How to add/mock the Nuxt Auth library when testing components in Nuxt with Jest

JS newbie here.

I have generated a Nuxt app and have implemented the @nuxt/auth middleware globally in my nuxt.config.js. It's working as expected in my app.

Now I would like to test some of my components that reference the $auth object.

// ~/components/hello_component.vue

<template>
  <div>
    <div v-if="$auth.loggedIn">
      <h1>Hi, {{ userName }}</h1>
    </div>
  </div>
</template>

<script>
export default {
  data () {
    userName: "Archduke Chocula"
  }
}
</script>

I have a test that looks like this:

// ~/spec/components/hello_component.spec.js

import { mount } from '@vue/test-utils'
import Hello from '@/components/hello_component.vue'

describe('Hello Component', () => {
  test('is a Vue instance', () => {
    const wrapper = mount(Hello)
    expect(wrapper.isVueInstance()).toBeTruthy()
  })
})

Which causes the following error

Error in render: "TypeError: Cannot read property 'loggedIn' of undefined"

So clearly I need to define auth somewhere, so my questions are:

1. Where and how should I add this dependency to my tests (per test? globally for all tests?)?
2. How can I mock the response of the loggedIn method so that I can test scenarios where I'm either logged in/out?
3. Is there a way to mock the Nuxt environment in my tests so that I can test my components etc as if they were mounted in Nuxt? Is that a even a good idea?

Thanks in advance for any help!

You can mock your $auth object it by passing the mock in an options object when calling mount

import { mount } from '@vue/test-utils'
import Hello from '@/components/hello_component.vue'

const authMock = {
  loggedIn: true
};

describe('Hello Component', () => {
  test('is a Vue instance', () => {
    const wrapper = mount(Hello, {
      mocks: {
        $auth: authMock
      }
    })
    expect(wrapper.isVueInstance()).toBeTruthy()
  })
})

You can extend the mock however your like, or change the values that it returns for each test.