The Electromagnetic Counterpart of the Binary Neutron Star Merger LIGO/Virgo GW170817. VII. Properties of the Host Galaxy and Constraints on the Merger Timescale

The recent discovery of gravitational waves (GWs) from binary black hole (BBH) mergers (Abbott et al. 2016a, 2016b, 2017) has launched a new era of astronomy. However, realizing the full potential of GW astronomy for advancing our knowledge of the formation of compact object binaries requires the observation of electromagnetic (EM) counterparts and hence precise positions and association with specific galaxies and stellar populations. While BBH mergers are not expected to produce EM signals, a wide range of EM counterparts are expected for binary systems containing at least one neutron star (Metzger & Berger 2012).

On 2017 August 17 at 12:41:04 UT the Advanced Laser Interferometer Gravitational-wave Observatory and Advanced Virgo interferometer (ALAV) discovered the first GW event from the inspiral and merger of two neutron stars (GW 170817; Abbott et al. 2017; LIGO Scientific Collaboration & Virgo Collaboration 2017). A short burst of gamma-rays (GRB 170817) was independently discovered from the same sky location with a delay of about 2 s by Fermi-GBM (Goldstein et al. 2017) and INTEGRAL (Savchenko et al. 2017). About 0.5 days after the GW trigger our group used the Dark Energy Camera on the Blanco 4 m telescope to discover an optical counterpart ($i\approx 17.48$ and $z\approx 17.59$ mag) associated with the galaxy NGC 4993 at a distance of $d\approx 39.5$ Mpc (Allam et al. 2017; Soares-Santos et al. 2017), which was independently discovered by Coulter et al. (2017a, 2017b; dubbed SSS17a) and Yang et al. (2017; dubbed DLT17ck). The transient is also known as AT 2017gfo. The companion papers in this series present strong evidence that the optical counterpart is due to kilonova emission (Chornock et al. 2017; Cowperthwaite et al. 2017; Nicholl et al. 2017), with little or no contribution from a GRB afterglow due to viewing angle effects (Alexander et al. 2017; Margutti et al. 2017).

Until now, the only observational data informing the formation and evolution of binary neutron star (BNS) systems has been through studies of the Galactic population of BNS systems (e.g., Smarr & Blandford 1976; Burgay et al. 2003; Kalogera et al. 2004, 2007; Kramer & Stairs 2008) and short GRBs (Berger 2014 and references therein). Numerous open questions remain related to the initial conditions, rate, and population properties of BNS systems, as well as their eventual mergers and role in galactic r-process enrichment. For example, the distribution of delay times (i.e., the sum of the evolutionary time to form a BNS system and its time to merge) is a key output of population synthesis simulations (e.g., Voss & Tauris 2003; Belczynski et al. 2006; Dominik et al. 2012). Similarly, the observed locations of short GRBs within their hosts provides constraints on natal kicks and the possibility of globular clusters as formation sites (Fong et al. 2010; Church et al. 2011; Fong & Berger 2013).

Here, we use our follow-up observations and archival data of NGC 4993 to measure the precise location of the BNS system at the time of merger and to infer the physical properties of the host, in particular its star formation history, which serves as a proxy for the BNS merger delay time, and hence the initial binary separation. We compare these results to Galactic BNS systems and results from population synthesis models.

Throughout the Letter, we use AB magnitudes corrected for Galactic extinction, with $E(B-V)=0.105$ (Schlafly & Finkbeiner 2011), and the following cosmological parameters: ${H}_{0}=67.7$ km s⁻¹ Mpc⁻¹, ${{\rm{\Omega }}}_{m}=0.307$, and ${{\rm{\Omega }}}_{{\rm{\Lambda }}}=0.691$ (Planck Collaboration et al. 2016).

2.1. Hubble Space Telescope (HST) Observations

As described in Cowperthwaite et al. (2017) we obtained HST target-of-opportunity observations of the optical counterpart of GW170817 on 2017 August 28 using the Advanced Camera for Surveys (ACS) with the F475W, F625W, F775W, and F850LP filters, the Wide Field Camera 3 (WFC3) IR channel with the F160W and F110W filters, and the WFC3 UVIS channel with the F336W filter (PID: 15329; PI: Berger). The data analysis is described in Cowperthwaite et al. (2017).

In Figure 1, we show a color image of NGC 4993 with an inset showing the location of the optical counterpart of GW170817 (${m}_{{\rm{F}}625{\rm{W}}}\approx 22.9$ mag at this epoch) created using our 2017 August 28 HST/ACS images (F850LP, F625W, and F475W). The galaxy exhibits a smooth surface brightness profile typical of elliptical galaxies, but with a complex dust structure near the nucleus.

