Filter

1. A filter comprising a columnar honeycomb structure part, the columnar honeycomb structure part comprising:

a plurality of first cells each extending from a first bottom surface to a second bottom surface of the columnar honeycomb structure part, the first bottom surface being opened and the second bottom surface being plugged for the plurality of first cells;

a plurality of second cells each extending from the first bottom surface to the second bottom surface of the columnar honeycomb structure part, the first bottom surface being plugged and the second bottom surface being opened for the plurality of second cells; and

porous cordierite partition walls that define the first cells and the second cells, the partition walls having an average pore depth of 1.5 μm or more and 3.5 μm or less as measured by a laser microscope, and a porosity of from 50 to 60% as measured by a mercury porosimeter.

2. The filter according to claim 1 , wherein the partition walls have the average pore depth of 2.5 μm or more and 3.5 μm or less as measured by the laser microscope.

3. The filter according to claim 1 , wherein the partition walls have a maximum pore depth of 40 μm or less as measured by a laser microscope.

4. The filter according to claim 1 , wherein the partition walls have a maximum pore depth of 20 μm or more and 26 μm or less as measured by a laser microscope.

5. The filter according to claim 1 , wherein the partition walls have an average equivalent circle pore diameter of 10.5 μm or less as measured by a laser microscope.

6. The filter according to claim 1 , wherein the partition walls have an average equivalent circle pore diameter of 5 μm or more and 10 μm or less as measured by a laser microscope.

7. The filter according to claim 1 , wherein the partition walls have an average pore diameter of 5 μm or more and 13 μm or less as measured by a mercury porosimeter.

8. The filter according to according to claim 1 , wherein the partition walls have a thickness of 150 μm or more and 260 μm or less.