Detecting and Locating Electromagnetic Counterparts to Gravitational Wave Sources Using Galactic Dust Scattering Halos

For the foreseeable future, it will be necessary to find electromagnetic emission from gravitational wave (GW) sources in order to fully exploit the unique power of gravitational wave observations for astrophysics and cosmology. If such counterparts can be identified, the redshifts of GW events can be determined; they can then be combined with absolute luminosity distances, using the GW sources as standard sirens. Determining the precise position of the events also breaks parameter degeneracies, and will provide insight into the nature and evolution of the progenitors, their relation to the host galaxies, and the nature of the electromagnetic emission.

The relatively poor angular localization capabilities of the current network of GW observatories complicates prompt searches for electromagnetic counterparts. Binary mergers involving a neutron star are expected and now known to produce both prompt and afterglow electromagnetic radiation (Abbott et al. 2017), but the more powerful binary black hole mergers have so far not been detected in electromagnetic radiation. There are several suggested mechanisms for producing an electromagnetic signal (e.g., Perna et al. 2016; de Mink & King 2017), which predict potentially detectable radiation over a range of wavelengths, on a variety of timescales.

Here, we explore a technique that allows a search for X-ray emission, which provides a "respite" of order a day, even if any prompt emission went undetected. X-rays will be scattered by Galactic dust particles, incurring travel-time delays of several hours up to about a day. The resulting time-variable scattering halo has a highly distinctive brightness pattern and a predictable time evolution. Its center can be determined with a precision in the arcsecond range, depending on the number of scattered photons detected. We briefly describe the X-ray scattering mechanism, its manifestation in the Galactic context, a search strategy, and some brief remarks on archive searches for "orphan" halos. Such orphans of course do not have GW data, but, if detected, they may teach us about detectable event rates and suggest optimum search strategies.

X-ray wavelengths are much smaller than the characteristic size of astrophysical dust grains, and since the (real part of the) index of refraction of the dust material (silicates, carbon compounds) in the X-ray band is very close to unity, the interaction of the radiation with the grains can be described by simple Fraunhofer diffraction (Overbeck 1965; Hayakawa 1970; Martin 1970). Characteristic scattering angles are therefore of order $\theta \sim \lambda /a=4.3{(a/1\mu {\rm{m}})}^{-1}{(E/1\mathrm{keV})}^{-1}$ arcmin (with a the particle diameter and E the photon energy). If a flash of X-rays from a source at large extragalactic distance strikes a layer of scattering particles in the Galaxy, at a distance d from the observer, a circular annulus-shaped halo of scattered photons will appear; the halo slowly expands with time. Photons scattered through an angle θ arrive with a delay $t\,={(d/2c){\theta }^{2}=7000(d/100\mathrm{pc})(\theta /4^{\prime} )}^{2}$ s after the prompt flash. Such halos are indeed seen around variable Galactic sources (examples are Cygnus X-3, Predehl et al. 2000; Nova Cygni 1992, Draine & Tan 2003; Circinus X-1, Heinz et al. 2015; V404 Cygni, Beardmore et al. 2016; Heinz et al. 2016), around the locations of gamma-ray bursts (GRBs 031203, Vaughan et al. 2004; 050724, Vaughan et al. 2006; 050713A, Tiengo & Mereghetti 2006; 061019, 070129, Vianello et al. 2007; 160623A, Pintore et al. 2017), and around soft-gamma-ray repeater SGR J1550–5418 (Halpern 2009). It is worth pointing out that a scattering halo from any intergalactic dust will be unobservably faint; the total number of scattered photons will be spread over a range of delay times of order $t={(D/2c){\theta }^{2}\approx 900(D/400\mathrm{Mpc})(\theta /4^{\prime} )}^{2}$ yr (Corrales 2015). X-rays scattered by dust in the host galaxy will arrive as an apparent point-source afterglow, with essentially no spatial extent.

