A COMPREHENSIVE STUDY OF DETECTABILITY AND CONTAMINATION IN DEEP RAPID OPTICAL SEARCHES FOR GRAVITATIONAL WAVE COUNTERPARTS

As discussed in Section 1, the merger of NS–NS or NS–BH binaries is expected to produce a faint, rapidly evolving optical/NIR transient powered by the radioactive decay of r-process elements formed in the ejecta. From a wide range of simulations it has been shown that the ejecta have a typical mass range of M_ej ∼ 10⁻³–10⁻¹ M_⊙ with velocities of β_ej ∼ 0.1–0.3, which depend on the initial mass asymmetry in the binary (Rosswog et al. 1999, 2013; Rosswog 2005; Bauswein et al. 2013a). The ejecta are expected to be neutron-rich, with typical electron fractions of Y_e ≲ 0.1 (Metzger et al. 2010).

A critical property for understanding kilonova emission is the opacity, because the ability of photons to diffuse through the ejecta determines the timescale, peak luminosity, and the spectral energy distribution of the transient. Metzger et al. (2010), using the models of Li & Paczyński (1998, LP98 hereafter), found that a typical Fe-peak element opacity (κ ∼ 0.1 cm² g⁻¹ for λ ∼ 0.3–1 μm) leads to a peak time of t_p ∼ 1 day, with a bolometric peak luminosity of L_p ∼ 10⁴¹ erg s⁻¹, and a photospheric temperature of T_p ≈ 10⁴ K (i.e., a peak in the UV). However, subsequent work by Kasen et al. (2013) and Barnes & Kasen (2013) found that r-process materials have much larger opacities with κ ∼ 10–100 cm² g⁻¹ for λ ∼ 0.3–3 μm. This leads to a transient that is longer-lived (t_p ∼ days), fainter (L_p ∼ 10⁴⁰ erg s⁻¹), and much redder (T_p ≈ 3000 K, e.g., a peak in the NIR). These results have been confirmed in simulations by other groups (e.g., Tanaka & Hotokezaka 2013; Grossman et al. 2014; Tanaka et al. 2014). A discussion of the effects of modifications to the standard kilonovae models on our results can be found in Appendix B.

In this work, we construct kilonova light curves using the time-resolved spectra of Barnes & Kasen (2013). They consider a grid of models with M_ej = 10⁻³, 10⁻², and 10⁻¹ M_⊙ and with β_ej = 0.1, 0.2, and 0.3. Unless otherwise noted we only consider the average ejecta properties of M_ej = 10⁻² M_⊙ and β_ej = 0.2 since we do not know the distribution of ejecta properties a priori. We compute light curves using the DECam filter transmission curves^{2 ,3} with the luminosity L_ϕ, through a filter ϕ, at a time t, being given by

$$\begin{eqnarray}&&{L}_{\phi }(t)=\displaystyle \frac{\int d\lambda {L}_{\lambda }(t,\lambda )\phi (\lambda )}{\int d\lambda \phi (\lambda )}\end{eqnarray} \tag{ 1 }$$

where L_λ(t, λ) is the model-specific luminosity and ϕ(λ) is the filter transmission as a function of wavelength. A representative plot of the spectra at 1 day and 1 week, along with the resulting r-, i-, and z-band light curves is shown in Figure 1.

Zoom In Zoom Out Reset image size

The tidal disruption of a WD by a NS or BH binary companion can produce an isotropic optical transient powered by the radioactive decay of ⁵⁶Ni synthesized in the ejecta. The ejecta have an expected mass of M_ej ≈ 0.3–1.0 M_⊙, velocity v_ej ≈ (1–5) × 10⁴ km s⁻¹, and ⁵⁶Ni mass of ${M}_{{56}_{\mathrm{Ni}}}$ ≈ 10^−4.5–10^−2.5 M_⊙ (Metzger 2012). These properties are primarily determined by the mass of the WD, with more massive progenitors producing higher ejecta mass, velocities, and ⁵⁶Ni masses. The resulting light curves have a typical peak timescale of t_p ∼ week and a peak bolometric luminosity of L_p ∼ 10³⁹–10^41.5 erg s⁻¹.

The two scenarios we consider here are the mergers of (1) a 0.6 M_⊙ C–O WD with a 1.4 M_⊙ NS and (2) a 1.2 M_⊙ O–Ne WD with a 3 M_⊙ BH. The models of Metzger (2012) only include bolometric light curves. To produce i- and z-band light curves we compute an effective temperature using the LP98 models with M_ej ≈ 0.5 M_⊙ and v_ej ≈ 2.8 × 10⁴ km s⁻¹ for scenario 1, and M_ej ≈ 1 M_⊙ and v_ej ≈ 4.6 × 10⁴ km s⁻¹ for scenario 2 (see Figure 7 of Metzger 2012). We integrate the resulting blackbody curve over the DECam filters using Equation (1) and compare to the bolometric luminosity to generate bolometric corrections. For the WD–NS merger, we find T_p ≈ 6000 K leading to ${m}_{\mathrm{bol}}-{m}_{{\rm{i}}}\approx -1.9$ mag and ${m}_{\mathrm{bol}}-{m}_{z}\approx -2.2$ mag. The WD–BH merger calculation yields T_p ≈ 7850 K leading to ${m}_{\mathrm{bol}}-{m}_{{\rm{i}}}\approx -2.2$ mag and ${m}_{\mathrm{bol}}-{m}_{z}\approx -2.6$ mag. We assume that these corrections are constant in time. The bolometric corrections are applied to the light curves of Metzger (2012) to generate the light curves used in this analysis (see Figure 2).

Zoom In Zoom Out Reset image size

The accretion of material onto an O–Ne WD near the Chandrasekhar mass can cause the degenerate star to undergo electron capture in its interior, resulting in the formation of a NS, rather than a thermonuclear explosion. This process is known as AIC. If the WD is rapidly rotating then a stable accretion disk will form. The disk will cool and become radiatively inefficient, driving powerful outflows with a characteristic ejecta mass of M_ej ∼ 10⁻² M_⊙ and velocity β_ej ∼ 0.1. The outflowing material has an electron fraction of Y_e ∼ 0.5 due to neutrino radiation from the proto-NS and synthesizes a few × 10⁻³ M_⊙ of ⁵⁶Ni powering an optical transient (Metzger et al. 2009b). Radiative transfer calculations by Darbha et al. (2010), motivated by the models of Metzger et al. (2009b), provided light curves of AIC events. They found that the resulting transient is rapidly evolving, with the light curve peaking at t_p ∼ 1 day with a bolometric luminosity of L_p ∼ 2 × 10⁴¹ erg s⁻¹.

We use the models of Darbha et al. (2010) to compute i- and z-band light curves using the same methodology as in Section 2.2. The effective blackbody temperature has an assumed fiducial value of T_p ≈ 5800 K from the models of Dabhra et al. (2010, see their Figure 3). The resulting bolometric corrections are therefore ${m}_{\mathrm{bol}}-{m}_{{\rm{i}}}\approx -1.9$ mag and ${m}_{\mathrm{bol}}-{m}_{z}\approx -2.2$ mag. We assume that these corrections are constant in time and apply them to the bolometric light curves to generate i- and z-band light curves (Figure 2).

