ContinuousWave monochromatic H1 direct class

Specification ID: cw-monochromatic-h1-direct-class/v2.

Definition field	Catalog value
Model ID	`ContinuousWaveH1Direct`
Reference composition	`cw-monochromatic-h1-direct-class/v2`
Scope	Direct Torch/JAX ContinuousWave class: selected float64 CPU monochromatic principal-axis 2f strain at H1, GPS epoch in 2015–2016.
Domain and modes	`time`; `(2, 2)`
Native backends	`torch`, `jax`
Scoped verification claims	2

Option	Default	Native choices	Reference-only choices
`call_route`	`direct_class`	`direct_class`	None
`detector`	`H1`	`H1`	None
`spindown`	`f1=f2=0`	`f1=f2=0`	None
`amplitude_input`	`h0`	`h0`, `ellipticity_distance`	None

Scope and status

This version covers selected float64 CPU outputs from the direct Torch/JAX ContinuousWave class with detector="H1", f1=f2=0, and the principal-axis \(2f_{\rm rot}\) branch. Both h0 and (ellipticity,distance) input routes are checked. It is a sampled implementation-verification claim. The class also permits other detectors and spin-down parameters; those calls are outside this version.

Inputs, conventions, and options

t and t0 are GPS seconds, with samples in the 17-second GPS–UTC interval from 2015-07 to 2016-12. t0=1126259462 seconds sets both intrinsic frequency and zero circular-orbit phase. f0 is GW frequency in Hz, twice the stellar rotation frequency. ra, dec, psi, and phi0 are radians; cos_iota is dimensionless. Either h0 is given directly or the class computes it from ellipticity, SI distance, and i_zz in kg m². The source is principal-axis, non-precessing, and monochromatic. The project model uses a circular 1-AU orbit, obliquity 0.4090928042223289 rad, and sidereal year 365.256363004 days. Earth rotation uses IAU 1982 GMST with UTC substituted for UT1. The unchanged amplitude, clock, phase, antenna, and strain components retain their v1 IDs; v2 adds the independently sourced cw.direct_h1.site.v1 gate.

Mathematics and components

Jaranowski, Królak and Schutz (1998), PDF Eqs. (23)–(24) give \(h_0=4\pi^2GI_{zz}\epsilon f_0^2/(c^4d)\) after mapping their rotation frequency to the native GW frequency. With \(\Delta t=t-t_0\), Eq. (18)'s geometric Roemer delay is \(\tau=\mathbf n\cdot (\mathbf r_{\rm orbit}+\mathbf r_{\rm H1})/c\). The circular orbit and its phase origin are project conventions. The monochromatic limit of Eq. (14) is \(\Phi=\phi_0+2\pi f_0(\Delta t+\tau)\).

JKS PDF Eqs. (1)–(6) form \(F_+\) and \(F_\times\) from the H1 arm tensor at the Greenwich sidereal angle. Eqs. (19)–(22), at the principal-axis angle, give

\[h(t)=h_0\left[\frac{1+\cos^2\iota}{2}F_+(t)\cos\Phi(t) +\cos\iota F_\times(t)\sin\Phi(t)\right].\]

The scalar reference computes these equations directly. The native class contracts the JKS four-amplitude basis, so the test also checks the full composition and convention signs.

Component ID	Source and scope
`cw.direct_h1.amplitude.v1`	JKS PDF Eqs. 23–24; both native amplitude routes
`cw.direct_h1.clock.v1`	Aoki 1982 GMST, UTC approximation and fixed leap offset
`cw.direct_h1.delay_phase.v1`	JKS PDF Eqs. 14, 18; monochromatic circular-orbit adapter
`cw.direct_h1.antenna.v1`	JKS PDF Eqs. 1–6; conditioned on supplied H1 site vectors
`cw.direct_h1.strain.v1`	JKS PDF Eqs. 19–22 and native four-amplitude composition
`cw.direct_h1.site.v1`	LIGO T980044-10, §2.1 and Table 4, Hanford Earth-fixed/geodetic vertex and arm directions at published precision

Implementation mapping

diffgw_reference.continuous_wave_direct_class.monochromatic_h1_sample uses mpmath and the existing paper-literal quadrupole and phase-response references. It does not import native waveform functions or constants. The H1 vertex and normalized arm vectors are explicit conditioning inputs from the detector object in the tight 2e-8 normalized comparison. A separate survey_h1_sample supplies the decimal values printed in LIGO Table 4; these constants are independent of the native detector definitions. The two native ContinuousWave classes run their own amplitude, timing, antenna, basis, and strain code paths.

Evidence and limitations

The maintained whole-class test covers both backends at two sky/frequency configurations, five GPS sample times per amplitude route, and selected \(f_0\) and \(\phi_0\) derivatives. The separate source-site gate uses LIGO T980044-10 Table 4: the native H1 vertex is 0.0432 m from the printed Earth-fixed vertex, inside the 0.05 m per-coordinate rounding interval. Independently converting the printed geodetic position with §2.1's WGS-84 constants yields a vertex within 0.3 mm numerically; the printed latitude, longitude, and height limit the physical precision to coarser than that arithmetic match. The two arm-direction separations are about 0.79 µrad, inside the table's 1.93 µrad estimated angular error. The native x/y arm components do not all round to Table 4's printed digits, so this does not source their inherited full precision. A separate whole-strain comparison at the published site uses a 5e-6 h0 gate allowing for the two estimated arm errors, printed-vector truncation, and vertex phase error at 71 Hz; the tight conditioned gate remains 2e-8.

IERS Bulletin C49 supports the 17-second GPS–UTC offset. IERS EOP 14 C04, MJD 57279 reports UT1–UTC = +0.2553711 s at 2015-09-14 0h UTC. The test confirms the native clock follows the declared UTC substitution; the measured difference from the corresponding UT1 sidereal angle is about 1.86e-5 rad. There is no time-varying Earth-orientation input or physical timing claim. The circular orbit has no planetary ephemeris, Einstein/Shapiro delay, binary orbit, or proper motion. The JKS historical H1 arm table was corrected by Anderson; it is not used as an exact H1 oracle. Native nonzero spin-down terms contain higher powers of the delay than JKS Eq. (14), recorded by a strict expected-failure diagnostic and excluded here. This claim establishes neither external binary compatibility nor astrophysical or domain-wide physical accuracy.

Reproduce the checks

Run python -m pytest -q tests/test_continuous_wave_direct_class_math_reference.py and python -m pytest -q tests/test_continuous_wave_phase_response_reference.py with the optional reference, Torch, and JAX dependencies installed. Run python scripts/generate_waveform_library_table.py --check to verify generated catalog tables.