Dust also scatters longer wavelength light, and one could search for scattering halos at UV and optical wavelengths. The difficulty will be that while the scattering cross sections in UV and optical are higher than in X-rays, the scattering angles are much larger, and the halo will be spread out over a large area. Thus, even at early times, the surface brightness of UV or optical light scattered by Galactic dust will be very low, too low in fact to be detectable.

We estimate the expected number of scattered photons. The total energy release in gravitational waves in GW150914 was about 3 M_⊙c². If a fraction were to emerge in X-rays, then the photon fluence Φ would be, assuming a luminosity distance of 400 Mpc and an average or characteristic photon energy of 1 keV, ${\rm{\Phi }}\approx 1700{\epsilon }_{-5}{(D/400\mathrm{Mpc})}^{-2}$ photons cm⁻², where ${\epsilon }_{-5}\,\equiv \epsilon /{10}^{-5}$. First, we briefly consider the chances that the direct emission would be missed. For the energy release and distance just quoted, the fluence would be 2.3 × 10⁻⁶ erg cm⁻², which, if the energy came out in gamma-rays, places it in the range of the median for gamma-ray bursts. We now know that neutron star–neutron star mergers in fact give rise to (short) gamma-ray bursts, but if black hole–black hole (BH–BH) mergers do not give rise to gamma-ray emission, gamma-ray monitoring experiments will of course miss them; and none have been seen in fact. Perhaps more to the point in the present context is the possibility that an all-sky X-ray monitor will see the primary event. The one such monitor in current operation is the MAXI experiment (Matsuoka et al. 2009). The detection limit in this experiment, in 5 ks exposure, is 7 × 10⁻¹⁰ erg cm⁻² s⁻¹ in the 2–30 keV band, or a fluence of 3.5 × 10⁻⁶ erg cm⁻². MAXI may well miss such an event. Likewise, Swift/BAT will miss the prompt events as bright as ₋₅ = 1 if they are relatively soft or of relatively long duration.

Galactic interstellar dust has average grain sizes a of a few tenths of a micron, and mass density ∼1/100 of the gas mass density (Draine 2011). The average number density of the interstellar medium is about 1 H atom cm⁻³, so the grain number density is ${n}_{d}=1.3\times {10}^{-12}{(a/0.1\mu {\rm{m}})}^{-3}{(\rho /3{\rm{g}}{\mathrm{cm}}^{-3})}^{-1}$ cm⁻³; ρ is the mass density of the grain material. Using an integrated scattering cross section $\sigma =6.3\times {10}^{-11}{(\rho /3{\rm{g}}{\mathrm{cm}}^{-3})}^{2}{(a/0.1\mu {\rm{m}})}^{4}{E}_{\mathrm{keV}}^{-2}$ cm² (Mauche & Gorenstein 1986; we suppress a weak dependence on the nuclear charge-to-mass ratio of the dust material), we estimate a characteristic scattering optical depth of ${\tau }_{d}\approx 2.5\,\times {10}^{-2}(a/0.1\,\mu {\rm{m}})(\rho /3\,{\rm{g}}\,{\mathrm{cm}}^{-3}){E}_{\mathrm{keV}}^{-2}(d/100\,\mathrm{pc})$ for a path length of 100 pc. The fraction of scattered photons is equal to τ_d at these small optical depths, so the number of photons in a scattering halo, per unit collecting area of the X-ray telescope, will be ${N}_{\mathrm{halo}}\sim 45{\epsilon }_{-5}(a/0.1\,\mu {\rm{m}})(\rho /3\,{\rm{g}}\,{\mathrm{cm}}^{-3}){E}_{\mathrm{keV}}^{-2}$ cm⁻², for a source distance of 400 Mpc and a dust path length of 100 pc. A significant fraction of the sky has higher dust column density and therefore a larger number of scattered photons for a given assumed value of ; for instance, approximately 10% of the sky has a foreground neutral H column density of N_H ≥ 10²² cm⁻². In general, however, these higher column densities are found at lower Galactic latitude, where the foreground emission from the Galaxy and its halo may also be higher. A more detailed evaluation of the expected number of photons for random source positions in the sky is outside the scope of this paper.