Detonation of a sufficiently large accreted He envelope (M_He ∼ 0.2 M_⊙) on the surface of a C–O WD can generate shock waves that then propagate to the core, leading to the total detonation of the WD. In simulations performed by Sim et al. (2012), two possible detonation scenarios were considered. The first, edge-lit double detonation (ELDD), occurs when the initial detonation takes place at the surface of the WD. This produces a transient that is expected to reach a peak bolometric luminosity of L_p ∼ 10⁴² erg s⁻¹ at t_p ∼ 8 days. The second scenario is the compression-shock double detonation (CSDD), where the core is compressed by the shock wave and C–O detonation occurs closer to the center of the WD. The transient is brighter than in the ELDD scenario with a peak bolometric luminosity of L_p ∼ 4 × 10⁴² erg s⁻¹ and a correspondingly longer rise time (t_p ≳ 10 days). In the CSDD scenario the transient is also longer-lived with no significant decline in brightness for ∼30 days.

The slow evolution of the CSDD model light curve relative to kilonovae means that it can be easily removed from consideration as a contaminant on the basis of timescales alone. However, we still consider the ELDD scenario because the more rapid rise time and comparably faster decline mean that it could serve as a potential contaminant. We make use of bolometric light curves from the simulations of Sim et al. (2012) to compute DECam i- and z-band light curves as in Section 2.2. The ELDD spectrum is approximated as a blackbody with a characteristic temperature of T_p ≈ 4800 K using the model spectra of Sim et al. (2012, see their Figure 7). The bolometric corrections are found to be ${m}_{\mathrm{bol}}-{m}_{{\rm{i}}}\approx -1.7$ mag and ${m}_{\mathrm{bol}}-{m}_{z}\approx -1.9$ mag. We assume that these corrections are constant in time and apply them to the bolometric light curves to generate i- and z-band light curves (Figure 2).

Another possible WD-based transient is the detonation of an outer shell of helium on the surface of the WD. This can occur when the mass accretion rate from the donor is low enough that burning in the He shell becomes thermally unstable. The specific term "type .Ia" was coined as a reference to He detonation in an AM Canum Venaticorum system (AM CVns) where the donor star is degenerate or semi-degenerate and accreting He-rich material onto a C–O or O–Ne WD (Bildsten et al. 2007; Shen et al. 2010). The typical envelope mass is M_env ∼ few × 10⁻²–10⁻¹ M_⊙ and the detonation ejects the bulk of the envelope at a typical velocity of v_ej ∼ 10⁴ km s⁻¹. This leads to a transient with a typical peak time of t_p ∼ 2–10 days and a peak bolometric luminosity of L_p ∼ 5 × 10⁴¹–5 × 10⁴² erg s⁻¹ (Shen et al. 2010).

We produce type .Ia light curves from the time-resolved spectra computed from the models of Shen et al. (2010). We consider the models 0.6 + 0.2 M_⊙, 0.6 + 0.3 M_⊙, 1.0 + 0.05 M_⊙, and 1.2 + 0.05 M_⊙, where the first number is the WD mass and the second number is the mass of the He envelope. We integrate the spectra over the DECam filter transmission curves as described in Section 2.1 (Figure 2).

Drout et al. (2014) discovered ten rapidly evolving transients in the Pan-STARRS1 Medium Deep Survey. These events are characterized by a time above half-maximum of less than 12 days and have typical absolute magnitudes of M ≈ −16.5 to −20 mag. These objects have blue colors with g − r ≲ −0.2 at peak (Drout et al. 2014). While the existing sample is small these events may end up being a significant contaminant in the fast-cadence, wide-field GW searches investigated here. Therefore, we consider the i- and z-band light curves of three objects from Drout et al. (2014): PS1-10ah, PS1-10bjp, and PS1-11qr. They possess sufficient pre-peak data for our analysis while providing a representative range of timescales and luminosities for the sample (Figure 2).

SNe Ia result from the thermonuclear explosion of a C–O WD. While these SNe have timescales much longer than those of kilonovae and other transients considered in this section, their high volumetric rate and large luminosity mean that a deep optical search for kilonovae will detect large numbers of SNe Ia. This makes them a particularly likely contaminant in such searches. We focus our analysis on the event SN2011fe discovered in M101 by the Palomar Transit Factory (Nugent et al. 2011a) due to the high quality of available data. In addition to being one of the closest known SNe Ia (μ = 29.04 ± 0.19, Shappee & Stanek 2011), SN2011fe was discovered a mere 12 hr after explosion (Nugent et al. 2011b), leading to coverage starting at −15 days relative to the B-band peak (Pereira et al. 2013). In this work, we use the 32 spectral observations compiled by Pereira et al. (2013) to produce DECam i- and z-band light curves as a function of redshift, including K-corrections, using the process described in Section 2.1 (Figure 2).

Classical novae (CNe) are close binary systems where a WD accretes hydrogen from a companion star that has filled its Roche lobe. If the accretion rate is sufficiently low then the hydrogen envelope on the WD will reach the critical temperature and density necessary to undergo thermonuclear runaway. The resulting energy deposition drives rapid expansion and mass loss in the surface layers of the unburnt hydrogen, powering the nova transient (Warner 2003). The typical luminosity of such an event is M_V ≈ −7.5 mag, but ∼1% of nova reach a peak luminosity of M_V ∼ −10 mag (Shafter et al. 2009). Despite their low luminosity compared to other transients considered in this work the high rate of CNe (∼35 yr⁻¹ per Milky Way/M31 type galaxy, Darnley et al. 2006; Shafter et al. 2011) means they could be a significant foreground contaminant.

In this analysis, we consider the event SN2010U as our fiducial CN. It is an unusually luminous (M_V ≈ −10 mag) and rapidly evolving (t_decline ≈ 3.5 days) CN discovered in NGC 4214 (Nakano & Kadota 2010; Czekala et al. 2013). We utilize the r-band light curve presented in Czekala et al. (2013) as it is well sampled and contains data points prior to maximum light. We model the spectrum of SN2010U as a blackbody with T_p ≈ 8000 K as per the spectral fits in Czekala et al. (2013). We integrate this spectrum over the DECam transmission filters to compute the r − i and r − z colors. We find r − i ≈ −0.43 mag and r − z ≈ −0.85 mag. We apply these colors to the r-band light curves from Czekala et al. (2013) to produce i- and z-band light curves (Figure 2).

Stellar flares, primarily from M dwarfs, are another potential contaminant in fast-cadence wide-field optical searches (Becker et al. 2004; Kulkarni & Rau 2006; Berger et al. 2013). These flares have characteristic timescales of minutes to hours (e.g., Berger et al. 2013) and temperature of T_p ∼ 10⁴ K, leading to an appearance as fast and blue transients. As a result, M-dwarf flares will only appear as a significant contaminant in kilonova searches that rely on single-epoch detection, primarily in g- and r-bands in which the kilonova timescale is shorter than in the redder bands. We return to this point in Section 6. The sky-projected M-dwarf flare rate at the depths relevant for kilonova searches is large, ∼10 deg⁻² day⁻¹ (Kulkarni & Rau 2006). On the other hand, as was demonstrated by Berger et al. (2013), deep observations in the i- and z-bands can easily reveal the underlying M dwarfs and hence reduce the potential for contamination from flares.

