Resolving the Decades-long Transient FIRST J141918.9+394036: An Orphan Long Gamma-Ray Burst or a Young Magnetar Nebula?

We observed J1642+3948 as fringe finder and J1419+3821 (located at only 13 from FIRST J1419+3940) as phase calibrator. We scheduled a phase-referencing cycle of 4.5 minutes on the target and 1.5 minutes on the phase calibrator, achieving a total time of ∼4.5 hr on FIRST J1419+3940.

The interferometric data were reduced using AIPS⁸ (Greisen 2003) and Difmap (Shepherd et al. 1994) following standard procedures. A priori amplitude calibration was performed using the known gain curves and system temperature measurements recorded individually on each station during the observation. We used nominal system equivalent flux density (SEFD) values for the following stations: Jodrell Bank Mark2, Tianma, and the e-MERLIN stations. We manually flagged data affected by radio frequency interference (RFI) and then we fringe-fitted and bandpass-calibrated the data using the fringe finder and the phase calibrator. We imaged and self-calibrated the phase calibrator in Difmap to improve the final calibration of the data. The obtained solutions were then transferred to the target, which was subsequently imaged.

We note that Tianma did not produce reliable system temperature values during the experiment. Most of these measurements failed, and the existing ones exhibited a much larger scatter than usual. Therefore we used the nominal SEFD for amplitude calibration. This typically produces a satisfactory a priori calibration that can be further improved during imaging and self-calibration. Tianma, however, provides the longest east–west baselines in our array with no equivalent baselines to compare with, and it also does not have short spacings to establish a reliable station calibration. In this case imaging and parameterization of source properties by model-fitting is complicated due to the fact that some source parameters may correlate with the Tianma station gain (Natarajan et al. 2017).

Figure 1 displays the visibility amplitudes and phases as a function of projected baseline length in units of observing wavelength. The top panel shows the initial calibration, with the Tianma data highlighted in red. The low amplitudes may be consistent with a source that is very compact in general, but well resolved in the east–west direction. The bottom panel shows the data after we apply an amplitude correction factor for Tianma, based on a source model obtained by only using the stations with robust calibration. The required scaling factor was about three, implying that the station could have been much less sensitive than expected.

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Due to the uncertainty with the Tianma calibration, we decided to take the following procedure to analyze the data. Instead of fitting an elliptical-Gaussian model brightness distribution to the uv-data in model fitting, we assumed a circular-Gaussian brightness distribution. This is expected to be less sensitive to uncertainties in station gain calibration (Natarajan et al. 2017). In addition, we looked at the results derived from the following cases: Tianma removed from the data set, Tianma present with nominal gain calibration, and Tianma present but with its gain scaled to be in agreement with the most compact possible solution (as explained above). As we will see in Section 3, the fitted source sizes differ somewhat, but in all cases they support the same main conclusion: that our target is resolved on milliarcsecond scales.

The high-time-resolution Effelsberg data were analyzed to search for individual millisecond bursts or a periodic signal. First, using PRESTO's rfifind, we identified specific time samples and frequency channels contaminated by RFI. The regions highlighted by rfifind and the frequency range 1610–1631 MHz, associated with RFI from the Iridium satellites, were masked prior to conducting the analysis. We then dedispersed the 4-bit data using the PRESTO tool prepsubband for 2500 trial dispersion measures (DMs) in the range 0–1210.8 pc cm⁻³. The resulting dedispersed time series were then searched for single pulses above a 6σ threshold using PRESTO's single_pulse_search.py, which applies a matched-filter technique using boxcar functions of various widths, and in our search was sensitive to burst durations in the range 40.96 μs and 0.02 s. Dynamic spectra of the identified single-pulse candidates were generated and inspected by eye to distinguish between astrophysical signals and RFI.

In addition, a Fourier-domain search was performed on each individual dedispersed time series using PRESTO's accelsearch, in order to search for periodic signals. Potential periodic signals were sifted using ACCEL_sift.py, and the remaining candidates were inspected by eye after folding using prepfold.

The RFI mitigation process was unable to remove all instances of RFI in the data. We calculate that of the ∼4.3 hr Effelsberg on-source time, approximately 92.4% was examined for bursts and periodic signals. Note the discrepancy between the Effelsberg on-source time (∼4.3 hr) and the EVN on-source time (∼4.5 hr), which is due to Effelsberg's longer slew time compared with other antennas.

The aforementioned analysis strategy was verified using similar data targeting pulsar PSR B2020+28. We performed a blind search and detected both individual pulses and the known periodicity of this pulsar.

