Solar inertial modes: Observations, identification, and diagnostic promise

Laurent Gizon; Robert H. Cameron; Yuto Bekki; Aaron C. Birch; Richard S. Bogart; Allan Sacha Brun; Cilia Damiani; Damien Fournier; Laura Hyest; Kiran Jain; B. Lekshmi; Zhi-Chao Liang; Bastian Proxauf

doi:10.1051/0004-6361/202141462

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Volume 652 (August 2021)

A&A, 652 (2021) L6

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Table A.1.

Solar inertial modes detected in HMI ring-diagram flow maps for 2010–2020.

m	(j, s)	Mode frequency ^(a)	Significance ^(b)	Critical latitude ^(c)	Latitude at max ()	max(u_θ)	max(u_ϕ)	Linewidth	Excess power range
		[nHz]		at r = R_⊙	[multiples of 7.5°]	[m s⁻¹]	[m s⁻¹]	[nHz]	(not activity related)
Equatorial Rossby modes:
3	(θ, +)	−269 ^(d)	> 8 σ_L	59°	0°	1.5	1.2	< 24	[−280, −200] nHz
4	(θ, +)	−208 ^(d)	7.5 σ_L	45°	0°	1.6	1.1	< 37	[−250, −190] nHz
5	(θ, +)	−171 ^(d)	> 8 σ_L	37°	0°	1.0	–	< 12	[−210, −150] nHz
6	(θ, +)	−147 ^(d)	5.7 σ_L	31°	0°	1.3	–	< 24	[−170, −125] nHz
7	(θ, +)	−130.7 ± 2.8 ^(d)^(e)	> 8 σ_L	25°	7.5°	1.5	–	9.9 ± 2.4	[−175, −110] nHz
8	(θ, +)	−110.9 ± 2.4 ^(d)^(e)	> 8 σ_L	22°	0°	2.0	–	10.6 ± 1.0	[−135, −65] nHz
9	(θ, +)	−122 ^(d)	> 8 σ_L	22°	0°	1.1	–	< 12	[−135, −55] nHz
10	(θ, +)	−110 ^(d)	> 8 σ_L	19°	0°	1.4	–	< 24	[−145, −70] nHz

High-latitude inertial modes:
1	(ϕ, +)	−86	> 8 σ_H	58°	≥67.5°	–	2.5	< 12	[−110, −50] nHz
1	(ϕ, −)	−86.3 ± 1.6 ^(e)^(f)	> 8 σ_H	58°	≥67.5°	3.0	9.8	7.8 ± 0.2	[−150, −10] nHz
2	(ϕ, +)	−171 ^(f)	> 8 σ_H	58°	60°	–	2.3	< 12	[−195, −100] nHz
2	(ϕ, −)	−151.1 ± 4.3 ^(e)^(f)	> 8 σ_H	56°	≥67.5°	2.5	3.4	30.6 ± 3.3	[−185, −90] nHz
3	(ϕ, +)	−224.7 ± 2.5 ^(e)^(f)	> 8 σ_H	53°	60°	1.6	1.8	9.7 ± 1.7	[−265, −180] nHz
4	(θ, +)	−294	3.9 σ_H	53°	≥67.5°	1.0	0.8	< 12	}[−310, −240] nHz
4	(θ, +)	−245	5.3 σ_H	49°	60°	1.1	1.1	< 24
5	(θ, −)	−343	5.3 σ_H	52°	60°	0.7	–	< 12	}[−355, −275] nHz
5	(ϕ, +)	−282	2.6 σ_H	47°	52.5°	0.8	0.8	< 24

Critical-latitude inertial modes:
1	(ϕ, +)	−37	> 8 σ_M	38°	37.5°	–	1.3	< 24 ^(g)
1	(ϕ, −)	−37	7.1 σ_M	38°	37.5°	0.5	0.9	< 12 ^(g)
1	(ϕ, −)	−12	> 8 σ_L	20°	30°	–	1.2	< 24
2	(ϕ, +)	−61	6.8 σ_M	34°	52.5°	–	1.1	< 24	}[−65, 0] nHz
2	(ϕ, +)	−12	> 8 σ_L	10°	22.5°	0.9	1.1	< 12
2	(ϕ, −)	−73	> 8 σ_H	38°	45°	0.8	1.3	< 12	}[−50, 30] nHz
3	(ϕ, −)	0	6.6 σ_L	n/a	15°	–	1.0	< 24 ^(g)
4	(ϕ, +)	−220	4.3 σ_H	46°	45°	–	0.5	< 12
4	(ϕ, +)	−110	4.4 σ_M	33°	37.5°	–	0.6	< 12	}[−120, 35] nHz
4	(ϕ, +)	−12	4.3 σ_L	n/a	15°	0.6	1.0	< 12 ^(g)
4	(ϕ, +)	24	5.5 σ_L	n/a	0°	–	1.4	< 24
4	(ϕ, −)	−171	3.4 σ_H	41°	45°	–	0.6	< 12
4	(ϕ, −)	−24	> 8 σ_L	10°	22.5°	–	1.0	< 24	}[−50, 30] nHz
4	(ϕ, −)	24	5.9 σ_L	n/a	7.5°	–	1.0	< 24
5	(ϕ, +)	−135 ^(h)	3.7 σ_M	32°	37.5°	–	0.8	< 24
5	(ϕ, +)	−24	3.5 σ_L	5°	15°	–	1.0	< 24 ^(g)
5	(θ, −)	37	4.3 σ_L	n/a	15°	0.7	–	< 24
5	(θ, +)	−330	2.3 σ_H	51°	60°	0.7	–	< 24	}[−330, −190] nHz
5	(ϕ, −)	−294	2.1 σ_H	48°	52.5°	–	0.7	< 24
5	(ϕ, −)	−245	5.7 σ_H	44°	45°	–	0.8	< 12
5	(θ, +)	−86	4.0 σ_M	25°	37.5°	0.7	–	< 12
6	(θ, −)	−343 ^(h)	2.1 σ_H	47°	60°	0.5	–	< 12
6	(ϕ, +)	−306	3.3 σ_H	45°	60°	–	0.4	< 12
6	(θ, −)	−61	2.0 σ_M	18°	30°	0.6	–	< 12
6	(ϕ, +)	−24	4.5 σ_M	n/a	15°	–	1.1	< 12
6	(ϕ, −)	−245 ^(h)	2.7 σ_H	40°	45°	–	0.5	< 12
6	(ϕ, −)	37	2.5 σ_L	n/a	7.5°	–	0.7	< 12 ^(g)
7	(θ, −)	−196	2.4 σ_H	33°	45°	0.7	–	< 24 ^(g)
7	(ϕ, +)	−86	3.6 σ_L	20°	22.5°	–	0.6	< 12
7	(θ, +)	−73	3.0 σ_M	18°	0°	0.5	–	< 12
7	(ϕ, −)	0	3.6 σ_L	n/a	22.5°	–	0.7	< 24
9	(ϕ, +)	0	5.3 σ_L	n/a	15°	0.7	0.6	< 12
9	(θ, +)	−269	2.5 σ_H	34°	45°	0.5	–	< 12
10	(θ, −)	−49	3.3 σ_M	6°	22.5°	0.5	–	< 12
10	(θ, +)	−282	2.9 σ_H	33°	45°	0.3	–	< 12

Notes. Frequencies are defined in the Carrington frame.

^(a)

The search range was limited to 1 ≤ m ≤ 10 and |ω/2π| ≤ 400 nHz.

^(b)

The statistical significance of each peak is given in terms of the standard deviation computed for the most significant of the latitudinal averages shown in Figs. C.2–C.11 (σ_L for low latitudes, σ_M for mid latitudes, and σ_H for high latitudes).

^(c)

“n/a” means not applicable (no critical latitude at the surface, only deeper).

^(d)

Mode reported by Löptien et al. (2018).

^(e)

Mode parameters measured with a Lorentzian fit.

^(f)

Frequency near that reported by Hathaway & Upton (2021).

^(g)

Measured during the quiet Sun period 2018–2020.

^(h)

Outside the activity frequency range, however not significant during the quiet Sun period 2018–2020.

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