We also consider short-duration optical variability from AGNs. AGNs typically show strong variability on month- or year-long timescales, making AGN outbursts too long in duration to be confused with a kilonova. However, recent work has detected rare cases of day-long or shorter variability in the NIR. Genzel et al. (2003) observed an H-band flare in Sgr A* during which the source brightened by a factor of 5. This flare lasted ∼30 minutes, with a characteristic rise time of ∼2–5 minutes. Such short-timescale flares can be ruled out as kilonova contaminants by requiring a detection on more than a single night. Flares with longer durations are also unlikely to be significant contaminants. Totani et al. (2005) performed V- and i-band observations of six AGNs, selected on the basis of their variability, over a period of four days. They found typical variability of only ∼1%–5% above their host galaxy luminosity. More recent work by Ruan et al. (2012) studied the variability of a sample of Fermi-selected blazars. They found that these sources showed a typical rms variability of ∼0.6 mag on timescales of ∼10 days. Therefore, AGNs are unlikely to exhibit sufficiently large variability to be confused with a kilonova.

An additional important factor for understanding the impact of potential contaminants on fast-cadence, wide-field searches is their volumetric rates. We note that the rates for these types of objects are generally poorly understood due to the lack of strong observational constraints; the notable exceptions are SNe Ia and fast novae. The volumetric rates of potential contaminants are compiled in Table 1. No values are provided in the literature for the ELDD volumetric rate so we assign a fiducial value of 1% of the SN Ia rate, consistent with the other rapid transients in this study. The volumetric rate for SNe Ia is known to be a function of redshift, and we use an approximate average volumetric rate in redshift bins of Δz ∼ 0.25 out to z_max ∼ 0.75 (Li et al. 2011; Perrett et al. 2012; Graur et al. 2014 and references therein). These rates are listed in Table 2.

Table 1.  Expected Rates for Fast Transients

Object	${{\mathcal{R}}}_{{\rm{vol}}}$	zmax	${{\mathcal{R}}}_{{\rm{area}}}$	N	References
	(Mpc−3 yr−1)		(deg−2 yr−1)
Type .Ia	10−6	0.5	0.7	1.4	Bildsten et al. (2007)
WD–NS mergers	10−5	0.06	2 × 10−2	3 × 10−2	Thompson et al. (2009)
WD–BH mergers	10−5	0.06	2 × 10−2	3 × 10−2	Fryer et al. (1999)
AIC	10−6	0.06	2 × 10−3	3 × 10−3	Darbha et al. (2010)
ELDD	3 × 10−7	0.14	6 × 10−3	1 × 10−2	⋯
Pan-STARRS fast	5 × 10−6	0.5	3.5	7	Drout et al. (2014)
Fast CNe	3.5 × 10−4	0.009	2 × 10−3	4 × 10−3	Darnley et al. (2006)

Note. Expected rates for the various contaminants considered in Section 2. ${{\mathcal{R}}}_{{\rm{area}}}$ is computed assuming an isotropic distribution of sources in a volume defined by the comoving volume at z_max. The column N refers to the number of events expected during a search covering 100 deg² for 7 days. See Section 2.11 for details.

Download table as:  ASCIITypeset image

Table 2.  Expected Rates for Type Ia SNe

Redshift	${{\mathcal{R}}}_{{\rm{vol}}}$	${{\mathcal{R}}}_{{\rm{area}}}$	N
	(Mpc−3 yr−1)	(deg−2 yr−1)
0–0.25	3 × 10−5	3.5	21
0.25–0.50	4 × 10−5	25	153
0.50–0.75	5 × 10−5	65	394

Note. Expected rates for type Ia SNe in redshift bins of Δz = 0.25 out to z_max = 0.75. See Section 2.11, Graur et al. (2014), and references therein.

Download table as:  ASCIITypeset image

To estimate the expected number of events observed during a GW optical follow-up search we compute the number of sources per square degree per year. This is done by determining the maximum redshift to which the object can be observed to a limiting magnitude of z ≈ 23 mag (see Sections 2.1 and 4.1). This rate is then multiplied by the search area (A ∼ 100 deg²) and duration to get the number of expected sources for our observations. We compute the duration by assuming that a kilonova will be detected within approximately one day of the GW trigger. Therefore, we do not consider events that begin more than +2 days into the search. However, we do consider sources that begin up to twice their characteristic timescale (∼5 days for rapid transients and ∼20 days for SNe Ia) prior to the GW trigger, as they may remain visible when the search begins. The total duration is then 7 days for rapid transients and 22 days for SNe Ia. The number of expected sources is given in Tables 1 and 2. SNe Ia dominate the number of expected events with N ∼ 568 when summing across all redshift bins. Of the population of fast transients, only type .Ia and the Pan-STARRS fast transients are expected to have N ≳ 1. Despite the low expected occurrence rate for other fast transients, we still consider these sources in this analysis due to the large uncertainty in their rates.

We first investigate the issue of kilonova detectability, as well as observation of the light curve during the rise to peak brightness. We explore four observing strategies utilizing ∼1 week of observations in both i- and z-bands with the following cadences:

• One visit per night for the duration of the search (i.e., N1, N2, N3, N4, N5, N6).
• One visit per night on the first two nights, followed by a visit every other night (i.e., N1, N2, N4, N6).
• Two visits ∼3 hr apart on the first night, followed by one visit per night for the duration of the search (i.e., N1, N1, N2, N3, N4, N5, N6).
• Two visits ∼3 hr apart on the first night, followed by a visit every other night (i.e., N1, N1, N3, N5).

These strategies are chosen to probe a range of timescales while representing differing levels of time investment, and possible loss of coverage due to adverse weather during follow-up observations. During the course of this analysis, we found that the results of Strategies 1 and 3 do not differ strongly from those of Strategies 2 and 4, indicating that the presence of intra-night observations on the first night is the most relevant factor. Therefore, we will only discuss the results of Strategies 1 and 3. Further discussion of Strategies 2 and 4 can be found in Appendix A.

For each observing strategy we establish a grid of start times following a GW trigger and a 5σ limiting magnitude. The range of grid values is t_start = 3–24 hr in steps of 3 hr and m_lim = 21–27 AB mag in steps of 1 AB mag. The range of start times represents the fact that a GW trigger may occur when the source is not readily visible in the night sky, while the range of limiting magnitudes covers the depths achievable by current and future wide-field instruments. At each point on this grid we conduct 50,000 simulated observations, with an observation comprising: (1) a kilonova with M_ej = 10⁻² M_⊙ and β_ej = 0.2 placed at a distance of up to 200 Mpc using a uniform volume distribution; (2) the light curve of the kilonova is computed for the chosen distance using the methodology outlined in Section 2.1; (3) the observation times are computed based on the chosen strategy; for example, if the start time is 12 hr and strategy 1 is chosen, then observations will be conducted at 0.5 day, 1.5 day, 2.5 day, and so on; and (4) the source flux in riz-bands of DECam filters is measured at the selected times using the light curves computed in step (2). If the kilonova brightness exceeds the search depth in at least three epochs, the event is flagged as a detection. If there is an observed increase in brightness between two epochs, the event is also flagged as "rising."

