Did GW170817 harbor a pulsar?

TL;DR

This paper investigates whether GW170817's progenitor contained a pulsar by analyzing the size of a potential bow-shock cavity and its impact on afterglow timing, providing constraints on the pulsar's presence.

Contribution

It introduces a novel method to constrain the existence of a pulsar in GW170817 using afterglow onset timing and compares findings with Galactic binary systems.

Findings

Most Galactic merging systems would have created large cavities inconsistent with GW170817's afterglow timing.

The system J1913+1102, with a low-luminosity pulsar, aligns with GW170817's progenitor characteristics.

Constraints suggest GW170817's progenitor likely did not harbor a pulsar.

Abstract

If the progenitor of GW170817 harbored a pulsar, then a Poynting flux dominated bow-shock cavity would have been expected to form around the traveling binary. The characteristic size of this evacuated region depends strongly on the spin-down evolution of the pulsar companion, which in turn depends on the merging timescale of the system. If this evacuated region is able to grow to a sufficiently large scale, then the deceleration of the jet, and thus the onset of the afterglow, would be noticeably delayed. The first detection of afterglow emission, which was uncovered 9.2 days after the $\gamma$-ray burst trigger, can thus be used to constrain the size of a pre-existing pulsar-wind cavity. We use this information, together with a model of the jet to place limits on the presence of a pulsar in GW170817 and discuss the derived constraints in the context of the observed double neutron star binary population. We find that the majority of Galactic systems that are close enough to merge within a Hubble time would have carved a discernibly large pulsar-wind cavity, inconsistent with the onset timescale of the X-ray afterglow of GW170817. Conversely, the recently detected system J1913+1102, which host a low-luminosity pulsar, provides a congruous Milky Way analog of GW170817's progenitor model. This study highlights the potential of the proposed observational test for gaining insight into the origin of double neutron star binaries, in particular if the properties of Galactic systems are representative of the overall merging population.

Equations

$$L_{\mathrm{p}}\approx$$

$$L_{\mathrm{B}}$$

$$a_{30}\approx {\left(\frac{{\tau }_{\mathrm{GW}}}{1.2\times 10^{-2}\text{s}}\right)}^{1/4},$$

$$R_{\mathrm{s}}\approx 4.0\times 10^{18}{L}_{35}^{1/2}{n}_{\mathrm{ext},-4}^{-1/2}{V}_{\mathrm{k},2}^{-1}\mathrm{cm}.$$

$$R_{\mathrm{dec}}\approx 1.6\times 10^{18}{E}_{50}^{1/3}{n}_{\mathrm{ext},-4}^{-1/3}{\Gamma }_5^{-2/3}\mathrm{cm},$$

$$t_{\mathrm{dec}}$$

$$\displaystyle\approx 27.3\;{\bigg{(}{1+z\over 2}\bigg{)}}E_{50}^{1/3}n_{\rm ext,-4}^{-1/3}\Gamma_{5}^{-8/3}\;{\rm days}.$$

$$\left(\frac{R_{\mathrm{s}}}{R_{\mathrm{dec}}}\right)\approx 2.5L_{35}^{1/2}{\Gamma }_5^{2/3}{E}_{50}^{-1/3}{n}_{\mathrm{ext},-4}^{-1/6}{V}_{\mathrm{k},2}^{-1}.$$

$$R_{\mathrm{dec}}\lesssim R_{\mathrm{x}}\approx 5.5\times 10^{17}{\Gamma }_5^2\mathrm{cm}.$$

$$L\lesssim 2\times 10^{33}{\Gamma }_5^4{n}_{\mathrm{ext},-4}{V}_{\mathrm{k},2}^2\mathrm{erg}{\mathrm{s}}^{-1}.$$

$$\dot{P}=9.8\times 10^{-19}{\left(\frac{\mathrm{B}}{10^{10}\mathrm{G}}\right)}^2{\left(\frac{P_0}{100\mathrm{ms}}\right)}^{-1}\mathrm{s}{\mathrm{s}}^{-1}.$$

$$R_{\mathrm{s}}=1.6\times 10^{18}{n}_{\mathrm{ext},-4}^{-1/2}{V}_{k,2}^{-1}{B}_{10}{P}_{0,-1}^{-2}\mathrm{cm},$$

$$P_0=36{\left(\frac{P_{\mathrm{bin}}}{\mathrm{days}}\right)}^{0.4}\mathrm{ms},$$

$${\tau }_{\mathrm{GW}}=0.0725{\left(\frac{P_{\mathrm{bin}}}{0.1\mathrm{days}}\right)}^{8/3}\mathrm{Gyr},$$

$$R_{\mathrm{s}}=3.5\times 10^{18}{n}_{\mathrm{ext},-4}^{-1/2}{V}_{\mathrm{k},2}^{-1}{B}_9{\tau }_{\mathrm{GW},\mathrm{Gyr}}^{-0.3}\mathrm{cm}.$$

