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We used data from the Helioseismic and Magnetic Imager (HMI), and AtmosphericImaging Assembly (AIA) on the \textit{Solar Dynamics Observatory} (SDO) tostudy coronal loops at small scales, emerging in the quiet Sun. With HMIline-of-sight magnetograms, we derive the integrated and unsigned photosphericmagnetic flux at the loop footpoints in the photosphere. These loops are brightin the EUV channels of AIA. Using the six AIA EUV filters, we construct thedifferential emission measure (DEM) in the temperature range $5.7 - 6.5$ in log$T$ (K) for several hours of observations. The observed DEMs have a peakdistribution around log $T \approx$ 6.3, falling rapidly at highertemperatures. For log $T <$ 6.3, DEMs are comparable to their peak valueswithin an order of magnitude. The emission weighted temperature is calculated,and its time variations are compared with those of magnetic flux. We presenttwo possibilities for explaining the observed DEMs and temperatures variations.(a) Assuming the observed loops are comprised of hundred thin strands withcertain radius and length, we tested three time-dependent heating models andcompared the resulting DEMs and temperatures with the observed quantities. Thismodeling used Enthalpy-based Thermal Evolution of Loops (EBTEL), azero-dimensional (0D) hydrodynamic code. The comparisons suggest that a mediumfrequency heating model with a population of different heating amplitudes canroughly reproduce the observations. (b) We also consider a loop model withsteady heating and non-uniform cross-section of the loop along its length, andfind that this model can also reproduce the observed DEMs, provided the loopexpansion factor $\gamma \sim$ 5 - 10. More observational constraints arerequired to better understand the nature of coronal heating in the shortemerging loops on the quiet Sun.

Observations and modeling of the emerging EUV loops in the quiet Sun as seen with the Solar Dynamics Observatory