Concordance: In-Flight Calibration Of X-ray Telescopes Without .

The Goal The problems Discrepant results from X-ray observatories in orbit Cluster temperatures and fluxes Blazar fluxes from simultaneous observations SNR line fluxesImperfect ground cal, performance changes in flight‣ Instrument area priors ai differ from “true values” Ai Let flux fij cij /Tij /aiwhere ai prior on Aicij observed countsTij known exposure timeNo absolute calibrators across all bands in flight: no “true” Fj Specific task: derive Aî for optimal agreementHLM — 11/24/20 IACHEC2 /13Concordance Overview

Some Poor Methods Use the average flux as the ‘true’ flux: Fj fij If statistical weighting, answer depends on Tij and aiIf no weighting, then “agnostic” but not stableProblematic statistical inference: Aî cij Let flux fij cij /Tij /aiwhere ai prior on Aicij observed countsTijFjUse one instrument as “given”: Fj fXj for some XTij known exposure timeReference choice is subjectiveStill problematic statisticallyHLM — 11/24/20 IACHEC3 /13Concordance Overview

Better: Multiplicative Shrinkage(Chen ’19)HLM — 11/24/20 IACHEC4 /13Concordance Overview

Better: Multiplicative Shrinkageyij Bi Gj HLM — 11/24/20 IACHEC2σi2(Chen ’19) eij ,yij log(cij /Tij) , Bi log Ai , Gj log Fj4 /13Concordance Overview

Better: Multiplicative Shrinkageyij Bi Gj 2σi2(Chen ’19) eij ,yij log(cij /Tij) , Bi log Ai , Gj log FjBî Wi(ȳ′i Ḡi) (1 Wi)biWi HLM — 11/24/20 IACHECand̂Gj ȳ′ j B̄j 2Mσiτi 2 Mσi 24 /13Concordance Overview

Better: Multiplicative Shrinkageyij Bi Gj 2σi2(Chen ’19) eij ,yij log(cij /Tij) , Bi log Ai , Gj log FjBî Wi(ȳ′i Ḡi) (1 Wi)biWi EA prior uncertaintiesHLM — 11/24/20 IACHECand̂Gj ȳ′ j B̄j 2Mσiτi 2 Mσi 24 /13Concordance Overview

Better: Multiplicative Shrinkageyij Bi Gj 2σi2(Chen ’19) eij ,yij log(cij /Tij) , Bi log Ai , Gj log FjBî Wi(ȳ′i Ḡi) (1 Wi)biWi EA prior uncertaintiesHLM — 11/24/20 IACHECand 2Mσiτi 2 Mσi 24 /13̂Gj ȳ′ j B̄jData uncertaintiesConcordance Overview

Better: Multiplicative Shrinkageyij Bi Gj 2σi2(Chen ’19) eij ,yij log(cij /Tij) , Bi log Ai , Gj log FjBî Wi(ȳ′i Ḡi) (1 Wi)biỹ′ij ỹij 20.5σi, ȳ′i M 2 j 1 ỹ′ijσiM j 1 σi 2,ȳ′ j Wi EA prior uncertaintiesHLM — 11/24/20 IACHECandN 2 i 1 ỹ′ijσi,N i 1 σi 2 2Mσiτi 2 Mσi 24 /13̂Gj ȳ′ j B̄jḠi M 2̂ j 1 GjσiM j 1 σi 2,B̄j N 2̂ i 1 Biσi i I σi 2jData uncertaintiesConcordance Overview

Paper IInput Data 1E0102 with 13 instruments (N 13), O & Ne (M 2) Same 3 sets as in Paper I2XMM catalog targets, N 3, M 41; soft, medium, hardXCAL bright targets, N 3, M 94-108; soft, medium, hard New paper (Marshall , in prep.)Also Capella with Chandra gratings, N 8, M 15Added correlations of XMM hard, medium, softAdded correlations of O, Ne fluxes of 1E0102Sample Data (Marshall in prep.)Used heterogeneous tau valuesHLM — 11/24/20 IACHEC5 /13Concordance Overview