In Figure 4 we plot contours of the fraction of events detected for observing Strategies 1 and 3 in the riz-bands, as a function of survey depth and start time. The dashed lines represent the approximate 5σ limiting magnitudes of several wide-field telescopes assuming the appropriate number of pointings necessary to cover a ∼100 deg² error region with the required cadence.

Zoom In Zoom Out Reset image size

We find that the choice of observing strategy does not strongly impact the fraction of sources detected at a given depth. In particular, in r-band (Figure 4, left column) we find that for Strategy 1, the typical depth required to detect 50% of events is ≈25 mag, while a depth of ≈26 mag is required to detect 95% of events. This challenge is slightly alleviated by Strategy 3, which involves two observations on the first night. In this case, an early start time (≲6 hr) allows 50% (95%) of events to be detected at a depth of ≈24.3 (25) mag. Consequently, only Subaru HSC and LSST will be able to achieve the required depth for routine detections in r-band. The redder bands offer more favorable conditions, with the i-band 50% (95%) detection rate achieved at a depth of ≈23 (24) mag across both strategies. Lastly, we find that the z-band contours indicate that a depth of ≈22.2 (23) mag is required to achieve a 50% (95%) detection rate across both strategies. In these cases, DECam, Pan-STARRS2, and Subaru HSC can all achieve the required depths for routine detections in i- and z-bands. These values are summarized in Table 3.

While the particular choice of search strategy does not strongly impact the detection fraction at a given survey depth, the choice of strategy is important when trying to detect the brightening of a kilonova. We investigate this point in Figure 5, which shows contours for the fraction of events that are seen to brighten between any two epochs. These events must also meet the detection criterion utilized in Figure 4. As in Figure 4, the contours are plotted as a function of start time and search depth for each of the observing strategies and filters. In r-band, utilizing Strategy 1, a brightening phase is not detected even to a limiting magnitude of 27 mag. This is because the r-band light curve peaks in ≲1 day (Figure 1), necessitating a rapid early-time cadence to capture the event as it brightens. For Strategy 3, with two observations on the first night, brightening can be observed for 50% (95%) of events provided the observations reach a limiting magnitude of ≈24.3 (25) mag and begin within 8 (6) hr of the GW trigger.

Zoom In Zoom Out Reset image size

The detection of the light curve rise is more favorable in i- and z-bands. In general, the contours shown in Figure 5 are identical to those in Figure 4, but truncated as the start time becomes comparable to the peak time of the light curve. Therefore, brightening can be detected provided observations begin early enough and assuming the required depth is achieved. For i-band, with Strategy 1, we find that observations starting within 6 (8) hr of the GW trigger can detect brightening in 50% (95%) of events. With Strategy 3, the required start time for a detection rate of 50% (95%) extends out to 12 (14) hr. In z-band the observations can achieve detection rates of 50% (95%) provided they begin within 12 (15) hr of the GW trigger. The starting time can be extended to 18 (21) hr when Strategy 3 is utilized. The broader range of starting times allowed by Strategy 3 highlights the advantage of rapid follow-up of GW triggers. However, these initial simulations consider any observed brightening to be the detection of a rise. It may be the case that the actual change in brightness is not statistically significant, making a robust detection of a rise impossible.

We investigate the actual change in brightness relative to the instrument sensitivity using a modified version of our initial simulations. We no longer operate on the depth–start time grid, but instead consider a fiducial fixed depth of 24 AB mag in r- and i-bands and 23 AB mag in z-band (as appropriate for achieving an acceptable detection fraction). The start time is randomly selected using a uniform distribution ranging from 3 to 24 hr. The same observing strategies are employed and we run 50,000 iterations per strategy, utilizing the same procedure as before. We then compute the change in magnitude between the first two epochs (Δm₂₁ ≡ m₂ − m₁) and between the first and third epochs (Δm₃₁ ≡ m₃ − m₁). We employ the same detection criteria as in the previous simulations, requiring the source to be detected in at least three epochs. We consider sources that are observed to either rise or decline.

In Figure 6 we plot two-dimensional histograms of Δm₂₁ versus m₂ for observing Strategies 1 and 3 and each of the three filters. The resulting histogram is color-coded by the probability of a kilonova falling in that bin, with darker colors indicating a higher probability. We also compute the 2σ photometric error for an exposure time necessary to reach our chosen target depth in each filter using the DECam exposure calculator⁴ (hatched region). Sources that exhibit a change in magnitude that is smaller than this photometric error will not produce a statistically significant detection of a change in brightness. Figure 7 follows a similar construction, showing the two-dimensional histograms for Δm₃₁ versus m₃.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Using these results we determine the fraction of sources that do not exhibit a sufficient change in brightness to be identified as a transient after the second or third observation. We begin by considering the first row of Figures 6 and 7 (Strategy 1). Recall that for this strategy the time between the first and second epochs is ∼1 day. In this case, the rapid evolution of the r-band light curve means that there is always a detectable change in brightness, but the source will always be seen in decline. Furthermore, it is still the case that given the overall faintness of kilonovae in r-band, only ∼13% of sources will be detected at r ≈ 24 mag.

In i- and z-bands we find that ∼20%–40% of sources are missed due to an insufficient change in brightness. For Strategy 3, where the time between the first two observations is only ∼3 hr, over half of the sources (60%–70%) fail to exhibit a statistically detectable change in brightness. This indicates that the intra-night observations have a time baseline that is too short for detecting a change in brightness even for the fast kilonova timescale.

Figure 7 shows observations that are separated by a longer timescale (m₃ − m₁): for Strategy 1, the first and third epochs are separated by 2 days, while the same visits are separated by only 1 day for Strategy 3. For both strategies we find that r-band exhibits a sufficient change in brightness, with Δm₃₁ well outside the hatched region, but these sources are always observed to decline. As before, only ∼10%–20% of the sources are actually detectable at r ≈ 24 mag. In both i- and z-bands we find that it is possible to detect a change of brightness in a much higher fraction of sources compared to Δm₂₁. Strategy 1 shows that ∼15%–20% of sources will not show a sufficient change in brightness. The highest fraction of missed sources is ∼25%–40% for Strategy 3. This is expected given the short separation between epochs. Furthermore, while sources in r-band are only observed to decline, in i- and z-bands the rise can also be measured without requiring a ∼3 hr baseline. This further highlights the importance of having observations that are sufficiently separated in time to probe the kilonova light curve across a wide range of its evolution.

The rapid decline of ∼0.6–1.3 mag in r-band that is evident in Figures 6 and 7 hints at a possible detection strategy. Namely, the GW error region can be observed with a cadence of ∼1 day, with rapidly declining sources flagged. However, a depth of ≈26 mag is required for a high detection fraction even if we require only two detections (to separate kilonovae from stellar flares), so covering the large GW error region can only be achieved with LSST.

These detectability simulations indicate that using intra-night observations (Strategy 3) to detect the rise of the light curve is not an efficient use of time for follow-up observations since kilonovae generally do not exhibit a statistically significant change in brightness on this timescale. As shown in Figure 4, the choice of cadence does not drastically impact the likelihood of detection. Therefore, the most efficient solution, from a detectability standpoint, is Strategy 1. It provides a sufficient cadence to effectively detect kilonovae while maximizing the amount of area that can be covered in a single night. Observations should be carried out in i- and z-bands as the depths required to detect 95% of sources (≈24, 23 AB mag, respectively) are obtainable by existing and future facilities.