The Rayleigh–Gans approximation (phase shift across scatterer small, λ/a small) is convenient for rough analytical estimates of the cross section. In that case, the differential scattering cross section has an approximately Gaussian shape, $d\sigma /d{\rm{\Omega }}\approx \mathrm{constant}\,\times \,\exp {(-{\theta }^{2}/2{\theta }_{0})}^{2}$ cm² sr⁻¹, with ${\theta }_{0}\,=10.4{E}_{\mathrm{keV}}^{-1}{(a/0.1\mu {\rm{m}})}^{-1}$ arcmin (Mauche & Gorenstein 1986). This allows us to roughly calculate how the photons will be spread out in time. For convenience, first place the scattering dust in a single screen at a distance d. Then half the scattered light will be within an angle ${\theta }_{1/2}={(2\mathrm{ln}2)}^{1/2}{\theta }_{0}$, which corresponds to a time delay ${t}_{1/2}=(1/2)(d/c){\theta }_{1/2}^{2}$ $=\,6.6\,\times {10}^{4}{(d/100\mathrm{pc})(a/0.1\mu {\rm{m}})}^{-2}{(E/1\mathrm{keV})}^{-2}$ s, so half the light arrives within about a day.

More generally, at any given time delay, light arriving at the observer will have been scattered from material located on a paraboloid of revolution, with the axis of the paraboloid pointing at the light source, and the focus located at the observer (assuming the source to be located at infinity; Tylenda 2004). The exact shape and time evolution of the scattering halo will depend on the intersection of the paraboloid with the interstellar medium, and its distribution of dust, and average dust grain properties, close to the line of sight through the Galaxy.

Note that, in general, the halo from a thin layer of dust tilted with respect to the plane of the sky will be circular, but with a center that is offset from the direction to the source, and will be moving in the sky. If the tilt angle of the layer is α, then the physical offset of the center of the halo is equal to x = act, with $a=\tan \alpha$. Since scattering angles in X-rays are very small, most of the scattering seen comes from distant dust, and the angular offset of the center of the scattering halo is consequently small, of order $act/d\sim 2{(t/1{\rm{day}})(d/100{\rm{pc}})}^{-1}$ arcsec.

Sources located at lower Galactic latitudes will on average have larger dust columns, therefore potentially producing brighter halos with longer time delays. Dust distributed in "screen"-like overdensities along the line of sight will produce distinctly separate halos, and small-scale (≲1 pc) spatial inhomogeneities will produce incomplete annular shapes. However, the fundamental underlying topology of the X-ray scattering halo remains (nearly) circular, precisely or very closely centered on the location of the source.

The ultimate limit to detection of low-surface-brightness light is the level of (apparently) diffuse background in the images. We assume an experiment whose background is limited by the astrophysical X-ray background, with negligible contribution from intrinsic and cosmic-ray-induced detector noise. In the band around 1 keV and below, the astrophysical background is dominated by diffuse Galactic and circumgalactic line emission from hot gas (${T}_{e}\sim {10}^{6}\,{\rm{K}}$), as well as individual photons contributed by faint point sources. The soft X-ray background level and spectrum are highly variable as a function of position (Snowden et al. 1997). Since we will be considering relatively short exposures in random directions, using as wide an energy band as is useful, we may consider the average low-angular-resolution, low-spectral-resolution background intensity, ${I}_{E}\,\approx 10{(E/1\mathrm{keV})}^{-1.4}$ photons cm⁻² s⁻¹ keV⁻¹ sr⁻¹, as given by McCammon & Sanders (1990) as representative. This corresponds to 1.2 × 10⁻⁶ photons cm⁻² s⁻¹ arcmin⁻² in the band 0.5–2 keV. An annulus of radius 10' (delay time of order half a day) and width 01 (corresponding to an exposure time of 1000 s at delay time half a day) will have 8 × 10⁻³ photons cm⁻² (photons per unit telescope effective area) in background intensity, much below the reference halo intensity we have been discussing.

