1I/'Oumuamua-like objects's SFDs with older, current and future surveys

Interstellar Objects (ISOs) may provide direct evidence of planetesimals ejected from early-stage solar systems. Studying these objects and predicting their detection through various surveys is vital for enhancing our understanding of planetary formation. We show how ISO size distribution (SFD), f D D-q, controls expected detections in current and future surveys. We focus on TESS and the Vera Rubin Observatory LSST while analyzing Pan-STARRS and ATLAS. TESS is expected to detect 1 ISO from shallow SFDs (q<2.5). On the other hand, LSST is likely to detect 0.2-100 ISO yr-1 over its lifetime. ATLAS is likely to detect one non-cometary object for populations with q<3. We further estimate 0-8 detections of cometary like-3I/ATLAS objects by LSST in 10 years and 1 cometary object detected by TESS over its mission time, independent of the nucleus size distribution. By considering both 1I/'Oumuamua and 3I/ATLAS from the same SFD, our results suggest that more asteroid-like objects are produced rather than comets during the early stages of planetary formation. Imminent detections of ISOs by LSST will help constrain the slopes of the SFDs for asteroid-like and cometary ISOs better, and, if applicable, differentiate between them.