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We also retrieved and analyzed an archival observation of NGC 4993 from 2017 April 28 using ACS/WFC with the F606W filter (PID: 14840; PI: Bellini), which allows for an assessment of an underlying source at the location of the optical counterpart of GW170817. We determine the exact location of the optical counterpart in the archival image by performing astrometry relative to our HST images. The resulting astrometric uncertainty is only $0\buildrel{\prime\prime}\over{.} 0075$ ($1\sigma$) corresponding to 0.2 pixels. No obvious source is seen at the location of the optical counterpart (Figure 1); the region is dominated by the background galaxy light. To obtain a limit on the presence of a point source we use the IRAF/psf task to create a point-spread function from the image, and the IRAF/addstar task to then inject fake point sources of varying brightness at the optical counterpart's location. We find a $5\sigma$ upper limit of ${m}_{{\rm{F}}606{\rm{W}}}\gtrsim 26.0$ mag for a point source, corresponding to ${M}_{{\rm{F}}606{\rm{W}}}\gtrsim -7.2$ mag at the distance of NGC 4993.

2.2. Additional Archival Data

For the purpose of modeling the host galaxy spectral energy distribution (SED), we retrieved archival observations of NGC 4993, including UV and IR photometry from the GALEX, 2MASS, and WISE catalogs via the NASA/IPAC Extragalactic Database. For optical data we used deep grizy stacks from the Pan-STARRS1 3π survey (Chambers et al. 2016; Waters et al. 2016) and performed photometry using SExtractor (Bertin & Arnouts 1996). We use the MAG_AUTO magnitudes, which are measured using Kron apertures. The photometry is summarized in Table 1.

Table 1.  X-Ray to Radio Photometry of NGC 4993

Instrument	Band	Magnitude/Flux
Chandra	2–10 keV	$1.7\times {10}^{-14}$
GALEX	FUV	>18.86
GALEX	NUV	17.82 (0.09)
PS1	g	12.80 (0.02)
PS1	r	12.16 (0.01)
PS1	i	11.81 (0.01)
PS1	z	11.57 (0.01)
PS1	y	11.36 (0.02)
2MASS	J	10.98 (0.02)
2MASS	H	10.82 (0.02)
2MASS	K	11.02 (0.02)
WISE	W1	11.92 (0.01)
WISE	W2	12.59 (0.01)
WISE	W3	13.70 (0.04)
WISE	W4	13.86 (0.18)
ALMA	97.5 GHz	210 (20)
VLA	15.0 GHz	295 (18)
VLA	10.0 GHz	288 (20)
VLA	9.7 GHz	250 (55)
VLA	6.0 GHz	330 (20)

Note. All magnitudes are given in the AB system and are corrected for Galactic extinction. Radio fluxes are in μJy, and the unabsorbed X-ray flux is in $\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$.

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2.3. Radio and X-Ray Observations: An Active Galactic Nucleus (AGN) Origin

2.4. Optical Spectra

To determine the morphological properties of the host galaxy of GW170817, we measured and fit the surface brightness profile using the HST observations. We used GALFIT v3.0.5 (Peng et al. 2010) to fit the 2D surface brightness profile of NGC 4993 with a standard Sérsic function that is parameterized by the Sérsic index, n, the effective radius, r_e, and ${\mu }_{e}$, the surface brightness at r_e. For comparison, we also used the ellipse task in IRAF to fit isophotes to the galaxy images and then fit the resulting 1D isophotal intensity profile with a Sérsic function. In both methods, the Sérsic model is defined in such a way that r_e corresponds to the half-light radius. The best-fit Sérsic parameters from GALFIT are listed in Table 2.

Table 2.  Measured and Derived Properties of NGC 4993 and the Offset of the Optical Counterpart of GW170817

