DM contributions

When radio signals propagate through a plasma, the travel time is longer than the light travel time in a vacuum. The additional delay depends on the radio wave frequency, f, in units of GHz, and obeys a precise physical law of the form: t DM = 4.149 ms × (DM × f−2), where the DM is the integrated electron density along the line of sight in units of cm−3 pc. If travelling across cosmological distances there are several contributions to the observed DM—from the host, the intergalactic medium and the Milky Way. The quantity of interest is the intergalactic medium component because this can be used, in conjunction with redshift measurements, to perform a number of fundamental studies, for example, detecting the missing baryons10, determining the dark energy equation of state11 and, if the signal is linearly polarized, measuring magnetic field strengths in the intergalactic medium31. For these applications the DM contributions other than those from the intergalactic medium are essentially foregrounds which must be understood so that they can be removed. Here we examine each contribution in turn and note the uncertainties in each case; it is important to note that the precision in the observed DM value is high (see Table 1) and does not therefore contribute to the uncertainty in determining the DM for the intergalactic medium.

The Milky Way component consists of two parts, the first of which is that due to the interstellar medium. This is in principle known14, because the NE2001 model of the Galaxy’s electron density can determine this to an accuracy of approximately 20%. The second Milky Way component is the contribution from the dark matter halo, which is thought to exist, yet which is not included in the NE2001 model. We follow previous work21, which has calculated this term to be 30 cm−3 pc. It is unclear how to assign an uncertainty to this component so (considering that the other components are dominant regardless) we take it to be zero. The host component is suppressed by a factor of (1 + z)1. Its magnitude depends on both the nature of the progenitor and of the host galaxy.

The observed FRB signal can be used to constrain the progenitor’s local DM contribution—a non-negligible contribution could imply a high density of electrons to be located close to the source. Such a high density configuration32 could produce higher-order dispersion terms (that is, the pulse’s frequency dispersion would deviate from the quadratic form), could result in plasma frequencies comparable to the emitted frequency (that is, radiation would not escape), and could produce scattering in the pulse profile. None of these effects are observed for FRB 150418, implying that any local-progenitor DM component is negligible.

The host galaxy contribution has been examined recently22 for spiral, dwarf and elliptical galaxies. This work considered modified versions of NE2001, with various sub-components of the model included or excluded as appropriate and suitable scalings to the Hα luminosity applied. For an elliptical galaxy, which is relevant in the case of FRB 150418, the average DM contribution over all inclination angles is 37 cm−3 pc (this is the value before being suppressed by the (1 + z)1 factor) and we use this as our estimate of the host contribution. As this is based upon NE2001 we assume that a 20% uncertainty applies. In addition to the uncertainties mentioned already the intergalactic medium component itself is uncertain at the level of ~100 cm−3 pc, owing to inhomogeneities between different lines of sight through the intergalactic medium10.

SUPERB

SUPERB is a project ongoing at the 64-m Parkes radio telescope since April 2014 with goals of discovering FRBs and pulsars. The central frequency of the survey is 1.382 GHz, with a bandwidth of 400 MHz, of which about 340 MHz is typically usable. It uses optimized graphics processing unit codes for performing real-time radio frequency interference mitigation and searches for short-duration radio bursts and pulsars in relativistic binary systems. In the real-time search we use the following criteria to define candidate FRB events: (1) the DM of the burst must be at least 1.5 times the expected maximum Milky Way contribution; (2) the signal-to-noise ratio must be at least 10; (3) the signal cannot be detected in more than four beams of the 13-beam receiver used for the SUPERB project at Parkes—an event detected in more beams cannot originate from a boresight signal and therefore cannot be of a celestial origin; (4) the width must be less than or equal to 8.192 ms, that is, 128 times our native time sampling of 64 μs; and (5) the number of independent events detected in a 4-s window centred on the event in question must be no greater than 5. The lag between the FRB signal hitting the dish and our software informing us of the detection7 is only ~10 s. We further search the data, offline, with more stringent interference rejection and covering corners of parameter space ignored for expediency during the real-time search. We note that since instigating this search system at Parkes no FRB has been missed by the real-time search pipeline, including FRB 150418.

