How to unit test $on event in a service that has $rootScope injected?

I have a service that has $rootScope as a dependency ($rootScope is used in this service to listen for a logout event, which triggers the service clear some cached promises):

angular.module('myApp')
    .factory('myService', [
        '$rootScope',
        myService
    ]);

/**
 * Factory function for this service.
 */
function myService($rootScope) {

    var service = {};

    var myCachedPromise = undefined;
    var myOtherCachedPromise = undefined;

    /**
     * Watch for logout event. Expire cached promises when this happens.
     */
    $rootScope.$on('NOT_AUTHORIZED', onPageExpire);

    /**
     * Handler for log out/page expire event.
     */
    function onPageExpire() {
        console.log('Expiring caches!');
        annotationChart = undefined;
        gotAnnnotationData = undefined;
    }

    service.getSomeData = function() {
        myCachedPromise = myCachedPromise || $http.get('/api/whatever');
        return myCachedPromise;
    };

    service.getSomeOtherData = function() {
        myOtherCachedPromise = myOtherCachedPromise || $http.get('/api/whatever');
        return myOtherCachedPromise;
    };

    return service;
}

In my Jasmine test, I want to broadcast the NOT_AUTHORIZED event to trigger this service to call the onPageExpire function:

var myService,
    $rootScope;

beforeEach(module('myApp'));

beforeEach(inject(function(_$rootScope_, _myService_) {
    myService = _myService_;

    $rootScope = _$rootScope_;
}));

it('should expire cached promises on log out', function() {

    $rootScope.$broadcast('NOT_AUTHORIZED');
    $rootScope.$digest();

});

Through some poking and prodding, it seems to me that the $rootScope in my test and the $rootScope being injected into the instance of myService isn't actually the same object, so when I do the broadcast in my test, the event handler in the service is not fired.

How do I ensure the $rootScope in the instance of the service is the same one as I'm using in my test?