HDAC preliminary analysis
Line profile, Hydrogen distribution
Ralf Reulke2,Yuichi Ito1, Horst Uwe Keller1, Axel Korth1
1 : Max-Planck Institut fuer Sonnensystemforschung, Katlenburg-Lindau, 37191,
Germany
2 : Deutsches Zentrum für Luft- und Raumfahrt Institut für Verkehrsforschung,
Rutherfordstraße 2, 12489 Berlin, Germany
Cassini UVIS team meeting, Jan 4-6, 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC Status 2005:
- ~2700 data sets in Jan. 2005 (for 2004)
- ~2300 data sets in Jan. 2006 (for 2005)
- HDAC run in photometer mode most of the time,
sensitivity is stable
- modulation measurements
- Important observations in 2005: Titan
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
2005:
Scale=40
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC Status:
Radiometry
- Sensitivity changes over the whole year 2003/4/5
- Hot Model fits data
- Sensitivity is less than 30 cts/s/R
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC Status:
Radiometry
- Analysed data from IPHSURVEY sequences
- Data, which are constant within the sequence
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC Status:
Radiometry
- Analysed data from IPHSURVEY sequences
- Data, which are constant within the sequence
- Analysed the variance / mean value – relation
- n … number of incoming photons
- m … measured value
- µ … “Sensitivity”
⟨ m⟩ = μ ⋅ ⟨ n⟩
2
2
2
2
2
2
σ M = ⟨ ( m – ⟨ m⟩ ) ⟩ = μ ⋅ ⟨ ( n – ⟨ n⟩ ) ⟩ = μ ⋅ σ N
2
2
2
σM
μ ⋅σ
--------= ----------------N- = μ
μ ⋅ ⟨ n⟩
⟨ m⟩
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC Status:
Radiometry: Analysed the variance / mean value – relation
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC Status:
Radiometry: Absolute to FUV, Sensitivity = 28 cts/s/R
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Modulation mode:
1. H and D-Cell Modulation lower than expected
2. Shape of the modulation curve is different
Derived a new Power-Tau-relation from all existing
measurements
Results:
• Describes all measurements
• Stable situation for the last 3 years
Possible reasons:
• Loss of Hydrogen and/or change of
dissociation rate
• Filament or wall dependent
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC modulation analysis:
4 * HDAC conditioning in 2005
2005-090T09:4
2005-091T06:1
2005-146T18:2
2005-301T13:19:47
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC modulation:
-New program for HDAC
modulation analysis
- Integrates HotModel &
Spice
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC modulation:
-New program for HDAC
modulation
analysis
- Integrates HotModel &
Spice
Next steps:
- Optimizing parameters
- Accuracy estimation
σEstm = 0.0379 A
σLISM = 0.0391 A
Diff ≈ 1 mA
(1215.664 A, 1215.34 A)
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC modulation analysis:
HDAC modulation measurements during the other
Titan observations until end of mission
Need exact influence of other disturbing sources
(e.g. D-cell)
Need to compare the HDAC data with FUV data
(HDAC's red tail sensitivity)
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Parameter Estimation
• LISM-Model can be fitted by
⎛ λ2 ⎞
LH ( λ ) = A ⋅ exp ⎜ −
2 ⎟
⎝ 2 ⋅σ H ⎠
σH =
•
λ0
H
c
⋅
2kTsource
mH
Wu, F. M., Judge, D. L.: A reanalysis of the observed interplanetary hydrogen
Lyman alpha emission profiles and the derived local interstellar gas
