Timing Models

PINT, like TEMPO and TEMPO2, support many different ways of calculating pulse arrival times. The key tool for doing this is a TimingModel object, through which a whole range of Parameter are accessible. The actual computation is done by pieces of code that live in Component; during the parsing of a parameter file, these are selected based on the parameters present. Binary models are selected explicitly using the BINARY parameter, while each non-binary component is selected if some parameter unique to it is included (for example if ELAT is present, AstrometryEcliptic is selected). Ambiguous or contradictory parameter files are possible, and for these PINT raises an exception.

Components supported by PINT:

  • AbsPhase - Absolute phase model.

  • AstrometryEcliptic - Astrometry in ecliptic coordinates.

  • AstrometryEquatorial - Astrometry in equatorial coordinates.

  • BinaryBT - Blandford and Teukolsky binary model. (BINARY BT)

  • BinaryBTPiecewise - Model implementing the BT model with piecewise orbital parameters A1X and T0X. This model lets the user specify time ranges and fit for a different piecewise orbital parameter in each time range, (BINARY BT_piecewise)

  • BinaryDD - Damour and Deruelle binary model. (BINARY DD)

  • BinaryDDGR - Damour and Deruelle model assuming GR to be correct (BINARY DDGR)

  • BinaryDDH - DD modified to use H3/STIGMA parameter for Shapiro delay. (BINARY DDH)

  • BinaryDDK - Damour and Deruelle model with kinematics. (BINARY DDK)

  • BinaryDDS - Damour and Deruelle model with alternate Shapiro delay parameterization. (BINARY DDS)

  • BinaryELL1 - ELL1 binary model. (BINARY ELL1)

  • BinaryELL1H - ELL1 modified to use H3 parameter for Shapiro delay. (BINARY ELL1H)

  • BinaryELL1k - ELL1k binary model. (BINARY ELL1k)

  • ChromaticCM - Simple chromatic delay model.

  • DMWaveX -

  • DispersionDM - Simple DM dispersion model.

  • DispersionDMX - This class provides a DMX model - multiple DM values.

  • DispersionJump - This class provides the constant offsets to the DM values.

  • EcorrNoise - Noise correlated between nearby TOAs.

  • FD - A timing model for frequency evolution of pulsar profiles.

  • FDJump - A timing model for system-dependent frequency evolution of pulsar

  • FDJumpDM - This class provides system-dependent DM offsets for narrow-band

  • Glitch - Pulsar spin-down glitches.

  • IFunc - This class implements tabulated delays.

  • PLDMNoise - Model of DM variations as radio frequency-dependent noise with a

  • PLRedNoise - Timing noise with a power-law spectrum.

  • PhaseJump - Arbitrary jumps in pulse phase.

  • PhaseOffset - Explicit pulse phase offset between physical TOAs and the TZR TOA.

  • PiecewiseSpindown - Pulsar spin-down piecewise solution.

  • ScaleDmError - Correction for estimated wideband DM measurement uncertainty.

  • ScaleToaError - Correct reported template fitting uncertainties.

  • SolarSystemShapiro - Shapiro delay due to light bending near Solar System objects.

  • SolarWindDispersion - Dispersion due to the solar wind (basic model).

  • SolarWindDispersionX - This class provides a SWX model - multiple Solar Wind segments.

  • Spindown - A simple timing model for an isolated pulsar.

  • TroposphereDelay - Model for accounting for the troposphere delay for topocentric TOAs.

  • Wave - Delays expressed as a sum of sinusoids.

  • WaveX -

Supported Parameters

The following table lists all the parameters that PINT can understand (along with their aliases). The model components that use them (linked below) should give more information about how they are interpreted.

Some parameters PINT understands have aliases - for example, the parameter PINT calls “ECC” may also be written as “E” in parameter files. PINT will understand these parameter files, but will always refer to this parameter internally as “ECC”. By default, though, when PINT reads a parameter file, PINT will remember the alias that was used, and PINT will write the model out using the same alias. This can be controlled by the use_alias attribute of Parameter objects.