Determining the centroid position of a structure of linear (or angular) extent L with N detected photons has an uncertainty of roughly $L/\sqrt{N}$. In our case, L will be on scales from 0.1 to a few arcminutes, depending on whether scattering dust is mostly located in a single layer at a distance of order 100 pc or distributed more homogeneously (see Section 3), respectively. For any reasonable detection, the positional uncertainty in the location of the source is therefore likely to be of order 1''–10''.

The highest surface density of possible host galaxies results from assuming a detection volume corresponding to detection of massive BH–BH binaries. Chen & Holz (2016) estimate that the detection volume for 30 M_⊙–30 M_⊙ BH–BH binaries with the design sensitivity for the combination of LIGO and VIRGO has a radius of approximately 1.5 Gpc (assuming no further constraints on distance or position in the sky). Assuming a density of galaxies of 10⁻² Mpc⁻³, this results in an average separation between galaxies of 35''. The localization of the scattering halo centroid will therefore point to a unique host galaxy most of the time.

If the coalescence of two black holes is accompanied by a prompt burst of X-rays, of a brightness that corresponds to a conversion efficiency of order $\epsilon \sim {10}^{-5}$, then the prompt flare is of course easily detectable with current X-ray instrumentation for any event currently detectable in gravitational waves (but see our discussion of the MAXI instrument for the limitations of current all-sky monitors). But should the emission subside rapidly, the chances of finding it become small, given the large uncertainty of the GW localization. Precise localization may still be achieved in principle with a suite of observatories, starting with an all-sky γ-ray or hard X-ray monitor, and rapidly pointing telescopes of smaller field and higher angular resolution. This approach works for the localization of gamma-ray bursts, and therefore works for GW events that are accompanied by a gamma-ray burst, as was demonstrated by GW170817.

In the case of rapidly fading emission, we will instead be searching for extended scattering halos, which suggests very different search strategies and techniques. An X-ray scattering halo will linger for about a day. GW detections currently have a positional uncertainty of the order of hundreds of square degrees. The considerations given above suggest surveying this area within about a day. An optimum X-ray telescope would have of course as large a field of view as possible, with angular resolution a fraction of an arcminute. In practice, a field of about a square degree is probably the largest achievable while maintaining sensitivity up to photon energies of a few keV. Each of the fields would then be exposed for about 1000 s. An instrument with effective area of order 100 cm² would yield a total of roughly $4500{\epsilon }_{-5}(a/0.1\,\mu {\rm{m}})(\rho /3\,{\rm{g}}\,{\mathrm{cm}}^{-3}){E}_{\mathrm{keV}}^{-2}$ counts in a scattering halo, for a source at 400 Mpc and a Galactic dust layer 100 pc thick. Since the halo dims rapidly, an optimum strategy may be to take brief exposures and rapidly cover the search area multiple times. The X-ray instrumentation on Swift (specifically, the X-Ray Telescope, XRT; Burrows et al. 2005) is close enough to these parameters that a survey could be attempted.

To visualize what the scattering halo might look like, we simulate a Swift XRT field. Figure 1 shows an archival Swift 1311 s exposure taken with the XRT on 2012 July 12 (obsid 00046605002), centered approximately on (J2000) α = 09^h21^m30^s, δ = −26°18'30'' (Galactic (l, b) = (255.07, 16.84)), targeting the source PLCKERC 030G255.08+16.45 (seen near the center of the field). We chose this field randomly from a set of exposures located in an X-ray dark region of the sky, as determined from the ROSAT All-Sky Survey maps of the Galaxy (Snowden et al. 1997; the 3/4 keV maps). The field of view is approximately circular, with a radius of 1235. The image contains 260 counts, of which 26 are in the central point source. The observed background surface brightness is roughly consistent with the estimate given in Section 2. The Galactic neutral hydrogen column density along this line of sight is N_H = 8.7 × 10²⁰ cm⁻², a factor of a few larger than the average value we used in the feasibility discussion in Section 2.

