How can I run a PHP script in the background after a form is submitted?

Doing some experimentation with exec and shell_exec I have uncovered a solution that worked perfectly! I choose to use shell_exec so I can log every notification process that happens (or doesn't). (shell_exec returns as a string and this was easier than using exec, assigning the output to a variable and then opening a file to write to.)

I'm using the following line to invoke the email script:

shell_exec("/path/to/php /path/to/send_notifications.php '".$post_id."' 'alert' >> /path/to/alert_log/paging.log &");

It is important to notice the & at the end of the command (as pointed out by @netcoder). This UNIX command runs a process in the background.

The extra variables surrounded in single quotes after the path to the script are set as $_SERVER['argv'] variables that I can call within my script.

The email script then outputs to my log file using the >> and will output something like this:

[2011-01-07 11:01:26] Alert Notifications Sent for http://alerts.illinoisstate.edu/2049 (SCRIPT: 38.71 seconds)
[2011-01-07 11:01:34] CRITICAL ERROR: Alert Notifications NOT sent for http://alerts.illinoisstate.edu/2049 (SCRIPT: 23.12 seconds)

On Linux/Unix servers, you can execute a job in the background by using proc_open:

$descriptorspec = array(
   array('pipe', 'r'),               // stdin
   array('file', 'myfile.txt', 'a'), // stdout
   array('pipe', 'w'),               // stderr
);

$proc = proc_open('php email_script.php &', $descriptorspec, $pipes);

The & being the important bit here. The script will continue even if the original script has ended.

Of all the answers, none considered the ridiculously easy fastcgi_finish_request function, that when called, flushes all remaining output to the browser and closes the Fastcgi session and the HTTP connection, while letting the script run in the background.

An example:

<?php
header('Content-Type: application/json');
echo json_encode(['ok' => true]);
fastcgi_finish_request(); // The user is now disconnected from the script

// do stuff with received data,

PHP exec("php script.php") can do it.

From the Manual:

If a program is started with this function, in order for it to continue running in the background, the output of the program must be redirected to a file or another output stream. Failing to do so will cause PHP to hang until the execution of the program ends.

So if you redirect the output to a log file (what is a good idea anyways), your calling script will not hang and your email script will run in bg.