Full text

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1. Introduction

Since the discovery of the first double neutron star binary by Hulse & Taylor (1975), a total of 18 additional systems have been uncovered by radio surveys (Stovall et al., 2018). Although these double neutron star binaries will not merge for tens of millions of years (Burgay et al., 2003; Kim et al., 2015), they make it clear that such mergers were an inescapable aftermath of binary stellar evolution (Tauris et al., 2017).

The potential outcomes arising from the merger of compact binaries was first discussed by Lattimer & Schramm (1976). They studied the tidal disruption of a neutron star by a black hole and, although they claimed that the occurrence rate was likely too rare for them to explain the then recently discovered $\gamma$-ray burst sources (Klebesadel et al., 1973), enough material might be ejected from these systems to be a primary channel for heavy element nucleosynthesis. In almost a literal sense, Lattimer & Schramm (1976) set the stage for interpreting the exceptional discovery of GW170817 (Abbott et al., 2017a). Through the unprecedented monitoring efforts of GW170817 by the astronomical community (Abbott et al., 2017b; Coulter et al., 2017), there is now a consensus that neutron star mergers can synthesize copious amounts of $r$-process material (Kasen et al., 2017) and trigger short $\gamma$-ray bursts (or at least a class of them; Abbott et al., 2017c).

Observing such systems before they merge can provide us with key information about the physics of binary stellar evolution and the types of gravitational-wave signals we might expect to uncover with current and future observatories (Kalogera et al., 2001). Progress is currently hampered by the small number of systems uncovered (Stovall et al., 2018), which represents a minuscule fraction of the total estimated population (Scholz et al., 2015). However, the future holds enormous promise for the study of neutron star binaries due to the advent of large wide-field radio surveys and the nascent field of gravitational wave astronomy, which will allow the study of these populations in great detail. A combination of finding more systems before and after they merge has a great potential for constraining binary evolution but also uncovering fundamental physics of the merger. This motivates us to explore potential constraints on the pre-merger properties of the progenitor system of GW170817.

In this Letter we examine the consequences of the hypothesis that GW170817’s progenitor system hosted a pulsar. In Section 2 we show that if a pulsar is present in the system, then a Poynting flux dominated cavity would have formed in its surroundings, effectively displacing the interstellar medium. After a review of the relevant observations, in Section 3 we examine the conditions required for a pulsar wind cavity to grow to a sufficiently large size in order to prevent the deceleration of the relativistic ejecta in GW170817 and, as a result, delay the onset of the afterglow emission (Holcomb et al., 2014). We use this information, together with a model of the structure of the evacuated cavity to place stringent limits on the presence of a pulsar in GW170817. Finally, in Section 4 we discuss the derived constraints in the context of the observed binary neutron star population and determine the properties of the electromagnetic signatures expected from gravitational wave sources harboring pulsars.

2. The Pre-Merger Environment of GW170817

The optical source of GW170817 was found by Coulter et al. (2017) to be associated with the early-type galaxy NGC 4993 at a distance of about 40 Mpc, with the merger site located at a projected distance of about 2 kpc away from NGC 4993’s galactic center. These observations would seem to favor a progenitor formed $\gtrsim$ 1 Gyr ago from an isolated binary in the field, receiving a natal kick velocity, $V_{\rm k}$, of about $10^{2}$ km s*-1* (Abbott et al., 2017d), as expected from merging neutron star models (Fryer & Kalogera, 1998; Perna & Belczynski, 2002; Kelley et al., 2010; Osłowski et al., 2011; Behroozi et al., 2014). Based on the inferred projected distance and the properties of the host (Abbott et al., 2017d), we expect the typical ambient density, $n_{\rm ext}$, in which the event occurred to be around $10^{-4}$ cm*-3* (Perna & Belczynski, 2002), consistent with those inferred from afterglow modeling (e.g. Margutti et al., 2018).