FIRST J1419+3940 was detected on 2018 September 18 as a radio source that is compact on milliarcsecond scales (see Figure 2), with a flux density of 620 ± 20 μJy at a position of $\alpha ({\rm{J}}2000)\,=\,{14}^{{\rm{h}}}{19}^{{\rm{m}}}18\buildrel{\rm{s}}\over{.} 850722\,\pm \,0.23\,\mathrm{mas}$ $\delta ({\rm{J}}2000)\,=39^\circ {40}^{{\prime} }36\buildrel{\prime\prime}\over{.} 04520\pm 0.23\,\mathrm{mas}$, where the quoted uncertainties represent the 1σ confidence interval and take into account the statistical uncertainties in the image (0.2 mas in both α and δ), the uncertainty in the phase calibrator position (0.1 mas; Beasley et al. 2002; Gordon et al. 2016), and the estimated uncertainties associated with the phase-referencing technique (0.06 and 0.04 mas for α and δ, respectively; Pradel et al. 2006). The obtained position is consistent with the one reported from the FIRST survey (Law et al. 2018), as well as the preliminary results published in Marcote et al. (2018). The measured flux density on 2018 September 18 follows the declining trend of the light curve reported from observations with the Karl G. Jansky VLA (see Figure 3). Given the luminosity distance of 87 Mpc, the obtained flux density corresponds to an isotropic luminosity νL_ν = (9.4 ± 0.3) × 10³⁶ erg s⁻¹. Together with the last published VLA observation at 3.0 GHz, and considering the same value for our epoch (i.e., no declining trend is assumed), we can place a conservative 3σ upper limit on the spectral index between 1.6 and 3.0 GHz of α ≲ −0.65 (where S_ν ∝ ν^α).

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FIRST J1419+3940 is significantly resolved in the obtained images given the size of the synthesized beam (5.5 × 4.1 mas²), as the measured size is larger than the minimum resolvable size by the array (see Martí-Vidal et al. 2012; Natarajan et al. 2017, for a detailed explanation). By fitting a circular Gaussian to the uv-data we measure a source size of 4.3 ± 0.8 mas, where the uncertainty has been estimated through a χ² test. However, we note that the gain calibration of Tianma constitutes a potential source of systematic errors in the size measurement. To provide a more reliable measurement, we produced images without this station. Despite having poorer resolution (synthesized beam of 24 × 5.3 mas²), we obtained a size that is significant and consistent within uncertainties with the value quoted above (3.9 ± 0.9 mas). Finally, we imaged the source with the gain correction applied to Tianma (as mentioned in the previous section), which provides the most stringent lower limit on the source size (i.e., assuming a point-like source during calibration). In this case we measured a source size of 3.4 ± 0.7 mas. The contribution of the longest baselines is therefore not critical as we obtain consistent results from all cases. We summarize the results of these different analyses in Table 1.

For comparison, the phase calibrator, J1419+3821, exhibits a main compact component with a measured size of 1.1–2.9 mas in all cases. The fact that the measured sizes are significantly different—while they are seen along almost the same Galactic line of sight—means that they are most likely intrinsic sizes, rather than due to scatter broadening. At the high Galactic latitudes of ∼67° scatter broadening at GHz frequencies is almost negligible, and one would not expect strong variations of scattering size on small angular scales either (see, e.g., Pushkarev & Kovalev 2015).

We thus conclude that FIRST J1419+3940 is significantly resolved, with an angular size of ${3.9}_{-0.5}^{+0.4}{}_{-0.2}^{+0.3}\,\mathrm{mas}$, where the first uncertainties take into account the dispersion of the values from the different analyses, and the second ones consider the estimated statistical uncertainties on the value. Given that the angular diameter distance to the source is 83 Mpc (Law et al. 2018), we derive a projected physical size of 1.6 ± 0.3 pc. This size also implies a brightness temperature of T_b ∼ 1.1 × 10⁷ K, which clearly points to a nonthermal origin for the emission.

Law et al. (2018) estimated that the putative GRB producing the observed afterglow likely took place around ∼25–30 yr ago. Considering an estimated central date for the explosion of ∼1993 and taking into account the given uncertainties, the afterglow must have a mean expansion velocity of v = (3.0 ± 0.6) × 10⁴ km s⁻¹, or (0.10 ± 0.02)c, which is consistent with a mildly relativistic expansion. We note that the calculated expansion velocity is an average over the whole lifetime, during which a significant deceleration has likely occurred.

