) [6] cites the upper limit $m_{\gamma}<8.4\times 10^{-19}$ eV c*-2* ($=1.5\times 10^{-54}$ kg) [7] obtained by modelling the magnetic field of the solar system [7, 8]. However, this limit relies on assumptions about the form of the magnetic field and does not discuss measurement accuracy and errors. Another limit ($m_{\gamma}<4\times 10^{-52}$ kg) has been derived from atmospheric radio waves has been reported in [9]. A more conservative approach was followed in an analysis of Cluster data [10], leading to an upper limit between $7.9\times 10^{-14}$ and $1.9\times 10^{-15}$ eV c*-2* ($1.4\times 10^{-49}$ and $3.4\times 10^{-51}$ kg). It is clearly desirable to explore more direct and robust astrophysical constraints on a possible photon mass.

This was the motivation for a study we made [11] (see also [12]) showing how data from fast radio bursts (FRBs) could be used to constrain $m_{\gamma}$. These have durations in the millisecond range, and their signals are known to arrive with a frequency-dependent dispersion in time of the $1/\nu^{2}$ form. This is the dependence expected from plasma effects, but a similar dispersion $\propto m_{\gamma}^{2}/\nu^{2}$ could also arise from a photon mass. The dispersions induced by plasma effects and $m_{\gamma}$ both increase with distance (redshift $z$), but with different dependences on $z$. We note in this connection that the lower frequencies of FRB emissions give a distinct advantage over gamma-ray bursters and other sources of high-energy $\gamma$ rays for constraining $m_{\gamma}$, since mass effects are suppressed for higher-energy photons 111In contrast, sources of high-energy photons are better suited for probing models of Lorentz violation [13].. Moreover, using FRB emissions to constrain $m_{\gamma}$ is much more direct and involves fewer uncertainties than using the properties of astrophysical magnetic fields 222For an early consideration of possible astrophysical photon propagation delays, see [14]. For pioneering studies using astrophysical sources, see [15] (flare stars) and [16] (Crab nebula), and for an analogous subsequent study with greater sensitivity to the photon mass, see [17] (GRB 980703, $m_{\gamma}<4.2\times 10^{-47}$ kg). The most recent such studies are those in [18] (GRB 050416A, $m_{\gamma}<1.1\times 10^{-47}$ kg) and [19] (radio pulsars in the Magellanic clouds, $m_{\gamma}<2\times 10^{-48}$ kg). Our limit on $m_{\gamma}$ is significantly stronger..

That said, although the large dispersion measures (DMs) and other arguments led to the general belief that FRBs occur at cosmological distances, until recently no FRB redshift had been measured. The first claim to measure a redshift was made for FRB 150418 [20], and this was the example we used in [11] to show how FRB measurements could in principle be used to constrain $m_{\gamma}$. However, the identification of the host galaxy of FRB 150418 has subsequently been challenged [21], and is now generally not accepted [22].

Our interest in the possibility of using FRBs to constrain $m_{\gamma}$ has recently been revived, however, by the observation of repeated emissions from FRB 121102 [22]. These have permitted precise localisation of its host galaxy, which has made possible a precise determination of its redshift, $z=0.19273(8)$ [23]. This redshift determination makes it possible, in turn, to use data on FRB 121102 to provide a robust constraint on $m_{\gamma}$, as we discuss in this paper.

The dispersion measure (DM) is related to the frequency-dependent time lag of an FRB by

[TABLE]

In the absence of a photon mass, the time-lag of an FRB is given by integrating the column density $n_{e}$ of free electrons along the line of flight of its radio signal

[TABLE]

where $\nu_{p}=(n_{e}e^{2}/\pi m_{e})^{1/2}=8.98\cdot 10^{3}n_{e}^{1/2}$ Hz. Several sources contribute to this integrated column density of free electrons, notably the Milky Way galaxy, the intergalactic medium (IGM) and the host galaxy. The contribution to the DM (1) of an FRB at redshift $z$ from the IGM is given by the cosmological density fraction ${\rm\Omega_{IGM}}$ of ionized baryons [24, 25]:

[TABLE]

where $H_{0}=67.8(9)$ km/s/Mpc [6] is the present Hubble expansion rate 333We discuss later the impact of assuming a broader range $H_{0}=70(4)$ km/s/Mpc [26]., $G$ is the Newton constant, $m_{p}$ is the proton mass, and the redshift-dependent factor

[TABLE]

where $\Omega_{\Lambda}=0.692(12)$ and $\Omega_{m}=0.308(12)$ [6]. For comparison, the difference in time lags between photons of energies $E_{1,2}$ due to a non-zero photon mass has the form:

[TABLE]

where we use natural units $h=c=1$, and [27, 28]

[TABLE]

As already commented, the time lags due to the IGM and a possible photon mass have different dependences (4, 6) on the redshift. The uncertainties in the cosmological parameters and the measurement of the redshift measurement of FRB 121102 are taken into account in our analysis, with the uncertainties in the former being much more important, as we see later.

