diff --git a/CHANGES.rst b/CHANGES.rst
index f459e140..e038477c 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -6,6 +6,7 @@
 
 - drop support for python 3.9. [#232]
 
+- replace usages of ``copy_arrays`` with ``memmap`` [#230]
 
 0.6.1 (2024-04-05)
 ------------------
diff --git a/asdf_astropy/converters/unit/tests/test_quantity.py b/asdf_astropy/converters/unit/tests/test_quantity.py
index 2595131c..71c07ae2 100644
--- a/asdf_astropy/converters/unit/tests/test_quantity.py
+++ b/asdf_astropy/converters/unit/tests/test_quantity.py
@@ -4,9 +4,16 @@
 from asdf.testing import helpers
 from astropy import units
 from astropy.units import Quantity
+from astropy.utils.introspection import minversion
 from numpy.testing import assert_array_equal
 
 
+def asdf_open_memory_mapping_kwarg(memmap: bool) -> dict:
+    if minversion("asdf", "3.1.0"):
+        return {"memmap": memmap}
+    return {"copy_arrays": not memmap}
+
+
 def create_quantities():
     return [
         # Scalar:
@@ -77,7 +84,7 @@ def test_read_array_value():
 
 def test_memmap(tmp_path):
     """
-    Test that memmap (copy_arrays=False) works with quantities.
+    Test that memmap (memmap=True) works with quantities.
 
     Unfortunately, this is not a simple `isinstance(obj, np.memmap)`
     Instead it requires a more complicated check.
@@ -95,7 +102,7 @@ def test_memmap(tmp_path):
         af.write_to(file_path)
 
     # Update a value in the ASDF file
-    with asdf.open(file_path, mode="rw", copy_arrays=False) as af:
+    with asdf.open(file_path, mode="rw", **asdf_open_memory_mapping_kwarg(memmap=True)) as af:
         assert (af.tree["quantity"] == quantity).all()
         assert af.tree["quantity"][-1, -1] != new_value
 
@@ -105,7 +112,7 @@ def test_memmap(tmp_path):
         assert (af.tree["quantity"] != quantity).any()
         assert (af.tree["quantity"] == new_quantity).all()
 
-    with asdf.open(file_path, mode="rw", copy_arrays=False) as af:
+    with asdf.open(file_path, mode="rw", **asdf_open_memory_mapping_kwarg(memmap=True)) as af:
         assert af.tree["quantity"][-1, -1] == new_value
         assert (af.tree["quantity"] != quantity).any()
         assert (af.tree["quantity"] == new_quantity).all()
@@ -113,7 +120,7 @@ def test_memmap(tmp_path):
 
 def test_no_memmap(tmp_path):
     """
-    Test that turning off memmap (copy_arrays=True) works as expected for quantities
+    Test that turning off memmap (memmap=False) works as expected for quantities
     """
     file_path = tmp_path / "test.asdf"
     quantity = Quantity(np.arange(100, dtype=np.float64).reshape(5, 20), units.km)
@@ -128,7 +135,7 @@ def test_no_memmap(tmp_path):
         af.write_to(file_path)
 
     # Update a value in the ASDF file
-    with asdf.open(file_path, mode="rw", copy_arrays=True) as af:
+    with asdf.open(file_path, mode="rw", **asdf_open_memory_mapping_kwarg(memmap=False)) as af:
         assert (af.tree["quantity"] == quantity).all()
         assert af.tree["quantity"][-1, -1] != new_value
 
@@ -138,7 +145,7 @@ def test_no_memmap(tmp_path):
         assert (af.tree["quantity"] != quantity).any()
         assert (af.tree["quantity"] == new_quantity).all()
 
-    with asdf.open(file_path, mode="rw", copy_arrays=True) as af:
+    with asdf.open(file_path, mode="rw", **asdf_open_memory_mapping_kwarg(memmap=False)) as af:
         assert af.tree["quantity"][-1, -1] != new_value
         assert (af.tree["quantity"] != new_quantity).any()
         assert (af.tree["quantity"] == quantity).all()
diff --git a/pyproject.toml b/pyproject.toml
index 9a83b079..6f5461ba 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -94,6 +94,7 @@ extend-ignore = [
     "FIX", # flake8-fixme
     # Individually ignored checks
     "SLF001", # private-member-access
+    "FBT001", # boolean positional arguments in function definition
 ]
 extend-exclude = ["docs/*"]