We detected no astrophysical single pulses or periodic signals in the high-time-resolution Effelsberg data. We can estimate the expected DM toward FIRST J1419+3940 using Galactic electron density models (NE2001; Cordes & Lazio 2002, YMW16; Yao et al. 2017). For an extragalactic source, the observed DM can be divided into four components along the line of sight:

$$\begin{eqnarray}&&{\mathrm{DM}}_{\mathrm{obs}}={\mathrm{DM}}_{\mathrm{MW}}+{\mathrm{DM}}_{{\mathrm{MW}}_{\mathrm{halo}}}+{\mathrm{DM}}_{\mathrm{IGM}}+{\mathrm{DM}}_{\mathrm{host}}.\end{eqnarray} \tag{ 1 }$$

The Milky Way contribution to the DM along the line of sight is divided into the disk and spiral arm component, DM_MW, and the Galactic halo component, ${\mathrm{DM}}_{{\mathrm{MW}}_{\mathrm{halo}}}$. The former, DM_MW, is 44 and 39 pc cm⁻³ calculated using the NE2001 and YMW16 models, respectively. The uncertainties in these contributions are not well quantified, but are likely on the order of 20%. Using this, we can derive an approximate range of: 30 ≲ DM_MW ≲ 50 pc cm⁻³. We apply a Galactic halo contribution of ∼60–100 pc cm⁻³ to the DM (Prochaska & Zheng 2019). Given that the redshift of FIRST J1419+3940 is 0.01957 (Law et al. 2018), the mean intergalactic medium contribution to the DM is DM_IGM ≃ 20 pc cm⁻³ (Ioka 2003; Inoue 2004). We assume that the DM contribution of the host galaxy of FIRST J1419+3940, DM_host, is comparable to that of the host galaxy of FRB 121102: 55 ≲ DM_host ≲ 225 pc cm⁻³ (Tendulkar et al. 2017). Combining all individual components using Equation (1) results in the approximate range 160 ≲ DM_obs ≲ 400 pc cm⁻³.

From the single-pulse candidates reported using single_pulse_search.py, an astrophysical burst would be identifiable provided the signal-to-noise ratio (S/N) exceeds ∼10. We can estimate the fluence limit of our search using

$$\begin{eqnarray}&&F={({\rm{S}}/{\rm{N}})}_{\min }\displaystyle \frac{{T}_{\mathrm{sys}}}{G}\sqrt{\displaystyle \frac{{W}_{b}}{{n}_{\mathrm{pol}}\ {\rm{\Delta }}\nu }}\end{eqnarray} \tag{ 2 }$$

(following Cordes & McLaughlin 2003), where (S/N)_min is our detection threshold of 10, T_sys is the system temperature, G is the telescope gain, n_pol is the number of recorded polarizations, Δν is the total bandwidth, and W_b is the observed width of the burst. The observed width, W_b, accounts for broadening of the intrinsic width due to the finite time sampling of the data, intra-channel smearing, smearing due to DM-trial spacing, and scatter broadening. FRB 121102 has been shown to exhibit individual bursts with widths ≲30 μs (Michilli et al. 2018) and there have been observations of FRBs with widths as large as ∼30 ms (Petroff et al. 2016).⁹ Taking a DM of 300 pc cm⁻³ and intrinsic widths 30 μs–30 ms, we find our fluence limit ranges from 0.1 Jy ms to 8 Jy ms.

In order to compare our measurements with the scenarios proposed by Law et al. (2018), we need to compute the expected apparent size of the source. At the time of our observation, t_obs ∼ 30 yr ∼ 10⁴ days after the initial explosion, the external shock produced by the GRB jet upon deceleration into the interstellar medium (ISM) is expected to be non-relativistic, and to have become essentially spherical. Detailed, long-term numerical relativistic hydrodynamics simulations (Zhang & MacFadyen 2009) indeed show that the blast wave is well-described by the spherical, non-relativistic Sedov–Von Neumann–Taylor solution after a time $5{t}_{\mathrm{NR}}\approx 2\times {10}^{3}{E}_{\mathrm{iso},53}^{1/3}\,{n}_{1}^{-1/3}\,\mathrm{days}$, where t_NR is the light-crossing time of the Sedov length associated to the jet. The initial relativistic expansion phase, however, can still have effects on the relation between observed time and projected size. For that reason, we compute the jet deceleration dynamics and spreading employing the "trumpet" model from Granot & Piran (2012), which has been shown to be in good quantitative agreement with results from numerical relativistic hydrodynamics simulations. The observed size is estimated as the maximum projected size of the equal-arrival-time surface, relativistic beaming of radiation being negligible in our late-time observations. Using the same jet parameters as Law et al. (2018), namely an isotropic equivalent energy E_iso = 2 × 10⁵³ erg, an ISM number density n = 10 cm⁻³ and a viewing angle θ_v = 0.6 rad, and further assuming a jet half-opening angle θ_j = 0.1 rad (which implies a total jet energy E_jet ∼ 10⁵¹ erg), we obtain the size evolution shown by the red solid line in Figure 4, which is fully compatible with the measured one, assuming that the GRB took place in ∼1993. This disfavors the alternative scenario of a magnetar birth nebula, which would exhibit a significantly smaller size (≲0.1 pc), due to the much lower expansion velocity (Murase et al. 2016).

