NO PRECISE LOCALIZATION FOR FRB 150418: CLAIMED RADIO TRANSIENT IS AGN VARIABILITY

The analysis of Keane et al. (2016) examines the probability of the chance discovery of an unassociated radio transient in their search field, but not the probability of the chance discovery of a variable radio source. The odds of the latter are non-negligible, as implied by the presence of a second compact variable radio source within the Parkes beam (Keane et al. 2016). The five detections of the ATCA light curve of WISE 0716–19 are insufficient to reject the possibility that it is a variable radio source, as demonstrated empirically by our new data showing that it in fact is one (Section 4).

Precise statements regarding the probability of  a chance detection of a candidate matching the characteristics reported by Keane et al. (2016) cannot be made without information regarding the total number of FRB localization regions searched by the SUPERB project and the process by which candidate transients were filtered, which is not currently available. However, in a catalog of 3652 compact sources brighter than ∼0.1 mJy at 3 GHz produced for the Caltech-NRAO Stripe 82 Survey pilot (CNSSp), Mooley et al. (2016) find that ${3.9}_{-0.9}^{+0.5}$% of them are variable at the >30% level. They only classified two sources as transients, implying that variables outnumber transients by a factor of $\approx 70$ and that the "headline" chance coincidence probability of <0.1% reported by Keane et al. (2016) may be underestimated by a comparable amount. More generally, studies in which the analysis performed depends on the data taken will inevitably yield overconfident significance metrics due to the "garden of forking paths" effect (Gelman & Loken 2014).

Furthermore, the probability of a radio variable masquerading as a radio transient in the particular data set reported by Keane et al. (2016) may be even higher. Ofek et al. (2011) used the VLA to search a total area of 2.66 deg² for radio transients and variables. They find that 30% (30 out of 98) of sources brighter than 1.5 mJy at 5 GHz are variable at the 4σ level. Given the three radio sources with ${S}_{\nu }\gtrsim 0.1$ mJy detected in our VLA imaging (Section 4), which has a position and total area close to that of the Parkes search area, the expected number of radio variables in the field is therefore of order unity. Using the deep 5 GHz source counts of Fomalont et al. (1991), ∼16 sources brighter than 0.1 mJy are expected to be found in each Parkes beam. The typical Parkes search area may therefore host multiple variable radio sources.

Ofek et al. (2011) note that the rate of variables found in their survey is higher than comparable surveys and attribute this to their choice of observing frequency, the short averaging times of their observations, and the low Galactic latitude ($b\sim 6^\circ$–8°) of their survey. All of these factors apply to the observations of Keane et al. (2016), with WISE 0716–19 being found at $b\sim -3\_\_AMP\_\_fdg;2$. The correlation between low Galactic latitude and increased incidence of variability is well established and is due at least in part to higher levels of refractive scintillation through the denser ISM (Section 2.3; Spangler et al. 1989; Rickett 1990), implying that the increase in the number of variable sources is not only due to foreground objects.

It may be argued that the agreement between the redshift of WISE 0716–19 and the DM of FRB 150418, given standard cosmological assumptions, supports the conclusion that the two are associated. Here we demonstrate that consistency between these is not unlikely, even if the FRB and galaxy are unrelated.

We performed a Markov Chain Monte Carlo (MCMC) simulation to characterize the host galaxy redshifts that would have been found to be consistent with the DM of FRB 150418, given the assumptions made by Keane et al. (2016).¹ The parameters are summarized in Table 1; the model is defined by Equation (1) and the surrounding discussion in Keane et al. (2016). We add a small (1%) uncertainty on the fraction of baryons contained in the intergalactic medium (IGM). Using a likelihood defined by the measured FRB DM and the priors listed in Table 1, we sampled from the posterior using the emcee package (Foreman-Mackey et al. 2013), which implements the Goodman & Weare (2010) affine-invariant sampling algorithm. We used 256 walkers divided into 8 independent groups, each taking 8192 steps, and thinning by a factor of 16 and discarding the first half of the samples from each walker. The mean proposal acceptance fraction was 41%, and there were in total ∼8500 independent samples of the redshift z, accounting for the estimated chain autocorrelation length of ∼6 samples after thinning. The $\hat{R}$ convergence criterion for the redshift parameter reached 1.08, implying good convergence (Gelman et al. 2013).