PINT support for families of parameters, either specified by prefix (F0, F1, F2, … or DMX_0017, DMX_0123, …) or selecting subsets of parameters based on flags (JUMP -tel AO). These are indicated in the table with square brackets. Note that like the frequency derivatives, these families may have units that vary in a systematic way.

Parameters can also have different types. Most are long double floating point, with or without units; these can be specified in the usual 1.234e5 format, although they also support 1.234d5 as well as capitalized versions for compatibility. One or two parameters - notably A1DOT - can accept a value scaled by 1e12, automatically rescaling upon read; although this is confusing, it is necessary because TEMPO does this and so there are parameter files “in the wild” that use this feature. Other data types allow input of different formats, for example RAJ 10:23:47.67; boolean parameters allow 1/0, Y/N, T/F, YES/NO, TRUE/FALSE, or lower-case versions of these.

Name / Aliases

Description

Kind

Components

A0

DD model aberration parameter A0

s

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

A1

Projected semi-major axis of pulsar orbit, ap*sin(i)

ls

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

BinaryELL1k

A1DOT / XDOT

Derivative of projected semi-major axis, d[ap*sin(i)]/dt

ls / s

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

BinaryELL1k

A1X_{number}

ParameterA1variation

ls

BinaryBTPiecewise

B0

DD model aberration parameter B0

s

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BINARY

Pulsar System/Binary model

string

TimingModel

CHI2

Chi-squared value obtained during fitting

number

TimingModel

CHI2R

Reduced chi-squared value obtained during fitting

number

TimingModel

CLOCK / CLK

Timescale to use

string

TimingModel

CM

Chromatic measure

pc / (MHz2 cm3)

ChromaticCM

CMEPOCH

Epoch of CM measurement

d

ChromaticCM

CM{number}

1’th time derivative of the chromatic measure

pc / (yr MHz2 cm3)

ChromaticCM

CORRECT_TROPOSPHERE

Enable Troposphere Delay Model

boolean

TroposphereDelay

DECJ / DEC

Declination (J2000)

deg

AstrometryEquatorial

DILATEFREQ

Whether or not TEMPO2 should apply gravitational redshift and time dilation to observing frequency (Y/N; PINT only supports N)

boolean

TimingModel

DM

Dispersion measure

pc / cm3

DispersionDM

DMDATA

Was the fit done using per-TOA DM information?

boolean

TimingModel

DMEFAC {flag} {value}

A multiplication factor on the measured DM uncertainties,

number

ScaleDmError

DMEPOCH

Epoch of DM measurement

d

DispersionDM

DMEQUAD {flag} {value}

An error term added in quadrature to the scaled (by EFAC) TOA uncertainty.

pc / cm3

ScaleDmError

DMJUMP {flag} {value}

Wideband DM value offset.

pc / cm3

DispersionJump

DMRES

DM residual after fitting (wideband only)

pc / cm3

TimingModel

DMWXCOS_{number}

Cosine amplitudes for Fourier representation of DM noise

dmu

DMWaveX

DMWXEPOCH

Reference epoch for Fourier representation of DM noise

d

DMWaveX

DMWXFREQ_{number}

Component frequency for Fourier representation of DM noise

1 / d

DMWaveX

DMWXSIN_{number}

Sine amplitudes for Fourier representation of DM noise

dmu

DMWaveX

DMX

Dispersion measure

pc / cm3

DispersionDMX

DMXR1_{number}

Beginning of DMX interval

d

DispersionDMX

DMXR2_{number}

End of DMX interval

d

DispersionDMX

DMX_{number}

Dispersion measure variation

pc / cm3

DispersionDMX

DM{number}

1’th time derivative of the dispersion measure

pc / (yr cm3)

DispersionDM

DR

Relativistic deformation of the orbit

number

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

DTH / DTHETA

Relativistic deformation of the orbit

number

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

ECC / E

Eccentricity

number

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

BinaryELL1k

ECL

Obliquity of the ecliptic (reference)

string

AstrometryEcliptic

ECORR {flag} {value} / TNECORR {flag} {value}

An error term that is correlated among all TOAs in an observing epoch.

