Which stars can see Earth as a transiting exoplanet?
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This is a common sci-fi trope (“Contact”), but I have no idea whether it’s actually true that our radio emissions would be trivially detectable tens of light years away.
Very, very unlikely that someone can hear us, even if they tried. Space is huge.
Edit: I think there are thousands of stars within 200ly of Earth.
Could be more efficient, but this interactive does the trick; shows how loaded our neighborhood is.
Going to hamburger menu -> settings -> show labels brings it to a crawl, though filtering objects helps that a bunch.
Showing only stars with known planets is rather interesting.
https://en.wikipedia.org/wiki/Proxima_Centauri
http://www.icc.dur.ac.uk/~tt/Lectures/Galaxies/LocalGroup/Ba...
One of the papers cited in the OP argues that a good indicator that there's something interesting about a planet is the combination of molecular oxygen and methane in its atmosphere - the former is a strong oxidiser, while the latter is a reducing gas, so there's some dynamic system producing free methane in the atmosphere.
You can see the list of stars which would have recently started seeing the first glimpses of the BMEWS Line radars here: https://en.wikipedia.org/wiki/List_of_star_systems_within_55...
Obviously many other radars (DEW, Hen House, etc.) are doing the same thing, but BMEWS has continuous operation and power on its side.
There's also little chance of those beams will ever hit the same observer. The inverse square law also means that a potential observer would need to be in a relatively small radius from our system.
First, the ionosphere bounces a lot of radio traffic right back down to the planet, amateur radio operators (like me) use that to talk to stations farther away on planet but it doesn't go into space.
Second the frequencies that do travel through the ionosphere are typically aimed at satellites (geosynchronous or lower) and are scaled to have a level of power that gets there reliably but without an overly large margin for error.
Third, the Sun is a very "noisy" source of RF energy and someone looking this way at us would also be looking at the Sun as well (if you're looking at transits). In terms of radio frequencies that they could perhaps analyze it would require a lot of filtering.
The analysis we've done on transiting planets so far is based on spectroscopy using the star as a huge light source and looking for how that light is filtered by the 'edges' of the planet. (so through the atmosphere of the planet).
If they are doing that, then the change in atmosphere composition over the last 1000 years seems like it would be detectable.
Interesting to think what conclusions would be drawn in these scenarios. Obviously atmospheric composition has drastically changed over the eons - I wonder what sort of civilization could detect these kind of longterm changes, and if they wouldn't have better observational capabilities than what we assume here given they have persistent knowledge over "long" timespans
Oxygen however. Just the fact that our atmosphere is as far out of equilibrium as it is.
They might notice a change in our atmosphere's composition, but honestly a 200 ppm to 400 ppm change of some trace gas over the course of two hundred years could have many much simpler explanations than "intelligent life dug up all the carbon and burned it".
Some people start longer discussions ("ragchews") from there. Though this is more common in regional communication. Topics can be all kinds of things, like exciting new ham radio topics ("there's a new ham radio satellite going up!"), where they've travelled (especially nice if you've been where the other person lives), their life history, health (not dead yet! me neither!) etc. Lots of random small talk. The main rule is to stay away from anything that could cause disagreement, like politics and religion.
This may not sound terribly interesting, but keep in mind that for many, this is really just the last step after a lot of time spent e.g. building and setting up new equipment or whatever. Also depending on propagation conditions (which vary wildly), just understanding the other person is a challenge in itself. The actual talking is often more of a side benefit.
Above is mostly assuming SSB (voice). Other modes are different. For example, with CW (morse) exchanges will generally be more concise. Then there's more "useful" modes, for example you could send/receive email over Winlink via a digital mode like VARA. This doesn't really benefit from extreme reach, but depending on which bands you have antennas for, the next station might be e.g. a thousand miles away, so this is more of a mid-range thing. In contrast, some digital modes like WSPR focus entirely on propagation research (/ antenna testing), and _automatically_ communicate the callsign, transmit power, location and _nothing else_, but getting (automated) reports from stations on the other side of the globe that have heard your very modestly powered transmissions feels pretty rewarding.
Also note that there are phenomena that give you long range, like grayline DX (good propagation along the day/night line), tropospheric ducting (bounces earth->sky->sky->sky->...->earth) and moonbounce/EME (earth->moon->earth). Trying these is fun in itself even without meaningful information exchanged. There's also ham radio satellites; including one in geostationary orbit (Es'hail 2). If you hit one, you can hit more or less your entire continent. There the fun is using the satellite; the reach is generally a welcome side effect.
At some point between 50 and 100 light years the Omni directional radio waves blend with the background radiation.
I have seen projections of "plausibly easy" detection up to 50 light years. They difference between the number of stars that are 50 light years vs 40 light years is about 2x, so the calculation of how many stars are in range is actually very sensitive to emission range. There are 64 stars 50 ly out, and almost 500 up to 100ly out.
That's still not that many though, given the 500 billion stars in our galaxy. It seems only plausible that an ET intelligence would detect us if they have seeded the galaxy with probes - in which case their would probably be one listening in our own system anyway.
In short, even our largest, most sensitive radio telescopes are far too small to detect omnidirectional (e.g., FM radio) leakage from Sol's nearest celestial neighbor. Unless an exoplanet directs a coherent radio beam at Earth, we'd need an antenna larger than the planet to detect a signal amid the noise.
Here's the calculation, in case you're curious: one light year is about 10^16 meters; a sphere of radius 4.25 ly has an area of 2 10^34 m2. The BBC antenna emits in the 200 kHz band, so a single photon has an energy of (plank const) x (frequency) = (6.6 10^-34) x (200 10^3) = 1.3 10^-28. The antenna has a power of 500 kW, so that translates into 3.8 10^33 photons per second. That means at Proxima's distance each square meter will be crossed by a photon about once every 5.4 seconds. The James Webb telescope has a receiving area of 25 m2, so you end up with a bit less than 5 photons per second.
[1] https://en.wikipedia.org/wiki/Droitwich_Transmitting_Station
The current agreement is that level IV Civilizations should stay "Uncontacted" :
I think realistic resolutions in kilometers per pixel are theoretically possible even with existing technology (assuming we can build the swarm and position it in the right place quite far from the Sun and then maintain communication).
The disadvantage is you need many separate fleets of drones to map more than one target.
I haven't watched this YT video recently, but I think he also touches on a Sol-scope and a Jupiter-scope https://www.youtube.com/watch?v=jgOTZe07eHA
It is remarkable what astronomers/physicists have achieved though.
TL;DR a powerful enough laser that is well collimated would work.