The Host Galaxy and Redshift of the Repeating Fast Radio Burst FRB 121102

I Introduction

Fast radio bursts (FRBs) are bright ($\sim$Jy) and short ($\sim$ms) bursts of radio emission that have dispersion measures (DMs) in excess of the line of sight DM contribution expected from the electron distribution of our Galaxy. To date 18 FRBs have been reported — most of them detected at the Parkes telescope (Lorimer et al. 2007; Thornton et al. 2013; Burke-Spolaor & Bannister 2014; Keane et al. 2012; Ravi et al. 2015; Petroff et al. 2015; Keane et al. 2016; Champion et al. 2016; Ravi et al. 2016) and one each at the Arecibo (Spitler et al. 2014) and Green Bank telescopes (Masui et al. 2015).

A plethora of source models have been proposed to explain the properties of FRBs (see e.g. Katz 2016, for a brief review). According to the models, the excess DM for FRBs may be intrinsic to the source, placing it within the Galaxy; it may arise mostly from the intergalactic medium, placing a source of FRBs at cosmological distances ($z\sim 0.2-1$) or it may arise from the host galaxy, placing a source of FRBs at extragalactic, but not necessarily cosmological, distances ($\sim 100$ Mpc).

Since the only evidence to claim an extragalactic origin for FRBs has been the anomalously high DM, some models also attempted to explain the excess DM as a part of the model, thus allowing FRBs to be Galactic. All FRBs observed to date have been detected with single dish radio telescopes, for which the localization is of order arcminutes, insufficient to obtain an unambiguous association with any object. To date, no independent information about their redshift, environment, and source could be obtained due to the lack of an accurate localization of FRBs. Keane et al. 2016 attempted to identify the host of FRB 150418 on the basis of a fading radio source in the field that was localized to a $z=0.492$ galaxy. However, later work identified the radio source as a variable active galactic nucleus (AGN) that may not be related to the source (Williams & Berger 2016; Bassa et al. 2016; Giroletti et al. 2016; Johnston et al. 2017).

Repeated radio bursts were observed from the location of the Arecibo-detected FRB 121102 (Spitler et al. 2016; Scholz et al. 2016), with the same DM as the first detection, indicating a common source. As discussed by Spitler et al. 2016, it is unclear whether the repetition makes FRB 121102 unique among known FRBs, or whether radio telescopes other than Arecibo lack the sensitivity to readily detect repeat bursts from other known FRBs.

Chatterjee et al. 2017 used the Karl G. Jansky Very Large Array (VLA) to directly localize the repeated bursts from FRB 121102 with 100-mas precision and reported an unresolved, persistent radio source and an extended optical counterpart at the location with a chance coincidence probability of $\approx 3\times 10^{-4}$ — the first unambiguous identification of multi-wavelength counterparts to FRBs. Independently, Marcote et al. 2017 used the European VLBI Network (EVN) to localize the bursts and the persistent source and showed that both are co-located within $\sim 12$ milliarcseconds.

Here we report the imaging and spectroscopic follow-up of the optical counterpart to FRB 121102 using the 8-m Gemini North telescope.

II Observations and Data Analysis

The location of FRB 121102 was observed with the Gemini Multi-Object Spectrograph (GMOS) instrument at the 8-m Gemini North telescope atop Mauna Kea, Hawai’i. Imaging observations were obtained with SDSS $r^{\prime}$, $i^{\prime}$ and $z^{\prime}$ filters on 2016 October 24, 25, and November 2, under photometric and clear conditions with $0\farcs 58$ to $0\farcs 66$ seeing. Exposure times of 250 s were used in the $r^{\prime}$ filter and of 300 s in the $i^{\prime}$ and $z^{\prime}$ filters with total exposures of 1250 s in $r^{\prime}$, 1000 s in $i^{\prime}$ and 1500 s in $z^{\prime}$. The detectors were read out with $2\times 2$ binning, providing a pixel scale of $0\farcs 146$ pix-1. The images were corrected for a bias offset, as measured from the overscan regions, flat fielded using sky flats and then registered and co-added.

The images were astrometrically calibrated against the Gaia DR1 Catalog (Gaia Collaboration et al. 2016). To limit the effects of distortion, the central $2\farcm 2\times 2\farcm 2$ subsection of the images were used. Each of the $r^{\prime}$, $i^{\prime}$, and $z^{\prime}$ images were matched with 35 – 50 unblended stars yielding an astrometric calibration with 7 – 9 mas root-mean-square (rms) position residuals in each coordinate after iteratively removing $\sim 4-5$ outliers. The error in the mean astrometric position with respect to the Gaia frame is thus $\sim 1-2\,$mas.