If the binary progenitor of GW170817 hosted a pulsar, then a bow shock cavity would have resulted from its interaction with the external medium, the characteristic size of which depends primarily on the pre-merger luminosity of the system. For an inspiraling binary with at least one pulsar, there are two widely commonly accepted mechanisms for energy dissipation. The first one is the traditional spin-down luminosity

[TABLE]

where $\tau_{\rm p}=P/\dot{P}$ is the pulsar spin-down time scale ($\tau_{{\rm p},9}=\tau_{\rm p}/10^{9}\text{ yr}$), $B$ is the strength of the magnetic field ($B_{9}=B/10^{9}\text{ G}$) and we have taken $R=12$ km and $M=1.4M_{\odot}$ as fiducial parameters.

The second one is the energy dissipation due to the torque on the binary by the magnetic field of the pulsar (Lai, 2012),

[TABLE]

where $\zeta_{\phi}$ is the azimuthal twist, which we take to be equal to the $\zeta_{\phi}\approx 1$ upper bound. This is because the flux tube will break up when $\zeta_{\phi}\gtrsim 1$ and, as a result, the linkage between the two binary components will be disconnected (Lai, 2012). The orbital separation $a$ ($a_{30}=a/30\text{ km}$), whose evolution is driven by gravitational wave emission, is given by

[TABLE]

where $\tau_{\rm GW}=a/\dot{a}$ is the merging time scale.

The binary progenitor of GW170817 would have then formed a bow shock (Fig. 1) with a characteristic size $R_{\rm s}$ given by (Wilkin, 1996, 2000)

[TABLE]

Here $L$ is the isotropic luminosity ($L_{35}=L/10^{35}{\rm erg\;s}^{-1}$), $n_{\rm ext}$ is the number density of the medium ($n_{\rm ext,-4}=n_{\rm ext}/10^{-4}\;{\rm cm}^{-3}$) and $V_{{\rm k},2}=V_{\rm k}/10^{2}\text{ km s}^{-1}$. Equation 4 becomes accurate in the limit of efficient cooling and is found to be in good agreement with sizes of cavities carved by anisotropic and non-axisymmetric MHD pulsar winds (Vigelius et al., 2007; Barkov & Lyutikov, 2018).

For small kick velocities ($V_{\rm k}\lesssim$ 10 km s*-1*), equation 4 fails to provide an accurate description for the size of the cavity and a spherically symmetric solution becomes more accurate (Medvedev & Loeb, 2013a, b). However, given that the neutron star binary progenitor in GW170817 likely received a velocity in excess of 100 km s*-1* (Abbott et al., 2017d), we expect equation 4 to provide us with a reasonable estimate for the characteristic size of the evacuated region.

3. Afterglows IN PRE-MERGER CAVITIES and Implications for GRB 170817A

In the study of short $\gamma$-ray burst afterglows from neutron star mergers one commonly considers expansion into a uniform medium (e.g, Perna & Belczynski, 2002). In the absence of a pulsar companion, the length scale of shock deceleration $R_{\rm dec}$ in the standard afterglow model (Rees & Meszaros, 1992; Meszaros & Rees, 1993) is given by

[TABLE]

where $E_{50}=E/(10^{50}\text{erg})$ is the isotropic-equivalent energy output of GRB 170817A and $\Gamma_{5}=\Gamma/5$ is the bulk Lorentz factor. The values of $E$ and $\Gamma$ have been selected here to match those inferred (along our line of sight) from observations of GW170817 (Murguia-Berthier et al., 2017; Lazzati et al., 2018; Margutti et al., 2018; Mooley et al., 2018; Matsumoto et al., 2019). This sets a characteristic deceleration time as measured by an observer along our line of sight (Rees & Meszaros, 1992; Meszaros & Rees, 1993; Zhang et al., 2006)

[TABLE]

The relativistic expansion is then gradually slowed down, and the blastwave evolves in a self-similar manner, as shown in the red curve of Fig. 2. However, since the wind of the pulsar meets the interstellar medium at some point, the evolution of the blast wave can be modified, as shown in the black curve of Fig. 2. In this case, the shock front expands unobstructed within the mass-evacuated pulsar wind cavity until it reaches the contact discontinuity, which is placed here at $R_{\rm s}=(5/2)R_{\rm dec}(n_{\rm ext})$. The afterglow lightcurves presented in Fig. 2 make use of the Mezcal special relativistic hydrodynamical calculations presented in Holcomb et al. (2014), in which we have assumed, for simplicity, that the blastwave is adiabatic and effectively spherical.

