Scalar emission from binary neutron stars in scalar-tensor theories with kinetic screening

This paper employs 3+1 numerical simulations to demonstrate that kinetic screening in shift-symmetric scalar-tensor theories non-monotonically affects scalar emission from binary neutron stars—either suppressing or enhancing the quadrupolar amplitude depending on the ratio of the screening radius to the radiation wavelength—and reveals that while unequal-mass binaries revive a scalar dipole, cosmologically motivated parameters may only moderately suppress scalar radiation in systems like the double pulsar.

The Gist

Imagine the universe is a giant, invisible ocean. In our standard understanding of physics (General Relativity), this ocean is made of space and time, and massive objects like stars create ripples in it called gravitational waves.

But what if there's a second, hidden ocean? This paper explores a theory where a mysterious "scalar field" (let's call it the Ghost Wind) also flows through the universe. This Ghost Wind interacts with stars, potentially creating its own kind of "wind waves" that we might detect.

The problem is that this Ghost Wind is tricky. Near heavy objects like neutron stars, it has a built-in "shield" that makes it act like normal physics, hiding its weird effects. This is called Kinetic Screening. It's like a force field that turns off the Ghost Wind's special powers when you are close to a star, so we don't notice it in our solar system.

The authors of this paper wanted to see what happens when two neutron stars dance around each other. Do they emit waves of this Ghost Wind? And how does the "shield" affect those waves?

Here is what they found, using a mix of math and super-computer simulations:

1. The "Shield" is Not a Simple Switch

For a long time, scientists thought the shield worked like a simple dimmer switch: the closer you are to the star, the dimmer the Ghost Wind gets.

The authors discovered it's actually more like a volume knob that behaves strangely.

• When the waves are very short (high pitch): The shield works well. It mutes the Ghost Wind, making the signal much quieter than expected.
• When the waves are long (low pitch): The shield actually turns up the volume. Instead of being quiet, the Ghost Wind becomes louder than it would be without the shield at all!

This is a "non-monotonic" behavior, meaning the effect doesn't just go down; it goes down, then goes up, depending on the size of the wave compared to the size of the shield.

2. The Dance of Two Stars

The team simulated two neutron stars orbiting each other.

• If the stars are twins (equal mass): They spin perfectly symmetrically. In this case, the "Ghost Wind" only has one main way to wiggle (a quadrupole, like a balloon being squeezed from two sides). The strange volume knob effect described above happens here.
• If the stars are different sizes: The symmetry breaks. Now, a new type of wave appears (a dipole, like a lighthouse beam). This new wave grows stronger as the difference in size between the stars gets bigger. However, the "volume knob" effect on the main squeeze-wave (quadrupole) stays mostly the same, even if the stars aren't identical twins.

3. The Technical Hurdle: The "Traffic Jam"

To run these simulations, the team hit a major roadblock. When they tried to set up the starting position of the stars on the computer, the math equations would crash. It was like trying to drive a car where the speed limit suddenly drops to zero the moment you try to move; the computer couldn't handle the "traffic jam" in the math.

To fix this, they invented a new mathematical "detour." Instead of trying to drive straight to the destination, they used a special relaxation method (like gently pushing a heavy box until it settles) to find the starting position without crashing the computer. This allowed them to simulate scenarios where the "shield" is huge compared to the distance between the stars—a situation previous computers couldn't handle.

4. What This Means for Real Stars

The authors looked at a famous real-life system: the Double Pulsar (two neutron stars orbiting each other).

• The "shield" around these stars is estimated to be about 100 billion kilometers wide (roughly the distance light travels in a year).
• The waves they emit are about 1 billion kilometers long.
• Because the waves are smaller than the shield, the shield should mute them. However, because the shield isn't infinite, it only mutes them by a factor of "a few tens."

The Bottom Line:
The paper shows that the "shield" hiding this Ghost Wind isn't a perfect wall. It acts like a complex filter that can either silence the signal or amplify it, depending on the "pitch" of the waves. This means that when astronomers look for these signals in the future, they can't just assume the signal will be weak. They have to account for this weird, non-linear behavior where the shield might actually make the signal louder in certain conditions.

Technical Summary

1. Problem Statement

The paper investigates the emission of scalar radiation from binary neutron star (BNS) systems within shift-symmetric K-essence scalar-tensor theories. These theories feature a non-canonical kinetic term ($K(X)$) that enables kinetic screening (or k-mouflage), a mechanism that suppresses deviations from General Relativity (GR) in high-density regions (inside a screening radius $r_*$) while allowing them to manifest at cosmological scales.

Key Challenges Addressed:

• Numerical Instability: In the fully nonlinear regime, the scalar field equations in K-essence can suffer from Keldysh-type breakdowns, where characteristic speeds diverge, making standard time-evolution of static configurations impossible. This is particularly acute when the screening radius $r_*$ is much larger than the orbital separation of the binary.
• Gap in Understanding: Previous studies yielded conflicting results:
  • Full numerical relativity simulations of merging BNSs suggested scalar quadrupole emission was largely unsuppressed (or even enhanced).
  • Perturbative studies of isolated stars suggested efficient suppression of quadrupoles when the radiation wavelength $\lambda$ is smaller than $r_*$.
  • Previous decoupling-limit studies of Neutron Star-Black Hole (NS-BH) binaries showed monotonic suppression of the quadrupole, but this setup lacked the symmetry of equal-mass BNSs where the dipole vanishes.
• Goal: To determine how kinetic screening affects scalar radiation (dipole and quadrupole) in BNS systems across different regimes of the screening radius relative to the radiation wavelength, specifically addressing the non-monotonic behavior hinted at in prior literature.