Property	Optical	NIR
n	3.9 (0.4)	5.1 (0.3)
re (arcsec)	16.2 (0.7)	18.1 (1.6)
re (kpc)	3.3 (0.1)	3.7 (0.3)
${\sigma }_{\mathrm{OT}}$ (arcsec)	0.0017	0.0006
${\sigma }_{\mathrm{gal}}$ (arcsec)	0.0006	0.0001
δR.A. (arcsec)	−5.1796	−5.1730
δDecl. (arcsec)	−8.9208	−8.9265
Offset (arcsec)	10.315 (0.007)	10.317 (0.005)
Offset (kpc)	2.125 (0.001)	2.125 (0.001)
Offset (re)	0.64 (0.03)	0.57 (0.05)
Fractional Flux	0.54	⋯
Derived Parameters
AVa	$\lt 0.11$
log(${\mathrm{SFR}}_{100\mathrm{Myr}}/{M}_{\odot }$ yr−1)	$-{2.00}_{-0.66}^{+0.44}$
$\mathrm{log}({M}_{* }/{M}_{\odot }$)	${10.65}_{-0.03}^{+0.03}$
log($M/{M}_{\odot }$)	${10.90}_{-0.03}^{+0.03}$
${t}_{\mathrm{half}}$ (Gyr)	${11.2}_{-1.4}^{+0.7}$
${t}_{\mathrm{age},\mathrm{spec}}$ (Gyr)	${13.2}_{-0.9}^{+0.5}$
$[\mathrm{Fe}/{\rm{H}}]$	${0.08}_{-0.03}^{+0.02}$
$[\mathrm{Mg}/\mathrm{Fe}]$	${0.20}_{-0.02}^{+0.03}$

Note. Sérsic parameters are from GALFIT. Optical and NIR columns are averages of the values from the optical and NIR HST observations in several filters. $[\mathrm{Fe}/{\rm{H}}]$, $[\mathrm{Mg}/\mathrm{Fe}]$, and ${t}_{\mathrm{age},\mathrm{spec}}$ are from modeling of the spectrum and all other derived properties are from modeling of the SED.

^a95% upper limit.

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In general, we find that the surface brightness profile of NGC 4993 can be well-described by a single $n\sim 3.9$ Sérsic component with ${r}_{e}\sim 3.3\,\mathrm{kpc}$ and modest ellipticity (axis ratio ∼0.85). After subtracting the best-fitting GALFIT models from our data, the residual images suggest the presence of shell and asymmetric structure that are especially prominent in the F160W image (see Figure 1). There are at least four concentric shells apparent in the F160W residual image with clear boundaries. In Figure 1, we also show the residual image in the F475W filter, zoomed to show the complex dust structure surrounding the nucleus. There is a large, approximately a few kiloparsecs, dust lane in a stretched out "s" shape, which appears to be connected to a smaller scale, ∼0.1 kpc, dust ring surrounding the brightest pixels. Both the shell and dust structures may be indicative of past galaxy mergers (e.g., Hernquist & Quinn 1988; Kormendy & Djorgovski 1989).

4.1. Offset

4.2. Fractional Flux

We model the UV to mid-IR SED of NGC 4993 using Prospector-α, a 14-parameter galaxy SED model (Leja et al. 2017a) that is built in the Prospector inference framework (B. Johnson et al. 2017, in preparation) and is optimized to fit UV–IR galaxy broadband photometry. Prospector-α uses a Bayesian Markov Chain Monte Carlo (MCMC) approach to modeling galaxy SEDs. In brief, the model fits a six-component non-parametric star formation history (SFH), a two-component dust attenuation model with a flexible attenuation curve, stellar metallicity, and a flexible dust emission model powered via energy balance. Nebular line and continuum emission are added self-consistently through use of CLOUDY model grids from Byler et al. (2017). This fit additionally includes a mid-IR AGN component described in Leja et al. (2017b). SFR and stellar mass measurements from this fitting assume a Chabrier initial mass function.

In Figure 2, we show the observed SED and best-fit model. We find a low current star formation rate (averaged over the last 100 Myr) of log(SFR${}_{100\mathrm{Myr}}$/${M}_{\odot }$ yr⁻¹) $=\,-{2.0}_{-0.7}^{+0.4}$, a total mass formed in stars of log($M/{M}_{\odot }$) $=\,{10.90}_{-0.03}^{+0.03}$, and a stellar mass of log($M/{M}_{\odot }$) $={10.65}_{-0.03}^{+0.03}$ (defined as the current mass in stars and stellar remnants). There is no significant dust extinction with a 95% upper limit of ${A}_{V}\lt 0.11$. Of particular interest here is the SFH, shown in eight temporal bins in Figure 2. We find an exponentially declining SFH with a peak star formation rate $\approx 10\,\mathrm{Gyr}$ ago of about 10 ${M}_{\odot }$ yr⁻¹. The SFH prior moderately favors a continuous star formation rate. The declining SFH in the posterior is thus driven by the photometry rather than the model priors.

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Using the SFH, we can calculate the fraction of stars produced by a given time to obtain the stellar mass build-up history, which we also show in Figure 2. Half of the stellar mass was formed by ${11.2}_{-1.4}^{+0.7}$ Gyr ago (t${}_{\mathrm{half}}$, the half-mass assembly time), due to the high SFR at early times, and 90% was formed by ${6.8}_{-0.8}^{+2.2}$ Gyr ago. We list the main physical parameters resulting from the SED modeling in Table 2.

