Understanding formation of young, distributed low-mass stars and clusters in the W4 cloud complex

It is well known that most of the stars form in rich clusters. However, recent $Spitzer$ observations have shown that a significant number of stars also form in distributed mode, origin of which is not well understood. In this work, we aim to investigate clustered and distributed mode of star formation in the W4 complex. To do so, we identified and characterized the young stellar population associated with the region using homogeneous infra-red data-sets obtained from 2MASS, GLIMPSE, MIPS and WISE surveys. We make stellar surface density and minimum spanning tree maps to identify young clusters, and use {\it Spitzer} images to identify irradiated structures, such as elephant trunk-like structures (ETLSs) and pillars in the region. The surface density distribution of the young stellar objects (YSOs) reveals three new clusterings and $\sim$ 50\% distributed protostars in the H{\sc ii} region. The clusters are of low-mass nature but significantly younger than the central cluster IC~1805. We identified $\sim$ 38 ETLSs in the region, a majority of which consist of one or a few stars at their tips. We find these stars are low-mass ($<$ 2~M$_\odot$) YSOs, located at the outskirts ($>$ 17 pc) of the cluster IC~1805 and are part of scattered distributed population. We argued that the star formation in the ETLSs of W4 is going on possibly due to triggering effect of expanding W4 bubble. Although high-resolution photometric and spectroscopic data would be required to confirm the scenario, nonetheless, we discuss the implications of this scenario for our understanding of distributed low-mass star formation in cloud complexes as opposed to other mechanisms such as turbulent fragmentation and dynamical ejection.