Investigators using a child protection database traced the child porn to an IP address used at the observatory in July, the warrant states.
The FBI also spoke with the chief observer at the facility, who said he'd found a laptop running in empty offices, which had images on it that were 'not good' and appeared to be child porn, KRQE reported.
The FBI began monitoring the network to see the time of day that the child porn was being sent and received, and found it only matched the presence of one employee: the overnight janitor.
The laptop was confiscated, and the chief observer told investigators that the janitor "feverishly started looking through the facility" when he realized it was missing.
The janitor began making paranoid comments about "lax security at the facility" and said it was "only a matter of time before the facility got ".
The chief observer became concerned for his personal safety after the janitor stated that he "believed there was a serial killer in the area" and that the killer might enter the observatory and execute someone.
At that point the agencies that operate the facility decided to shut it down out of an abundance of caution.
The janitor is the main suspect, although he has yet to be charged in the case.
The observatory has terminated its contract with the cleaning company that employed the janitor, which is owned by the janitor's parents.
For over a week, the sudden closure and evacuation of the facility sparked a swirl of rumours and conspiracy theories.
Secrecy persisted even as local media reported the FBI has showed up to the site, and Blackhawk helicopters were seen circling overhead.
In the week following the initial evacuation, the public proposed all sorts of explanations, with some even suggesting aliens could be at the root of it all.
The frenzy of speculation forced James McAteer, a New Mexico State University professor who is also the director of the Sunspot Solar Observatory, to issue a statement saying that the "telescope did not see aliens."
"All data will be made public in its unaltered form. Nothing is hidden or kept secret," McAteer assured the vexed public.
Among the more down to Earth suggestions, some people proposed that the facility may have suffered a leak at its Richard B. Dunn Solar Telescope, which relies on a mercury float bearing.
However, the team that operates the telescope confirmed last week that there had not been a mercury incident.
Acknowledging the secrecy, Association of Universities for Research in Astronomy (AURA), which manages the facility, said it chose not to release any details due to the investigation.
"We recognize that the lack of communications while the facility was vacated was concerning and frustrating for some," AURA said in a statement.
"However, our desire to provide additional information had to be balanced against the risk that, if spread at the time, the news would alert the suspect and impede the law enforcement investigation. That was a risk we could not take."
AURA says they've since determined it's safe for staff to return.