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To this image, we added simulated scattering halos. We simulated halos for two different extreme cases. In the first, we assume that the dust is located in a single scattering screen at a distance d, oriented perpendicularly to the line of sight. In this case, at any time we see light scattered through a single angle, and this angle increases slowly with time. The width of the annular halo is determined by the length of the exposure time. We assumed an annular halo of radius 7' (corresponding to a delay time of 6 hr on dust located at a distance of 100 pc) and width 021, corresponding to an exposure time of 1300 s. The halo contains 60 photons, corresponding to ₋₅ = 1, for the effective area of the XRT and an exposure time of 1300 s. The center of the annulus is at approximately α = 09^h21^m05^s, δ = −26°15'00''. Vignetting in the telescope has not been taken into account. The finite angular resolution of the telescope has approximately been taken into account by widening the annulus to 03 (the half-power diameter of the telescope point-spread function). This halo is shown in Figure 1.

In the second case, we assumed uniformly distributed dust out to a distance of 100 pc. In this case, at any given time the entire paraboloid-shaped "iso-delay surface" lights up, producing scattered light seen at angles starting at the angle corresponding to the most distant dust on the paraboloid, and increasing outward. The contribution from each patch of dust is weighted with the differential scattering cross section, for which we assume the Gaussian distribution discussed in Section 2. We assumed a Gaussian width of θ₀ = 5', corresponding to grain size a = 0.2 μm (at photon energy E = 1 keV), and 1300 s exposure at 6 hr after the flash. The halo contains 300 photons, corresponding to ₋₅ = 5. In this case, the apparent extent of the halo is dominated by the angular width of the scattering cross section, not the range of delay times. The appearance of the scattered X-rays is that of a "hollow" halo. This halo is shown in Figure 2.

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Given the average background in the image, we expect the annular halo area in Figure 1 to contain 6.5 background counts. Phrased in terms of naive counting statistics, the 60 scattered photons correspond to a ∼24σ excess over the expected background, yet the halo, while discernible, is not immediately obvious under visual inspection. The extended halo produced by uniformly distributed dust, shown in Figure 2, has approximately 150 photons in its inner part (radii between 7' and 9'). That area has an expected background count of 49, so the 150 photons constitute a 21σ excess. Again, the halo is visible but would probably easily be missed if it were slightly less bright or somewhat less compact. For this second simulation, we assumed ₋₅ = 5, probably unrealistically high. We used a high value, increasing to the point where it made a faint halo visible in the image, just to underscore the need for unorthodox (for high-energy astrophysics) data analysis techniques. At the nominal value of  = 10⁻⁵, the halo would have been marginally significant: 30 photons in an annulus between 7' and 9', which would have 49 background photons, or a 4.3σ excursion, in naive terms. But the halo would be indiscernible in the image.

From these considerations, it does appear that, in order to attain the highest sensitivity, a sophisticated image analysis procedure should be employed, based on the fact that halo photons should occupy full or partial, narrow or wide, but still perfectly circular annuli.

A systematic search was in fact conducted with Swift starting 53.5 hr after the arrival of the gravitational signal of GW150914 (Evans et al. 2016a), including a raster of the LMC. By this time, the radius of the halo would have been $21{(d/100\mathrm{pc})}^{-1/2}$ arcmin and growing. Likewise, a search was performed starting 39.0 hr after GW151226 (Evans et al. 2016b), 13.9 hr after GW170104 (Evans et al. 2017b), 17.5 hr after GW170608 (Evans et al. 2017c), and 8.6 hr after GW170814 (Evans et al. 2017d). No possible counterpart point source was found in any of these searches.

Of course, in the case of GW170817, the source location is known, which removes a major uncertainty from the halo search. Swift obtained two early XRT data sets, at t₀ + 53,802 s (for 1986 s exposure) and at t₀ + 85,758 s (for 1988 s exposure) (Evans et al. 2017a); t₀ is the arrival time of the gravitational wave signal. The foreground Galactic column density of neutral H in this line of sight is N_H = 7.6 × 10²⁰ cm⁻², a few times the reference value we used in the feasibility discussion. At these times, a scattering halo from a single dust screen at d = 100 pc would have had a radius of θ = 11.3(d/100 pc)^1/2 arcmin and θ = 14.0(d/100 pc)^1/2 arcmin, respectively, with widths of approximately 02. About half of the annulus is in, but at the edge of, the field in the first observation. It would not have been in the field of the second observation. We conducted an informal visual search for a scattering halo, but did not find an obvious signal. This finding is probably inconclusive, since the pointing of the telescope was not optimal. In the context of the properties of the population of GRBs with detected afterglows, the flux limits for GRB 170817 are in the lower quartile of the X-ray flux distribution (Evans et al. 2017a), and the resulting prediction for the brightness of a scattering halo is only of order one or two counts.

