Fermi Gamma-ray Space Telescope

Barycentric Correction

Ideally a detector in an inertial frame should observe a pulsar in an inertial frame. However, Fermi is not in an inertial frame: the spacecraft is in orbit around the Earth, which in turn is in orbit around the Sun. In addition, the spacecraft is in the gravitational potential well of the Earth and of the Sun, resulting in general relativistic effects. The pulsar may be in a binary system, with the resulting effects from the binary orbit and gravitational potential well. The transformation from Fermi's frame to an inertial frame and from the pulsar's frame to an inertial frame can be achieved by 'correcting' the arrival time of a photon produced by the pulsar to what it would have been had it been emitted and received in inertial frames. Since the Solar System is assumed to be nearly in an inertial frame—the System's acceleration is assumed to be negligible—the correction places the hypothetical ideal receiver at the Solar System's barycenter, hence this correction is called the 'barycentric correction.' Note that Jupiter's mass displaces the Solar System's barycenter so that it is slightly outside the Sun.

The transformation to inertial frames can be broken into a number of physical effects. Since these effects are small relative to the travel time of the photon from the pulsar to Fermi, they can be added linearly. Analysis of the relative magnitudes of these effects shows that the dominant effects result from the difference in photon travel time and the potential well of the Earth and Sun.

The event arrival times are usually converted in a series of steps, resulting in sequence of different time systems:

Conversion Convert from Convert to Light travel time Time system conversion
Geocentric correction Mission Elapsed Time Geocentric time ±23 ms at maximum From Mission Elapsed Time to Terrestrial Time (TT)
Barycentric correction Geocentric time Barycentric time ±500 s at maximum From TT to Barycentric Dynamical Time (TDB)
Binary demodulation Barycentric time Binary-demodulated time Depends on binary parameters None

The Fermi pulsar tools carry out this arrival time correction using Fermi-specific routines based on the FTOOL faxbary; faxbary has been thoroughly tested and used for various other missions. The position of the Earth relative to the Solar System barycenter is calculated from JPL Planetary Ephemeris DE-405 as a default. Because some pulsar timing is done using the older DE-200 Planetary Ephemeris, it is possible to select this system within the pulsar tools.

For micro-second precision timing, relativistic effects are not negligible. Such effects include: the Shapiro delay in the Solar System, aberration due to the motion of the spacecraft around the Earth and the motion of the Earth around the Sun, and relativistic delay at the source (for binary pulsars only). These effects are included in the Fermitools.

Performing the Barycentric Correction

To perform the barycentric correction we need the list of event arrival times at the spacecraft, the position of the spacecraft at these times, and the pulsar's position in the sky. Thus, the user must supply the tool with an event file (with the arrival times), a spacecraft file (with a history of the spacecraft position), and the RA and Dec of the pulsar.

In routine analysis of a pulsar with a known ephemeris, gtpphase does the barycentric correction at run time without changing the original arrival times of the events in the data stream.

For permanent conversion of the arrival time of the event to the barycenter, the tool gtbary replaces the arrival time for each event in the input event file with the corrected arrival times. The input and output event files can have the same name (although there is an option for providing an alternate name), and the tool's operation is irreversible. This conversion would be appropriate when searching for an unknown or poorly-known pulsar period.

The time range in the spacecraft file must begin before, and end after, the time range in the event file; the beginning or end times of these two time ranges should not be the same.

The Fermitools assume that the spacecraft position in the spacecraft file is given in meters. This will normally not be a concern since the software that creates the spacecraft file follows this convention. However, if you create a new spacecraft file, or modify an existing one, do not use a different length unit (e.g., centimeters or kilometers) for the position.

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