# How are the atomic clocks synchronised between worldwide VLBI telescopes?

I know that VLBI needs precise synchronised atomic clocks to calculate the baseline distance between the radio telescopes at cm level. But i cant´t find any information how the atomic clocks are kept synchronised over long distances (several thousand kilometres around the world). As far as i know GPS is not accurate enough.... How are atomic clocks kept synchronised on all VLBI telescopes ?

Thanks a lot :)

• Good question. My guess is they use some form of TWSTFT. That article is a stub, but the NIST link looks pretty good. The BIPM site probably has all the details of how they synch the 400 clicks in the TAI network. – PM 2Ring Nov 4 '19 at 12:20
• Many thanks :) That sounds like a possible solution to keep the time synchronized:) Thanks a lot :) – Andy Nov 4 '19 at 13:28
• eventhorizontelescope.org/blog/eht-update mentions GPS synchronisation. I think accuracy far beyond the norms of GPS can be obtained when multiple radio telescopes observe the same GPS satellite at the same time. – Steve Linton Nov 4 '19 at 15:51
• eventhorizontelescope.org/science has even more. It seems they use the GPS for microsecond accuracy and the hydrogen maser for picosecond relative accuracy within a recording and then solve for the remainign inaccuracy in the sychronisayttion as part fo the correlation – Steve Linton Nov 4 '19 at 15:56
• @SteveLinton looks like combining your comments would constitute an answer – Carl Witthoft Nov 4 '19 at 19:34

You don't have to have an absolute time standard reference for each telescope in a VLBI array, and it isn't feasible to do so at the precision needed to track the phase of 1.3mm waves with a frequency of $$2.3\times 10^{11}$$ Hz.

What you have is a very precise and stable local oscillator (a hydrogen maser) that timestamps all the data recorded locally. This is supplemented by GPS signals to put the data roughly in the same absolute timeframe - or "coarse synchronisation", as the M87 VLBI data-processing paper by Akiyama et al (2019) puts it.

The data are recorded and brought together for correlation. Each pair of signals (from a pair of telescopes) is roughly corrected for where they are on the Earth, the expected phase delays due to the atmosphere and the timestamp recorded from GPS. This process can only be done for about 1 second of data at a time before coherence is lost due to changes in atmospheric conditions.

Each correlation dataset is then fed into a global optimisation algorithm that allows small variations in phase due to clock errors and atmospheric variability or delays in the electronics at each site. The aim is to maximise the visibility of the inteference fringes. You might think that this approach might have too many degrees of freedom, but of course you cannot arbitrarily change the phase offset at one station without upsetting the fringe visibility seen between that station and other stations. The gist of this can be gathered by looking at the wikipedia entry on closure phase, though the actualy algorithms used for VLBI appear to be considerably more sophisticated.

They don’t have to synchronize the atomic clocks at each telescope. Instead, they synchronize the collections using GPS (so the telescopes observe the same target in the same frequency range at the same time), as shown in the diagram from this paper.

When the data is brought together, they use differences between the arrival times of quasar data to calculate relative antenna locations. From this paper from NASA:

During geodetic VLBI observations, signals emitted by distant sources of radio frequency energy (quasars) are received and recorded at several antennas. At each antenna (VLBI station) a very stable frequency standard (hydrogen maser) provides a reference signal that enables time tagging of the quasar signals as they are being recorded. For each VLBI experiment, correlation of the time-tagged, recorded information from the participating antennas yields the differences among the arrival times of any specific quasar radio wave at the antennas. These time differences are used to calculate the locations of the antennas with respect to each other.

• Credit to Steve Linton's comments above for putting me on the right track to this answer. – Connor Garcia Dec 5 '20 at 20:12