In general, if the pre-merger pulsar wind is weak enough that the blastwave would not be significantly slowed down by the time it expands beyond the pulsar wind cavity $R_{\rm s}\ll R_{\rm dec}$, then we expect its evolution as we see it to take place in a uniform medium (red curve in Fig. 2). Alternatively, we expect the presence of the pulsar wind cavity to inevitably delay the onset of the afterglow when $R_{\rm s}\gtrsim R_{\rm dec}$ (black curve in Fig. 2). It is thus useful to examine the range of conditions that fulfill this later requirement. Taking the ratio of equations 4 and 5, we derive

[TABLE]

This ratio is modestly dependent on $L$ and $\Gamma$ but weakly dependent on $n_{\rm ext}$ and $E$.

In Fig. 3 we compare the relative contribution of $L_{\rm B}$ and $L_{\rm p}$ to $R_{\rm s}$ by separating it into $R_{\rm s}^{\rm B}=R_{\rm s}(L_{\rm B})$ and $R_{\rm s}^{\rm p}=R_{\rm s}(L_{\rm p})$. In order to calculate the size of the cavity produced by $L_{\rm B}$ we must make the transformation $\tau_{\rm GW}\rightarrow\tau_{\rm GW}+R_{\rm s}^{\rm B}/c$ in order to correctly compute $R_{\rm s}^{\rm B}$ (Holcomb et al., 2014). This is because $L_{\rm B}$ propagates to the bow-shock interface within a finite amount of time and there is a lag of $R_{\rm s}^{\rm B}/c$ before $R_{\rm s}^{\rm B}$ can react to changes in $L_{\rm B}$. For this reason, the size of the cavity at the time of merger (equation 4) should be computed using $L_{\rm B}$, which, after making the substitution that $a\sim(\tau_{\rm GW})^{1/4}\sim(R_{\rm s}^{\rm B}/c)^{1/4}$ in equation 2, gives $R_{\rm s}^{\rm B}\propto B^{16/29}$ (Fig. 3). We find that $L_{\rm p}$ dominates for most realistic values of $B$ and $\tau_{\rm p}$, while $L_{\rm B}$ becomes only relevant when $B>10^{12}$ G (likely to be unrealistic as it assumes no field decay). In addition, in Fig. 3 we plot two values of $R_{\rm dec}$, corresponding to the deceleration radii inferred from afterglow observations of GW170817 (Lazzati et al., 2018; Margutti et al., 2018) along our line of sight (black dashed line) and along the jet’s axis (grey dashed line), respectively. Since $R_{\rm s}$ can in some cases exceed $R_{\rm dec}$, we expect that afterglows emanating from neutron star mergers to noticeably trail the prompt emission, in particular when the observer is near the axis of the jet (e.g. Murguia-Berthier et al., 2014). We comment further on this in Section 4.

Observations summarized in Abbott et al. (2017b) show that the first detection of afterglow emission in GW170817 was uncovered at $t=9.2$ days at X-ray wavelengths. This can be used to set a constraint on the X-ray emitting radius, $R_{\rm x}$, as measured by an observer along our line of sight

[TABLE]

This in turn implies that the mass required to decelerate the ejecta was not pushed out beyond $R_{\rm dec}$ by the Poynting flux emanating from the pulsar companion and, as such, it suggests that $R_{\rm s}\lesssim R_{\rm dec}\lesssim R_{\rm x}\approx 5.5\times 10^{17}\Gamma_{5}^{2}\;{\rm cm}$. The fulfillment of the condition $R_{\rm s}\lesssim R_{\rm x}$ naturally translates into a limit on the pre-merger wind luminosity

[TABLE]

Here the bulk Lorentz factor (along our line of sight), $\Gamma$, is highly constrained by the condition that $2.3\;{\rm days}\lesssim t_{\rm dec}\lesssim 9.2\;{\rm days}$ (Margutti et al., 2018), which can be rewritten using equation 6 as $1.1E_{50}^{1/8}n_{\rm ext,-4}^{-1/8}\lesssim\Gamma_{5}\lesssim 2.05E_{50}^{1/8}n_{\rm ext,-4}^{-1/8}$. This is in agreement with arguments connected with the estimated opacity of the $\gamma$-ray emitting region (Matsumoto et al., 2019), for material moving our line of sight.