FRB 150418 was detected in beam 4 of the 21-cm multi-beam receiver. The FRB profile was fitted simultaneously for time of arrival, DM, width, amplitude and dispersion index using 4 and 8 different sub-bands. The results were consistent with an unresolved pulse, where the width is purely given by the dispersion smearing across the 390.625-kHz filterbank channels. Uncertainties were determined using CERN’s MINUIT packages (http://seal.web.cern.ch/seal/snapshot/work-packages/mathlibs/minuit/). The burst was found to have a DM of 776.2(5) cm−3 pc, and a dispersion index of β = −2.00(1), where the dispersion delay is proportional to vβ, and so is consistent with propagation through a cold plasma.

The gain of beam 4 is well fitted by a Gaussian25 with FWHM of 14.1 arcmin, so to derive corrected values for the flux density, fluence, and so on we boost the measured values by a factor of exp(ln2(2θ/FWHM)2), where θ is the offset of the signal from the beam centre. The offset between the ATCA position determined from the first epoch (RA 07 h 16 min 34.557 s, dec. −19° 00′ 39.954′′) and the centre of the Parkes beam (RA 07 h 16 min 30.9 s, dec. −19° 02′ 24.4′′) is θ = 1.944 arcmin, yielding a boost factor of 1.054. The observed peak flux density, if the FRB were at the centre of the beam, is 2.2 Jy with a corresponding fluence of 1.9 Jy ms; correcting these to the location of the host galaxy, we estimate values of 2.4 Jy and 2.0 Jy ms.

A calibration observation was taken 17 min post-burst and the polarization calibration was performed using the PSRCHIVE software package33. On the basis of observations of PSR J1644–4459, a bright polarized pulsar which we use to calibrate the off-axis response, taken three days before the FRB, we determine that the difference in the Jones matrix coefficients is not statistically different off-boresight. Therefore the boresight calibration was used to determine the polarization fraction of the pulse. This FRB is not seen to have a large linear polarization L, the rotation-measure-corrected linear polarization is L/I = 8.5 ± 1.5% (where I is total intensity) and the circular polarization is consistent with zero. An additional systematic uncertainty exists in the leakage of total intensity to polarization. Our analysis of PSR J1644–4459 provides an upper limit on the magnitude (but not orientation) of the leakage vector that is <6% of the total intensity, meaning that the true L/I value may be either smaller or larger than quoted by up to this amount. Owing to the low linear polarization the rotation measure estimate is not very precise at 36 ± 52 rad m−2. As the rotation measure is consistent with zero, examination of the intergalactic medium magnetic field strength is not possible with this FRB, although for completeness we note that the 3σ upper limit on the electron weighted intergalactic medium magnetic field strength is ~0.4 μG for this line of sight. There is no evidence for a large host contribution to the rotation measure for this FRB, although we note that an extremely large rotation measure exceeding 105 rad m−2 would result in depolarization within a single frequency channel, meaning we are insensitive to such large values.

The Murchison Widefield Array (MWA)34 was shadowing our Parkes observations but did not detect a counterpart. The resulting 3σ fluence upper limit of 1,050 Jy ms at 185 MHz gives us the first simultaneous multi-frequency observation of an FRB, and hence the first broadband limit on the spectral index. The spectral index limit from the Parkes and MWA data combined is α > −3.0. Properties of the FRB are summarized in Table 1.

Follow-up observations

After the discovery of the FRB we triggered observations at numerous telescopes and performed a calibration observation at Parkes. We continued to observe with the Parkes telescope, obtaining 4.5 h of observation over the course of the next 7.5 h, in order to search for any repeat bursts. The MWA was shadowing during the discovery observation and continued to track the FRB position for another ~7.5 h. The ATCA was on source 2 h after the burst and also observed until T + 7.5 h (where T is the time of the FRB) when the source set at both Parkes and ATCA. Swift was on source 8 h after the burst, and 10 h after the burst the Lovell telescope continued the monitoring for 2.5 h. On April 19 and 20 we obtained optical observations with Subaru, and on April 20 and 21 continued to search for repeated radio bursts with the Effelsberg, Sardinia and Parkes radio telescopes. The longer term follow-up campaign consisted of radio imaging (four further ATCA epochs, three GMRT epochs), high time resolution radio (with the Lovell telescope), X-ray (one further Swift epoch), optical photometry (with the Palomar telescope) and optical spectroscopy (with the Keck and Subaru telescopes). We did not detect any subsequent bursts in our high time resolution radio follow-up (limiting flux densities in Extended Data Table 1); however, regular emission at a much weaker level cannot be ruled out. The follow-up observations are summarized in Extended Data Table 1. We additionally note that no γ-ray burst was detected in temporal coincidence, or in the months before, by telescopes on either of the Fermi or Swift satellites. Furthermore, at a comoving distance of 1.8 gigaparsecs or a luminosity distance of 2.8 gigaparsecs, this galaxy is beyond the LIGO35 horizon for gravitational wave signatures from short γ-ray bursts.

