Can Small-scale Magnetic Fields Be the Major Cause for the Near-surface Effect of the Solar p-mode Frequencies?

Small-scale magnetic fields are not only the fundamental element of the solar magnetism, but also closely related to the structure of the solar atmosphere. The observations have shown that there is a ubiquitous tangled small-scale magnetic field with a strength of 60 $\sim$ 130\,G in the canopy forming layer of the quiet solar photosphere. On the other hand, the multi-dimensional MHD simulations show that the convective overshooting expels the magnetic field to form the magnetic canopies at a height of about 500\,km in the upper photosphere. However, the distribution of such small-scale ``canopies" in the solar photosphere cannot be rigorously constrained by either observations and numerical simulations. Based on stellar standard models, we identify that these magnetic canopies can act as a global magnetic-arch splicing layer, and find that the reflections of the solar p-mode oscillations at this magnetic-arch splicing layer results in significant improvement on the discrepancy between the observed and calculated p-mode frequencies. The location of the magnetic-arch splicing layer is determined at a height of about 630\,km, and the inferred strength of the magnetic field is about 90\,G. These features of the magnetic-arch splicing layer derived independently in the present study are quantitatively in agreement with the presence of small-scale magnetic canopies as those obtained by the observations and 3-D MHD simulations.