The non-detection of the X-ray afterglow at $2.3\;{\rm days}$ can, in principle, be used to place tighter constraints on the characteristic size of the emitting region under the assumption that the afterglow data are consistent with a quasi-spherical, sub-energetic explosion (Fig 2). However, given that the flow is likely to be collimated into jets (Lazzati et al., 2018; Margutti et al., 2018), the exact observed afterglow properties are expected to vary depending upon the angle, $\theta_{\rm obs}$, from the symmetry axis of the jet at which they are viewed. For example, if one assumes a homogeneous sharp-edged jet (Murguia-Berthier et al., 2017), an off-axis observer will see a rising afterglow light curve at early times (as the flow decelerates and the Lorentz factor decreases with time) peaking when the jet Lorentz factor reaches $\sim 1/\theta_{\rm obs}$ and approaching that seen by an on-axis observer at later times. In this case, equation 9 provides us with a conservative underestimate of the pre-merger wind luminosity.

The constraint on the pre-merger luminosity should be thus taken as an order of magnitude estimate at present and is currently consistent with the presence of an un-recycled (i.e. low luminosity) pulsar. However, as we show below, it allows for meaningful constraints to be placed on the nature of a potential pulsar binary companion, in particular if the properties of the Galactic neutron star binaries are indicative of the general merging population. This is because a large number of Galactic systems would have been expected to carve discernible cavities. If merging binaries hosting low-luminosity pulsars are, on the other hand, common, then we expect no clear delay between the onset of the afterglow and the prompt emission.

In Fig. 4 we translate the condition $R_{\rm s}\lesssim R_{\rm x}$ to constraints in the $P$-$\dot{P}$ diagram. The region of interest is separated into two distinct zones: low field pulsars with long spin-down time scales and high field pulsars. In the latter case, the necessary conversion $\tau_{\rm GW}\rightarrow\tau_{\rm GW}+R_{\rm s}^{\rm B}/c$ was made. For the low field pulsars, which depend on their spin to generate pre-merger luminosity, an additional constraint should be that $\tau_{\rm p}\gtrsim\tau_{\rm GW}$. For this reason, we have truncated the region of interest in Fig. 4 to include low pulsar field systems with $\tau_{\rm p}\gtrsim 10$ Myr as inferred from the typical merging times of double neutron star binaries (Fig. 5). For high field pulsars, on the other hand, the constraints are independent of $\tau_{\rm p}$ (equation 2). After translating the condition that $R_{\rm s}\lesssim R_{\rm x}$ into a constraint on the pulsar $P$-$\dot{P}$ diagram, Fig. 4 shows that roughly half of all Milky Way double neutron star binaries fall outside the constraints. To get a sense for the likelihood that such systems are indeed representative, we have included in Fig. 4 the contours from the double neutron star binary population synthesis modeling of Osłowski et al. (2011). With the caveat that the uncertainties of population synthesis are significant, a sizable fraction of binaries lie within the excluded region and all of these systems are in the low field, long lived pulsar branch.

4. Discussion

It is clear from the above discussion that the uniform environment expected to surround double neutron star binaries at the time of merger can be altered if the system hosts a pulsar. The spin-down luminosity of the pulsar companion is expected to be carried away in a magnetized wind that expands into the surrounding medium, decelerating as it sweeps up ejecta from the interstellar medium, eventually forming a bow shock cavity. The onset of the afterglow can thus be noticeably delayed from the prompt emission if the size of the resultant cavity is larger than the shock deceleration length scale in the undisturbed interstellar medium. This condition is easily satisfied for high field pulsars $B\gtrsim 10^{13}$ G, irrespective of the spin-down age (equation 2). However, this is only valid under the assumption of no significant magnetic field decay. The processes regulating pulsar field decay are still highly debated, yet it is expected to occur on a timescale that is shorter then the lifetime of the system (Osłowski et al., 2011; Chashkina & Popov, 2012; Igoshev et al., 2014; Klus et al., 2014). If, as expected, magnetic field decay occurs, then the pulsar lifetime $\tau_{\rm p}$ becomes a key parameter, as younger pulsars are expected to produce more extended cavities at a given magnetic field strength.

If the magnetic field strength doesn’t change significantly with time, $L_{\rm p}$ can be written in terms of the pulsar’s age (equation 1) by assuming that its initial period $P_{0}$ was much shorter than the current period. From dipole radiation we know that

[TABLE]

Substituting this, along with $\tau_{\rm p}=P/\dot{P}$ for the spin down luminosity, into equation 4 we get

[TABLE]

where $P_{0,-1}=P_{0}/100{\rm ms}$. Now, from Tauris et al. (2017) we have a relation between the (birth) spin period and the orbital period of the binary

[TABLE]

which, in turn, relates to the gravitational merger timescale

[TABLE]

where we have assumed zero eccentricity, which provides a reasonable approximation for the merger time of most galactic double neutron star binaries.