We used the Source Extractor (Bertin & Arnouts 1996) software to detect and extract sources in the coadded images. The $r^{\prime}$ and $i^{\prime}$ images were photometrically calibrated with respect to the IPHAS DR2 catalog (Barentsen et al. 2014) using Vega-AB magnitude conversions stated therein. We measure isophotal integrated magnitudes of $m_{r^{\prime}}=25.1\pm 0.1$ AB mag and $m_{i^{\prime}}=23.9\pm 0.1$ AB mag for the optical counterpart of FRB 121102. The error value includes the photometric errors and rms zero-point scatter. Ongoing observations will provide full photometric calibration in $g^{\prime}$, $r^{\prime}$, $i^{\prime}$, and $z^{\prime}$ bands and will be reported in a subsequent publication.

Spectroscopic observations were obtained with GMOS on 2016 November 9 and 10 with the 400 lines mm-1 grating (R400) in combination with a $1\arcsec$ slit, covering the wavelength range from 4650 to 8900 Å. A total of nine 1800 s exposures were taken with $2\times 2$ binning, providing a spatial scale of $0\farcs 292$ pix-1 and an instrumental resolution of 4.66 Å, sampled at $1.36$ Å pix-1. The conditions were clear, with $0\farcs 8$ to $1\farcs 0$ seeing on the first night, and $0\farcs 9$ to $1\farcs 1$ on the second. To aid the spectral extraction of the very faint counterpart, the slit was oriented at a position angle of $18\fdg 6$, containing the counterpart to FRB 121102 as well as an $m_{r^{\prime}}=24.3$ AB mag, $m_{i^{\prime}}=22.7$ AB mag foreground star, located $2\farcs 8$ to the South (shown later in Figure 3).

The low signal-to-noise of the spectral trace of the FRB counterpart on the individual bias-corrected long-slit spectra complicated spectral extraction through the optimal method by Horne 1986. Instead, we used a variant of the optimal extraction method of Hynes 2002 by modelling the spectral trace of the reference object by a Moffat function (Moffat 1969) to determine the position and width of the spatial profile as a function of wavelength. Because of the proximity of the reference object to the FRB counterpart (20 pix), we assume that the spatial profile as a function of wavelength is identical for both. We note that though the counterpart is slightly resolved in the imaging observations, the worse seeing during the spectroscopic observations (by a factor 1.2 to 1.9) means the seeing dominates the spatial profile. The residual images validate this assumption; no residual flux is seen once the extracted model is subtracted from the image. To optimally extract the spectra of the FRB counterpart, the reference object as well as the sky background, we then simultaneously fit the spatial profile at the location of the counterpart and at the location of the reference object on top of a spatially varying linear polynomial for each column in the dispersion direction.

Wavelength calibrations were obtained from arc lamp exposures, modelling the dispersion location to wavelength through 4th order polynomials, yielding rms residuals of better than 0.2 Å. The individual wavelength calibrated spectra were then combined and averaged. The instrumental response of the spectrograph was calibrated using an observation of the spectrophotometric standard Hiltner 600 (catalog ) (Hamuy et al. 1992; Hamuy et al. 1994), which was taken on 2016 November 7 as part of the standard Gemini calibration plan with identical instrumental setup as the science observations. The flux-calibrated spectrum of the reference object gives a spectroscopic AB magnitude of $m_{i^{\prime}}\approx 22.6$, about 11% higher than derived from photometry. Given that the spectrophotometric standard was observed on a different night with worse seeing ($1\farcs 4$), we attribute this difference to slit losses and scale the flux of the observed spectra of the reference object and the FRB counterpart by a factor 0.89.

III Results and Analysis

Finally, the bottom right panel of Figure 3 plots the Gaussian centroids on the International Celestial Reference Frame (ICRF) through the astrometric calibration of the $r^{\prime}$, $i^{\prime}$, and $z^{\prime}$ images against Gaia. The positional uncertainties in each axis are the quadratic sum of the astrometric tie against Gaia (of order 2 mas) and the centroid uncertainty on the image (between 20 and 50 mas). The Gaia frame is tied to the ICRF defined via radio VLBI to a $\sim$1 mas precision (Mignard et al. 2016), much smaller than the centroid uncertainty. We find that the position of the persistent radio source seen with the EVN at an observing frequency of 5 GHz with a 1-mas precision (Marcote et al. 2017), is offset from the galaxy centroids by $186\pm 68$ and $163\pm 32$ mas in the line-dominated $r^{\prime}$ and $i^{\prime}$ images, and $286\pm 64$ mas in the continuum-dominated $z^{\prime}$ image. Though offset from the centroids, the persistent radio source is located within the effective radii of the different bands.