Table 1.  Parameters of the Model Used in DM MCMC Analysis

Parameter	Symbol	Units	Prior
Host galaxy redshift	z	...	$U({10}^{-4},20)$ a
Host galaxy DM	${{\rm{DM}}}_{{\rm{host}}}$	cm−3 pc	$N(37,37\times 20\%)$ b
Milky way DM	${{\rm{DM}}}_{{\rm{MW}}}$	cm−3 pc	$N(188.5,188.5\times 20\%)$
Milky way halo DM	${{\rm{DM}}}_{{\rm{halo}}}$	cm−3 pc	$N(30,5)$ c
Dark energy content of universe	${{\rm{\Omega }}}_{{\rm{\Lambda }}}$	...	$N(0.721,0.025)$
Matter content of universe	${{\rm{\Omega }}}_{m}$	...	$N(0.233,0.023)$
Baryonic content of universe	${{\rm{\Omega }}}_{b}$	...	$N(0.0463,0.0024)$
Present-day Hubble parameter	H0	km s−1 Mpc−1	$N(70.0,2.2)$
Fraction of baryons in IGM	${f}_{{\rm{IGM}}}$	...	$N(0.90,0.01)$

Notes.

^aDenotes a uniform distribution between the specified bounds. ^bDenotes a normal distribution with the specified mean and standard deviation. ^cUncertainty estimated from Figure 2 of Dolag et al. (2015).

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Figure 2 shows the redshift posterior samples marginalized over all other parameters. Given the model and data, host galaxy redshifts in the range 0.42–0.65 can be judged to be consistent with the measured DM of FRB 150418 at the 1σ level. The true range of host redshifts consistent with the data is broader than this—and our analysis is thus conservative—even if the assumption of an extragalactic origin is maintained, because other DM models are valid. For example, if, as we argue, the elliptical galaxy is not associated with FRB 150418 and the true host is allowed to be a spiral rather than elliptical galaxy, its DM contribution could be significantly larger than the value assumed in the present model, broadening the distribution of allowed redshifts to include lower values.

Radio AGNs are generally found at redshifts comparable to those allowed by the FRB DM measurement (e.g., Condon et al. 1998). In its unbiased search for radio variables and transients, the CNSSp discovered 142 such objects in observations at 2–4 GHz. Of the 35 variables with variability timescales less than 1 week, there are 13 measured redshifts, ranging from 0.15 to 0.84, with a mean of 0.45. We further note that 90% (32/35) of these variables are classified as AGNs. Of the full sample of CNSSp variables with redshift measurements, 22% (15/69) and 41% (28/69) are within the 1σ and 2σ limits of the posterior, respectively. A radio source selected on the basis of its variability is therefore not unlikely to have a redshift compatible with the DM of FRB 150418.

The only confirmed slowly evolving extragalactic radio transients are synchrotron-emitting blastwaves, which exhibit a clear relationship between evolutionary timescale and luminosity (Metzger et al. 2015). From the observed flux of ${F}_{\nu }(5.5\ \mathrm{GHz})\sim 0.27$ mJy at a midpoint of ${\rm{\Delta }}t=0.2$, and assuming expansion at $v\approx c$, we infer a brightness temperature of ${T}_{B}\approx 5\times {10}^{15}$ K, which clearly requires relativistic expansion, with an inferred Lorentz factor of ${\rm{\Gamma }}\approx 6$ to avoid the inverse Compton catastrophe limit of ${T}_{B}\approx {10}^{12}$ K. Thus, if the observed emission is due to a synchrotron-emitting blastwave, it will obey the basic relativistic afterglow evolution of GRBs (Sari et al. 1998, 1999; Granot & Sari 2002). The synchrotron emission model is characterized by three break frequencies—self-absorption (${\nu }_{a}$), peak (${\nu }_{m}$) and cooling (${\nu }_{c}$)—and an overall flux density normalization (${F}_{\nu ,m}$). These parameters in turn determine the physical properties of the blastwave: isotropic kinetic energy (${E}_{K,{\rm{iso}}}$), density (n), and fractions of post-shock energy in the relativistic electrons (${\epsilon }_{e}$) and magnetic fields (${\epsilon }_{B}$). The power-law distribution of the relativistic electrons is further determined by an index p, such that $N(\gamma )\propto {\gamma }^{-p}$ at $\gamma \geqslant {\gamma }_{m}$. This model has been used to study GRB afterglows for the past 15 years.

