Understanding the connection between active galactic nuclei and star-formation (the AGN-SF connection) is one of the longest standing problems in modern astrophysics. In the age of large Integral Field Unit (IFU) surveys, studies of the AGN-SF connection greatly benefit from spatially resolving AGN and SF contributions to study the two processes independently. Using IFU data for 54 local active galaxies from the S7 sample, we present a new method to separate emission from AGN activity and SF using mixing sequences observed in the [NII]$λ6584$/H$α$ vs. [OIII]$λ5007$/H$β$ Baldwin-Phillips-Terlevich (BPT) diagram. We use the new decomposition method to calculate the H$α$ star-formation rate and AGN [OIII] luminosity for the galaxies. Our new method is robust to outliers in the line-ratio distribution and can be applied to large galaxy samples with little manual intervention. We infer star-formation histories (SFHs) using pPXF, conducting detailed recovery tests to determine the quantities that can be considered robust. We test the correlation between the AGN Eddington ratio, using the proxy L[OIII]/$σ_*^4$, and star-formation properties. We find a moderately strong correlation between the Eddington ratio and the star-formation rate (SFR). We also observe marginally significant correlations between the AGN Eddington ratio and the light-weighted stellar age under 100 Myr. Our results point to higher AGN accretion being associated with young nuclear star formation under 100 Myr, consistent with timelines presented in previous studies. The correlations found in this paper are relatively weak; extending our methods to larger samples, including radio-quiet galaxies, will help better constrain the physical mechanisms and timescales of the AGN-SF connection.

翻译：理解活动星系核与恒星形成之间的关联（AGN-SF关联）是现代天体物理学中长期存在的核心问题之一。在大规模积分场单元巡天时代，通过空间分辨AGN与SF的贡献来独立研究这两个过程，极大地促进了AGN-SF关联的研究。基于S7样本中54个本地活动星系的IFU数据，我们提出了一种利用[NII]λ6584/Hα与[OIII]λ5007/Hβ鲍德温-菲利普斯-特列维奇图观测到的混合序列来分离AGN活动与恒星形成辐射的新方法。运用该分解方法，我们计算了这些星系的Hα恒星形成率与AGN的[OIII]光度。新方法对线比分布中的异常值具有鲁棒性，且可应用于大规模星系样本而无需过多人工干预。我们使用pPXF推断了恒星形成历史，并通过详细的恢复测试确定了可视为稳健的物理量。我们检验了以L[OIII]/σ_*^4为代理的AGN爱丁顿比与恒星形成特性之间的相关性，发现爱丁顿比与恒星形成率之间存在中等强度的相关性。同时，我们观测到AGN爱丁顿比与100 Myr以下的光度加权恒星年龄之间存在边缘显著的相关性。我们的结果表明较高的AGN吸积率与100 Myr以下的年轻核区恒星形成相关，这与先前研究提出的时间线一致。本文发现的相关性相对较弱；将我们的方法扩展到包含射电宁静星系在内的更大样本，将有助于更好地约束AGN-SF关联的物理机制与时间尺度。