Electromagnetic outflows in a class of scalar-tensor theories: Binary neutron star coalescence

As we showed in previous work, the dynamics and gravitational emission of binary neutron-star systems in certain scalar-tensor theories can differ significantly from that expected from general relativity (GR) in the coalescing stage. In this work we examine whether the characteristics of the electromagnetic counterparts to these binaries—driven by magnetosphere interactions prior to the merger event—can provide an independent way to test gravity in the most strongly dynamical stages of binary mergers. We find that the electromagnetic flux emitted by binaries in these scalar-tensor theories can show deviations from the GR prediction in particular cases. These differences are quite subtle, thus requiring delicate measurements to differentiate between GR and the type of scalar-tensor theories considered in this work using electromagnetic observations alone. However, if coupled with a gravitational-wave detection, electromagnetic measurements might provide a way to increase the confidence with which GR will be confirmed (or ruled out) by gravitational observations.

Figure 1

Separation shown as a function of $t_{\text{merger}}-t$ in log scale, being $t_{\text{merger}}$ the time at which the stars come into contact (i.e. the separation equals $R_{*}+R_c$). The panels display the $\mathbf{LE}$ (top-left panel), $\mathbf{HE}$ (top-right panel), $\mathbf{LU}$ (bottom-left panel), and $\mathbf{HU}$ (bottom-right panel) binaries, for $\tilde{\beta }=-4.5$ (dotted lines), $-4.2$ (dashed lines), and GR (solid lines). Recall that magnetic field effects on the binary’s motion are negligible, thus the differences in the trajectories are solely due to the underlying gravity theory. In the $\mathbf{LE}$ binary, the trajectories for the three cases are almost identical, as there is almost no scalarization until very late in the inspiral. These examples show that at any given separation, the time to merger is shorter (or equal) in ST theories than in GR.

Figure 2

Orbital frequency as a function of separation (in log scale), for the same parameters shown in Fig. 1.

Figure 3

Scalar charge for the same binaries as in Fig. 1, as a function of the orbital frequency, for $\tilde{\beta }=-4.5$ (dotted lines) and $-4.2$ (dashed lines). The top panels correspond to equal-mass binaries, and both stars have the same scalar charge for a given value of $\tilde{\beta }$. On the other hand, the bottom panels correspond to unequal-mass binaries, and the scalar charges are different. In these cases in particular, the upper line with the same style (i.e. the same value of $\tilde{\beta }$) refers to the more massive star.

Figure 4

Luminosity vs time to merger, for the same parameters shown in Fig. 1. Different lines in each panel indicate the ratio between the secondary and primary magnetic fields (from top to bottom): $b=0.1$ (in red), $b=0.01$ (in green), $b=0.001$ (in blue), and a nonmagnetized secondary (i.e. $b=0$, in black).

Figure 5

Luminosity as a function of orbital frequency, for the same parameters shown in Fig. 4.

Figure 6

Time derivative of the luminosity as a function of time to merger, for the same parameters shown in Fig. 4. Note that the differences are less significative for the low-mass binaries.

Figure 7

Total energy radiated in electromagnetic waves (i.e. the time integral of the luminosity) as a function of time elapsed from an initial separation of approximately 180 km for the same parameters shown in Fig. 4. Insets show zoom-ins of the total energy radiated at late times, when the binary is close to the merger.

Figure 8

Fractional change of the luminosity, $FCL\equiv |{\mathcal{L}}_{\text{ST}}-{\mathcal{L}}_{\text{GR}}|/{\mathcal{L}}_{\text{GR}}$, for the $\mathbf{LE}$ (top-left panel), $\mathbf{HE}$ (top-right panel), $\mathbf{LU}$ (bottom-left panel), and $\mathbf{HU}$ (bottom-right panel) binaries as a function of orbital and GW frequencies (assuming $b=0.1$ for concreteness and for clarity’s sake). The solid black line shows the $FCL$ of a ST with $\tilde{\beta }=-4.5$ with respect to GR, while the dashed red line represents the $FCL$ of a ST with $\tilde{\beta }=-4.2$ (again with respect to GR).

Figure 9

Eccentric binaries: evolution of the separation for a binary governed by GR and ST with $\tilde{\beta }=-4.5$ and scalar charges of the binary’s components (for binaries governed by ST with $\tilde{\beta }=-4.5$ and $\tilde{\beta }=-4.2$ for comparison purposes) as a function of time to merger, for an equal-mass binary (top panels) and an unequal-mass binary (bottom panels), for low-eccentricity orbits (left column) and high-eccentricity orbits (right column) (see text for the details on the exact masses and eccentricities). As the orbit progresses, and scalar charges become significant, the eccentricity is reduced more rapidly in the ST cases as illustrated by the increasingly reduced differences between local maxima and minima of the binary’s separation.

Figure 10

Luminosity vs time to merger, for the same parameters shown in Fig. 9. For clarity’s sake we show here the two extremal magnetic ratios considered, $b=0.1$ and $b=0$ (i.e. a nonmagnetized companion).

Figure 11

Energy radiated by eccentric binaries, as a function of the time elapsed from an initial binary separation of approximately 220 km, for the same parameters shown in Fig. 9. We show, in contiguous panels, three different magnetic ratios (from left to right within each plot): $b=0.1$ (in red), 0.01 (in green), and 0.001 (in blue). Note that in the case of low-eccentricity orbits (left column), the radiated energy has a smoother (continuous) trend, while in the case of high-eccentricity orbits (right column) the radiated energy is more jagged; this is a consequence of the oscillatory features in the luminosity, and ultimately the effect of the different dynamics of each binary.