We now use our simulated observations to explore the contaminant population in the framework of the rise time–color–magnitude phase space outlined in Section 3. We accomplish this by repeating the simulations for each of the contaminants considered in Section 2. We then utilize the simulated observations to compute analogues to the rise time–color–magnitude phase space for both kilonovae and the contaminant population. In this manner we can produce a version of the phase space that takes into account a distribution of contaminants with realistically sampled light curves given the choice of cadence, depth, and start time appropriate to wide-field follow-up observations of a GW trigger.

We begin by employing the same four observing strategies as in the previous simulations. We again consider observations at a fixed depth of ≈24 AB mag in i-band and ≈23 AB mag in z-band, with the observations beginning 3–24 hr after the GW trigger. The simulations include 50,000 iterations, each consisting of: (1) a contaminant placed at a random, volume-weighted redshift. We consider contaminants at much larger distances than 200 Mpc to account for the fact that many contaminants are more luminous than kilonovae; the choice of z_max is indicated in Figure 8. (2) The contaminant light curve is randomly placed out of phase with respect to the start time of observations. We consider contaminants that occur approximately twice their characteristic timescale prior (5–20 days) and up to 2 days after the start of observations. The latter value is motivated by the results of the previous section in which we showed that kilonovae should be detectable within 1–2 days, and therefore, sources that first appear more than 2 days after the start of the observations can be rejected. Once the phase offset is determined the observation times are computed and the source brightness in i- and z-bands is computed at each epoch. (3) The observed peak of the z-band light curve is measured. (4) The i − z color is computed at the epoch where z-band attains its maximum value. (5) The rise time is defined as the time between the z-band peak and the first observation in which the source is detected. In cases where the source is only observed in decline, then the decline time is defined as the time between the first observation and the last observation in which the source is detected.

Zoom In Zoom Out Reset image size

In Figure 8 we plot the rise time–color slice of the three-dimensional phase space for each observing strategy. In addition to the nine kilonovae models, we consider four groups of sources with each given an equal contribution. The first group of contaminants is SNe Ia (Figure 8, leftmost column). The second group comprises the four type .Ia SNe models (Figure 8, second column). We form the third group from all of the low-luminosity, fast transients (i.e., AIC, WD–NS/BH mergers, ELDD, and CNe; Figure 8, third column). Lastly, the fourth group of contaminants contains the three Pan-STARRS fast transients (Figure 8, rightmost column).

To analyze the results, we first bin sources by their rise times, which fall in discrete values due to the cadence of the observations. For each rise time bin, we then bin the source populations by i − z color in equally spaced bins from −1.5 to +1.5 mag. For each bin, we compute the fraction of detected sources in that bin relative to the total number of detected sources.

As we showed in Section 3, kilonovae stand out from the contaminant population primarily on the basis of their redder colors, even when luminous contaminants are considered to higher redshifts (e.g., SNe Ia, Pan-STARRS fast transients). For all choices of observing strategy there is essentially no overlap in i − z color between the kilonova population and any of the contaminant populations. We note that across both observing strategies ∼12% of SNe Ia, ∼7% of type .Ia, and ∼8% of Pan-STARRS fast transients exhibit i − z ≳ 0, while none have i − z ≳ 0.4 mag. However, all kilonovae exhibit i − z ≳ 0.4 mag. These numbers are relative to the total number of events observed during the rise and do not include sources that are observed only in decline (see below). Consequently, i − z color remains a strong discriminant for separating kilonovae from the contaminant population.

So far we have neglected the potential effect of extinction in reddening the i − z colors of the contaminant sources. If the extinction is sufficiently large an intrinsically blue contaminant may be reddened into the regime of kilonova i − z colors. However, this extinction will also cause the source to appear dimmer and may therefore push it below the detection limit. To quantify the effects of extinction we use the Milky Way extinction curve with R_V = 3.1. Figure 8 indicates that a reddening of E(i − z) ≈ 1 mag is required to shift the contaminant population into the region of phase space occupied by kilonovae. This will result in an extinction of A_V ≈ 6.3 mag, A_i ≈ 3.9 mag, and A_z ≈ 2.9 mag. However, in our simulation nearly all (≳97%) of the contaminants that pass the detection cuts have m_z ≳ 20 mag meaning, that an extinction of 2.9 mag will dim these sources below our z-band detection limit of ≈23 mag. Thus, reddening due to dust extinction does not seem to be a concern.

We also consider the possibility of separating kilonovae by their rise time. In Figure 3, the entire set of kilonovae models showed generally shorter timescales relative to the contaminant population with rise times of ≲4 days. However, when the contaminants are placed out of phase with the GW trigger, and the observing cadence is taken into account, we find contaminants that present an apparent shorter rise time. This effect is the most prominent in the Pan-STARRS fast transients and miscellaneous fast transients, for which ∼55%–60% and ∼65%–75% of detected sources show a rise time of ≲4 days, respectively. We also find that ∼35%–45% of detected type .Ia SNe show a rise time that is ≲4 days. Lastly, for SNe Ia, ∼20%–25% of detected sources will present a rise time of ≲4 days. Thus, rise time alone is not a strong discriminant for separating kilonovae from the contaminant population.

In Section 3, we considered the peak z-band magnitude as the third data point in our phase space. However, in a magnitude-limited search, the population of contaminants will be dominated by events at the furthest distance to which they can be detected. Here we instead track the evolution of the source brightness by computing the difference in z-band magnitude between the source at the observed peak (m_z,peak) and the first observation in which it is detected (m_z,0), denoted as ${\rm{\Delta }}{m}_{z}\equiv {m}_{z,{\rm{peak}}}-{m}_{z,0}.$ We show the rise time-Δm_z slice of the three-dimensional phase space in Figure 9. The basic layout of the figure is identical to that of Figure 8, but sources are offset by ±5 hr to improve visibility.

Zoom In Zoom Out Reset image size

We find that kilonovae exhibit Δm_z ≈ −3.5–0 mag, where larger changes in brightness are associated with longer rise times. SNe Ia only exhibit values of Δm_z comparable to those of kilonova when the observed rise time is ∼6 days (the duration of our search), well beyond the range of observed rise times for kilonovae. When the rise time is ≲6 days, the average change in brightness is negligible (Δm_z ≈ 0.05 mag). This is because shorter rise times only occur near peak when the light curve evolution is slow. This slow evolution will make SNe Ia easy to reject relative to the much more rapidly evolving kilonovae. We note a small fraction of events with Δm_z ≈ −2 mag and rise times of 4–5 days. These account for ≲0.2% of detected SNe Ia and are the result of an event occurring in a range of redshifts where the set of spectral features that produce the second peak of SNe Ia appear in z-band. Thus, SNe Ia can be rejected based on Δm_z, rise time, and i − z color. For the other contaminant populations the separation is not as clean. This is not unexpected since rapid evolution was a strong consideration when constructing our list of potential contaminants. This highlights the critical importance of selecting kilonovae on the basis of their i − z color along with their rapid rise times.

