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According to wikipedia the 1859 Carrington Event was caused by a coronal mass ejection (CME) of plasma.
As it's plasma and not photons it stands to reason that the CME would not be traveling at the speed of light but how fast would it be traveling at? Or does that amount vary?
Of course just because the CME is traveling at a certain speed it doesn't necessarily follow that we'd instantly detect it the moment it left the suns surface either.
Could be as much as an hour.
Looking at NASA's Space Weather Prediction Centre page on CMEs
Imminent CME arrival is first observed by the Deep Space Climate Observatory (DSCOVR) satellite, located at the L1 orbital area. Sudden increases in density, total interplanetary magnetic field (IMF) strength, and solar wind speed at the DSCOVR spacecraft indicate arrival of the CME-associated interplanetary shock ahead of the magnetic cloud. This can often provide 15 to 60 minutes advanced warning of shock arrival at Earth – and any possible sudden impulse or sudden storm commencement; as registered by Earth-based magnetometers.
To supplement Rory Alsop's answer, it is also possible to detect some CMEs through X-ray observations of the Sun. We have a few satellites continually monitoring the Sun, and if we're lucky we'll see the CME when it erupts. That gives an early warning on the order of a day. "Lucky" because it is coming right at us, so sometimes it's not obvious. Active regions on the Sun (like sunspots) are often associated with CMEs. We can keep a close eye on them and be on alert when they are lined up with Earth.