Imaging transients

The radio transient sky is not very well studied at frequencies of 5.5 GHz and 7.5 GHz to the flux density levels relevant to this study. Additionally there are no archival data of the FRB field with which to compare our follow-up observations. To estimate the likelihood of the 6-day fading transient being detected by chance in our ATCA follow-up of the Parkes FRB field we first considered a previous ATCA study16. This is the only such work performed on the same timescales and at the same observing frequency using the ATCA. In that work, which also covered a wider area of sky than our FRB follow-ups and to a deeper level, no transient sources were discovered. A 95% (99%) confidence upper limit event rate of <7.5 deg−2 (<11.1 deg−2) with a flux density of >69 μJy/beam was obtained. Scaling this to obtain the expectation of a transient with flux density in excess of 200 μJy yields an upper limit event rate of <1.5 deg−2 (<2.2 deg−2). Considering the 0.04-deg2 field-of-view of a Parkes beam, which corresponds to the uncertainty in the FRB’s position, the upper limit on the expected number of events in our follow-up observations is thus <0.06 (<0.09). We can rephrase this by interpreting the upper limit number of expected events as the upper limit on λ, the Poisson rate parameter; then the probability of a chance temporal coincidence is P(1; λ) = λexp(−λ). This yields an upper-limit probability of <6% (<8%).

One can also obtain estimates of the false-positive rate from considering studies36,37,38,39,40 at other telescopes. As other studies are not ideally matched in terms of observing frequency and sensitivity, one must scale the findings appropriately. For example, for studies performed at different observing frequencies we must scale the flux densities by a spectral index; we adopt the spectral index of our 6-day transient as measured in the first epoch of our follow-up. Additionally, sensitivity levels must be scaled to the 200-μJy level; for this operation we adopt the standard N ∝ S−3/2 scaling. With this approach we consider a recent deep Very Large Array study18 which operated at 2–4 GHz. Applying the appropriate scaling, this study yields an expected number of events in our follow-up observations of <0.001 (<0.002) at 95% (99%) confidence. The equivalent upper limit chance temporal coincidence probability is <0.1% (<0.2%). This result is more constraining than the ATCA-derived numbers by a factor of at least 60. From this assessment we deem it statistically unlikely that we would have detected, by chance, this fading negative spectral index radio source at this location and time, resulting in our interpretation that this source is likely to be associated with the FRB.

Ideally, we might expand upon this calculation by estimating probabilities of chance coincidence in each independent wave-band (radio, optical and X-ray) in our follow-up campaign, and then compute a joint probability of a transient occurring in any of the bands. It is unclear what the appropriate statistics are for the X-ray and optical bands, but if we take the observed γ-ray burst and supernova rates as indicative, we find that the upper limit expectation in these wave bands is much smaller than in the radio bands. Deeper all-sky radio transient surveys are therefore the key to tightening constraints on transient associations like that reported here.

Optical analysis

The i′ optical profile of the Galaxy was fitted with a Sersic function of the form I(r) ∝ exp(−kR1/n). The best-fit parameters (see Extended Data Fig. 2) are a Sersic index of n = 3.6 ± 0.5, consistent with the n = 4 value seen in elliptical galaxies. The half-light radius is R e = 6.9 ± 1.2 pixels, or R e = 1.4 ± 0.2 arcsec. At z = 0.492 the angular diameter distance is 1.62 gigaparsecs so that this implies R e = 10.9 ± 1.8 kpc as the physical half-light radius of the galaxy. The profile fitting also yields an estimate of the major to minor axes ratio for the galaxy of b/a = 0.68 ± 0.03. We note that there are additional systematic uncertainties involved in the fit of the Sersic index, depending on the exact method of sky subtraction employed; our analysis suggests that the systematic errors are probably of equal magnitude to the statistical errors quoted above.

