Rachel Howe

 Rotation profile  Rotation changes over the solar cycle  The torsional oscillation  Tachocline fluctuations  Frequency and parameter changes  Global frequency shifts  Local frequency shifts  Looking for interior changes

 So-called ‘torsional oscillation’ is a pattern of weak slower and faster zonal flows migrating from mid- latitudes to the equator and poles over the solar cycle.  First observed by Howard and Labonte (1980) in surface observations  Surface Doppler measurements from Mt Wilson go back to (Ulrich 2001).

 Woodard and Libbrecht (1993) saw hints in BBSO data.  Seen in early MDI f- mode data by Kosovichev & Schou (1997)

 Seen in 4 years of GONG and 3 years of MDI data by Toomre et al. (2000), Howe, Komm & Hill (2000), Howe et al. (2000)  Penetration depth at least 0.92 R.

 Antia and Basu (2001) drew attention to high- latitude, poleward-moving part of phenomenon.

 Vorontsov et al (2003) showed that the phenomenon involves much of convection zone, and analyzed the signal in terms of 11- year sinusoidal variations.

MDI OLA MDI RLS GONG RLS Howe et al 2005

 We now have a full 11yr cycle of observations!  Animation based on 11+11/2 year sinusoids.

MDI LOCAL MDI GLOBAL DOPPLER Howe et al, 2006

Howe et al. 2009

 Torsional oscillation pattern involves most of convection zone  Related to timing of solar cycle  Strength may not be related to cycle strength  High-latitude flows show this cycle is not like the last one (or maybe the one before that.)

See Howe et al. (2000; Science 287, 2456)

Basu & Antia (2001; MNRAS 324, 498)

A. 0.71, eq. residuals B. Power spectrum C. Power in max. power frequency bin, vs latitude D. Power in max. power frequency bin, vs radius.

 Rule 1: Everything varies with everything else  Rule 2: It’s always more complicated  Well established that p-mode frequency increases with solar activity  Response to activity increases with activity (until it starts decreasing again.)

 From Libbrecht,  Amplitude peaks, linewidth has plateau around 3mHz.

 Differences from model are tiny.  Anomaly at base of convection zone – heavy element settling?  But things look worse with more recent opacity values.

 ACRIM (Woodard & Noyes 1985, 1988, Gelly, Fossat & Grec 1988)  BiSON, Mark I (Palle et al. 1989, Elsworth et al. 1990) Chaplin et al. 2007

Slight systematic shift between MDI and GONG

Howe et al. 2002

(Antia et al 2001, Howe et al 2002)

(Howe, Komm & Hill 2002)

 Mode frequencies are higher in active regions  (Hindman et al, 2000).  Also, amplitude decreases and linewidth increases.

 Method- dependent  Also depends on position on disk (or detector)

 Sound speed and flow patterns below a sunspot

 Bogart et al. 2008, Sol. Phys.

 Komm, Howe and Hill 2002

 Frequency shifts correlate with surface flux in time and space, at a wide range of scales  BUT remember Rule 2: It’s always more complicated  Is there interesting information in the deviations from the trends?

From Tripathy et al., 2007 Solar Phys. 243, 105

Broomhall et al. 2011

 Frequency shifts are strongly correlated with surface activity, but such changes are mostly shallow.  Finding subsurface changes in structure (sound speed/density) requires careful removal of surface effects

 Lefebvre & Kosovichev 2005, Lefebvre, Kosovochev & Rozelot 2007 – radius change in shallow subsurface layers. Fig. 1.- Radial variation as a function of the fractional radius, obtained as a solution of the inversion of f-mode frequencies by a least-squares regularization technique. The reference year is The error bars are the standard deviation after averaging over a set of random noise added to the relative frequencies. The averaging kernels for this inversion are well localized between and 0.996, with a typical half- width of

 Basu & Mandel (2004), Verner, Chaplin & Elsworth (2006) – evidence for solar-cycle change in amplitude of He ionization zone signature (0.98 R ) from GONG, MDI, BiSON data.

 Eff-Darwich et al 2002 – upper limit of 3e-5 on stratification change at base of convection zone

 Chou & Serebryanskiy 2005, Serbryanskiy & Chou 2005 – possible wave speed change near bottom of convection zone.

 Baldner & Basu, 2008  l ≤ 176, 2 ≤ n ≤16  Principal Component Analysis  Interior changes at latitudes below 45 deg.

 Helioseismology reveals changes in dynamics deep in the convection zone.  Improved knowledge of convection-zone dynamics may help predict future cycles.  Solar activity at the surface influences mode parameters.  Detection of interior structural change is still difficult.