How to send a private message on Twitter using CURL?

Question

PHP

I set the parameters via CURLOPT_POSTFIELDS:
$param_arr = array(
'screen_name' => $recipient_screen_name,
'text' => $text,
'oauth_access_token' => $oauth_access_token // 111111111-XxXxXxXxXxXxXxXxXxXxXxXxXxXx
);
and send
$ch = curl_init($url); // url = https://api.twitter.com/1.1/direct_messages/new.json
curl_setopt( $ch, CURLOPT_POST, true );
curl_setopt( $ch, CURLOPT_POSTFIELDS, $param_arr );
curl_setopt( $ch, CURLOPT_HEADER, true );
curl_setopt( $ch, CURLOPT_RETURNTRANSFER, true );
$curl_res = curl_exec($ch);
$curl_err = curl_errno($ch);
curl_close($ch);
In response:
{"errors":[{"code":215,"message":"Bad Authentication data."}]}
What other parameters are needed for authorization?