We also conducted an informal prompt visual search for a halo of the Swift images for GW150914 and GW151226, but found none. In view of the unusual characteristics of the halos, we cannot quantify this non-detection in terms of surface brightness or source luminosity at this time.

Finally, the question naturally arises whether scattering halos may accidentally have been preserved in all-sky surveys. Those detections of course would not have gravitational wave counterparts, but they may tell us about event rates and suggest detection methods. The only sensitive imaging all-sky survey in X-rays was the ROSAT All-Sky Survey (1990/1991; Voges et al. 1999). If currently detectable gravitational wave events occur at a rate of ∼r per year, then, since ROSAT surveyed approximately 720 deg² per day, for a consecutive period of 180 days, the probability that it caught a scattering halo is very roughly p = (r/365) × (720/4 × 10⁴) per day. The probability that the survey contains at least one halo is then equal to $1-{(1-p)}^{180}\approx 180p$ $=\,4.9\,\times {10}^{-5}\times 180\times r=0.036$ for r = 4 yr⁻¹ (this same argument applied to the much more frequent gamma-ray bursts suggests that there must be a few GRB afterglow halos in the survey). Despite their much longer lifetimes, the Chandra and XMM-Newton observatories may be less likely to have caught an orphan halo, since they spend most of their observing time pointed at small areas on the sky. Instead of surveying 720 deg² in a day, XMM-Newton typically observes one or two fields, of order 0.25 deg², in a day. Even though it has been conducting observations for a time period 40 times longer than the ROSAT All-Sky Survey, the probability of it having covered an "orphan" GW halo is approximately 5 × 10⁻⁴; the corresponding figure for Chandra is smaller since its field of view is smaller. This argument is of course based on the crude assumption that the detection probability is unity for any overlap of a halo with a survey field, and does not take flux or surface brightness sensitivity into account. Due to larger collecting areas and longer exposure times, the large observatories have an advantage in detecting fainter halos that may not show up in the ROSAT All-Sky Survey—or indeed in the recently begun eROSITA All Sky Survey (Predehl 2017). A proper evaluation of the potential of the Chandra and XMM-Newton archives therefore requires making fairly detailed assumptions for the luminosity function of the X-ray emission, among others, and is outside the scope of the present paper.

We have suggested a technique for locating electromagnetic counterparts to gravitational wave sources that addresses the limited intrinsic localization capability of current networks of gravitational wave observatories, and the potential delay in alerts. Any X-ray emission associated with the event, if sufficiently bright, will leave a time-dependent echo of X-rays scattered by dust in our Galaxy, which will be visible even if the prompt event was missed. The characteristic light travel-time delays through the Galaxy will be of order hours to a day. The halo's intrinsic geometry is circular, with the center of the halo located at, or within a few arcseconds of, the source of the radiation. Localization to ∼1''–10'' is likely. The density of candidate host galaxies on the sky is such that this is sufficient accuracy to allow for unique identification. The expected surface brightness is of course directly dependent on the source luminosity, which is a matter of speculation, but mechanisms have been suggested that imply radiative efficiencies that would put the predicted brightness into the range of detectability with current X-ray instrumentation.

We thank Slavko Bogdanov, Eric Gotthelf, Kohtaro Yamakawa, Terri Brandt, Szabi Marka, and the students in the Introduction to Astrophysics I class for helpful discussions. We thank our anonymous referee for a critical reading and very helpful comments that improved the manuscript.

This research has made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory.