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Coronal heating is a big question for modern astronomy. Daily measurement of 985 solar spectral irradiances (SSIs) at the spectral intervals 1-39 nm and 116-2416 nm during March 1 2003 to October 28 2017 is utilized to investigate characteristics of solar rotation in the solar atmosphere by means of the Lomb -Scargle periodogram method to calculate their power spectra. The rotation period of coronal plasma is obtained to be 26.3 days, and that of the solar atmosphere at the bottom of the photosphere modulated by magnetic structures is 27.5 days. Here we report for the first time that unexpectedly the coronal atmosphere is found to rotate faster than the underlying photosphere. When time series of SSIs are divided into different cycles, and the ascending and descending periods of a solar cycle, rotation rate in the corona is also found to be larger than that in the photosphere, and this actually gives hidden evidence: it is small-scale magnetic activity that heats the corona.

Differential rotation is the basis of the solar dynamo theory. Synoptic maps of He I intensity from Carrington rotations 2032–2135 are utilized to investigate the differential rotation of the solar chromosphere in the He I absorption line. The chromosphere is surprisingly found to rotate faster than the photosphere below it. The anomalous heating of the chromosphere and corona has been a big problem in modern astronomy. It is speculated that the small-scale magnetic elements with magnetic flux in the range of (2.9–32.0) × 1018 Mx, which are anchored in the leptocline, heat the quiet chromosphere to present the anomalous temperature increase, causing it to rotate at the same rate as the leptocline. The differential of rotation rate in the chromosphere is found to be strengthened by strong magnetic fields, but in stark contrast, at the photosphere strong magnetic fields repress the differential of rotation rate. A plausible explanation is given for these findings.

Rotation is a significant characteristic of the Sun and other stars, and it plays an important role in understanding their dynamo actions and magnetic activities. In this study, the rotation of the solar chromospheric activity is investigated from a global point of view with an over 40 yr Mg ii index. We determined the time-varying rotational period lengths (RPLs) with the synchrosqueezed wavelet transform, which provides high temporal and frequency resolution; furthermore, we compared the RPLs with the photospheric and coronal RPLs obtained from the sunspot numbers and the 10.7 cm radio flux data. The significance of the RPLs is taken into consideration. We found that the RPLs of the chromosphere exhibit a downward trend, as do those of the photosphere and corona; in addition, their RPLs at the recent four solar maxima also show a declining trend. This suggests that the rotation of the solar atmosphere has been accelerating during the recent four solar cycles, which is inferred to be caused by the declining strength of solar activity. The variations of the solar atmospheric RPLs show periodicities of multiple harmonics of the solar cycle period, and it is modulated by the solar activity cycle.

Solar chromosphere and coronal heating is a big question for astrophysics. Daily measurement of 985 solar spectral irradiances (SSIs) at the spectral intervals 1-39 nm and 116-

The rotational characteristics of the solar photospheric magnetic field at four flux ranges are investigated together with the total flux of active regions (MFar) and quiet regions (MFqr). The first four ranges (MF1–4) are (1.5–2.9) × 1018, (2.9–32.0) × 1018, (3.20–4.27) × 1019, and (4.27–38.01) × 1019, respectively (the unit is Mx per element). Daily values of the flux data are extracted from magnetograms of the Michelson Doppler Imager on board the Solar and Heliospheric Observatory. Lomb–Scargle periodograms show that only MF2, MF4, MFqr, and MFar exhibit rotational periods. The periods of the first three types of flux are very similar, i.e., 26.20, 26.23, and 26.24 days, respectively, while that of MFar is longer, 26.66 days. This indicates that active regions rotate more slowly than quiet regions on average, and strong magnetic fields tend to repress the surface rotation. Sinusoidal function fittings and cross-correlation analyses reveal that MFar leads MF2 and MF4 by 5 and 1 days, respectively. This is speculated to be related with the decaying of active regions. MF2 and MFar are negatively correlated, while both MF4 and MFqr are positively correlated with MFar. At the timescale of the solar activity cycle, MFar leads (negatively) MF2 by around one year (350 days), and leads MF4 by about 3 rotation periods (82 days). The relation between MF2 and MFar may be explained by the possibility that the former mainly comes from a higher latitude, or emerges from the subsurface shear layer. We conjecture that MF4 may partly come from the magnetic flux of active regions; this verifies previous results that were obtained with indirect solar magnetic indices.

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The daily sunspot numbers of the whole disk as well as the northern and southern hemispheres from January 1, 1945 to December 31, 2010 are used to investigate the temporal variation of the rotational cycle length through the continuous wavelet transformation analysis method. The auto-correlation function analysis of daily hemispheric sunspot numbers shows that the southern hemisphere rotates faster than the northern hemisphere. The results obtained from the wavelet transformation analysis are: there exists no direct relationship between the variation trend of the rotational cycle length and the variation trend of solar activity in the two hemispheres; the rotational cycle length of both hemispheres has no significant period appearing at the 11 years, but has significant period of about 7.6 years. Analysis concerning the solar cycle dependence of the rotational cycle length shows that in the whole disk and the northern hemisphere acceleration seems to appear before the minimum time of solar activity. Furthermore, the cross-correlation study indicates that the rotational cycle length of the two hemispheres has different phases, and the rotational cycle length of the whole disk as well as the northern and southern hemispheres also has phase shifts with the corresponding solar activity. What's more, the temporal variation of North-South (N-S) asymmetry of the rotational cycle length is also studied; it displays the same variation trend as the N-S asymmetry of solar activity in a solar cycle as well as in the considered time interval, and it has two significant periods of 7.7 and 17.5 years. Moreover, the N-S asymmetry of the rotational cycle length and the N-S asymmetry of solar activity are highly correlated. It's inferred that the northern hemisphere should rotate faster at the beginning of solar cycle 24.