As per the ethical guidelines of this community, your post should be of good quality and that is the primary requirement. How good you are in your write up and how you present further attract readers to your post. Here I am saying reader means I am differentiating readers from your followers. We all know how the upvotes and followers are a kind of synthetic things here in this community and that is a bitter truth. You can see there are many posts who have got hundreds of upvotes and so many followers to an author. But how many actually read your post, that is important. So the number of upvotes does not necessarily mean the number of readers to your post. That is because of so many bots, curation trail etc. So you may say, that is one of the limitations. So the key thing in my perspective is an actual number of readers.
Now coming to your question "what necessitates a post to be visible". For visibility, your post has to be up the rank in the trending page and if that happens then you may get more visibility. How many will be reading your article comes the next and that all depends on how interesting your topic is, how good you are in presenting an article, how good you are in the particular subject matter of the article, etc.
The tools to make your post to the trending page is the use of upvote bots and yes they are really powerful tools to make the post up the trending page. So the point is that the author needs good upvote size to make it to the trending page. So in order to meet this, an author needs a promotional service using which it can buy upvotes and makes it to the trending page. This will not only increase the chances of better visibility but also better engagement from the community & subsequent earning. The leading promotional service in regards to vote buying are offered by instant bots like Minnowbooster, Smartmarket and bid bots like buildawahle, smartsteem, and many more which you can find the list in steembottracker.com
Please bear in mind that in order to use the promotional tools offered by many services here in Steem community, there is a threshold to the minimum standard of the post to use this service promotional service, so that low quality post is not upvoted to make it to the trending page. Most of the promotional services have a ToS in place, which doesn't support low-quality post, in order to meet the community guidelines. So the primary requirement is always at least above average quality post.
After putting up a good quality post and after using the promotional tool, if it makes it to the trending page then it will have larger visibility and better productive engagement from the community. Last but not the least, it also attracts whales to read the article and if the content is good enough to impress upon them positively, then it may further get good upvotes from the whales. In this way, you can get more visibility, more readers and more earning as well.
I believe that one of the ways of making a post visible is by using bid bot,there have been ill-talks about using bid bot because it doesn't encourage quality write ups as someone can just make post not valuable and use bid bot to get a good upvote, despite this disadvantage it also makes post visible as your post could appear under the trending posts which whales could even see and upvote if your article is good