IV Discussion and Conclusions

We use the Schlegel et al. 1998 estimate of the Galactic extinction along this line of sight From the IRSA Dust Extinction Calculator http://irsa.ipac.caltech.edu/applications/DUST/, $E_{B-V}=0.781$. Using $R_{V}=3.1$, we find $A_{V}=2.42$, and use the Cardelli et al. 1989 Galactic extinction curve to correct the spectrum with band extinctions of $A_{r^{\prime}}=2.15,A_{i^{\prime}}=1.63,$ and $A_{z^{\prime}}=1.16$ mag. We note that the Schlafly et al. 2010; Schlafly & Finkbeiner 2011 recalibrated extinction model predicts a slightly lower extinction of $E_{B-V}=0.673$. The results described below are insensitive to differences in the extinction at this level. We do not apply $k$-correction to the magnitudes as they are not needed for the precision discussed here.

IV.2 Physical Properties of the Host

The host of FRB 121102 is a small galaxy with a diameter of $\lesssim 4$ kpc, inferred from the continuum-dominated $z^{\prime}$-band image. The absolute magnitudes, including the emission line fluxes and after correcting for the Milky Way’s extinction, are $M_{r^{\prime}}=-17.0$ AB mag and $M_{i^{\prime}}=-17.7$ AB mag, identifying the host as a dwarf galaxy.

The mass-to-light ratio $\Upsilon_{*}$ is dependent on the star formation history and the initial mass function for star formation. As an estimate, we use $\Upsilon_{*}^{R}\approx 2-3\,M_{\sun}\,L_{\sun}^{-1}$ based on the dynamics of dwarf galaxies with high star formation rates (Lelli et al. 2014), implying a stellar mass $M_{*}\sim 4-7\times 10^{7}\ M_{\sun}$. As dwarf galaxies are usually gas-rich (Papastergis et al. 2012, e.g. ), we expect that this estimate is a lower limit to the host baryonic mass. We also note that dwarf galaxies are typically dark matter dominated (Côté et al. 2000), and so the total dynamical mass is likely to be larger.

We use the $R_{23}$ (Kewley & Dopita 2002), $N2$, $O3N2$ (Pettini & Pagel 2004), and the recently defined diagnostic of Dopita et al. 2016 to estimate the metallicity where,

As the [O II]$\lambda$3727 line is outside our spectral coverage and [N II]$\lambda 6584$ is not detected, we can only set an upper limit to the metallicity. Using the extinction-corrected line fluxes, we measure,

The host properties are similar to those of extreme emission line galaxies (Atek et al. 2011, EELGs; ), young, low-mass starbursts which have emission lines of rest-frame equivalent widths greater than 200Å.

IV.3 Ionized Gas Properties in the Host

The Balmer lines from the host also allow us to estimate the properties its ionized ISM and its contribution to the total DM of FRB 121102.

This value is fairly large compared to measurements of the local Galactic disk. The WHAM $\rm H\alpha$ survey, for example, gives values of tens of pc cm-6 in the Galactic plane and about 1 pc cm-6 looking out of the plane (Hill et al. 2008). However, lines of sight to distant pulsars and studies of other galaxies give EM values in the hundreds (Reynolds 1977; Haffner et al. 2009).

The implied optical depth for free-free absorption at an observation frequency $\nu$ (in GHz) is

Free-free absorption for FRB 121102 is therefore negligible even at 100 MHz. This suggests that the radio spectra of the bursts and possibly the persistent source are unaffected by absorption and are inherent to the emission process or to propagation effects near the sources, confirming the inference made by (Scholz et al. 2016) based on the widely varying spectral shapes of the bursts alone.

The EM implies a DM value sometimes given by ${\rm DM}=({\rm EM}f_{\rm f}L)^{1/2}$, where $f_{\rm f}$ is the volume filling factor of ionized clouds in a region of total size $L$ (Reynolds 1977). As summarized in Appendix B of Cordes et al. 2016, additional fluctuations decrease the DM derived from EM, giving a source-frame value,

where $\epsilon\leq 1$ is the fractional variation inside discrete clouds due to turbulent-like density variations and $\zeta\geq 1$ defines cloud-to-cloud density variations in the ionized region of depth $L_{\rm kpc}$ in kpc. Here we have used ${\rm EM}_{\rm s}\ =600$ pc cm-6 and assumed 100% cloud-to-cloud variations ($\zeta=2$) and fully modulated electron densities inside clouds ($\epsilon=1$).

