The sun ignited about 4.6 Billion Years ago, so anyone around 4.6 billion light years away (a little more due to expansion of the universe) could see that there are planets orbiting a star that’s capable of sustaining life could see it with a big enough telescope.
https://en.wikipedia.org/wiki/Sun
Tectonics and water would have been around on Earth for around that same amount of time, so as soon as the Sun fired up, it was showing the universe that there was a planet with water on it.
https://en.wikipedia.org/wiki/Origin_of_water_on_Earth
The Great Oxidation Event happened around 2.5 billion years ago, so anyone 2.5 billion light years away would be able to see it with a big enough telescope, and know that something interesting happened that suddenly released a bunch of Oxygen.
We’ve been ramping up technology for 10,000+ years, but really started dumping interesting chemicals into the atmosphere when the industrial revolution started around 250 years ago (so 10,000 - 250 light years away.)
https://en.wikipedia.org/wiki/Industrial_Revolution
We started firing off nukes in the 1940s, so probably the last 80 years we started showing the universe that we’re nuclear technological intelligence.
So depending on how far away someone is trying to observe us, they’d be able to see different life stages.
Even in another nearby galaxy, they could see the spectral lines of these signatures if they had our telescopes, and used gravitational lensing. They could even park something like the Hubble Space Telescope a couple hundred AU away from their star and use it as a giant telescope to see us from extremely far distances.
Well how far is extremely far? The article you linked says
This would give a resolution of about 10 square kilometers for objects 100 light-years away.
The galaxy is 87k light years across. Is such a resolution good enough to determine the atmospheric composition of any planet in our galaxy? What about other galaxies?
Obviously there is a delay based on the speed of light where time needs to pass before changes can be seen, but I’m wondering what the radius is where these things become invisible no matter how much time passes, if there is such a limit. There might be intelligent life elsewhere in the universe but not in our galaxy, so if the edge of the galaxy was the limit that would be relevant to our security.
You don’t need resolution to do spectral analysis. They’re talking about identifying specific features, which isn’t what we’re talking about.
An ideal situation would be to look at a star (you only need to be able to pick out a single star, which you can do in other galaxies in the right conditions) and have a planet pass between that star and us. You’d see the change in color of the light and from that you can determine a lot about the planet’s atmosphere.
With our current technology, you have to get pretty lucky to have gravitational lensing opportunity along with a planetary transit, but that’s just assuming our level of tech.
With a powerful enough telescope, if you can pick out the specific planet and not get overwhelmed by it’s star’s light, you can do it without being lined up with the star.
If you’re a high tech enough civilization to be an actual threat to another planet, then you can build telescopes in space. If you build telescopes in space, they can be giant, and positioned wherever you want them. If that’s the case then you can likely directly measure the atmosphere of any planet big enough to support life in the entire galaxy, along with plenty of samples in the nearby galaxy.
But also, if you are assuming an alien race that has the capability to transit intergalactic distances in an amount of time that would make them a threat to us, then that means they already have some sort of technology that is so far beyond anything we can currently imagine, that we can already assume they know we are here.
If they can’t traverse those distances, then it doesn’t matter if they know we’re here.
~60 light years.
We’ve been broadcasting for longer, but everything we sent before Cold War Era military RADAR would get filtered out by the atmosphere or drowned out by the sun’s radiation.
Turns out everything since would be hopelessly scrambled almost immediately upon leaving the suns magnetic field and being subjected to the galactic wind (solar wind but… galactic) And we’re only getting more radio quiet as more and more communication becomes wired so we good.