us

EcorrNoise

EDOT

Eccentricity derivative respect to time

1 / s

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

EFAC {flag} {value} / T2EFAC {flag} {value}, TNEF {flag} {value}

A multiplication factor on the measured TOA uncertainties,

number

ScaleToaError

ELAT / BETA

Ecliptic latitude

deg

AstrometryEcliptic

ELONG / LAMBDA

Ecliptic longitude

deg

AstrometryEcliptic

EPHEM

Ephemeris to use

string

TimingModel

EPS1

First Laplace-Lagrange parameter, ECC*sin(OM)

number

BinaryELL1

BinaryELL1H

BinaryELL1k

EPS1DOT

First derivative of first Laplace-Lagrange parameter

1e-12 / s

BinaryELL1

BinaryELL1H

EPS2

Second Laplace-Lagrange parameter, ECC*cos(OM)

number

BinaryELL1

BinaryELL1H

BinaryELL1k

EPS2DOT

Second derivative of first Laplace-Lagrange parameter

1e-12 / s

BinaryELL1

BinaryELL1H

EQUAD {flag} {value} / T2EQUAD {flag} {value}

An error term added in quadrature to the scaled (by EFAC) TOA uncertainty.

us

ScaleToaError

FB{number}

0th time derivative of frequency of orbit

1 / s

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

BinaryELL1k

FD10JUMP {flag} {value}

System-dependent FD parameter of polynomial index 10

s

FDJump

FD11JUMP {flag} {value}

System-dependent FD parameter of polynomial index 11

s

FDJump

FD12JUMP {flag} {value}

System-dependent FD parameter of polynomial index 12

s

FDJump

FD13JUMP {flag} {value}

System-dependent FD parameter of polynomial index 13

s

FDJump

FD14JUMP {flag} {value}

System-dependent FD parameter of polynomial index 14

s

FDJump

FD15JUMP {flag} {value}

System-dependent FD parameter of polynomial index 15

s

FDJump

FD16JUMP {flag} {value}

System-dependent FD parameter of polynomial index 16

s

FDJump

FD17JUMP {flag} {value}

System-dependent FD parameter of polynomial index 17

s

FDJump

FD18JUMP {flag} {value}

System-dependent FD parameter of polynomial index 18

s

FDJump

FD19JUMP {flag} {value}

System-dependent FD parameter of polynomial index 19

s

FDJump

FD1JUMP {flag} {value}

System-dependent FD parameter of polynomial index 1

s

FDJump

FD20JUMP {flag} {value}

System-dependent FD parameter of polynomial index 20

s

FDJump

FD2JUMP {flag} {value}

System-dependent FD parameter of polynomial index 2

s

FDJump

FD3JUMP {flag} {value}

System-dependent FD parameter of polynomial index 3

s

FDJump

FD4JUMP {flag} {value}

System-dependent FD parameter of polynomial index 4

s

FDJump

FD5JUMP {flag} {value}

System-dependent FD parameter of polynomial index 5

s

FDJump

FD6JUMP {flag} {value}

System-dependent FD parameter of polynomial index 6

s

FDJump

FD7JUMP {flag} {value}

System-dependent FD parameter of polynomial index 7

s

FDJump

FD8JUMP {flag} {value}

System-dependent FD parameter of polynomial index 8

s

FDJump

FD9JUMP {flag} {value}

System-dependent FD parameter of polynomial index 9

s

FDJump

FDJUMPDM {flag} {value}

System-dependent DM offset.

pc / cm3

FDJumpDM

FDJUMPLOG

Whether to use log-frequency (Y) or linear-frequency (N) for computing FDJUMPs.

boolean

FDJump

FD{number}

Polynomial coefficient of log-frequency-dependent delay

s

FD

FINISH

End MJD for fitting

d

TimingModel

F{number}

Spin-frequency

Hz

Spindown

GAMMA

Time dilation & gravitational redshift

s

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

GLEP_{number}

Epoch of glitch 1

d

Glitch

GLF0D_{number}

Decaying frequency change for glitch 1

Hz

Glitch

GLF0_{number}

(‘Permanent frequency change for glitch 1’,)