Under this assumption, equation 11 reduces to

[TABLE]

This implies that the eventual delay between the afterglow and the prompt emission $\approx R_{s}/(2c\Gamma^{2})$ depends on the merging timescale, and, as such, offers a direct observational test on the assembly properties of the progenitor system. These constraints are likely to be more stringent for mergers in which the jet axis is near the observer’s direction and the time delay between the prompt and afterglow emission is expected to be much shorter (equation 6).

Fig. 5 shows the distribution of orbital periods and eccentricities for the 17 double neutron star binary population in the Milky Way field, as well as B2127$+$11C, a dynamically assembled system (Grindlay et al., 2006; Lee et al., 2010) located in the globular cluster M15. Lines of constant merger time due to gravitational wave radiation are indicated in black; a sizable fraction of those have orbital periods too long for the systems to merge within a Hubble time due to gravitational wave radiation; only two DNSs are allowed by the constraints on $P$ and $\dot{P}$.111This is a relatively robust result. If, for example, the derived limit on the pre-merger luminosity was an order of magnitude less stringent (based on the uncertainties associated with $n_{\rm ext}$ and $V_{\rm k}$), only two additional systems will be allowed by the $P$ and $\dot{P}$ constraints. One of these is the unconfirmed double neutron star binary, J1906$+$0746, that hosts a young, un-recycled pulsar. Its companion could be a massive white dwarf, but is likely a recycled pulsar that is either too weak or beamed away from Earth (van Leeuwen et al., 2015). The other system that satisfies the $P$-$\dot{P}$ condition, the recently detected system J1913$+$1102 (Lazarus et al., 2016; Ferdman & PALFA Collaboration, 2018), provides a potential Milky Way analog of the progenitor of GW170817. Given the uncertainties in the afterglow modeling, we urge caution in the strict application of our results. For example, if the limit on the pre-merger wind luminosity given by equation 9 is reduced by a factor of 6 (well within the derived uncertainties in our estimation of the size of the cavity), the two pulsars with merging ages between 1 and 10 Gyrs in Fig. 5 will be able to satisfy the revised constraints in the $P$-$\dot{P}$ plane. The precise measurement of the time delay between the prompt and afterglow emission can thus help provide key constraints on the pre-merger history of the binary system

4.1. PSR J1913+1102: a Milky Way analog of the double neutron star progenitor of GW170817

Among the DNSs in the Milky Way, J1913$+$1102 is somewhat unique: whereas all other Galactic DNSs that will merge within a Hubble time have characteristic ages $<$0.5 Gyr, J1913$+$1102’s characteristic age is 2.7 Gyr, a delay time of similar order to the last star formation episode of NGC 4993 (Hjorth et al., 2017; Palmese et al., 2017; Im et al., 2017). Furthermore, its $P$ and $\dot{P}$ translate to $L\approx 5\times 10^{32}$erg s*-1* and $B\approx 2\times 10^{9}$G, characteristics that fit within the constraints we place here based on the $\approx$9 day delay between the arrival of the prompt emission and the onset of the afterglow. These constraints were derived assuming a peculiar velocity of 100 km s*-1*. A dispersion measure-derived distance combined with a proper motion measurement of J1913$+$1102 indicates it is moving with a tangential velocity of $\approx$400 km s*-1*; however without knowledge of the system’s radial velocity it is difficult to determine the velocity of J1913$+$1102 relative to the local standard of rest.

Despite this caveat, J1913$+$1102 produces one of the best Milky Way analogs currently available with which to compare to the progenitor of GW170817. Besides satisfying the total mass requirements (as most other Galactic neutron star binaries; Abbott et al., 2017a), J1913$+$1102 is a large mass ratio ($q\approx 1.35$) system, suggesting larger amount of tidal ejecta upon merger as estimated for GW170817 (Kilpatrick et al., 2017; Kasen et al., 2017). This analysis highlights the potential of the observational tool presented in this paper. Space- and ground-based observations over the coming years should allow us to uncover the detailed nature of these most remarkable binaries.

We are especially grateful to C. Holcomb and F. De Colle for extended collaboration and V. Kaspi and S. Ransom for discussions. We also thank the referee for many useful suggestions improving the exposition of this paper. We are indebted to the David and Lucile Packard Foundation, the Heising-Simons Foundation, the Danish National Research Foundation (DNRF132) and NSF (AST-1911206) for support.