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In Imperial armor imperial guard codex, the listing for renegades and heretics lets you use from imperial guard liest the Artillery earthshaker battery and Artillery Earth shaker battery carriage.
The difference being that the battery carriage comes with 4 imperial guards.
The listing for Earthshaker battery carriage also says ability: Artillery : that if there are no guardsmen near to operate it, it is removed from play.
The earthshaker battery does not have this under ability, just under keywords.

Can i use Earthshaker battery without having imperial guard troops around them to operate them?

The rules for that unit have been updated in the corresponding faq.

FAQs and errata can be found here https://www.dakkadakka.com/dakkaforum/posts/list/736188.page

from what i read in the faqs it does not address my question.
the only revision says that
Artillery Battery: When this unit is set up on the
battlefield, all models are set up in unit coherency.
From that point onwards, all the Artillery models
are treated as one unit and all the Guardsmen Crew
are treated as another. Guardsmen Crew may only be
chosen as a target in the Shooting phase.

so nothing about earth shaker battery requiring a proximity guardsmen model to be operational

Ah ok.
So we are talking about the difference between the old FW kits.
In the earth shaker battery, the crew are mounted on the platform itself, so don't have a separate profile.
In the carriage battery, the crew walk alongside.

So yes you can fire the battery without needing operators, as they come on the model.

If a weapon doesn't have a restriction or requirement on the Datasheet if doesn't have it.