We demonstrated in Figure 5 that it is challenging to detect a kilonova during the rise to peak. Therefore, in our simulations we also consider the behavior of sources that are observed in decline. We construct an identical phase space by replacing the rise time with the decline time, as defined above. Figure 10 shows the decline time–color slice of this phase space. The layout is identical to Figure 8. As before, the kilonova population presents i − z colors that are consistently redder than those of the contaminant population, with all detected events exhibiting i − z ≳ 0.3 mag. Furthermore, the fraction of contaminants seen in decline that exhibit i − z ≳ 0 is essentially unchanged compared to those observed on the rise. Additionally, all of the contaminants considered still exhibit i − z ≲ 0.3 mag, so therefore color can still be utilized as a strong discriminant.

Zoom In Zoom Out Reset image size

The efficacy of a cut on decline time is diminished compared to a cut on rise time. Both kilonovae and the contaminant population cover the entire distribution of possible decline times from ∼2–6 days. A notable exception is SNe Ia, which all exhibit a decline time of ∼6 days (the duration of the search), because if the source is already in decline at the start of the observations, it will remain detectable for the entire duration of the search. Only ∼20%–25% of kilonovae exhibit a decline time of ≲6 days, making this an ineffectual cut. On the other hand, the slow evolution is beneficial for separating the SNe Ia population from a kilonova if template images at ≳10 days are utilized. In this scenario, the kilonova will have faded away while SNe Ia will remain visible, allowing them to be easily rejected.

Figure 11 shows the decline time–Δm_z slice of the phase space. In this context we define ${\rm{\Delta }}{m}_{z}\equiv {m}_{z,{\rm{last}}}-{m}_{z,{\rm{0}}},$ where m_z,last is the z-band magnitude from the last observation in which the source is detected. Kilonovae exhibit a change in brightness of Δm_z ≈ 0–4 mag, with a weak trend for larger changes in brightness being associated with longer observed decline times. The SNe Ia and Pan-STARRS fast transients exhibit an average change in brightness of only Δm_z ≈ 0.1 mag and Δm_z ≈ 0.2 mag, respectively, making the potential for contamination low. However, as with the rise time–Δm_z space, the type .Ia and miscellaneous fast transients exhibit changes in brightness that are comparable to those of kilonovae. This makes cuts on Δm_z less practical for these sources.

Zoom In Zoom Out Reset image size

The key point emerging from our simulations is that i − z color is a strong discriminant for selecting kilonovae, regardless of observing strategy, and whether a kilonova is observed on the rise or decline. In fact, if we consider sources observed during the rise to peak, and we require that i − z ≳ 0 mag, we may eliminate ∼84%–87% of detected SNe Ia and Pan-STARRS fast transients, ∼90%–94% of detected type .Ia, and ∼100% of detected miscellaneous fast transients without removing any kilonovae from the selection. If we additionally require that the rise time is ≲4 days, then we eliminate ∼94% of detected SNe Ia and ∼98% of detected type .Ia. If we also require that $| {\rm{\Delta }}{m}_{z}| \gtrsim 0.1$ mag, we eliminate ∼99% of SNe Ia.

Considering sources observed in decline, the cuts on i − z color and Δm_z remain effective but a cut on decline time does not provide any additional information. Quantitatively, if we apply cuts of i − z ≳ 0 mag and $| {\rm{\Delta }}{m}_{z}| \gtrsim 0.1$ mag we eliminate ∼80% of SNe Ia, ∼60% of type .Ia, ∼81% of Pan-STARRS fast transients, and ∼100% of the miscellaneous fast transients. If we also require that the decline time is ≲5 days we eliminate ∼100% of the SNe Ia and ∼94% of the Pan-STARRS fast transients, but lose ∼46% of the kilonova population. However, if additional observations are taken at ≳10 days then these kilonovae can be recovered. But, given that cuts made on sources observed to rise are more effective, then in order to maximize the chances of a kilonova detection and identification during a GW follow-up campaign it is essential to obtain both i- and z-band data as close to the GW trigger as possible.

We now investigate how the absence of a pre-existing template affects our ability to reject contaminants. We carry out our simulations in the following way. The flux in the first observation (the template) is subtracted from the later observations. Noise calculations are handled identically to those outlined above for the detectability simulation, and we impose the same detection criterion for events. The rise/decline time phase-space coordinates are computed using the same definition as in Section 4.2. The challenge then is computing an analog for the values of the i − z color and Δm_z when the source flux is not known absolutely (due to the presence of source flux in the template image).

When there is source flux in the template image we are only able to measure a difference in flux between the template and science image. We denote this as Δf_ϕ ≡ f_s,ϕ − f_t,ϕ where f_s,ϕ is the flux observed in the science image and f_t,ϕ is the flux observed in the template image, both in some bandpass ϕ. We can then define an AB magnitude using the standard formula ${m}_{\phi }^{\star }=-2.5\mathrm{log}| {\rm{\Delta }}{f}_{\phi }| -48.6,$ where the star denotes magnitudes computed from a difference in flux. The ${\phi }_{1}-{\phi }_{2}$ color for bandpasses ϕ₁ and ϕ₂ is then ${m}_{{\phi }_{1}}^{\star }-{m}_{{\phi }_{2}}^{\star }.$ In the case where $| {\rm{\Delta }}{f}_{\phi }|$ is large, and consequently the detection is of high statistical significance, we approach the limit where the source flux in the template is negligible and a reasonable approximation for the true magnitude and color of the source can be obtained. However, for less significant detections, the measured color will not be an accurate measurement of its true value.

Lastly, we construct a straightforward analog to the rise/decline time–Δm slice of our phase space. In the case of a rising source, we compute ${m}_{z}^{\star }$ using the largest positive difference in flux between the template image and the science images. If the source is observed only in decline then the largest negative difference in flux is used. This will allow us to understand how rapidly a source evolves relative to others in this study (e.g., kilonovae versus contaminants).

In Figure 14 we plot the rise time–color slice using the same layout as in Figure 8. Inspecting the kilonovae across both observing strategies, we note that when the observed rise time is small (≲1 day, i.e., when the difference in time between the template and first science image is small) then the color is not well constrained due to $| {\rm{\Delta }}f|$ being too small to obtain an accurate measurement. However, the fraction of kilonovae with a rise time of ≲1 day is only ∼5%–8%. We also note that the fraction of detected kilonovae with t_rise ≲ 1 day that exhibit i − z ≈ −2 to +0.5 mag (i.e., in the range that overlaps with contaminants) is at most ∼1% for Strategy 3 and ≲1% for Strategy 1. More importantly, when the observed rise time is longer (≳2 days), then $| {\rm{\Delta }}f|$ is large enough that the i − z color can be well constrained and it is generally i − z ≳ 1 mag. This is consistent with the color measured when a pre-existing template is available (Figure 8). The fraction of detected kilonovae that present a rise time of ≳2 days is ∼45%–55%. This fraction is dominated by kilonovae models with an ejecta mass of M_ej = 10⁻¹ M_⊙ and β_ej = 0.1 or 0.2.

