News Release
14 September 2021
Chiba University
Nagoya University

Solar mystery about differential rotation
was solved with supercomputer “Fugaku”
The solar differential rotation was reproduced for the first timewith the highest-resolution simulation
Associate Professor Hideyuki Hotta (Graduate School of Science, Chiba University) and Professor
Kanya Kusano (Institute for Space-Earth Environmental Research, Nagoya University)
succeeded to precisely reproduce the thermal convection and the magnetic field in the solar
interior in the super high-resolution calculation on supercomputer “Fugaku”*1. As a result, thebasic structure of the solar differential rotation, that is, the equator region rotates faster thanthe polar region, was also reproduced without any artificial manipulation.
The calculation ability of “Fugaku” enabled us to reproduce the sun on the computer. We
continue carrying out higher-resolution calculations. Our effort will be a big step towards solving
the biggest solar mystery, the 11-year solar cycle*2.
This research was published in Nature Astronomy (13 September 2021).
■ Introduction: Convective conundrum
While the earth rotates rigidly, the sun has different
rotation periods in different latitudes, called differentialrotation*3. This fact has been known since 1630.
Currently, we know that the solar equatorial regions rotate
faster than the polar regions; the former rotates with aperiod of 25 days, and the latter with a period of 30 days.
The differential rotation is thought to have essential rolesin the sunspot formation and the solar activity cycle.
The solar interior is filled with turbulent*4 thermal
convection*5. The energy generated by the nuclear fusion
around the solar center is transported by the radiation in
the radiation zone (70% of the solar radius). In theconvection zone, which is the outer 30% of the sun,thermal convection transports the energy. This turbulent
motion is expected to construct and maintain the solar
differential rotation.
The solar internal convection structure*6
reproducedin Fugaku. The entropy, which isHowever, previous numerical simulations
could notsuitable to describe the thermal convection isreproduce the solar differential rotation. Even with theshown. Orange and blue regions correspond tohigh-resolution calculation on K-computer (~100 million
the warm and cool, respectively.
grid points), it simulated that the poles rotate faster thanthe equator, contrary to the actual solar profile. This phenomenon occurred because thesimulations could not precisely calculate turbulent thermal convection. The problem is called“the convective conundrum,” a long-term mystery in solar physics.

■ Research achievement
We carried out an unprecedentedly high-resolution simulation, which is only achievablewith “Fugaku,” to solve the convective conundrum. As the high turbulent solar interior
investigation requires a substantial numerical resource, we used 5.4 billion points to simulate
the solar convection zone. As a result, we succeeded in reproducing the solar-like differentialrotation; the fast equator and the slow pole.
The previous calculations have shown that the magnetic energy was smaller than the turbulent
energy in the solar convection zone. The magnetic field, therefore, had been thought to haveminor roles. The calculation in this study shows that the energy of strong magnetic fields ismore than twice the turbulent energy. Our view on the solar interior is significantly changed.
Also, we found that the magnetic field has essential roles in the construction and themaintenance of the solar differential rotation.

Low
８5 million

Middle680 millionHigh
5.4 billion

The realSun
The longitudinally averaged differential rotation on the meridional plane reproduced in the numericalsimulations. The color indicates the angular velocity. The yellow corresponds to the faster rotation.

■ Future perspective
The solar differential rotation has an essential role in the origin of the solar magnetic field.
Understanding the solar differential rotation is a vital step in solving the biggest solar mystery,the 11-year solar activity cycle.
Although we found that the high-resolution simulations could reproduce the solar interior, wehave not used the full abilities of “Fugaku” yet. We will continue carrying out higher-resolution
simulations to challenge the 11-year cycle mystery.
■ Researcher's comment (Assoc. prof. Hideyuki Hotta)
Since we expected it would take a longer time to solve the problem, we are surprised and happy
to obtain the result.

The solar differential rotation is closely related to the biggest solar mystery, the 11-year cycle.
We are excited to continue the research for the next goal.
■ Glossary*1) Supercomputer Fugaku: A supercomputer settled in RIKEN as a successor of the Kcomputer. The computer has obtained the first place in four categories of thesupercomputer ranking for three consecutive terms from June 2020 to June 2021.
Currently, Fugaku is the world's fastest supercomputer. The main operation started on 9March 2021.
*2）11-year solar cycle: The number of sunspots cycles every 11 years. The mechanism has
not been understood yet.
*3） Differential rotation: There are different rotation periods in different latitudes. Like theearth, the rotation which does not depend on the latitude is called rigid rotation.
*4） Turbulence: A chaotic and uneven movement in a liquid or gas. The antonym is the laminarflow which indicates the ordered flow.
*5） Thermal convection: Phenomena in which the heated substances such as air or waterrise and cool air/water descend, which occurs in hot water in a bus tab. In the solar interior,
the energy generated by the nuclear fusion warms the convection zone from the bottom,
and the thermal convection occurs permanently.
*6） Numerical simulation: Equations that are thought to describe the solar interior are solved
numerically. A tremendous amount of calculation is needed to reproduce the solar situation,and high-performance computers are required.
■ Research team・ Associate Professor Hideyuki Hotta, Graduate School of Science Chiba University
・ Professor/Manager Kanya Kusano Institute for Space-Earth Environmental Research,Nagoya University■ ProjectThis project is supported by MEXT as a Program for Promoting Researches on theSupercomputer Fugaku (Toward a unified view of the universe: from large-scale structures toplanets, grant no. 20351188 (PI: J. Makino), and Joint Institute for Computational Fundamental
Sciences (JICFuS). Calculations are carried out on “Fugaku” provided by the RIKEN Center for
Computational Science, the Supercomputer Flow at Nagoya University, and the Cray ATERUI II
provided by the Center for Computational Astrophysics, National Astronomical Observatory ofJapan. This project is also supported by MEXT/JSPS KAKENHI (grant No. JP20K14510 (PI: H.
Hotta), JP21H04492 (PI: K. Kusano), JP21H01124 (PI: T. Yokoyama), JP21H04497 (PI: H.
Miayahara)).
■ Publication information
Journal: Nature Astronomy
Title: Solar differential rotation reproduced with high-resolution simulation
Authors: H. Hotta, K. Kusano
DOI: https://doi.org/10.1038/s41550-021-01459-0
Movies and figures are available on the website.
http://www.astro.phys.s.chiba-u.ac.jp/~hotta/press/2021/

Contact information
Hideyuki Hotta, Graduate School of Science, Chiba University
TEL: +81 432902749 Email: hotta@chiba-u.jp