temperature and velocity; Astrophysical Journal, Vol. 239, pp. 389-394, 1980
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Parameter Estimation
I (τ i , j ) = A ⋅ ∫ H (λ ) ⋅ THH, D (λ ,τ i , j ) ⋅ L(λ )d λ + BD
• Model
i, j ∈[ 0, 7 ]
k ∈[0, 63]
yk + vk = a ⋅ Fk + bk
∑v
• Minimize νk or
⎡ y1 ⎤
⎢y ⎥
L = ⎢ 2⎥
⎢M⎥
⎢ ⎥
⎢⎣ yn ⎥⎦
2
⎡ v1 ⎤
⎢v ⎥
v = ⎢ 2⎥
⎢M⎥
⎢ ⎥
⎣ vn ⎦
= min
⎡ F1
⎢F
A=⎢ 2
⎢M
⎢
⎢⎣ Fn
0
0
1
0
1
M
0
0⎤
0 ⎥⎥
⎥
⎥
1 ⎥⎦
→
v T v = min
⎡ a ⎤
xˆ = ⎢
⎥
⎣b1K7 ⎦
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Adjustment Approach (Nonlinearities)
F (T ; λ ,K) = F (T0 ; λ ,K) +
L + v = Axˆ
→
∂F
⋅ dT + K
∂T 0
v = Axˆ - L
L = L − F0
Results:
σ~ 120 c/s
σb ~ 50…70 c/s
σT ~ 120 K
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Parameter Estimation
Nonlinearities
I (τ i , j ) = A ⋅ ∫ H (λ ) ⋅ THH, D (λ ,τ i , j ) ⋅ L(λ )d λ + BD
i, j ∈[ 0, 7 ] k ∈[0, 63] k = i ⋅ j
yk + vk = a ⋅ Fk + b j
Designmatrix
⎡ ⎛ ∂ϕ1 ( X ) ⎞
⎟⎟
⎢ ⎜⎜
⎢ ⎝ ∂X 1 ⎠ 0
⎢⎛ ∂ϕ 2 ( X ) ⎞
⎜
⎟
A = ⎢⎜ ∂X ⎟
1
⎝
⎠0
⎢
n ,u
⎢
M
⎢⎛ ∂ϕ ( X ) ⎞
⎟⎟
⎢⎜⎜ n
⎢⎣⎝ ∂X 1 ⎠ 0
⎛ ∂ϕ1 ( X ) ⎞
⎜⎜
⎟⎟
⎝ ∂X 2 ⎠ 0
⎛ ∂ϕ 2 ( X ) ⎞
⎜⎜
⎟⎟
⎝ ∂X 2 ⎠ 0
M
⎛ ∂ϕ n ( X ) ⎞
⎜⎜
⎟⎟
⎝ ∂X 2 ⎠ 0
⎛ ∂ϕ ( X ) ⎞ ⎤
⎟⎟ ⎥
L ⎜⎜ 1
⎝ ∂X u ⎠ 0 ⎥
⎛ ∂ϕ ( X ) ⎞ ⎥
⎟⎟ ⎥
L ⎜⎜ 2
⎝ ∂X u ⎠ 0 ⎥
⎥
O
M
⎛ ∂ϕ n ( X ) ⎞ ⎥
⎟⎟ ⎥
L ⎜⎜
⎝ ∂X u ⎠ 0 ⎥⎦
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Parameter Estimation
•
•
•
•
Derivative for LISM-Model
Number of unknown: 10
Number of equations: 16*(# measurements) = 448
Problem: „good“ start values for the iteration
2
⎛ λ −λ +λ 2 ⎞
(
∂I H A ( λ − λ0 + λd )
0
d) ⎟
=
⋅ exp ⎜ −
2
2
0
2
0
⎜ 2 ⋅ (σ ) T ⎟
∂T
2 ⋅ (σ H ) Ts
H
s ⎠
⎝
⎛ λ −λ +λ 2 ⎞
(
∂I H
0
d) ⎟
= exp ⎜ −
2
0
⎜ 2 ⋅ (σ ) T ⎟
∂A
H
s ⎠
⎝
∂I H
=1
∂B j
( j = 1K 7 )
⎛ λ −λ +λ 2 ⎞
(
∂I H A ( λ − λ0 + λd )
0
d) ⎟
⎜
=
⋅ exp −
2
2
0
0
⎜
⎟
∂λ0
(σ H ) Ts
⎝ 2 ⋅ (σ H ) Ts ⎠
(σ )
0
H
2
⎛ λ0
⎜ H
=⎜
⎜
⎝ c
⎞
2k
⎟
⎟ ⋅
⎟
⎟ mH
⎠
2
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Results:
• D-background is changing. For the last few measurements
we have the following results:
2005-091T06:1
• A0=6518 cts/s
• Bi = [41, -16, 21, 51, 70, 223, 319, 406]
2005-146T18:2
• A0 = 6544 cts/s
• Bi = [56, -12, -26, 23, 51, 238, 325, 419]
• Good estimate for Bi = [0, 0, 0, 0, 0, 200, 300, 400]
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC on Titan
- S17 19 19TI (t) Titan 2005-360T18:54 Dec26 Mon T9;
outbound 10,429 km flyby, v=5.6 km/s, phase=67 deg
- Modulation of H-Lyα line
- Adaptation of earlier calculation to actual cruse
- Comparison with modified sensitivity, SNR and τ
dependences
- Algorithm test, adaptation and improvements
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC Titan T9 fly-by:
∼9h & 3 different phases
departure
fly-by
approach
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
TITAN fly-by
Closest approach:
Name:
HDAC2005_30_17_53_20_UVIS_019TI_HDAC001_PRIME
ODC-ID: 1145
Sequenz: 16 modulation steps × 72 samples each
H-Cell: 0777777777777777
D-Cell: 0707070707070707
54 Sequences
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
FUV-Data
• FUV2005_361_04_35_43_UVIS_019SW_IPHSURVEY027_RIDER
• 2005-361T04:35:45.89 - 2005-361T13:33:15.90
•
•
• FUV2005_362_04_18_40_UVIS_019SW_IPHSURVEY001_RIDER
• 2005-362T04:18:44.84 - 2005-362T11:09:09.84
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