Zoom In Zoom Out Reset image size

Turning to the contaminant population, we find that several of the source classes have poorly constrained colors with some events exhibiting i − z > 0 mag. We can assess the impact of these contaminants by utilizing the rate data in Tables 1 and 2. This is achieved by multiplying the expected fraction of sources in a region of the phase space by the number of sources expected to occur during the search. This gives the actual number of sources detected. As expected, SNe Ia are the most numerous contaminant with ∼3–12 sources expected to exhibit i − z ≳ 0 mag. Strategy 3 produces the smallest number of SNe Ia detections (∼3–5). For the Pan-STARRS fast transients, we find that the number of sources exhibiting i − z ≳ 0 mag is ∼3 across both strategies. Lastly, we expect $\ll 1$ type .Ia and miscellaneous fast transients to exhibit i − z ≳ 0 mag. If we additionally require that the rise time is ≲4 days the number of detected SNe Ia is reduced to ∼1–7. This does not affect the number of detected Pan-STARRS fast transients. Ultimately, we do not expect the lack of a pre-existing template to significantly hinder our ability to separate kilonovae from contaminants on the basis of their i − z color and timescale, if the source is observed during the rise to peak.

Figure 15 shows the rise time–${m}_{z}^{\star }$ slice of our phase space. We first note the wide range of values for ${m}_{z}^{\star }$ that appear in our simulations. This arises from considering contaminants over a wide redshift range or, in the case of the kilonovae, over a range of model parameters. We further note that there does not appear to be an obvious cut utilizing ${m}_{z}^{\star }$ that helps to distinguish kilonovae from the contaminant population. However, we can separate kilonovae from the contaminant populations by utilizing a cut on timescale as all of the kilonovae exhibit a rise time of ≲4 days. Therefore, if we require that sources exhibit a rise time of ≲4 days, then we expect to eliminate ∼100 SNe Ia, ∼1 Pan-STARRS fast transient, and $\ll 1$ type Ia and miscellaneous fast transients, without rejecting any kilonovae.

Zoom In Zoom Out Reset image size

Despite the lack of a clear separation between the kilonovae and contaminant populations in ${m}_{z}^{\star },$ the requirement that sources exhibit a ${m}_{z}^{\star }$ greater than 5σ in the difference images does reduce the overall number of contaminants detected. Utilizing this criterion, the detection rates for SNe Ia and Pan-STARRS fast transients (the two most numerous contaminants) on the rise is ∼1% for both populations, down from ∼60% and ∼25%, respectively, in the case of a pre-existing template. The downside of this approach is that ∼10%–15% of kilonovae are also lost. These sources can be recovered with a late-time template, but they will not be detected in real time.

In Figure 16 we plot the decline time–color slice of our phase space. We find that there is no longer a clear separation in color between the kilonovae and contaminant populations. This is true for all contaminants and across all observing strategies. This effect is the result of the apparent slow evolution of the light curve during the decline phase relative to the template flux. This can occur if the observations straddle the peak of the light curve or if the source simply evolves more slowly after peak. However, we can separate kilonovae from the contaminant populations by utilizing a cut on timescale as all of the contaminants predominantly exhibit a decline time of ≳6 days (the maximal value given the duration of our search). Therefore, if we require that sources exhibit a decline time of ≲5 days, then we expect no SNe Ia, type .Ia and Pan-STARRS fast transients, and $\ll 1$ miscellaneous fast transient to be detected, but this cut will reject ∼15%–20% of kilonovae.

Zoom In Zoom Out Reset image size

Figure 17 shows the decline time–${m}_{z}^{\star }$ slice of the phase space. As in the case of sources detected on the rise, there is no clear cut on ${m}_{z}^{\star }$ that will help to separate the kilonovae from any contaminants. Furthermore, a cut on decline time (e.g., ≳6 days) does not yield any new information beyond what is gained from the decline time–color slice of the phase space. However, as before, utilizing a detection criterion on ${m}_{z}^{\star }$ does reduce the total number of contaminants detected. This effect is enhanced for sources such as SNe Ia and the Pan-STARRS fast transients, as they show slower post-peak evolution in their light curves. Here, the detection rates for these sources, when seen on the decline, is $\ll 1\%$ in both cases. This is down from ∼20% and ∼15%, respectively, in the case of a pre-existing template. However, the detection criterion on ${m}_{z}^{\star }$ reduces the kilonovae detection rates by ∼5%.

Zoom In Zoom Out Reset image size

We now summarize the efficacy of cuts based on i − z color, timescale, and change in flux for separating kilonovae from the contaminants when a pre-existing template is not available. For sources observed during the rise to peak, requiring i − z ≳ 0 mag eliminates ∼98% of detected SNe Ia, ∼91% of detected type .Ia, ∼100% of detected miscellaneous fast transients, and ∼56% of detected Pan-STARRS fast transients while eliminating ≲0.1% of detected kilonovae. If we additionally require that the rise time is ≲4 days, then we eliminate ∼99% of detected SNe Ia, ∼94% of detected .Ia SNe, and ∼59% of detected fast Pan-STARRS transients, without altering the fraction of kilonovae eliminated. In this scenario, an additional cut on ${m}_{z}^{\star }$ does not yield any additional information.

For sources observed only in decline, a cut of i − z ≳ 0 mag eliminates ∼50% of detected SNe Ia, ∼99% of detected type .Ia, and ∼100% of detected miscellaneous fast transients. The fraction of detected Pan-STARRS fast transients eliminated is essentially zero for both observing strategies. The cut of i − z ≳ 0 mag color also eliminates ∼15% of detected kilonovae. If we additionally require that the decline time is ≲5 days then we remove ∼100% of the contaminant population but also eliminate ∼60%–80% of detected kilonovae. No additional information is gained from a cut on ${m}_{z}^{\star }.$ Therefore, cuts on i − z color and timescale are less effective when the source is observed on the decline only. This highlights the need for the rapid triggering of follow-up observations.

Despite these challenges, the best approach in the absence of a pre-existing template is unchanged from the results of Section 4.2. The optimal follow-up cadence is still Strategy 1, which allows good sampling of the light curve while maximizing the area that can be covered in a single night of observations. However, we note that the previously recommended depths of 24 AB mag in i-band and 23 AB mag in z-band are only expected to detect ∼50%–75% of kilonovae in this scenario (Figure 12). The i − z color still provides a strong constraint for separating kilonovae from contaminants but it is most reliable when the kilonova can be observed during the rise to peak. If this is not feasible due to other observational constraints, then it is best to resort to obtaining template images once the kilonova has faded in the optical (≳10 days).

Ejecta can be produced by the outflows from a post-merger accretion disk (Dessart et al. 2009; Fernández & Metzger 2013; Fernández et al. 2015). Fernández & Metzger (2013) performed numerical two-dimensional hydrodynamical simulations of accretion disks and found that ∼10% of the initial disk mass is ejected over timescales of ∼1 s. These ejecta are a neutron-rich wind with an electron fraction of Y_e ∼ 0.2, producing conditions that are favorable for r-process nucleosynthesis. This type of outflow will therefore not drastically alter the observational properties of the kilonova.

Recent work by Fernández et al. (2015) found that the amount of ejected mass is a function of the spin of the remnant black hole, with more rapidly spinning black holes leading to higher ejecta masses by a factor of several. Furthermore, they found that Y_e increased monotonically with black hole spin due to an increased early-time neutrino luminosity from a rapidly spinning black hole. They found that in the most extreme cases (a ≳ 0.8), the system could eject ∼10⁻⁵–3 × 10⁻³ M_⊙ of material with Y_e ≳ 0.25. Specifically, an ejecta mass of ∼10⁻³ M_⊙ will produce a blue component in the kilonova light curve with νL_ν ≈ 7.5 × 10⁴⁰ erg s⁻¹ at ∼6500 Å (r ≈ 22.5 mag at 200 Mpc) and a peak time of ≲1 day (Kasen et al. 2014). This is significantly brighter in r-band than the kilonovae models discussed previously, but the short timescales make observing this component challenging.