Hz

Glitch

GLF1_{number}

(‘Permanent frequency-derivative change for glitch 1’,)

Hz / s

Glitch

GLF2_{number}

(‘Permanent second frequency-derivative change for glitch 1’,)

Hz / s2

Glitch

GLPH_{number}

Phase change for glitch 1

number

Glitch

GLTD_{number}

Decay time constant for glitch 1

d

Glitch

H3

Shapiro delay parameter H3 as in Freire and Wex 2010 Eq(20)

s

BinaryDDH

BinaryELL1H

H4

Shapiro delay parameter H4 as in Freire and Wex 2010 Eq(21)

s

BinaryELL1H

IFUNC{number}

Interpolation control point pair (MJD, delay)

s

IFunc

INFO

Tells TEMPO to write some extra information about frontend/backend combinations; -f is recommended

string

TimingModel

JUMP {flag} {value}

Phase jump for selection.

s

PhaseJump

K96

Flag for Kopeikin binary model proper motion correction

boolean

BinaryDDK

KIN

Inclination angle

deg

BinaryDDK

KINIAU

Inclination angle in the IAU convention

deg

BinaryDDK

KOM

The longitude of the ascending node

deg

BinaryDDK

KOMIAU

The longitude of the ascending node in the IAU convention

deg

BinaryDDK

LNEDOT

Log-derivative of the eccentricity EDOT/ECC

1 / yr

BinaryELL1k

M2

Companion mass

solMass

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1k

MP

Pulsar mass

solMass

BinaryDDGR

MTOT

Total system mass in units of Solar mass

solMass

BinaryDDGR

NE_SW / NE1AU, SOLARN0

Solar Wind density at 1 AU

1 / cm3

SolarWindDispersion

NHARMS

Number of harmonics for ELL1H shapiro delay.

integer

BinaryELL1H

NTOA

Number of TOAs used in the fitting

integer

TimingModel

OM

Longitude of periastron

deg

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

BinaryELL1k

OMDOT

Rate of advance of periastron

deg / yr

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

BinaryELL1k

PB

Orbital period

d

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

BinaryELL1k

PBDOT

Orbital period derivative respect to time

number

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1H

BinaryELL1k

PEPOCH

Reference epoch for spin-down

d

Spindown

PHOFF

Overall phase offset between physical TOAs and the TZR TOA.

number

PhaseOffset

PLANET_SHAPIRO

Include planetary Shapiro delays

boolean

SolarSystemShapiro

PMDEC

Proper motion in DEC

mas / yr

AstrometryEquatorial

PMELAT / PMBETA

Proper motion in ecliptic latitude

mas / yr

AstrometryEcliptic

PMELONG / PMLAMBDA

Proper motion in ecliptic longitude

mas / yr

AstrometryEcliptic

PMRA

Proper motion in RA

mas / yr

AstrometryEquatorial

POSEPOCH

Reference epoch for position

d

AstrometryEquatorial

AstrometryEcliptic

PSR / PSRJ, PSRB

Source name

string

TimingModel

PWEP_{number}

(‘Epoch of solution piece 1’,)

d

PiecewiseSpindown

PWF0_{number}

Frequency of solution piece 1

Hz

PiecewiseSpindown

PWF1_{number}

Frequency-derivative of solution piece 1

Hz / s

PiecewiseSpindown

PWF2_{number}

Second frequency-derivative of solution piece 1

Hz / s2

PiecewiseSpindown

PWPH_{number}

(‘Starting phase of solution piece 1’,)

number

PiecewiseSpindown

PWSTART_{number}

(‘Start epoch of solution piece 1’,)

d

PiecewiseSpindown

PWSTOP_{number}

(‘Stop epoch of solution piece 1’,)

d

PiecewiseSpindown

PX

Parallax

mas

AstrometryEquatorial

AstrometryEcliptic

RAJ / RA

Right ascension (J2000)

hourangle

AstrometryEquatorial

RM

Rotation measure

rad / m2

TimingModel

RNAMP

Amplitude of powerlaw red noise.

