The star formation rate function (SFRF) and specific star formation rate function (sSFRF) from observations are impacted by the Eddington bias, due to uncertainties in the estimated star formation rate (SFR). We develop a novel method to correct the Eddington bias and obtain the intrinsic SFRF and sSFRF from the Sloan Digital Sky Survey (SDSS) Data Release 7. The intrinsic SFRF is in good agreement with measurements from previous data in the literature that relied on UV SFRs but its high star-forming end is slightly lower than the corresponding IR and radio tracers. We demonstrate that the intrinsic sSFRF from SDSS has a bimodal form with one peak found at sSFR ∼ 10^−9.7 yr⁻¹ representing the star-forming objects while the other peak is found at sSFR ∼ 10⁻¹² yr⁻¹ representing the quenched population. Furthermore, we compare our observations with the predictions from the IllustrisTNG and Illustris simulations and affirm that the “TNG” model performs much better than its predecessor. However, we show that the simulated SFRF and CSFRD of TNG simulations are highly dependent on resolution, reflecting the limitations of the model and today’s state-of-the-art simulations. We demonstrate that the bimodal, two peaked sSFRF implied by the SDSS observations does not appear in TNG regardless of the adopted box-size or resolution. This tension reflects the need for inclusion of an additional efficient quenching mechanism in the TNG model.

由于估计的恒星形成率（SFR）的不确定性，来自观测的恒星形成率函数（SFRF）和特定恒星形成率函数（sSFRF）受到爱丁顿偏差的影响。我们开发了一种新方法来纠正爱丁顿偏差并从斯隆数字巡天 (SDSS) 数据版本 7 中获得本征 SFRF 和 sSFRF。本征 SFRF 与文献中依赖于 UV SFR 的先前数据的测量值非常一致但它的高恒星形成端略低于相应的红外和无线电示踪剂。我们证明了SDSS的固有sSFRF具有双峰形式，其中一个峰值出现在sSFR ∼ 10 ^-9.7 yr ^-1代表恒星形成物体，而另一个峰值出现在sSFR ∼ 10 ^-12yr ^-1代表淬火人口。此外，我们将我们的观察结果与 IllustrisTNG 和 Illustris 模拟的预测进行比较，并确认“TNG”模型的性能比其前身要好得多。然而，我们表明 TNG 模拟的模拟 SFRF 和 CSFRD 高度依赖于分辨率，反映了模型的局限性和当今最先进的模拟。我们证明，无论采用何种框尺寸或分辨率，SDSS 观察所暗示的双峰、两个峰值 sSFRF 都不会出现在 TNG 中。这种张力反映了在 TNG 模型中包含额外的有效淬火机制的需要。