Another modification can be caused by a surviving hypermassive neutron star (HMNS). The HMNS is a potential result of NS–NS mergers, but in simulations it often collapses rapidly (t ≲ 100 ms) to form a black hole (Sekiguchi et al. 2011). The prompt formation of a black hole is an implicit assumption in the kilonova models discussed so far in this paper. However, if the total mass of the binary is less than a critical value, the HMNS can survive for a longer period of time (Bauswein et al. 2013a; Kaplan et al. 2014). In this scenario, the resulting neutrino luminosity will raise the electron fraction of the disk wind ejecta and will suppress r-process nucleosynthesis. Thus, the lanthanide-free disk wind material will produce a brighter, bluer, and shorter-lived component in the kilonova light curve (e.g., Metzger & Fernández 2014; Metzger & Piro 2014, and the references therein). This emissions component will have a strong viewing angle dependence, with the polar regions being more strongly irradiated by neutrinos than the equatorial regions, which will remain obscured by lanthanide-rich material. Consequently, the blue early component is more pronounced when the merger is observed along the polar axis.

Metzger & Fernández (2014) found that the luminosity and timescale of this initial blue component are strongly dependent on the lifetime of the HMNS, with typical values (∼100 ms) leading to peak luminosity that is a factor of a few times brighter than the red kilonova component, with a timescale of a few days for emission along the polar direction. The light curves of this early-time component were computed in detail using wavelength-dependent radiative transfer calculations by Kasen et al. (2014). They found that for an HMNS with a lifetime of ∼100 ms, the initial blue component will have a peak luminosity of νL_ν ≈ 1.3 × 10⁴¹ erg s⁻¹ at ∼6500 Å (r ≈ 22 mag at 200 Mpc) and a peak time of ∼2 days. Kasen et al. (2014) also compared the blue component to the r-process-powered emission from a 10⁻² M_⊙ torus of dynamical ejecta. They found that the blue component will be visible for polar viewing angles (θ ≲ 15°). The fraction of sources expected to be observed at this viewing angle is ∼7θ² ∼ 0.48 (Metzger & Berger 2012). However, at these viewing angles the kilonova emission will be overwhelmed by the optical afterglow of an on-axis SGRB that may accompany the merger. Furthermore, if the source is observed at large viewing angles (θ ≳ 15°) then the emission will become obscured by the dynamical torus and the r-band emission will then peak at ≳23.7 mag (∼2 mag fainter than the polar case for a torus mass of 10⁻² M_⊙).

Lastly, we consider the case in which a small fraction of the neutron-rich ejecta is expanding so rapidly that it avoids the initial phase of r-process nucleosynthesis. This effect has been seen in several general relativistic simulations (Bauswein et al. 2013b; Goriely et al. 2013; Just et al. 2015). In particular, Bauswein et al. (2013b) found that for a small fraction of the ejecta (∼10⁻⁵–10⁻⁴ M_⊙), the expansion timescale was sufficiently rapid (≲5 ms) that it evades neutron capture. These neutrons will undergo β-decay and release energy into the ejecta. Given that the photon diffusion time is of the order of a few hours in the outer layers of the ejecta, a significant fraction of this energy will manage to produce radiation. The light curves of this "neutron precursor" were modeled by Metzger et al. (2014). They found that the β-decay from the population of free neutrons at the leading edge of 10⁻⁴ M_⊙ of ejecta can produce a transient with a timescale of ∼1–2 hr and a peak r-band magnitude of ≈22.2 mag at 200 Mpc.

We now investigate the effect of these speculative models on the early-time detectability of kilonovae using r-band observations. We construct the light curves for the long-lived HMNS from the time-resolved spectra modeled by Kasen et al. (2014) using the procedure outlined in Section 2.1. These spectra are for a HMNS lifetime of 100 ms with a dynamical torus with 10⁻² M_⊙ of neutron-rich material observed at a viewing angle of cosθ = 0.95 (θ ≈ 18°). For the neutron precursor, we use the r-band light curve provided by Metzger et al. (2014), for 10⁻⁴ M_⊙ of free neutrons with an electron fraction of Y_e ≈ 0.05 and opacity of κ ≈ 30 cm² g⁻¹. These light curves are plotted in Figure 20 along with those from the dynamical ejecta-only model for M_ej = 10⁻² M_⊙ and β_ej = 0.2 used in Sections 4 and 5.

Zoom In Zoom Out Reset image size

We repeat the detectability simulations discussed in Section 4.1 for the two speculative light curves in Figure 20, which are co-added in flux space to the light curve for the dynamical ejecta from Barnes & Kasen (2013). The general simulation procedure and criteria for detection are identical to those described in Section 4.1. The contours are plotted in Figure 21. The r-band contours for the dynamical ejecta only (Figure 4) are reproduced for comparison.

Zoom In Zoom Out Reset image size

Inspecting the case of a long-lived HMNS, we first note that the typical depth required to detect 50% (95%) of events is 23.4 (24) mag across both observing scenarios. This is shallower than the depth required for the dynamical ejecta alone, but still within reach of the larger telescopes. If intra-night observations are utilized (e.g., Strategy 3), then the 50% detection fraction contour is at 23 mag for observations within 6 hr of the GW trigger. The other contours are unaffected. For the neutron precursor model, the typical depth required to detect 50% (95%) of events is 24.7 (25.9) mag for observing Strategy 1, comparable to those required for the dynamical ejecta alone because the precursor is short-lived. When Strategy 3 is utilized, the 50% detection fraction contour begins at 23.6 mag for observations starting 3 hr after the GW trigger. It then monotonically declines to 24.7 mag by 24 hr. This is because a neutron precursor is short-lived, and only early-time observations benefit from its high luminosity.

Contour plots showing the detection of a rise to peak are shown in Figure 22. As in Section 4.1, a rise is defined as any observed brightening between epochs. We note that for Strategy 1 the source is always seen in decline for all three models. In the case of a long-lived HMNS brightening is observed in 50% (95%) of events for observations starting ≲5 (≲3) hr of the GW trigger and reaching a depth of ≈23 (24) mag. For a neutron precursor, brightening in the source is never observed. This is because the source peaks in ∼2 hr, while a reasonable start time is longer.

Zoom In Zoom Out Reset image size

Ultimately, the case of a long-lived HMNS irradiating the ejecta shows the strongest potential impact on kilonova r-band detectability. However, this component has a strong dependence on viewing angle and thus will not always be observed. In addition, this component is still faint, requiring observations that achieve a depth of ≈24 mag in r-band to detect 95% of the sources. This scenario is highly speculative and requires further study of the neutron star equation of state and post-merger behavior to assess the likelihood that the post-merger remnant will avoid the prompt collapse to a black hole. The scenario involving a neutron precursor does not drastically impact r-band detectability unless an observing strategy with rapid intra-night cadence is employed (i.e., a baseline of ∼1 hr).