number

PLRedNoise

RNIDX

Spectral index of powerlaw red noise.

number

PLRedNoise

SHAPMAX

Function of inclination angle

number

BinaryDDS

SIFUNC

Type of interpolation

number

IFunc

SINI

Sine of inclination angle

number

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

BinaryELL1

BinaryELL1k

START

Start MJD for fitting

d

TimingModel

STIGMA / VARSIGMA, STIG

Shapiro delay parameter STIGMA as in Freire and Wex 2010 Eq(12)

number

BinaryDDH

BinaryELL1H

SWM

Solar Wind Model (0 is from Edwards+ 2006, 1 is from You+2007,2012/Hazboun+ 2022)

integer

SolarWindDispersion

SWP

Solar Wind Model radial power-law index (only for SWM=1)

number

SolarWindDispersion

SWXDM_{number}

Max Solar Wind DM

pc / cm3

SolarWindDispersionX

SWXP_{number}

Solar wind power-law index

number

SolarWindDispersionX

SWXR1_{number}

Beginning of SWX interval

d

SolarWindDispersionX

SWXR2_{number}

End of SWX interval

d

SolarWindDispersionX

T0

Epoch of periastron passage

d

BinaryBT

BinaryBTPiecewise

BinaryDD

BinaryDDS

BinaryDDGR

BinaryDDH

BinaryDDK

T0X_{number}

ParameterT0variation

d

BinaryBTPiecewise

T2CMETHOD

Method for transforming from terrestrial to celestial frame (IAU2000B/TEMPO; PINT only supports ????)

string

TimingModel

TASC

Epoch of ascending node

d

BinaryELL1

BinaryELL1H

BinaryELL1k

TIMEEPH

Time ephemeris to use for TDB conversion; for PINT, always FB90

string

TimingModel

TNCHROMIDX

Chromatic measure index

number

ChromaticCM

TNDMAMP

Amplitude of powerlaw DM noise in tempo2 format

number

PLDMNoise

TNDMC

Number of DM noise frequencies.

number

PLDMNoise

TNDMGAM

Spectral index of powerlaw DM noise in tempo2 format

number

PLDMNoise

TNEQ {flag} {value}

An error term added in quadrature to the scaled (by EFAC) TOA uncertainty in units of log10(second).

dex(s)

ScaleToaError

TNREDAMP

Amplitude of powerlaw red noise in tempo2 format

number

PLRedNoise

TNREDC

Number of red noise frequencies.

number

PLRedNoise

TNREDGAM

Spectral index of powerlaw red noise in tempo2 format

number

PLRedNoise

TRACK

Tracking Information

string

TimingModel

TRES

TOA residual after fitting

us

TimingModel

TZRFRQ

The frequency of the zero phase TOA.

MHz

AbsPhase

TZRMJD

Epoch of the zero phase TOA.

d

AbsPhase

TZRSITE

Observatory of the zero phase TOA.

string

AbsPhase

UNITS

Units (TDB assumed)

string

TimingModel

WAVEEPOCH

Reference epoch for wave solution

d

Wave

WAVE_OM

Base frequency of wave solution

1 / d

Wave

WAVE{number}

Wave components

s

Wave

WXCOS_{number}

Cosine amplitudes for Fourier representation of red noise

s

WaveX

WXEPOCH

Reference epoch for Fourier representation of red noise

d

WaveX

WXFREQ_{number}

Component frequency for Fourier representation of red noise

1 / d

WaveX

WXSIN_{number}

Sine amplitudes for Fourier representation of red noise

s

WaveX

XOMDOT

Excess longitude of periastron advance compared to GR

deg / yr

BinaryDDGR

XPBDOT

Excess Orbital period derivative respect to time compared to GR

number

BinaryDDGR

XR1_{number}

Beginning of paramX interval

d

BinaryBTPiecewise

XR2_{number}

End of paramX interval

d

BinaryBTPiecewise

For comparison, there is a table of parameters that TEMPO supports.