Local heat release rate is one of the most concerned parameters in the combustion processes. However, this parameter is hard to be measured directly in the experiments. Therefore local heat release rate indicators have been sought and evaluated, and many works focus on the study in the gaseous laminar or turbulent premixed flames. The motivation of this work is to explore and validate heat release rate indicators for auto-igniting n-heptane droplets. To this end, direct numerical simulation (DNS) is performed with a detailed chemical reacting mechanism. Results show that the product of mass fractions of OH and CH 2 O is a proper indicator when the local auto-ignition prevails and the temperature rises quickly. The elementary reactions involved are analyzed, which shed light on the construction and performance of heat release rate indicators. Some new definitions of the indicators are proposed and evaluated. The proportional relationship between the indicator and the actual local heat release rate is determined. The heat release associated with different combustion regimes are distinguished, which reveals the dominant role of premixed flames in the droplets auto-ignition processes. Currently, most of the reported HRIs are for gaseous laminar and turbulent premixed flames. Their validity and performance in the two-phase combustion or in higher hydrocarbons flames need be evaluated. More importantly, the mechanism of what makes it a proper HRI or how to find a good HRI has not been investigated systematically. The quantitative relationship between the indicator and the actual local heat release rate is not yet determined in the turbulent studies. This paper aims to make a contribution to the above issues by numerical simulation. Direct numerical simulation (DNS) is performed to study the HRIs for the auto-igniting n-heptane droplets distributed in the hot vitiated flow.DNS is believed to resolve the turbulence completely, and it has been extended to the study of two-phase combustion. Auto-ignition of the liquid droplets in hot circumstance is one interested topic of DNS (Baba and Kurose 2008;Fujita et al. 2013;Kitano et al. 2013). The specific methods include two dimensional (2D) DNS coupled with the detailed reacting mechanism (Wang and Rutland 2007;Yoo et al. 2009;Wang and Rutland 2005) and 3D DNS coupled with the simplified reacting mechanism (Wang et al. 2012;Schroll et al. 2009;Wang et al. 2014). The effects of the relevant parameters, e.g. the overall equivalence ratio, the droplet diameter and its distribution, the initial gas temperature, pressure on ignition delay time were examined Rutland 2005, 2007;Im et al. 1998). So far, 3D DNS coupled with the detailed reacting mechanism (Borghesi et al. 2013) is rare due to huge requirement of calculation resources. Meanwhile, DNS also favors to the optimization of the related models in gaseous or two-phase combustion simulation. For instance, the droplets evaporation model coupled with the detailed chemical reacting mechanism is a concerned issue. Recently...