TITAN fly-by (Closest Approach)
Dark: H=0 & D=0 (Background)
Blue: H=7 & D=0
Green: H=7 & D=7
Signal from 13-19 kcts/s ≈ 460-680 R
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Results
• Max. modulation – 0.75
• Modulation is proportional
to Doppler-velocity
• Photometry influenced by
changes of viewing
directions (see steps)
• Steps are correlated to
change in view angle
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
HDAC at Titan
-Modulation of H-Lyα
-Comparison with modified τ dependence
-Large H-density & modulation is low (tab. from
Reghely)
H-density
Modulation
(Model 1)
Modulation
(Model 2)
0.1
0.12
0.6
1
0.23
0.67
10
0.47
0.77
UVIS Science Team Meeting
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
Modulation
Measurement
process
Photometer Mode:
Modulation Mode:
UVIS Science Team Meeting
∫ H(λ ) ⋅1⋅ S(λ )dλ
I( τ) = ∫ H(λ ) ⋅ T(λ, τ) ⋅ S(λ )dλ
I0 =
04 Jan. 2006
HDAC Instrument – Cassini/Huygens Mission
2. HDAC Experiment:
Cell Transmission
T(λ) = e
−σ⋅n⋅L⋅Φ (λ)
UVIS Science Team Meeting
04 Jan. 2006
Obs & Calc data
Similar tendency
Different tendency
HDAC FOV detects
limb scattered light.
Angle (Sun-Titan-s/c)
[deg]
Omni-directional
flux [Raileigh]
Calculated intensity from an initial Titan model profile
Comparison with observation data
Angle (Sun-Titan-s/c)
=90deg
Closest approach
Minutes after PHASE2
Fitting result
Variation of chi-square value
with no of iterations
Comparison of obs & cal data
with no of iterations
Chi-square
Calculation result from
an initial profile
converged
19000 km
3000 km
Obtained altitude profile
# In T9 observation, we had information of Hydrogen
corona distribution between 3000km-19000km alt.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
200.000
400000.
240.000
798105.
280.000 1.59243e+006
320.000 3.17731e+006
360.000 6.33957e+006
400.000 1.26491e+007
440.000 2.52383e+007
480.000 5.03570e+007
520.000 1.00475e+008
560.000 2.00475e+008
600.000 4.00000e+008
630.000 2.83178e+008
660.000 2.00475e+008
690.000 1.41925e+008
720.000 1.00475e+008
750.000 7.11312e+007
780.000 5.03570e+007
810.000 3.56500e+007
840.000 2.52383e+007
870.000 1.78673e+007
900.000 1.26491e+007
930.000 8.95488e+006
960.000 6.33957e+006
990.000 4.48807e+006
1020.00 3.17731e+006
1050.00 2.24937e+006
1080.00 1.59243e+006
1110.00 1.12735e+006
1140.00
798105.
1170.00
565015.
1200.00
399698.
2715.79
66435.7
4231.58
1584.36
5747.37
96.5387
7263.16
14.6508
8778.95
2.54202
10294.7 0.448676
11810.5 0.110039
13326.3 0.0623054
14842.1 0.0285319
16357.9 0.00842478
17873.7 0.00186005
19389.5 0.000333962
20905.3 5.71462e-005
22421.1 9.81674e-006
23936.8 1.71253e-006
25452.6 2.99051e-007
26968.4 5.22215e-008
28484.2 9.11916e-009
30000.0 1.59243e-009
Retrieved
Hydrogen distribution
Simulation scheme
(Analysis scheme)
By using the formula, we can estimate the SNR of D
H(D) LYMAN-A
TH(n)
<ANSWER>
SIMULATION OF
IMAGING
TD(n)
BGIS(n)
Deuterium retrieval
Formula
BGSiginc(n)
# Expected deuterium intensity
with its standard err
BGDARK(n)
BGNONLY-A(n)
NOTE : Cell only controll H & D Lyman alpha
emisson, other parameters must be adopted
from the pre-observation, parallel observation
by the grating spactrometer
6 parameters
Temperature (assumed) + Gaussian profile assumed
HDAC Instrument – Cassini/Huygens Mission
Anhang
UVIS Science Team Meeting
04 Jan. 2006