Prospects for axion searches with Advanced LIGO through binary mergers

The observation of gravitational waves from a binary neutron star merger by LIGO/VIRGO and the associated electromagnetic counterpart provides a high precision test of orbital dynamics, and therefore a new and sensitive probe of extra forces and new radiative degrees of freedom (d.o.f.). Axions are one particularly well-motivated class of extensions to the Standard Model leading to new forces and sources of radiation, which we focus on in this paper. Using an effective field theory (EFT) approach, we calculate the first post-Newtonian corrections to the orbital dynamics, radiated power, and gravitational waveform for binary neutron star mergers in the presence of an axion. This result is applicable to many theories which add an extra massive scalar d.o.f. to general relativity. We then perform a detailed forecast of the potential for Advanced LIGO to constrain the free parameters of the EFT, and map these to the mass $m_a$ and decay constant $f_a$ of the axion. At design sensitivity, we find that Advanced LIGO can potentially exclude axions with $m_a\lesssim {10}^{-11}\mathrm{eV}$ and $f_a\sim ({10}^{14}-{10}^{17})\mathrm{GeV}$. There are a variety of complementary observational probes over this region of parameter space, including the orbital decay of binary pulsars, black hole superradiance, and laboratory searches. We comment on the synergies between these various observables.

Figure 1

Schematic plot of the strain vs time for a GW waveform emitted during a binary merger in the presence of an axion. The arrows indicate whether the effects of the axion hasten or delay the merger, and therefore shorten or lengthen the chirp (and increase or decrease its pitch, respectively).

Figure 2

Leading order diagrams. In the diagrams above and in Figs. 3, 4, 5 below, the solid black lines are the geodesics of the neutron stars, the dashed lines represent the propagator of the scalar field, and the wiggly lines are the propagator of the graviton.

Figure 3

1PN diagrams proportional to $G{\mathbf{v}}^2$. See Fig. 2 for a description of the diagrammatic representation. The crosses in the diagrams above represent the insertion caused by the PN expansion of the propagator.

Figure 4

1PN diagrams proportional to $G^2$.

Figure 5

1PN diagrams with 3-vertices.

Figure 6

Corrections from the scalar field on $T^{00}$ and $T^{kk}$ at 1PN.

Figure 7

Diagrams contribute to scalar radiation at leading order, $v^2$ and $p{v}^2$.

Figure 8

Corrections from the scalar field proportional to $p{v}^4$.

Figure 9

Forecasted marginalized constraints on scalar charge and Compton wavelength. We consider a fiducial model of a binary system with $M_1=1.2M_{\odot }$, $M_2=1.24M_{\odot }$ and $D_L=40\mathrm{Mpc}$ and evolve it in the absence of axions. We sample the likelihood function assuming the noise properties of Advanced LIGO at design sensitivity on the full parameter space. The plot shows the forecasted marginalized $3\sigma$ constraints on the ($q-\lambda$) plane (left) and the $(q_1/M_1-\lambda )$ plane (right).

Figure 10

Forecasted marginalized constraints on the axion parameter space. Colored regions below the curves can be constrained by analyzing data of the LIGO detections of NS-NS (blue) and NS-BH (red) mergers. The forecasted constraints are found by performing MCMC sampling in the small $m_a$ limit (the horizontal solid lines) and in the large $m_a$ limit (the curly solid lines). We connect these forecasted constraints by linear interpolation (the dashed lines). Note that the parameters of the NS-BH case were chosen to contrast with the NS-NS case. In reality, astrophysical black holes would have larger masses [71]. For the same scalar mass, a larger black hole mass would weaken the constraint. For example, for a $4M_{\odot }$ black hole, the constraint weakens by a factor of 2. For comparison, we also show the existing constraints (in gray) from direct measurements of the Sun, from measurements of the orbital decay of binary pulsar systems [31] and from black hole super-radiance through black hole spin measurement [23]. A wider range of the axion parameter space can be probed by direct searches of continues wave at LIGO as well as indirect measurement of black hole spin distribution [23, 24, 72]. The region above the dotted purple line are parameter spaces where an axion profile can be sourced by a neutron star. The black line shows the parameters of a QCD axion, while the dotted gray horizontal line marks the value of the reduced planck scale $M_{\mathrm{pl}}$.

Figure 11

Phase difference caused by the scalar with different PN GR expressions. We consider a binary of masses $1.2M_{\odot }$ and $1.24M_{\odot }$, and calculate the total phase difference (integrated from 10 Hz to 1000 Hz) caused by the scalar. The contours show the total phases between the cases with and without scalar differ by $1.\lambda$ is in units of the total inverse mass.