We also model the optical spectrum of NGC 4993 with the alf stellar population synthesis modeling code (Conroy & van Dokkum 2012; Conroy et al. 2017), a two-component star formation history, the metallicity, and the abundances of 18 different elements. This complex model space is fit with MCMC techniques, with the continuum shape removed with high-order polynomials. For the present analysis we focus on three key quantities: the mass-weighted age, [Fe/H] metallicity, and [Mg/Fe], each of which is well-constrained by the data. The data and best-fit model are shown in Figure 2; the model provides an excellent fit. From the posterior distributions of the fitted parameters, we find a median mass-weighted age of ${13.2}_{-0.9}^{+0.5}$ Gyr, a median metallicity of $[\mathrm{Fe}/{\rm{H}}]={0.08}_{-0.03}^{+0.02}$, and $[\mathrm{Mg}/\mathrm{Fe}]={0.20}_{-0.02}^{+0.03};$ the age inferred here is consistent with the SED modeling results.

Using the SFH determined from the SED modeling, we can infer a probability distribution for the BNS merger timescale, and hence the initial binary separation. We note that the inspiral timescale dominates over the stellar evolution timescale (which is at most tens of Myr). The cumulative stellar mass build-up history, shown in Figure 2, can therefore be interpreted as the integral of the merger timescale probability distribution. The inferred old age of the stellar population and the exponentially declining SFH, lead to a median merger time of ${11.2}_{-1.4}^{+0.7}$ Gyr and a 90% confidence interval of $6.8\mbox{--}13.6\,\mathrm{Gyr}$. Due to the lack of observational constraints on the intrinsic population delay time distribution (DTD), this interpretation makes the assumption that all merger times are equally probable. To check the influence of this assumption on the result, we recalculate the merger time probability distribution with the SFH weighted by a ${\tau }^{-1}$ DTD (truncated at 0.1 Gyr), which results in a median merger time of ${10.3}_{-0.8}^{+1.1}$ Gyr (Figure 2). While slightly shorter, the resulting merger time estimate is not significantly changed, due to the exponentially declining SFH.

The merger timescale depends on both the initial separation (a₀) and eccentricity (e₀) of the system (Peters 1964):

$$\begin{eqnarray}&&{\tau }_{\mathrm{merg}}({a}_{0},{e}_{0})=\displaystyle \frac{12}{19}\displaystyle \frac{{c}_{0}^{4}}{\beta }\\ &&\quad \times {\displaystyle \int }_{0}^{{e}_{0}}\displaystyle \frac{{e}^{29/19}{[1+(121/304){e}^{2}]}^{1181/2299}}{{(1-{e}^{2})}^{3/2}}{de},\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}&&{c}_{0}=\displaystyle \frac{{a}_{0}(1-{e}_{0}^{2})}{{e}_{0}^{12/19}}{[1+(121/304){e}_{0}^{2}]}^{-870/2299}\end{eqnarray} \tag{ 2 }$$

and β is a constant related to the total and reduced mass. Here we assume nominal neutron star masses of 1.4 M_⊙ since at the time of writing the measured neutron star masses from the GW data were not publicly available. We can therefore convert our inferred median and 90% confidence merger timescale to a₀ as a function of e₀; see Figure 3. For ${e}_{0}\lesssim 0.5$ we find ${a}_{0}\approx 3.9\mbox{--}4.7$ ${R}_{\odot }$ with a median of $\approx 4.5$ R_⊙. However, if the initial eccentricity of the system was large (${e}_{0}\gtrsim 0.8$), then the initial separation could be tens of ${R}_{\odot }$.

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In Figure 3, we also show the initial separations and eccentricities for the simulated population of BNS systems from Dominik et al. (2012) using their standard model (sub-model A) with solar metallicity, appropriate for NGC 4993. The population has an overdensity roughly centered along the contour for ∼100 Myr, though there is considerable spread in the initial separations and thus timescales for a given eccentricity. At low eccentricity (${e}_{0}\lesssim 0.2$) the distribution of separations peaks at about a factor of 2–3 less than the separation of the progenitor of GW170817, though even at these eccentricities the spread is large. Interestingly, the region of ${a}_{0}-{e}_{0}$ parameter space for the progenitor of GW170817 is mid-range compared to the Galactic BNS systems.

