Glossary of symbols¶
Parameter |
Symbol |
Remarks |
|---|---|---|
pulsar’s semi-major axis |
\(a_\mathrm{p}\) |
|
amplitude of pulsar’s orbital scaled-effective-velocity modulation |
\(A_\mathrm{p}\) |
|
harmonic coefficient in scaled-effective-velocity equation for cosine of pulsar’s orbital phase |
\(A_\mathrm{p,c}\) |
|
harmonic coefficient in scaled-effective-velocity equation for sine of pulsar’s orbital phase |
\(A_\mathrm{p,s}\) |
|
amplitude of Earth’s orbital scaled-effective-velocity modulation |
\(A_\oplus\) |
|
harmonic coefficient in scaled-effective-velocity equation for cosine of Earth’s orbital phase |
\(A_\mathrm{\oplus,c}\) |
|
harmonic coefficient in scaled-effective-velocity equation for sine of Earth’s orbital phase |
\(A_\mathrm{\oplus,s}\) |
|
factor modifying amplitude of pulsar’s sinusoid amplitude |
\(b_\mathrm{p}\) |
|
factor modifying amplitude of Earth’s sinusoid amplitude |
\(b_\oplus\) |
|
speed of light |
\(c\) |
|
constant scaled-effective-velocity offset |
\(C\) |
|
effective distance |
\(d_\mathrm{eff}\) |
|
distance to the pulsar system |
\(d_\mathrm{p}\) |
|
distance to the screen |
\(d_\mathrm{s}\) |
from Earth |
pulsar’s orbital inclination |
\(i_\mathrm{p}\) |
\(0^\circ \leq i_\mathrm{p} < 180^\circ\), with \(i_\mathrm{p} = 90^\circ\) for an edge-on orbit; for \(i_\mathrm{p} < 90^\circ\), the binary rotates counterclockwise on the sky (from north through east), for \(i_\mathrm{p} \geq 90^\circ\) it rotates clockwise |
Earth’s orbital inclination |
\(i_\oplus\) |
with respect the line of sight to the pulsar system |
pulsar’s radial-velocity amplitude |
\(K_\mathrm{p}\) |
|
pulsar’s orbital period |
\(P_\mathrm{orb,p}\) |
|
Earth’s orbital period |
\(P_\mathrm{orb,\oplus}\) |
|
fractional pulsar–screen distance |
\(s\) |
from pulsar to screen |
time |
\(t\) |
|
time of Earth’s equinox |
\(t_\mathrm{eqx}\) |
|
pulsar’s time of ascending node |
\(t_\mathrm{asc,p}\) |
|
Earth’s time of ascending node |
\(t_\mathrm{asc,\oplus}\) |
|
pulsar’s mean orbital speed |
\(v_\mathrm{0,p}\) |
|
Earth’s mean orbital speed |
\(v_\mathrm{0,\oplus}\) |
|
effective velocity |
\(v_\mathrm{eff,\parallel}\) |
component along the screen direction |
contribution of the pulsar’s systemic motion to the effective velocity |
\(v_\mathrm{eff,\parallel,p,sys}\) |
component along the screen direction |
velocity of the lens |
\(v_\mathrm{lens,\parallel}\) |
component along the screen direction |
pulsar’s orbital velocity |
\(v_\mathrm{p,orb,\parallel}\) |
with respect to the pulsar system’s barycentre; component along the screen direction |
velocity of the pulsar system’s barycentre |
\(v_\mathrm{p,sys,\parallel}\) |
with respect to some local standard of rest (e.g., the Solar System’s barycentre); component along the screen direction |
velocity of the observatory/Earth |
\(v_\mathrm{\oplus,\parallel}\) |
component along the screen direction |
equatorial coordinates of Earth’s ascending node |
\(X_\mathrm{asc,\oplus}\) |
|
equatorial coordinates of pulsar system |
\(X_\mathrm{p}\) |
|
auxiliary variable for finding pulsar’s orbital inclination |
\(Z\) |
|
pulsar system’s right ascension |
\(\alpha_\mathrm{p}\) |
|
pulsar system’s ecliptic latitude |
\(\beta_\mathrm{p}\) |
|
pulsar system’s declination |
\(\delta_\mathrm{p}\) |
|
pulsar’s ascending node–screen angle |
\(\Delta\Omega_\mathrm{p}\) |
|
Earth’s ascending node–screen angle |
\(\Delta\Omega_\oplus\) |
|
curvature |
\(\eta\) |
|
observing wavelength |
\(\lambda\) |
|
pulsar system’s ecliptic longitude |
\(\lambda_\mathrm{p}\) |
|
pulsar system’s proper motion in right ascension |
\(\mu_\mathrm{p,sys,\alpha\ast}\) |
including the \(\cos(\delta_\mathrm{p})\) term |
pulsar system’s proper motion in declination |
\(\mu_\mathrm{p,sys,\delta}\) |
|
position angle of the lensed images |
\(\xi\) |
measured from the celestial north, through east, to the line of images formed by the lens; \(0^\circ \leq \xi < 180^\circ\) |
pulsar’s orbital phase |
\(\phi_\mathrm{p}\) |
measured from the ascending node |
Earth’s orbital phase |
\(\phi_\oplus\) |
measured from the ascending node with respect to the pulsar system |
pulsar’s orbital scaled-effective-velocity modulation phase offset |
\(\chi_\mathrm{p}\) |
|
Earth’s orbital scaled-effective-velocity modulation phase offset |
\(\chi_\oplus\) |
|
pulsar’s longitude of ascending node |
\(\Omega_\mathrm{p}\) |
measured from the celestial north through east; \(0^\circ \leq \Omega_\mathrm{p} < 360^\circ\) |
Earth’s longitude of ascending node |
\(\Omega_\oplus\) |
measured from the celestial north through east; \(0^\circ \leq \Omega_\oplus < 360^\circ\) |