TEMPO2 tutorial
George Hobbs (饺子), Research Scientist
CSIRO Australia Telescope National Facility,
International Young Scientist of NTSC
george.hobbs@csiro.au
Content
• TEMPO2 is a software package. It implements “pulsar timing”
algorithms.
• Section 1: What TEMPO2 has been used for. Overview of
TEMPO2
• Section 2: How to use TEMPO2
• Section 3: How to develop TEMPO2
• Major TEMPO2 developers (software and algorithms): G. Hobbs, R. Edwards,
R. Manchester, W. Coles, X. You, M. Keith, F. Jenet, D. Yardley, J. Verbiest, …
CSIRO. TEMPO2
What has tempo2 been used for in
2010/2011?
• Searching for gravitational wave signals (e.g., Yardley et al. 2011,
Yardley et al. 2010, Abbott et al. 2010, van Haasteren et al. 2010)
• Using pulsars as navigational aids (Ruggiero 2011)
• Statistical analysis of timing residuals (e.g., Na, X. S. et al., 2011,
Hobbs et al. 2010)
• Studying emission geometry (e.g., Noutsos et al., 2011)
• Searching for gamma-ray pulsars (Ray et al., 2010)
• Determining pulsar masses (Demorest et al. 2010)
• Studying pulsations from main-sequence stars (Ravi et al. 2010)
• Tests of relativity (Weisberg et al. 2010)
• Measuring Jupiter’s mass (Champion et al. 2010)
• Observations of glitches (Chukwude et al. 2010)
• Analysis of accreting millisecond X-ray pulsar (Patruno et al. 2010)
• Relativistic spin precession (Manchester et al. 2010)
CSIRO. TEMPO2
What does tempo2 do?
• USAGE 1:
• Start with file of pulse arrival times
• Start with model of a pulsar’s spin, astrometric and orbital
parameters
• -> pulsar timing residuals
• USAGE 2:
• Start with pulsar timing model
-> predict the pulse phase and frequency at a given
observatory at a given time
CSIRO. TEMPO2
A parameter file (.par)
Pulsar name,
astrometric,
rotational,
dispersion
measure and
orbital
parameters
Fit for this
parameter?
Realisation of
terrestrial time
Solar system
ephemeris
Weighted fit?
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An arrival time file (.tim)
States that this is a tempo2
format file
Filename or identifier
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Observing
frequency (MHz)
Site arrival
time (MJD)
Telescope
code
Uncertainty on
arrival time (us)
User defined
flags
How does tempo2 work?
• The algorithms are based on those implemented in TEMPO1
• Details in Hobbs, Edwards & Manchester (2006) and Edwards,
Hobbs & Manchester (2006)
Clock
corrections
Einstein delay
Shapiro delay
Roemer delay
Conversion of
site-arrivaltime to pulse
emission time
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Atmospheric
delays
Dispersive
delay
Secular
motion (e.g.,
radial velocity)
Orbital
motion
Details: clock correction
• Must convert from the observatory time standard to a
realisation of terrestrial time TT. Use set of text files containing
the difference between two time standards: pks2gps.clk,
gps2utc.clk, utc2tai.clk, tai2tt_bipm2011.
You’ll find these
files in
$TEMPO2/clock
directory
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Details: Einstein delay
• Pulse arrival times (in terrestrial time) must be converted to the
frame of the Solar System Barycentre.
• TEMPO2 uses the tabulated results of Irwin & Fukushima
(1999)
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Details: Roemer delay
• The Roemer delay is the vacuum light travel time between the
pulse arriving at the observatory and the equivalent arrival time
at the SSB.
pulsar
R kˆ
K = Unit vector
pointing at
pulsar.
Obtained from
RA, DEC,
PMRA,
PMDEC
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Use observatory coordinate file
to know position of observatory
k

Earth
R
R is vector from observatory
to SSB. Use JPL ephemeris,
observatory coordinates and
earth orientation parameters
SSB
Roemer delay
Pulsar in
ecliptic
Ecliptic latitude
= 90 deg
CSIRO. Gravitational wave detection
Details: Shapiro delay
• Time delay caused by the passage of the pulse through large
gravitational fields. Tempo2 includes delay caused by Sun (<
110us), Jupiter (<180ns), Saturn (<58ns), Neptune (<12ns) and
Uranus (<10ns)
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Details: dispersive delay
• D is the dispersion constant. DM (cm-3pc) = 2.410 x 10-16 D
• f is the frequency of the radiation at the Solar System
barycentre
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Details: binary system
• For pulsars in binary
systems, tempo2 includes
parameters describing the
orbital motion.
