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Main memory (DRAM) significantly impacts the power and energy utilization of the overall server system. Non-Volatile Memory (NVM) devices, such as Phase Change Memory and Spin-Transfer Torque RAM, are suitable candidates for main memory to reduce energy consumption. But unlike DRAM, NVMs access latencies are higher than DRAM and NVM writes are more energy sensitive than DRAM write operations. Thus, Hybrid Main Memory Systems (HMMS) employing DRAM and NVM have been proposed to reduce the overall energy depletion of main memory while optimizing the performance of NVM. This paper proposes eMap, an optimal heap memory object placement planner in HMMS. eMap considers the object-level access patterns and energy consumption at the application level and provides an ideal placement strategy for each object to augment performance and energy utilization. eMap is equipped with two modules, eMPlan and eMDyn. Specifically, eMPlan is a static placement planner which provides one time placement policies for memory object to meet the energy budget while eMDyn is a runtime placement planner to consider the change in energy limiting constraint during the runtime and shuffles the memory objects by taking into account the access patterns as well as the migration cost in terms of energy and performance. The evaluation shows that our proposed solution satisfies both the energy limiting constraint and the performance. We compare our methodology with the state-of-the-art memory object classification and allocation (MOCA) framework. Our extensive evaluation shows that our proposed solution, eMPlan meets the energy constraint with 4.17 times less costly and reducing the energy consumption up to 14% with the same performance. eMDyn also satisfies the performance and energy requirement while considering the migration cost in terms of time and energy.