The host contribution to the measured DM is a factor $(1+z)^{-1}$ smaller than the source frame DM The factor of $(1+z)^{-1}$ is a combination of the photon redshift, time dilation and the frequency-2 dependence of cold plasma dispersion.. Also, the line of sight to the FRB source may sample only a fraction of $\widehat{\rm DM}_{\rm s}$ depending on if it is embedded in or offset from the $\rm H\alpha$-emitting gas. For an effective path length through the ionized gas $L_{\rm FRB}\leq L$, we then have

IV.4 Implications for Source Models

Chatterjee et al. 2017 reported the locations of the radio bursts, the optical and variable radio counterparts and the absence of millimeter-wave and X-ray emission. Marcote et al. 2017 have shown that the bursts and the persistent radio source are colocated to within a linear projected separation of 40 pc, suggesting that the two emission sources should be physically related, though not necessarily the same source. The radio source properties are consistent with a low luminosity AGN or a young ($<$1000 yr) supernova remnant (SNR) powered by an energetic neutron star (Murase et al. 2016, e.g. ).

The optical properties of the galaxies reported here do not add support to the AGN interpretation although it cannot be conclusively ruled out. The BPT diagnostics for the host (Figure 2) show no indication of AGN activity. However, this may not be conclusive as the majority of radio-loud AGN show no optical signatures of activity (Mauch & Sadler 2007). This is further supported by five low luminosity AGN with no optical signatures have also recently been discovered (Park et al. 2016). However, these objects are almost exclusively hosted in galaxies with much larger stellar masses ($\sim 10^{10}\,M_{\sun}$). We also note that the radio source is offset from the optical center of the galaxy by 170–300 mas, corresponding to a transverse linear distance of 0.5–1 kpc, nearly a quarter to half of the radial extent, which is not consistent with a central AGN, but such offsets have been seen before in dwarf galaxies, e.g. Henize 2-10 (Reines et al. 2011).

The high star formation rate is consistent with the presence of a young SNR or a cluster of young massive stars (i.e. an OB association), which would naturally link FRBs to neutron stars which are the favored progenitor models.

It is interesting to note that the only FRB host directly identified so far is a low metallicity dwarf galaxy rather than, say, an extremely high-star-formation-rate galaxy such as Arp 220 or a galaxy with a very powerful AGN or some other extreme characteristics. Dwarf galaxies are also a small fraction of the stellar mass in the Universe (Papastergis et al. 2012). Ravi et al. 2016 also suggested that the extremely low scattering of FRB 150807 compared to its DM may be linked to its origin from a low-mass ($<10^{9}\,M_{\sun}$) galaxy. However, the strong polarization and scattering properties of FRB 110523 do suggest the presence of turbulent magnetized plasma around the source (Masui et al. 2015), suggesting that individual FRB environments may be quite diverse.

If FRBs are indeed more commonly hosted by dwarf galaxies in the low redshift Universe, they would share this preference with two other classes of high-energy transients — long duration gamma-ray bursts and superluminous supernovae, both of which prefer low-mass, low-metallicity, and high star formation rate hosts (e.g., Fruchter et al. 2006; Perley et al. 2013; Vergani et al. 2015; Perley et al. 2016, and other works). Indeed, superluminous supernovae are prefentially hosted by EELGs (Leloudas et al. 2015). If this relation is true, it may point to a link between FRBs and extremely massive progenitor stars, possibly extending to magnetars that have been associated with massive progenitor stars (Olausen & Kaspi 2014, e.g. ).

IV.5 Future Optical Follow-Up of FRBs

A link between FRBs and dwarf galaxies will impact future multi-wavelength follow-up plans. Without the precise localization for FRB 121102 (Chatterjee et al. 2017), the host galaxy is scarcely distinguishable from other objects in the deep Gemini images.

Due to the trade-off between field of view and localization precision, FRB search projects that have a large FRB detection rate such as CHIME (Kaspi V. M. et al,. 2017, in preparation), UTMOST (Caleb et al. 2016), and HIRAX (Newburgh et al. 2016) will localize high signal to noise detections to only sub-arcmin precision. If FRB hosts are star-forming galaxies with strong emission lines, slitless objective prism spectroscopy could efficiently distinguish these objects from a field of stars and elliptical galaxies, leading to putative host identifications without very precise localization. However, this strongly depends on the link between FRBs and their host properties and the homogeneity of FRBs — which will first have to be confirmed with more interferometric localizations.

We note, of course, that our above discussion regarding the possible relationship between FRBs and dwarf galaxies in general is based on a single data point of a repeating FRB, which may not be representative of the broader FRB population (see Spitler et al. 2016; Scholz et al. 2016, for more details).

References