How does increased density and colder temperature affect the Jeans Mass ($M_J$)?

It results in a lower Jeans Mass, allowing smaller clumps to collapse

The Jeans Mass ($M_J$) is a critical threshold that dictates whether a region of gas will spontaneously collapse under its own weight. It is highly sensitive to the local environmental conditions, specifically temperature and density. If the gas becomes denser, the gravitational attraction between adjacent particles is enhanced more rapidly than the thermal pressure can resist it. Similarly, lowering the temperature reduces the kinetic energy and thus the internal thermal pressure resisting gravity. Consequently, a denser and colder region will have a lower Jeans Mass. A lower $M_J$ means that smaller amounts of mass are required within that region to achieve gravitational dominance, thereby facilitating the initiation of collapse in smaller clumps.