HMI Team 4/30/03

Kuhn - HMI Science Interests:Limb photometry and astrometry

• HMI, with 4Kx4K (or even 2Kx2K) pixel resolution will improve limb astrometry and photometry in some respects by over an order of magnitude

• HMI roll calibration and lessons learned from MDI thermal environment may do better than an order of magnitude improvement in some astrometric goals

HMI Team 4/30/03

Focus areas

• Limb Astrometry– rotational constraints through limb harmonics– secular radius variations– limb seismology (low frequency modes)

• Limb brightness– thermal magnetic diagnostics– limb seismology

HMI Team 4/30/03

Limb astrometry

dr

Angle of arrival fluctuations define dr

dI

Photometric gain uncertainty (flatfielding) defines dr

In practice limb isn’t knife edge, spacecraft pointing jitter is about 0.01 pixel,long term stability limitations are due to optics and thermal drifts [1px=2”]

mas 0.4r pixels limb 3000

mas 20 dr intensity rms 1%

HMI Team 4/30/03

Shape, rotation, and gravitational figure

(-1)

(10) (50)

HMI Team 4/30/03

Shape and gravitational potential

Coefficient l=2 (Uncertainty) l=4 (Uncertainty)density -5.87E-06 8.00E-08 6.16E-07 3.20E-08pressure -5.84E-06 5.93E-07observed -5.27E-06 3.80E-07 1.30E-06 5.10E-07J -2.22E-07 3.84E-09

HMI Team 4/30/03

Emilio et al.: No W measured -- limits only

c/yrmilliarcse 0.98.1 /

mas) 5 100 (vs.

cmilliarcse 321 ||

sec

dtdr

rcycleBush et al. 2002 sees different “temperature”trend after SoHO vacation.

HMI Team 4/30/03

Interpreting solar radius change

Log(W) Models

-4 -3 -2 -1 0

S&E ('79)

D&B ('80)

Gilliland ('84)

Spruit ('82)

II

rr

W

< 0.02

HMI Team 4/30/03

Oscillations: astrometry vs. Doppler measurements, random telegraph

2

2

2

2

2

2

0

20

2

2

24 ratios/n nt Displaceme

4 ratios/n Velocity

2/)2()(

/2

1

2)(

signal harmonic of amplitude velocity

noise telegraphof amplitude velocity

signal harmonic of period

s timeserieofduration

crossing zerobetween mean time

tP

tT

v

s

tT

v

s

PTsP

t

tvP

s

v

P

T

t

sig

noise

t=20

f=16

HMI Team 4/30/03

Astrometric advantages

on)(granulati10min t916.3006.

mode-r

hr-10

mode-g

hr-2

mode-p

min-5P

snrsnr

rv

r

HMI Team 4/30/03

P-mode limb oscillations

ti

tli

et

elt

),(),(

),(),( )(

P-mode 5min limbshape oscillations

15cm/s 10 microarcsec

dominates lk with b

)(cosP ),(Y

klm

lmlm

ikl

lkklmeb

r

HMI Team 4/30/03

G-modes in velocity and displacement

1600 days of MDI astrometry (l=6)

Appourchaux et al. (2000)

HMI Team 4/30/03

Low frequency oscillations

HMI Team 4/30/03

Another branch of the solar dispersion relation: r-modes

100m x 90,000km

HMI Team 4/30/03

Antishadows

HMI Team 4/30/03

Focus areas

• Limb Astrometry– rotational constraints through limb harmonics– secular radius variations– limb seismology (low frequency modes)

• Limb brightness– thermal magnetic diagnostics– limb seismology