When ATC mention 'radar contact', what does that mean?
In what conditions ATC might contact you and mention 'radar contact' in the call? and what would be the appropriate responses?
The FAA's Pilot/Controller Glossary gives both US and ICAO definitions:
RADAR CONTACT- a. Used by ATC to inform an aircraft that it is identified on the radar display and radar flight following will be provided until radar identification is terminated. Radar service may also be provided within the limits of necessity and capability. When a pilot is informed of “radar contact,” he/she automatically discontinues reporting over compulsory reporting points. [...]
b. The term used to inform the controller that the aircraft is identified and approval is granted for the aircraft to enter the receiving controllers airspace. (See ICAO term RADAR CONTACT.)
RADAR CONTACT [ICAO]- The situation which exists when the radar blip or radar position symbol of a particular aircraft is seen and identified on a radar display.
RADAR CONTACT LOST- Used by ATC to inform a pilot that radar data used to determine the aircraft’s position is no longer being received, or is no longer reliable and radar service is no longer being provided. The loss may be attributed to several factors including the aircraft merging with weather or ground clutter, the aircraft operating below radar line of sight coverage, the aircraft entering an area of poor radar return, failure of the aircraft transponder, or failure of the ground radar equipment.
Note that this is not a universal term, Canada uses "radar identified" instead. Their equivalent of the P/CG is the Glossary for Pilots and Air Traffic Services Personnel:
An expression used by ATC to inform the pilot of an aircraft when radar identification is established.
Fr: « Identifié radar »
U.S.: Expression for: “Radar identified”
No specific response is typically necessary (although acknowledging that you heard the transmission with a callsign or "roger" is appropriate). The call means that the controller sees your aircraft on radar & has confirmed that "this" target is "that" aircraft, i.e. your aircraft. He is now capable of providing ATC services that require the use of radar, such as radar vectors, separation, traffic calls, minimum altitude monitoring, etc. Not saying that he necessarily IS providing all of those things; there's a little bit of context to such things.
You can also hear, "radar contact lost" either when you are below the radar horizon due to terrain, or over the water too far away from from the radar site. This means that you're now, if flying IFR, operating under non-radar IFR rules, and things like making position reports at the mandatory reporting points now applies. (You don't have to make those reports while in radar contract.)
Interestingly, you may also (rarely) hear a military fighter call "radar contact" in response to a traffic call, meaning that he sees the traffic on radar, but not visually. Not sure if that's standard terminology for them in an ATC environment or not, but I've heard it a few times.
Context: You will typically get this the first time you contact an ATC facility and they reply with a squawk code. "Radar contact" is to tell you that they now know which blip (aka contact) on their radar display is you and are thus able to provide various radar services--though whether they actually will is another matter.
Notably, if you don't hear this, you're likely either below their radar coverage or talking to a facility that doesn't have radar at all. Obviously, they're not able to provide radar services in that case. They're likely to ask for position and altitude next so they know where you are relative to other aircraft. If they do see a primary radar return at the position you give them but no secondary, it's likely your transponder isn't working; in that case, they probably won't ask position again but will ask your altitude occasionally--and near a busy class B/C airspace, will likely tell you to keep out because having to verify that every time another plane comes near adds too much work.
Responses: If all they say is "radar contact" and nothing else, just acknowledge it with your callsign. Usually, though, they'll start giving you traffic advisories, and you'd reply to those with "looking" or "in sight". If you didn't specify why you're calling them on your callup, they may also ask you to "say intentions" so they know what to do with you--and may start giving you vectors accordingly, which you would need to repeat back as usual.