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