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

We investigate the scalar emission from binary neutron stars in shift-symmetric scalar-tensor theories with kinetic screening ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>K</a:mi> </a:math> -essence), using <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>3</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> numerical simulations in the decoupling limit. To construct static binary initial data in the regime where the screening radius <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>r</e:mi> <e:mo>*</e:mo> </e:msub> </e:math> greatly exceeds the orbital separation, we introduce a hyperbolization of the static field equations that bypasses the Keldysh-type breakdown affecting direct time evolutions. For equal-mass binaries, where the scalar emission is dominated by the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mo>ℓ</g:mo> <g:mo>=</g:mo> <g:mi>m</g:mi> <g:mo>=</g:mo> <g:mn>2</g:mn> </g:math> mode, kinetic screening acts nonmonotonically on the scalar radiation, suppressing or enhancing the quadrupolar amplitude depending on the relative size of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>r</i:mi> <i:mo>*</i:mo> </i:msub> </i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>λ</k:mi> <k:mn>22</k:mn> </k:msub> </k:math> (with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>λ</m:mi> <m:mn>22</m:mn> </m:msub> </m:math> the wavelength): for <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>λ</o:mi> <o:mn>22</o:mn> </o:msub> <o:mo>≪</o:mo> <o:msub> <o:mi>r</o:mi> <o:mo>*</o:mo> </o:msub> </o:math> it is suppressed relative to the Fierz-Jordan-Brans-Dicke (FJBD) case, while for <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>λ</q:mi> <q:mn>22</q:mn> </q:msub> <q:mo>≳</q:mo> <q:msub> <q:mi>r</q:mi> <q:mo>*</q:mo> </q:msub> </q:math> it is amplified above FJBD. For unequal-mass binaries a scalar dipole reemerges, growing linearly with the mass asymmetry, while the quadrupolar screening remains close to the equal-mass case down to mass ratios <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mo>∼</s:mo> <s:mn>0.6</s:mn> </s:math> . The nonmonotonic behavior of kinetic screening that we uncover has potential implications for gravitational-wave-based tests of gravity. The relativistic double pulsar, in particular, requires <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>r</u:mi> <u:mo>*</u:mo> </u:msub> <u:mo>≫</u:mo> <u:msup> <u:mn>10</u:mn> <u:mn>9</u:mn> </u:msup> <u:mtext> </u:mtext> <u:mtext> </u:mtext> <u:mi>km</u:mi> </u:math> to efficiently suppress the scalar quadrupole; for cosmologically-motivated <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi mathvariant="normal">Λ</w:mi> </w:math> , <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msub> <z:mi>r</z:mi> <z:mo>*</z:mo> </z:msub> <z:mo>∼</z:mo> <z:msup> <z:mn>10</z:mn> <z:mn>11</z:mn> </z:msup> <z:mtext> </z:mtext> <z:mtext> </z:mtext> <z:mi>km</z:mi> </z:math> (for a solar-mass source), giving only moderate suppression.