• Various binary models
exist. Suggest using “T2”
model that combines most
earlier binary models
CSIRO. TEMPO2
Using the pulsar timing model
• Have pulse emission time in the pulsar frame.
• Predict using the pulsar timing model
Pulse frequency (and time
derivatives)
Phase of pulse
sequence
Pulse
emission
time
Reference phase
Time at which
df/dt = n
• Can also include simple model of glitch events
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Timing residuals
Pulse
phase
Timing
residual for
i’th
observation
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Nearest integer
to fi
Pulse frequency
Example
Time
1
2
3
Measured arrival time with observatory clock
Measured arrival time in terrestrial time (Dc)
Measured arrival time in pulsar frame
Predicted arrival
times in pulsar frame
4
5
CSIRO. TEMPO2
Timing residual
Pulsar timing residuals
• If pulsar model predicts the observations perfectly (and the
conversion from the observatory to pulsar frame is perfect) then
R = 0 (within measurement uncertainty).
• If R != 0 then the pulsar model is (1) not accurate or (2) does
not include a physical process that affects the measured arrival
times or (3) the correction from the observatory to pulsar frame
is not correct.
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Pulsar timing residuals: incorrect F0
Pmodel > Ptrue
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Pulsar timing residuals: incorrect F1
Pmodel < Ptrue
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Pmodel > Ptrue
Pulsar timing residuals: incorrect position
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Pulsar timing residuals: incorrect proper motion
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Pulsar timing residuals
Good
parameters
Do not have a
phase
connected
solution
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Phase
wraps
Induced timing residuals from ISM and from
gravitational waves
10cm (~3000MHz)
20cm (~1400MHz)
Induced residuals
from gravitational
wave background
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50cm (~600MHz)
Incorrect conversion to pulsar frame
Champion et al. (2010): induced timing residuals from error in mass of Jupiter
of 5x10-10 Mo
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Predictive mode
• TEMPO2 can provide a polynomial approximation of the phase
and pulse frequency at the observatory for a specified time
interval.
• TEMPO1 creates polycos. TEMPO2 can create polycos, but
we recommend predictors.
• Predictors model the phase as a function of time using
Chebyshev polynomials.
• Tempo2 provides a ‘C library’ to read predictors
Observing frequency range (MHz)
• tempo2 –f mypar.par –pred "sitename mjd1 mjd2 freq1 freq2 ntimecoeff
nfreqcoeff seg_length"
Segment
length (s)
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Time range
Part 2
• Usage of tempo2 and example of pulsar timing
• TEMPO2 is written in C/C++ (with a little Fortran) and runs on linux
and MacOS.
• Main tempo2 website: http://www.atnf.csiro.au/research/pulsar/tempo2
(see “tutorials” and “Documentation”)
• Main tempo2 download site:
• http://sourceforge.net/projects/tempo2
• Tempo2 email distribution list:
• Sign up at http://pulsarastronomy.net (click on “Mailing Lists”)
• Contact: george.hobbs@csiro.au, use feedback form
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Running tempo2
• Need a pulsar model (use the ATNF pulsar catalogue –
http://www.atnf.csiro.au/research/pulsar/psrcat - type in pulsar
name and click ‘Get Ephemeris’)
• Get some pulse arrival times (use Parkes data archive – see
Jonathan’s talk and ‘pat’ in psrchive – see Willem’s talk)
• tempo2 –f psrname.par psrname.tim
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Using the “plk” graphical interface
• tempo2 –gr plk –f mypar.par mytim.tim
Which parameters to fit
Re-do
the fit
What
to plot
The
residuals
Press ‘h’
to get help
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Other useful graphical interfaces: spectrum
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Other useful graphical interfaces: plotMany
tempo2 –gr plotMany –f par1.par tim1.tim –f
par2.par tim2.tim –f par3.par par3.tim …
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The glitch plugin
Yu Meng (in preparation)
Pulse
frequency
Pulse
frequency
with
mean
removed
Pulse
frequency
derivative
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Glitch
events
Using “output” interfaces
• tempo2 –output general –s “Hello f0 = {f0_v} {f0_e}\n f1 = {f1_v}
{f1_e}\n” –f mypar.par mytim.tim
• tempo2 –output general2 –s “freq = {freq}, sat = {sat}, bat =
{bat}, res = {pre}\n” –f mypar.par mytim.tim
• tempo2 –output matrix –f mypar.par mytim.tim
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Part 3: Developing the software
• You should never need to modify the main tempo2 source
code. (Please report any bugs to george.hobbs@csiro.au)
• You should create new “plug-in packages”. These can be for
text output, a graphical interface, methods to select data or new
fitting algorithms.