The top (green) band in Fig. 1 shows the total DM $=558.1\pm 3.3$ pc cm*-3* measured for FRB 121102 [22]. The most conservative approach to constraining $m_{\gamma}$ would be to set to zero the other contributions, and assign this total DM to a possible photon mass. However, this is surely over conservative, and a reasonable approach is to subtract from the total DM the expected contribution from the Milky Way [22], DMMW, which is the sum of contributions from the disk [29]: DM${}_{\rm NE2001}\simeq 188$ pc cm*-3* and the halo: DM${}_{\rm halo}\simeq 30$ pc cm*-3* [23], to which we assign an overall uncertainty of 20%, namely $44$ pc cm*-3* [23], leaving the middle (blue) band in Fig. 1 that is centred at $340$ pc cm*-3*. From this we may also subtract the contribution from the IGM, which is estimated within the $\Lambda$CDM model to be $\simeq 200$ pc cm*-3* [24, 25, 23]. To this is assigned an uncertainty of $85$ pc cm*-3* associated with inhomogeneities in the IGM [30, 23], which is much larger than the 1.2% variation associated with uncertainties in the cosmological parameters (shown as the narrow magenta band). The bottom (pink) band in Fig. 1, centred at $140$ pc cm*-3*, shows the effect of subtracting these contributions from the measured DM for FRB 121102.

After subtracting these contributions, we are left with a residual DM $=140$ pc cm*-3* with a total uncertainty of $\pm 96$ pc cm*-3*, shown as the outer pink band, where the error is calculated by combining in quadrature the uncertainties in the experimental measurement of the total DM, the uncertainty in DMMW, and the uncertainties in DMIGM associated with the cosmological parameters $H_{0},\Omega_{\Lambda}$ and $\Omega_{m}$ and possible inhomogeneities. One cannot exclude the possibility that all the residual DM of FRB 121102 is due to the host galaxy, which is estimated to lie within the range $55\lesssim$ DM${}_{\rm Host}\lesssim 225$ pc cm*-3* [23]. However, in the absence of detailed information about the host galaxy, when constraining the photon mass we allow conservatively for the possibility that all the residual DM is due to $m_{\gamma}\neq 0$.

The curved band in Fig. 1 shows the possible contribution to the DM of FRB 121102 of a photon mass, as a function of $m_{\gamma}$: DM $=10^{5}m_{\gamma}^{2}H_{\gamma}/(415A^{2}h_{0})$, where $H_{\gamma}$ is given in (6), $A=1.05\cdot 10^{-14}$ ev s*-1/2* and $h_{0}\equiv H_{0}/100$km/s/Mpc. The width of this band is due to the uncertainties in the cosmological parameters $H_{0},\Omega_{\Lambda}$ and $\Omega_{m}$ [6], and the uncertainty in the determination of the redshift of FRB 121102. Assuming that the photon mass contribution to the total DM of FRB 121102 lies within the range allowed for the residual DM, after subtraction of the Milky Way and IGM contributions and taking their uncertainties into account, we find $m_{\gamma}\lesssim 2.2\times 10^{-14}$ eV c*-2* ($3.9\times 10^{-50}$ kg) 444This limit would increase to $m_{\gamma}\lesssim 2.3\times 10^{-14}$ eV c*-2* ($4.1\times 10^{-50}$ kg) if the more relaxed range $H_{0}=70(4)$ km/s/Mpc [26] were used for $H_{0}$. On the other hand, it would decrease to $m_{\gamma}\lesssim 1.8\times 10^{-14}$ eV c*-2* ($3.2\times 10^{-50}$ kg) if the minimum estimate of DMHost [23] was taken into account.. This limit is similar to, though slightly weaker than, that obtained from similar considerations of FRB 150418 [11, 12], whose redshift is now contested, as discussed earlier [21]. If FRB 150418 was indeed at a cosmological distance, using its DM value determined in [20] and the same values of $H_{e}(z)$ and $H_{\gamma}(z)$ as in the present analysis, we find that the inferred limits on $m_{\gamma}$ would coincide if FRB 150418 had a redshift $z=0.38$, instead of the value $z=0.492$ reported in [20] and challenged in [21].

How could this constraint be improved in the future? Clearly it is desirable to reduce the uncertainties in the modelling of the Milky Way and IGM contributions. Also, the limit could be strengthened by a redshift measurement for an FRB at higher $z$, if the uncertainty in the IGM contribution can be controlled. Finally, as remarked in [11], comparing the DMs for FRBs with different redshifts could enable the IGM and $m_{\gamma}$ contributions to be disentangled, in view of their different dependences (4, 6) on $z$.

A hitherto unexplored window at very low frequencies in the MHz-KHz region could be opened by a space mission consisting of a swarm of nanosatellites [31]. One possible configuration would be orbiting the Moon, where it would be sufficiently away from the ionosphere to avoid terrestrial interference, and would have stable conditions for calibration during observations. Such low frequencies would offer a sensitive probe of any delays due to a non-zero photon mass.

Acknowledgements

The research of J.E. and N.E.M. was supported partly by the STFC Grant ST/L000326/1. The work of A.S.S. was supported partly by the US National Science Foundation under Grants PHY-1505463 and PHY-1402964.