我有一个集合geo，它有以下索引：

> db.geo.getIndexes();
[
    {
        "v" : 1,
        "key" : {
            "_id" : 1
        },
        "name" : "_id_",
        "ns" : "geospatial.geo"
    },
    {
        "v" : 1,
        "key" : {
            "checkin_id" : -1
        },
        "name" : "checkin_id_-1",
        "ns" : "geospatial.geo"
    },
    {
        "v" : 1,
        "key" : {
            "loc" : "2dsphere",
            "created_at" : -1,
            "user_id" : 1
        },
        "name" : "loc_2dsphere_created_at_-1_user_id_1",
        "ns" : "geospatial.geo",
        "2dsphereIndexVersion" : 2
    },
    {
        "v" : 1,
        "key" : {
            "created_at" : -1
        },
        "name" : "created_at_-1",
        "ns" : "geospatial.geo",
        "expireAfterSeconds" : 31557600
    },
    {
        "v" : 1,
        "key" : {
            "loc" : "2dsphere",
            "created_at" : 1
        },
        "name" : "loc_2dsphere_created_at_1",
        "ns" : "geospatial.geo",
        "background" : true,
        "2dsphereIndexVersion" : 2
    }
]

但运行此查询：

db.geo.find(
   {
     loc:
       { $near :
          {
            $geometry: { type: "Point",  coordinates: [ -73.9667, 40.78 ] },
            $minDistance: 1000,
            $maxDistance: 5000
          }
       },
      created_at: {  $gte : new ISODate("2017-06-23T00:00:00Z") }
   }
)

或

db.geo.distinct(
    "user_id",
     {
     loc:
       { $near :
          {
            $geometry: { type: "Point",  coordinates: [ -73.9667, 40.78 ] },
            $maxDistance: 16093.4
          }
       },
     created_at: {  $gte : new ISODate("2017-06-23T00:00:00Z") }
 }

).length

它只是超时，从来没有处理。有什么想法，我在这里缺少一个索引？有7400万+文档在这个集合。
示例文档：

{
    "_id" : ObjectId("59740de9e5bfa822388b4567"),
    "checkin_id" : XXXXX,
    "user_id" : XXXX,
    "created_at" : ISODate("2017-07-23T02:44:36.000Z"),
    "loc" : {
        "type" : "Point",
        "coordinates" : [ 
            -88.2165, 
            42.3718
        ]
    }
}

更新：以下是executionStats结果：

{
    "cursor" : "S2NearCursor",
    "isMultiKey" : false,
    "n" : 57740,
    "nscannedObjects" : 77737,
    "nscanned" : 200823,
    "nscannedObjectsAllPlans" : 123823,
    "nscannedAllPlans" : 300660,
    "scanAndOrder" : false,
    "indexOnly" : false,
    "nYields" : 0,
    "nChunkSkips" : 0,
    "millis" : 1514,
    "indexBounds" : {

    },
    "allPlans" : [
        {
            "cursor" : "S2NearCursor",
            "isMultiKey" : false,
            "n" : 57740,
            "nscannedObjects" : 77737,
            "nscanned" : 200823,
            "scanAndOrder" : false,
            "indexOnly" : false,
            "nChunkSkips" : 0,
            "indexBounds" : {

            }
        },
        {
            "cursor" : "S2NearCursor",
            "isMultiKey" : false,
            "n" : 101,
            "nscannedObjects" : 46086,
            "nscanned" : 99837,
            "scanAndOrder" : false,
            "indexOnly" : false,
            "nChunkSkips" : 0,
            "indexBounds" : {

            }
        }
    ],
    "server" : "ut-geobrain-01:27017",
    "filterSet" : false,
    "stats" : {
        "type" : "GEO_NEAR_2DSPHERE",
        "works" : 258567,
        "yields" : 0,
        "unyields" : 0,
        "invalidates" : 0,
        "advanced" : 57740,
        "needTime" : 0,
        "needFetch" : 0,
        "isEOF" : 1,
        "children" : [ ]
    }
}