diff --git a/yt/data_objects/data_containers.py b/yt/data_objects/data_containers.py
index 69b3ccf1673..fd76f63fe63 100644
--- a/yt/data_objects/data_containers.py
+++ b/yt/data_objects/data_containers.py
@@ -2,7 +2,7 @@
 import weakref
 from collections import defaultdict
 from contextlib import contextmanager
-from typing import TYPE_CHECKING, List, Tuple
+from typing import TYPE_CHECKING, List, Optional, Tuple
 
 import numpy as np
 
@@ -76,7 +76,7 @@ class YTDataContainer(abc.ABC):
     _index = None
     _key_fields: List[str]
 
-    def __init__(self, ds, field_parameters):
+    def __init__(self, ds: Optional["Dataset"], field_parameters) -> None:
         """
         Typically this is never called directly, but only due to inheritance.
         It associates a :class:`~yt.data_objects.static_output.Dataset` with the class,
diff --git a/yt/data_objects/static_output.py b/yt/data_objects/static_output.py
index 4b126ba1908..795864435e9 100644
--- a/yt/data_objects/static_output.py
+++ b/yt/data_objects/static_output.py
@@ -28,7 +28,7 @@
 import numpy as np
 from more_itertools import unzip
 from sympy import Symbol
-from unyt import Unit, unyt_quantity
+from unyt import Unit, UnitSystem, unyt_quantity
 from unyt.exceptions import UnitConversionError, UnitParseError
 
 from yt._maintenance.deprecation import issue_deprecation_warning
@@ -1263,7 +1263,7 @@ def _assign_unit_system(
 
         self._unit_system_name: str = unit_system
 
-        self.unit_system = us
+        self.unit_system: UnitSystem = us
         self.unit_registry.unit_system = self.unit_system
 
     @property