Below are the terms understood by the VARTOOLS analytic expression evaluator
Operators:
a+b - Addition a-b - Subtraction a*b - Multiplication a/b - Division a%b - Floating point remainder (fmod function in C) a^b - Exponentiation a>b - Greater than comparison a>=b - Greater than or equal to comparison a<b - Less than comparison a<=b - Less than or equal to comparison a==b - Logical equals a!=b - Logical not equal a&&b - Logical "and" comparison a||b - Logical "or" comparison !a - Logical "not"
Functions:
exp(x) - exponential of x log(x) - natural logarithm of x log10(x) - base 10 logarithm of x. sqrt(x) - square root of x. abs(x) - absolute value of x. max(x,y) - the larger of x or y min(x,y) - the smaller of x or y hypot(x,y) - sqrt(x*x+y*y) sin(x) - trigonometric sine of x; input in radians cos(x) - trigonometric cosine of x; input in radians tan(x) - trigonometric tangent of x; input in radians sindegr(x) - trigonometric sine of x; input in degrees cosdegr(x) - trigonometric cosine of x; input in degrees tandegr(x) - trigonometric tangent of x; input in degrees asin(x) - inverse sine of x; output in radians acos(x) - inverse cosine of x; output in radians atan2(y,x) - 4 quadrant inverse tangent of y/x; output in radians asindegr(x) - inverse sine of x; output in degrees acosdegr(x) - inverse cosine of x; output in degrees atan2degr(y,x) - 4 quadrant inverse tangent of y/x; output in degrees sinh(x) - hyperbolic sine of x cosh(x) - hyperbolic cosine of x tanh(x) - hyperbolic tangent of x asinh(x) - inverse hyperbolic sine of x acosh(x) - inverse hyperbolic cosine of x atanh(x) - inverse hyperbolic tangent of x erf(x) - error function of x erfc(x) - complimentary error function of x gamma(x) - gamma function of x lgamma(x) - natural logarithm of the gamma function of x theta(x) - 1 for x >= 0, 0 for x < 0 round(x) - round x to the nearest integer ceil(x) - smallest integer that is >= x floor(x) - largest integer that is <= x rand() - random number drawn from a uniform distribution between 0 and 1 gauss() - random number drawn from a normal distribution with 0 mean and unit variance
Constants:
pi e
Special Variables:
NR - image index in the light curve starting from 0 NF - light curve index starting from 0
Functions in the "astrofuncs" library: to use these functions include "-F astrofuncs" in your call to VARTOOLS.
EccentricAnomaly(M,e) - returns the eccentric anomaly in radiansM - mean anomaly in radians e - eccentricityMeanAnomaly(dt,P) - returns the mean anomaly in radiansdt - time since periastron P - orbital periodMeanAnomalyConjunction(dt,P,e,omega) - returns the mean anomaly in radiansdt - time since conjunction (or transit) P - orbital period e - eccentricity omega - argument of periastron in degreesTransitQuadLD(dt,P,b,Rp/R*,a/R*,e,omega,u1,u2) - returns the relative flux of a source in transit using the Mandel & Agol 2002 semi-analytic transit model for quadratic limb darkening. A value of 1 is returned for out-of-transit observations, and a value less than 1 will be returned for in-transit observations.dt - time since transit P - orbital period b - impact parameter at conjunction normalized to the stellar radius Rp/R* - planet to stellar radius ratio a/R* - semi-major axis in units of the stellar radius e - eccentricity omega - argument of periastron in degrees u1 - first quadratic limb darkening coefficient u2 - second quadratic limb darkening coefficientTransitNonlinLD(dt,P,b,Rp/R*,a/R*,e,omega,a1,a2,a3,a4) - returns the relative flux of a source in transit using the Mandel & Agol 2002 semi-analytic transit model for a 4 parmeter non-linear limb darkening law. A value of 1 is returned for out-of-transit observations, and a value less than 1 will be returned for in-transit observations.dt - time since transit P - orbital period b - impact parameter at conjunction normalized to the stellar radius Rp/R* - planet to stellar radius ratio a/R* - semi-major axis in units of the stellar radius e - eccentricity omega - argument of periastron in degrees a1 - first limb darkening coefficient a2 - second limb darkening coefficient a3 - third limb darkening coefficient a4 - fourth limb darkening coefficientBroadeningProfile(delv,dt,P,lambda,vsini,b,Rp/R*,a/R*,e,omega,u1,u2) - returns the (distorted) line broadening function at a given wavelength for a star with a transiting planet.delv - (wl - wl0)*c_light/wl0, where wl is the wavelength to return the broadening function at, wl0 is the central wavelength of the line, and c_light is the speed of light in km/s. dt - time since transit P - orbital period lambda - projected obliquity angle in degrees vsini - projected equatorial rotation velocity of the star, in km/s b - impact parameter at conjunction normalized to the stellar radius Rp/R* - planet to stellar radius ratio a/R* - semi-major axis in units of the stellar radius e - eccentricity omega - argument of periastron in degrees u1 - first quadratic limb darkening coefficient u2 - second quadratic limb darkening coefficientTransitProjectedX(dt,P,lambda,b,Rp/R*,a/R*,e,omega) - returns the sky-projected X position of the center of a planet in its orbit in front of the star, in units of the stellar radius. The coordinate system used has the rotation axis of the star along the Y direction.dt - time since transit P - orbital period lambda - sky-projected obliquity angle in degrees b - impact parameter at conjunction normalized to the stellar radius Rp/R* - planet to stellar radius ratio a/R* - semi-major axis in units of the stellar radius e - eccentricity omega - argument of periastron in degreesTransitProjectedY(dt,P,lambda,b,Rp/R*,a/R*,e,omega) - returns the sky-projected Y position of the center of a planet in its orbit in front of the star, in units of the stellar radius. The coordinate system used has the rotation axis of the star along the Y direction.dt - time since transit P - orbital period lambda - sky-projected obliquity angle in degrees b - impact parameter at conjunction normalized to the stellar radius Rp/R* - planet to stellar radius ratio a/R* - semi-major axis in units of the stellar radius e - eccentricity omega - argument of periastron in degreesRV_E(E,e,omega,K) - returns the radial velocity of an object on a Keplerian orbit given the mean anomaly as the input time unit. The radial velocity will be in the same units as K.M - mean anomaly in radians e - eccentricity omega - argument of periastron in degrees K - RV semi-amplitudeRV_dt(E,e,omega,K) - returns the radial velocity of an object on a Keplerian orbit given the time from conjection of its companion as the input time unit (e.g., this is the radial velocity of a transiting planet host star given the time since transit). The radial velocity will be in the same units as K.dt - time from conjunction P - orbital period e - eccentricity omega - argument of periastron in degrees K - RV semi-amplitudeRV_dtp(E,e,omega,K) - returns the radial velocity of an object on a Keplerian orbit given the time from periastron as the input time unit. The radial velocity will be in the same units as K.dt - time from periastron P - orbital period e - eccentricity omega - argument of periastron in degrees K - RV semi-amplitude