We obtained the following photometry of the FRB host galaxy: with Subaru Suprime-Cam41 we determined AB magnitudes of 23.45(16) and 22.07(31), for the r′ and i′ bands respectively. Between the two Subaru epochs no variability is seen—a subtraction of the epochs yields an upper limit on any variation of 25.2 and 24.7 magnitudes (5σ). The galaxy is also detected in two WISE filters with Vega magnitudes of 15.204(0.044) and 15.050(082), for the W 1 and W 2 bands respectively. With the Palomar 200′′ (P200) telescope we obtained further information, obtaining Vega magnitudes of 18.92(10), 17.55(25) and 16.51(05) for the J, H and K s bands respectively. We corrected the observed photometry for the Milky Way extinction using A V = 3.7 mag and standard extinction coefficients42, and converted those magnitudes into flux densities using the established zero-points43,44. We fitted for the photometric redshift using the 2015 November version of EAZY45, finding 68% confidence limits for 0.48 < z < 0.56. This was robust to different choices of galaxy template, with good overall fits (χ2 of 5–8). We then fitted the spectral energy distribution of the host galaxy using MAGPHYS46. We were able to achieve an acceptable fit (see Extended Data Fig. 1) to all of the photometry with a model for a passive (≤0.2M ⊙ yr−1), massive (stellar mass ~1011M ⊙ ) galaxy with a modest amount of dust (in-host extinction A V in the range 0–4 mag). The exact fit was rather degenerate because of our limited wavelength coverage, with only the stellar mass well determined. Future observations at shorter wavelengths should be able to determine more robust properties.

The spectrum that confirmed the redshift was obtained on 2015 November 2 in a 3-h observation using FOCAS on the Subaru telescope. An earlier attempt to obtain a spectroscopic redshift on 2015 October 21 using DEIMOS on the Keck telescope in poorer sky conditions had proved difficult to calibrate and resulted in an imprecise redshift estimate, no better than the photometric estimate. In that case difficulties in calibration are compounded by the spectrum’s lack of any relevant emission lines. The well calibrated Subaru spectrum is found to be consistent with a reddened z = 0.492(8) early-type galaxy with E(B − V) = 1.2 ± 0.1 (Fig. 3), noting that r′ and i′ are approximations to restframe B and V filters. This implies absolute magnitudes of M B ≈ −21.6 and M V ≈ −22.1. As the galaxy is elliptical we can apply the Faber–Jackson relation47 to estimate the velocity dispersion of ~230 km s−1. From the virial theorem and the observed half-light radius we can thus estimate the stellar (and total) mass48 to be ~1011M ⊙ (and ~2 × 1012M ⊙ ). An upper limit to the Hα luminosity of 2.6 × 1040 erg s−1 (3σ) can be derived from the optical spectrum, and from this we can, in the standard way49, derive a star-formation rate of ≤0.2M ⊙ yr−1.

The very faint companion galaxy (r′ = 24.22(16) mag, i′ = 23.22(31) mag) visible to the northeast is not inconsistent with a galaxy at the same redshift. If confirmed the two galaxies may be in the process of merging. The absolute K-band magnitude of the galaxy is −25.7 mag (Vega). The radio continuum level can be estimated from this17 and is consistent with the quiescent level of the galaxy after the ~6-day fading event. This shows that the background level seen is not surprising for an early-type galaxy, and implies that the FRB afterglow had already faded below this level by the third ATCA epoch.

FRB 110523

After the initial submission of this manuscript a study was published8 announcing the discovery of FRB 110523, which we have compared and contrasted with FRB 150418 in the main text. There are now strong indications that there are two or more FRB progenitors, and we speculate that the observed pulse width may act as a useful discriminator between these. To this end we consider the time sampling and frequency resolution of the study that discovered FRB 110523, as well as its DM, in an effort to see whether the pulse was resolved in the Green Bank observations8. We would expect an unresolved FRB to have an observed width of no more than 1.08 ms, 1.14 ms and 1.26 ms in the highest, central and lowest frequency channels, respectively, in the Green Bank study8. This is inconsistent with the reported observed width (after the effects of scattering had been removed) at the 3σ to 4σ level, indicating that FRB 110523 appears to be resolved and therefore to have an intrinsic timescale of ~1 ms.