Elasticsearch aggregation performance takes a hit on relatively small dataset - elasticsearch

Question

We have a cluster of 3 Linux VMs (each machine has 2 cores, 8GB of RAM per core) where we have deployed an Elasticsearch 2.1.1 cluster, with default configuration. Store size is ~50GB for ~3M documents -so arguably fairly modest. We index documents ranging in size from tweets to blog posts. For each document, we extract "entities" (eg, if string "Barack Obama" appears in a document, we locate its character position and classify it into an entity type, in this case the type "person", or "statesman") from the text before indexing the document alongside its array of extracted entities.
Our mapping is as follows:
{
"mappings": {
"_default_": {
"_all": { "enabled": "false" },
"dynamic": false
},
"document": {
"properties": {
"body": { "type": "string", "index": "analyzed", "analyzer": "english" },
"timestamp": { "type": "date", "index":"not_analyzed" },
"author": {
"properties": {
"name": { "type": "string", "index": "not_analyzed" }
}
},
"entities": {
"type": "nested",
"include_in_parent": true,
"properties": {
"text": { "type": "string", "index": "not_analyzed" },
"type": { "type": "string", "index": "analyzed", "analyzer": "path" },
"start": { "type": "integer", "index":"not_analyzed", "doc_values": false },
"stop": { "type": "integer", "index":"not_analyzed", "doc_values": false }
}
}
}
}
}
}
Path analyzer is used on the entity type field (entity types are based on some hierarchical taxonomy, so the type is represented as a path-like string). The only other analyzed field is the body of the document. For some reason that I could expand on if necessary, we have to index the entities as nested types, though we are still including them in the parent document.
There are on average ~10 entities extracted per document, so ~30M entities in total. The cardinality for the entities field is thus fairly high (~2M unique values).
Our problem is that some of the aggregations we are doing are very slow (>30s). In particular, the following two aggregations:
{
"query": {
"bool": {
"must": {
"query": {
// Some query
}
},
"filter": {
// Some filter
}
}
},
"aggs": {
"aggData": {
terms: { field: 'entities.text', size: 50 }
}
}
}
And the same one, just replacing 'terms' aggregation with 'significant_terms':
{
"query": {
"bool": {
"must": {
"query": {
// Some query
}
},
"filter": {
// Some filter
}
}
},
"aggs": {
"aggData": {
significant_terms: { field: 'entities.text', size: 50 }
}
}
}
My questions:
Why are these aggregations prohibitively slow?
Is there something stupid/inefficient in the mapping strategy?
Does indexing the entities as a nested document while still keeping them in the parent document have an impact?
Is it simply that the cardinality of the entities field is just too big and Elasticsearch is not magic?