2. Methodology

The authors employ 3+1 numerical simulations in the decoupling limit, where the background metric is fixed to Minkowski space, and the scalar field evolves on this background sourced by effective point particles representing the neutron stars.

Key Technical Innovations:

• Hyperbolization of Static Equations: To construct static binary initial data in the regime where $r_* \gg$ orbital separation (a regime prone to Keldysh breakdown), the authors do not evolve the elliptic static equations directly. Instead, they hyperbolize the static field equations by introducing a relaxation time $\tau$ and a damping parameter $\eta$. This transforms the elliptic PDE into a hyperbolic one, allowing the system to relax smoothly from arbitrary initial data to the desired static binary configuration without encountering numerical instabilities.
• Effective Source Model: The neutron stars are modeled as effective point particles with scalar charges $\alpha_i = \alpha(1-2s_i)$, where $s_i$ is the sensitivity. For the simulations, sensitivities are set to zero ($s_1=s_2=0$) to isolate the effects of mass asymmetry, with the understanding that results can be rescaled for non-zero sensitivities.
• Simulation Setup:
  • Code: A 3D parallelized code (Simflowny) with Adaptive Mesh Refinement (AMR).
  • Process: Static binary data is generated via relaxation $\to$ Orbital angular velocity is ramped up to the Keplerian value $\to$ Outgoing scalar radiation is extracted.
  • Parameters: Mass ratios $\mu \in [0.5, 1.0]$, strong-coupling scale $\Lambda$ varied to change $r_*$, and orbital separation fixed at $a \approx 103$ km.

3. Key Contributions

1. Novel Numerical Technique: The successful application of hyperbolized relaxation to generate stable static binary initial data in K-essence theories, bypassing the Keldysh-type breakdown that previously hindered simulations in the $r_* \gg a$ regime.
2. Discovery of Non-Monotonic Screening: The paper establishes that kinetic screening acts non-monotonically on scalar radiation. The effect on the quadrupolar amplitude depends critically on the ratio of the screening radius $r_*$ to the radiation wavelength $\lambda_{22}$.
3. Extension to Equal-Mass Binaries: Unlike previous NS-BH studies where the dipole dominates, this work isolates the quadrupole channel in equal-mass binaries and characterizes its behavior, then systematically introduces mass asymmetry to study the re-emergence of the dipole.

4. Key Results

A. Equal-Mass Binaries ($\mu = 1$)

In this symmetric case, the dipole vanishes, and the $\ell=m=2$ quadrupole dominates. The amplitude $A$ relative to the Fierz-Jordan-Brans-Dicke (FJBD) case ($A_{FJBD}$) exhibits two distinct regimes:

• Short Wavelength Regime ($\lambda_{22} \ll r_*$): The scalar radiation is suppressed.
  • Scaling: $A \propto r_*^{-4/5}$.
  • This confirms perturbative predictions for isolated stars and explains why full numerical relativity simulations (which often access this regime) see suppression.
• Long Wavelength Regime ($\lambda_{22} \gtrsim r_*$): The scalar radiation is amplified above the FJBD value.
  • Scaling: $A \propto r_*^{2/5}$.
  • This explains the "enhanced" quadrupole seen in full numerical relativity merger simulations, which operate in a regime where the wavelength is comparable to or larger than the screening radius.
• Phase Shift: A phase shift in the waveform is observed, scaling as $\delta \chi \approx 0.78 \Omega r_*$.

B. Unequal-Mass Binaries ($\mu < 1$)

• Dipole Re-emergence: A scalar dipole ($\ell=m=1$) re-emerges, with its amplitude growing linearly with the mass asymmetry ($1-\mu$).
• Quadrupole Behavior: The quadrupole amplitude decreases quadratically with mass asymmetry. However, for mass ratios $\mu \gtrsim 0.6$, the screening behavior of the quadrupole remains indistinguishable from the equal-mass case.
• Dominance Transition: The dipole is expected to dominate over the quadrupole for $\mu \lesssim 0.35$, a regime where the system behaves more like the NS-BH case studied previously.

5. Significance and Implications

• Reconciling Literature: The non-monotonic behavior resolves the apparent contradiction between perturbative studies (which found suppression) and full numerical relativity simulations (which found enhancement). The difference lies in the relative size of the screening radius and the radiation wavelength.
• Gravitational Wave Tests: The findings have critical implications for testing gravity using BNS observations:
  • Double Pulsar (PSR J0737-3039): For cosmologically motivated values of $\Lambda$, the screening radius is $r_* \sim 10^{11}$ km, while the radiation wavelength is $\lambda_{22} \sim 10^9$ km. The system lies in the suppressed regime ($\lambda < r_*$), but the suppression is only moderate (a factor of $\sim 10-30$ relative to FJBD), not total. This suggests that current binary pulsar timing constraints may not rule out these theories as strictly as previously thought if the scaling is $r_*^{-4/5}$ rather than exponential.
  • Future GW Detectors: The enhancement regime ($\lambda > r_*$) implies that for certain parameter spaces, scalar-tensor theories could produce stronger signals than standard FJBD predictions, potentially making them easier to detect or distinguish from GR in specific frequency bands.
• Theoretical Robustness: The work demonstrates that the "naive" picture of a uniform cutoff for scalar emission is incorrect. The interplay between the source size, orbital frequency, and the strong-coupling scale creates a complex phenomenology that must be accounted for in waveform modeling.

In conclusion, this paper provides a robust numerical framework for studying K-essence binaries and reveals a rich, non-monotonic phenomenology for scalar radiation that fundamentally alters how we interpret constraints from binary pulsars and gravitational wave detectors.