Combining the location of GW170817 within its host and the merger timescale probability distribution, we can assess the velocity imparted to the system due to a natal kick. There are several unknown factors such as the formation location of the system, the fact that we can only measure a projected offset, and the exact gravitational potential of the host galaxy. However, given the long merger timescale and the measured location within the host's half-light radius, it is most likely that any natal kick was not strong enough to unbind the binary from the host on an escaping trajectory. Assuming the progenitor system was born near or within its current small offset, we can use the central stellar velocity dispersion (${\sigma }_{* }$) to set an upper limit on the kick velocity. The velocity dispersion is only marginally resolved in the host spectrum, yielding a nominal value of ${\sigma }_{* }\approx 150$ km s⁻¹ from the model fitting. As the dispersion is less than the instrumental resolution, we consider the instrumental resolution to be a conservative upper limit on the velocity dispersion and therefore the kick velocity, which yields ${v}_{{kick}}\lesssim 200$ km s⁻¹. This value is within the range of observed and simulated velocity distributions for Galactic BNS systems (Wong et al. 2010; Tauris et al. 2017).

Finally, we assess the possibility of a globular cluster origin for the progenitor of GW170817 (e.g., Lee et al. 2010). We compare the limit on an underlying point source at the location of the progenitor (≳−7.2 mag) to the globular cluster luminosity function (GCLF) for giant elliptical galaxies, which peaks at ${M}_{V}\approx -7.4$ mag, with the brightest observed system at ${M}_{V}\approx -10$ mag (Harris et al. 1991). Strader et al. (2006) found that the luminosity at the peak of the GCLF remains the same regardless of galaxy size for elliptical galaxies. Thus, the archival limit rules out the brighter half of the GCLF. Additional, deeper observations will be needed to definitively rule out a globular cluster at the position of the optical counterpart.

We presented new and archival data for NGC 4993, the host galaxy of the first BNS merger discovered through GW emission, and the first with an EM counterpart. Using these data we investigated the location of the progenitor within its host, determined critical properties of the galaxy and its stellar population, and placed constraints on the merger timescale, initial separation, and kick velocity of the BNS system. Our key findings are:

• 1.  
  The host galaxy of GW170817 is an elliptical galaxy that is well-described by a $n\approx 3.9$ Sérsic profile in the optical, but with significant fine shell structure in the NIR indicative of past galaxy mergers. We detect NGC 4993 with X-ray and radio luminosities that suggest the presence of a weak AGN.
• 2.  
  The offset of the BNS system from the nucleus of NGC 4993 is 2.1 kpc, with a normalized offset of 0.64 in the optical and 0.57 in the NIR, indicating that the merger took place within the host's half-light radius. The fractional flux value is 0.54, consistent with this conclusion.
• 3.  
  From modeling the UV to MIR SED we find an exponentially declining SFH, with a median stellar population age of ${11.2}_{-1.4}^{+0.7}$ Gyr. The present-day SFR is low, $\approx 0.01$ ${M}_{\odot }$ yr⁻¹.
• 4.  
  The median merger timescale is therefore ${11.2}_{-1.4}^{+0.7}$ Gyr for the progenitor of GW170817, with a 90% probability the BNS system formed between $6.8\,\mathrm{and}\,13.6\,\mathrm{Gyr}$ ago. Assuming a circular orbit and equal neutron star masses of 1.4 ${M}_{\odot }$, this corresponds to an initial separation of 3.9–4.7 ${R}_{\odot }$ with a median of 4.5 ${R}_{\odot };$ for large initial eccentricity the separation could be tens of ${R}_{\odot }$.
• 5.  
  Given the long merger timescale and small projected offset, we conclude that the binary system experienced at most a modest natal kick, with an upper limit of 200 km s⁻¹.

This Letter demonstrates the utility of detailed host galaxy studies for inferring the properties of BNS systems. Studying the host galaxies of future BNS mergers discovered by ALAV and localized by EM follow-up will allow for an observational measurement of the population DTD, a key parameter that informs the viability of BNS mergers as the dominant source of r-process enrichment in the universe. Comparison of the DTD as well as separations, natal kicks, and merger rates with population synthesis models will also yield great insight into uncertain phases, such as the common envelope phase, of massive star binary evolution.

The Berger Time-Domain Group at Harvard is supported in part by the NSF through grants AST-1411763 and AST-1714498, and by NASA through grants NNX15AE50G and NNX16AC22G. P.K.B. is grateful for support from the National Science Foundation Graduate Research Fellowship Program under grant No. DGE1144152. D.A.B. is supported by NSF award PHY-1707954. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Some of the data presented in this Letter were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts.

Facilities: HST (ACS - , WFC3) - , SOAR - , VLA - , ALMA - , CXO - .