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Creating a new text output format
• Print out the pulsar model parameters and the timing residuals
in your format
Must include tempo2.h
Must have this function
Pulsar number
Parameter of
interest
Time
derivative
Number of
observations
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Observation
number
Observation
parameter
Creating a new graphical interface
Must include this
function
Must define how
many pulsars to
process
Must process the
command line
arguments
Read parameter and
observation file(s)
Form barycentric
arrival times,
residuals and fit.
Repeat with postfit parameters
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Do your
plotting/analysis
Output format versus graphical interface
• Output format: tempo2 runs as usual then gives control to your
plugin to display the output (easy, but no control over fitting
etc.)
• Graphical interface: tempo2 provides control to your plugin from
the beginning (your plugin must call all the functions to read
data files, do the fit etc., but you have more control)
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The tempo2 toolkits
• To aid development the following toolkits are available:
• T2toolkit.h: find minimum and maximum values in array, find
RMS, mean, range, sort data array, create random numbers
• TKspectrum.h: routines for spectral estimation
• TKfit.h: fitting routines (e.g., SVD, Cholesky decomposition …)
• tempo2Util.h: calculate dot products, turns hh:mm:ss/dd:mm:ss
into degrees
• gwsim.h: gravitational wave simulation routines.
• (NOTE: Many people use “numerical recipes” routines in
plugins – these are copyright and the source code cannot be
made publically available – use the tempo2 toolkits instead)
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Debugging your installation
• Sometimes things don’t work!
• If it doesn’t compile: check that your version of gfortran, gcc
and g++ are the same! Check that pgplot has been correctly
installed.
• It compiles and runs, but doesn’t do anything:
run your code with
> tempo2 …. –f mypar.par mytim.tim –debug –displayVersion >
outfile
and then send your .par, .tim and outfile to
george.hobbs@csiro.au (or any tempo2 developer)
• Your plugin does not work. Check that you have installed the
plugin in $TEMPO2/plugins/
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Publishing results from tempo2
• For general usage, please cite: Hobbs, Edwards & Manchester
(2006)
• For details of the algorithms: Edwards, Hobbs & Manchester
(2006)
• For gravitational wave implementation: Hobbs et al. (2009)
• To enable complete reproducibility of results should include an
appendix including output of –displayVersion.
• Important: publish the clock reference (e.g., TT(TAI)) and Solar
System ephemeris model (e.g., DE405)
CSIRO. TEMPO2
Topics not covered in this presentation
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•
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•
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Simulating data (use fake, GWbkgrd … plugins)
Use of ‘flags’ (use –select, -pass, -filter options)
Atmospheric corrections
Xiaopeng’s Solar Wind model
FERMI gamma-ray plugin
Use of –fitfunc and –splug interfaces
Use of region files
Measuring dispersion measure variations
• Look at the tempo2 tutorials on
http://www.atnf.csiro.au/research/pulsar/tempo2
CSIRO. Gravitational wave detection
The future of tempo2
• Improved binary models
• Plugin to determine irregularities in terrestrial time standards
(see Ding Chen’s talk)
• In-built algorithms to model gravitational waves
• Methods to determine dispersion measure variations
• Improved methods for simulating data
• Algorithms to enable pulsar navigation
• Web-based access tools (so you do not need to install your
own version of tempo2)
•…
CSIRO. TEMPO2
Conclusions
• Tempo2 is a publically available software package for pulsar
timing: http://www.atnf.csiro.au/research/pulsar/tempo2
• Plugin-packages can be developed for specific research topics
• Tempo2 is suitable for all current high-precision pulsar timing
applications
• Tempo2 can process multiple pulsars simultaneously
• Download TEMPO2 and try it out!
• TEMPO2 真的是一个好东西，希望大家都来试试，你
会爱上它的！
• Supported by the Chinese Academy of Sciences #CAS KJCX2-YWT09 and NSFC 10803006. Australian Research Council QEII
Fellowship
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