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While the measured size agrees well with the GRB scenario proposed by Law et al. (2018), our measured flux density S_{1.6 GHz} = 620 ± 20 μJy is low when compared to the extrapolation of their model. More precisely, adopting the same assumptions as Law et al. (2018), namely quasi-isotropic, adiabatic expansion, Deep Newtonian regime and an electron power-law index p = 2.2, the flux density should follow S_ν ∝ ν^−0.6t^−0.96. Using the latest VLA detection as reference, which yielded a flux density of 1.1 ± 0.1 mJy at 1.52 GHz on 2015 May 11, and assuming the GRB to have happened in 1993, we should have measured S_{1.6 GHz} ≈ 930 ± 85 μJy at the time of our observation, which is ∼3.5σ (summing the uncertainties in quadrature) above our measured flux density. As noted by Law et al. (2018), the latest VLASS non-detection S_ν < 400 μJy at 3 GHz on 2017 October 11 already pointed to a faster decline after 2015. Several physical processes could lead to a steepening in the decay of the light curve, as follows.

• 1.  
  The conditions in the shocked fluid could be changing as a consequence of the transition to the non-relativistic, Deep Newtonian phase, e.g., the fraction _e of shock energy given to electrons could decrease, or the electron momentum distribution power-law index p could decrease from p = 2.2 toward ∼2 (Sironi & Giannios 2013). Both these effects would result in a steepening of the flux decay.
• 2.  
  Contrary to what is stated by Law et al. (2018), the steepening could also be due to the shock crossing a dip in the ISM density. According to the argument by Law et al. (2018), based on Nakar & Granot (2007) and Mimica & Giannios (2011), an ISM density drop would result only in a smooth, slow change in the light curve. This is essentially a consequence of the assumption that the shock is relativistic (Γ ≫ 1), in which case the angular timescale R/2Γ²c would be of the same order as the observer time t_obs, and therefore any change in the shock conditions would be smeared out over that timescale. In our case, conversely, the shock expansion speed is non-relativistic, and the angular timescale is ∼R/2c ≪ t_obs (using our size measurement, we have R/c ∼ 2.5 yr, which is significantly smaller than the explosion age t_obs ≳ 25 yr), so that a drop in the ISM density at a radius slightly smaller than the observed size ∼1.6 pc may justify the flux deficit. Such a drop could mark the outer radius of the star-forming region where the GRB exploded. Let us caution, though, that this requires some fine-tuning. In order for the shock to entirely cross the outer edge of the star-forming region in a short enough time, the latter should be approximately spherical and nearly concentric to the shock. By using the same shock dynamics model as in the previous section, we estimate the current shock expansion velocity to be v_s ∼ 0. 03c ≈ 9000 km s⁻¹. The shock thus traveled a distance ΔR ∼ 0.03 pc between the latest VLA detection at 1.5 GHz and our observation. The centers of the shock wave and the star-forming region, assumed spherical, should therefore be located less than ΔR away from each other. As the flux deficit we observe amounts to a factor ∼2/3 reduction with respect to the expected value, we can partially relax these requirements, allowing the outer edge of the star-forming region to have some structure—e.g., bumps, filaments, a non-spherical shape—as long as ∼1/3 (in terms of solid angle) of the shock wave still experiences a sharp density drop in the required time. This leads us to conclude that, while the arguments against an ambient medium density drop proposed by Law et al. (2018) do not hold in this case, this kind of explanation for the flux variation, while not impossible, remains rather unlikely.

Finally, we note that the flux deficit cannot be understood as due to scintillation-induced fluctuations, as the apparent size of the source is too large (Goodman 1997).