Complications I: Flux MeasurementsConcordance: find Ai where Cij Tij AiFj , A(E) Aiαi(E)Fluxes in band (E1, E2) derived by an inversion processInput: observation cijk for counts in channel kThen fit to model C′ijk tijai fijwhere fij E2 EnE(Θij)dE nij1E2 EG21.5-0.9 (Tsujimoto ’10)E2 E αi(E)qj(E)Φk(E)dE1E2 E qj(E)dE1 Tijkai fijqj(E)dE and Ã(E) aiαi(E) define shape1functions qj(E) and αi(E), the detector response is Φk(E), andNow, Cij kCijk , Tij HLM — 11/24/20 IACHEC k kΦk(E) 1Bautz ‘99ACIS RMFTijk6 /13Concordance Overview

Complications II: Eff. Area Correlations Assume we have EA parameters ξ ⃗ giving log Ã(E; ξ )⃗ B̃(E; ξ )⃗ withp( ξ )⃗⃗⃗⃗̂Then B(E) B̃(E; ξ )p( ξ )d ξ is the best (prior) estimate of B and 22⃗⃗ ξ ⃗ should be the prior’s variancêτ (E) [B̃(E; ξ ) B(E)] p( ξ )d Consider two energies, Ei and Ei′, then the correlation between these is In reality, a Monte Carlo method is used to compute the correlations 1⃗ ξ⃗̂ i)][B̃(Ei′; ξ )⃗ B(Ê i′)]p( ξ )dρi,i′ [B̃(Ei; ξ )⃗ B(Eτ(Ei)τ(Ei′) HLM — 11/24/20 IACHEC7 /13Concordance Overview

Complications III: Assessing Priors Collecting prior (fractional) uncertainties on effective areas Cal scientists assessed their instrumentsHLM — 11/24/20 IACHEC8 /13Concordance Overview

Concordance 1: 1E0102Large t forSuzakuHETGand S3corr’dw/ NeHLM — 11/24/20 IACHEC9 /13Concordance Overview

Concordance 2: 2XMM Based on 42 sources from the2XMM catalog Fixed t: no EA change required Result (hetero. t): 1% for pnUnaffected by pileupindicated, 5-7% for MOSHLM — 11/24/20 IACHEC10 /13Concordance Overview

Concordance 3: XMM Blazars 117 bright XMM sources fromMatteo Guainazzi PSF clipped to reduce effect ofpileup Result (fixed t): 5% adjustmentto pn indicated, 1-2% for MOS Result (hetero. t): 1% for pnindicated, 5-7% for MOSHLM — 11/24/20 IACHEC11 /13Concordance Overview

Concordance 4: Capella Lines from Chandra gratingspectraNe XNe x, Fe xxvii (15 Å), Fe xxvii (17 Å), O VIII 5 sets of adjacent observations comparedNot all instruments used eachtimeResult: 1generally consistent,LETGS are low of HETGSHLM — 11/24/20 IACHECO VIIIMarshall in prep.12 /13Concordance Overview

Conclusions We can bring observations intoConcordance Simple situations give reasonableanswers: consistent with otheranalyses More complex situations: Outliers handled with t distribution Instrument areas are time-dependentFluxes in bands are related globally, notindependentHLM — 11/24/20 IACHEC13 /13Concordance Overview

Preview: XMM v. ChandraHLM — 11/24/20 IACHEC14 /13Concordance Overview

In-Flight Calibration of X-ray Telescopes without Absolute References Herman L. Marshall (MIT), Vinay Kashyap, Jeremy Drake, Pete Ratzlaff, Paul Plucinsky (SAO), Matteo Guainazzi (ESA) Yang Chen (Harvard, UMich.), Xiao-Li Meng (Harvard), Xufei Wang (Harvard, Two Sigma), David van Dyk (ICL) HLM — 11/24/20 IACHEC /13 Concordance Overview