Compact radio sources—including both GRB afterglows and AGN jets—are furthermore subject to interstellar scintillation (ISS) by the interstellar medium of the Milky Way (Spangler et al. 1989; Rickett 1990). For the low Galactic latitude sightline to FRB 150418 the scattering measure is large, $\mathrm{log}(\mathrm{SM})\approx -2.4$ (Cordes & Lazio 2002), and hence frequencies below ${\nu }_{0}\approx 30$ GHz are subject to strong scintillation. We do not consider diffractive ISS to be important because the coherence bandwidth is $\delta \nu /\nu \approx {(\nu /{\nu }_{0})}^{17/5}\approx 20\;{\rm{MHz}}$, much narrower than the GHz bandwidth of the ATCA and VLA observations. However, strong refractive interstellar scintillation (RISS) is expected, with a modulation index (rms fractional variation) of ∼0.4 and 0.5 at 5.5 and 7.5 GHz, respectively. This level of variability will be present for any source that is compact relative to the characteristic RISS angular size ${\theta }_{s}$. Taking a scattering screen distance of 1 kpc, we find ${\theta }_{s}\sim 50\;\mu \mathrm{as}$ at 5.5 GHz (Walker 1998), corresponding to a linear scale of ∼0.2 pc at the redshift of WISE 0716–19. In our modeling of the radio emission below we account for the effect of RISS by adding the expected modulation of the model light curves in quadrature to the measurement uncertainties.

We model the radio light curve with the afterglow model of Granot & Sari (2002) using standard parameters for GRB afterglows: ${\epsilon }_{e}=0.1$, ${\epsilon }_{B}=0.01$, and p = 2.5. We note that the ATCA data indicate that ${\nu }_{a}\lt 5.5$ GHz, and moreover the radio data do not constrain ${\nu }_{c}$, which is typically located in the optical to X-ray regime. As a result, the model light curves are degenerate with respect to our choice of ${\epsilon }_{e}$ and ${\epsilon }_{B}$, with the inferred values of ${E}_{K,{\rm{iso}}}$ and n changing with the choice of values, but the light curves (and hence the quality of fit) remaining unchanged. We tested models with values of ${\epsilon }_{e}$ and ${\epsilon }_{B}$ varying between 0.1 and 10⁻⁶, and find identical ${\chi }_{r}^{2}$ values. We use models with both a spherical geometry and a jet, leaving the blastwave kinetic energy and the density as free parameters, as well as the jet opening angle in the latter model. We also include a constant term with a flux density of 0.09 mJy at 5.5 GHz and 0.065 mJy at 7.5 GHz to represent the steady component detected in the ATCA data at ${\rm{\Delta }}t\gtrsim 8;$ our 7.5 GHz steady component agrees with the ATCA upper limits and assumes a ${\nu }^{-1}$ spectrum for this component. The best-fit models are shown in Figure 3. Both models provide a poor fit to the data, with ${\chi }_{r}^{2}\approx 8.0$ (spherical; 8 degrees of freedom) and $\approx 8.8$ (jet; 7 degrees of freedom) assuming no RISS. The inclusion of RISS leads to ${\chi }_{r}^{2}\approx 1.5$ and $\approx 1.6$, respectively. In this latter case, we assume that the steady component scintillates as well; if it does not (i.e., is not compact), the ${\chi }_{r}^{2}$ values increase since the scintillation-induced uncertainty in the model is lower.

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We next compare these models to a simple steady source that is modulated purely by RISS. In this case we find a mean flux density of 0.135 mJy at 5.5 GHz and 0.100 mJy at 7.5 GHz (i.e., assuming a ${\nu }^{-1}$ spectrum). This simpler model results in ${\chi }_{r}^{2}\approx 6.4$ (8 degrees of freedom) when ignoring RISS and ${\chi }_{r}^{2}\approx 1.1$ when including RISS.

The synchrotron models are challenged by the data at ${\rm{\Delta }}t\lt 8$, which show a rapid evolution in spectral slope that is not expected from a synchrotron blastwave. More specifically, while the spectral indices of the first and third epochs of ATCA observations are not atypical, the second epoch implies an exceptionally steep $\alpha \lesssim -3.4$ between 5.5 and 7.5 GHz. This variation may be compatible with RISS, which has a correlation bandwidth ${\rm{\Delta }}\nu /\nu \sim 1$. Recent observations suggest that flares in faint AGNs can result in rapid spectral evolution: α evolved from −1.7 to $+0.4$ over 15 days in a source (VTC225411−010651) found in the CNSSp. We speculate that this mechanism is at work in this case as well.

Thus, while Keane et al. (2016; and similarly Zhang 2016) claim that the post-FRB radio data are consistent with a short GRB afterglow, the data actually favor other interpretations. The best formal fit to the data is of a model of a steady source modulated by the inevitable strong refractive scintillation. The rapid spectral evolution observed at ${\rm{\Delta }}t\lt 8$ may suggest the presence of an AGN flare. This spectral evolution is inconsistent with a synchrotron blastwave, such as for a short GRB afterglow.