The association of FRB 121102 with a persistent radio counterpart (Chatterjee et al. 2017; Marcote et al. 2017) led to the discovery of FIRST J1419+3940, the characteristics of which match those of the persistent source coincident with FRB 121102 (Ofek 2017; Law et al. 2018): i.e., a compact radio source with a similar luminosity and co-located with a star-forming region of a dwarf galaxy. It is, therefore, natural to compare FIRST J1419+3940 with the radio counterpart of FRB 121102.

The declining light curve of FIRST J1419+3940 contrasts with the persistent emission from FRB 121102 (Chatterjee et al. 2017, A. Plavin et al. 2019, in preparation). Another discrepancy that arises is that the obtained source size of FIRST J1419+3940 is significantly larger than the one associated with FRB 121102 (<0.7 pc; Marcote et al. 2017), implying a much higher expansion velocity. These differences can, naturally, be explained by a younger age of FIRST J1419+3940 (∼30 yr) when compared with FRB 121102 (∼100 yr; Metzger et al. 2017; Piro & Gaensler 2018). We note that although we conclude our observations are consistent with GRB jet expansion, we do not rule out the presence of a nebula driven by a highly magnetized neutron star contributing to a fraction of the radio emission observed. The presence of such nebula could cause the light curve to plateau at late times.

It has been hypothesized that the birth of a millisecond magnetar can connect FRB 121102 with long GRBs or SLSNe (Metzger et al. 2017). If we assume that millisecond magnetars can produce FRBs similar to what is observed in FRB 121102, and that a magnetized neutron star resides within the radio source FIRST J1419+3940, we might expect FRBs from this source. The comparable ages of FIRST J1419+3940 and FRB 121102 leads to our assumption that the compact object residing within FIRST J1419+3940 is emitting bursts with a comparable energy distribution and duty cycle to FRB 121102.

Bursts from the repeating FRB 121102 have been observed with fluences of ∼0.02 Jy ms (Gajjar et al. 2018) to ≳7 Jy ms (Marcote et al. 2017) and widths ranging from ≲30 μs (Michilli et al. 2018) to ∼8.7 ms (Spitler et al. 2016). Taking this range of fluence values at the luminosity distance of FRB 121102 (972 Mpc) and scaling to the luminosity distance of FIRST J1419+3940 (87 Mpc), gives an estimated fluence range of 2.5–870 Jy ms. For bursts with widths exceeding ∼9 ms, the fluence limit of our search increases beyond 2.5 Jy ms (see Section 3.2). Under the assumption that FIRST J1419+3940 is producing bursts with widths comparable to that of FRB 121102 and with an alignment (with respect to the observer) that is consistent with FRB 121102, single bursts from this source would be identifiable in the data.

The lack of short-duration bursts in our observation could imply that the source is in a quiescent state, similar to the behavior observed in FRB 121102 (Scholz et al. 2016; Gajjar et al. 2018). Alternatively, the hypothesized central compact object could be producing bursts that do not cross our line of sight. To ensure that our search was not affected by self-absorption, future observations of FIRST J1419+3940 at higher radio frequencies are required.

The potential connection of FRB 121102 with long GRBs or SLSNe has sparked targeted searches for millisecond-duration bursts and compact persistent radio sources at the positions of such events. In one such a search, Eftekhari et al. (2019) discovered a persistent radio source coincident with the SLSN PTF10hgi. An orphan GRB afterglow is explored as the potential origin of the emission, but is considered unlikely due to the high inferred isotropic jet energy, exceeding that of most observed long GRBs. Because the discovery of both this radio source and FIRST J1419+3940 were motivated by observations of FRB 121102 and its environment, we compare the inferred isotropic jet energy for both sources. The inferred properties of the radio source associated with PTF10hgi, assuming GRB jet expansion, is estimated as E_iso ∼ (3–5) × 10⁵³ erg, n = 10⁻³–10² cm⁻³ (Eftekhari et al. 2019). Although this energy range is larger than the majority of observed long GRBs, it is comparable to that of FIRST J1419+3940 (E_iso = 2 × 10⁵³ erg, n = 10 cm⁻³; Law et al. 2018). The results shown in the work presented here support the scenario in which FIRST J1419+3940 is an orphan GRB afterglow. Whether this is the case for PTF10hgi as well is not clear at this point, but we argue that the inferred high isotropic jet energy in itself does not exclude an off-axis jet origin. The ultimate probe of this scenario is very high angular resolution VLBI observations. Accurately measuring the source size at the redshift of PTF10hgi (about five times more distant than FIRST J1419+3940)—and especially considering its low flux density of ∼50 μJy—is very challenging, and may only be possible with a very sensitive future SKA-VLBI array (Paragi et al. 2015) observing at high frequencies (≳5 GHz).