Sensitivity Analysis Applied to Atomic Data Used for X-ray Spectrum Synthesis (and other topics) T. Kallman NASA/GSFC with crucial help from M. Bautista, J. Garcia, C. Mendoza, P. Palmeri Atomic data for spectral fitting and synthesis Sensitivity of model results to atomic data: DR and Auger Atomic data for ionization balance: DR

900 ksec Chandra HETG spectrum of NGC 3783 (Krongold et al 2004; Kaspi et al. 2001, 2003; Netzer et al. 2004; Blustin et al 2002) Chandra and XMM have provided spectra which have the best spectral resolution and sensitivity in the X-ray band obtained so far.. With surprising consequences: Discovery of outflowing X-ray gas Relatively low velocity Weak or absent emission Possibly large mass loss rate

The challenge of X-ray astronomy Calculate Ionization, T.. Synthesize spectum Agree? Choose inputs ( ,..) no Observed data (pulse height) Instrument response Synthetic data “xspec” “model” “science”

Photoionization modeling Traditional photoionization based on nebular approximation: clean separation of ionization balance from excitation But this neglects effects likely to be important in X-ray plasmas: high density and radiative excitation. We attempt to solve self-consistently for population kinetics, ionization, and radiative equilibrium. Atomic processes Photoionization (including inner shells, Auger decay Recombination (RR, DR, …) Collisional processes Compton scattering Charge transfer Emission/absorption associated with these processes A key challenge is the accumulation of complete, yet accurate atomic data. Radiation transfer is still highly simplified But we don’t really know how errors propogate..

Fit of photoionization model to Chandra HETG observation of NGC 3783  2 ~18516/8192, voff=700 km/s vturb=300 km/s wavelength (A) Component Fit, log  =2.2, 0.1  flux/density

Favored region  flux/density

Fitting absorption only is fraught, due to influence of scattering/reemission

Si VII-XI K lines

Al XIII Al XII

Fe XX-XXII

Fe XXII

Fe XXI

Fe M shell UTAs

Effect of atomic data Current model (Chianti V.5) (Using Chianti v.3) (cf. Berrington &Tully 1997 Chidichimo 2005 Landi and Gu 2006 Feldman 2000, Brown et al Fawcett et al Landi and Phillips 2005, Kucera 2000, Edlen 1984, Shirai et al. 2000, Butler and Zeippen 2001, Mclaughlin and Kirby 2001, Feldman et al. 1998, Young et al. 1998, Thomas and Neupert 1994, Brosius et al Eissner et al. 1999, NIST, Berrington et al. 2005)

what do we learn from Spectral fitting tests? ● We can get ~acceptable fits to some of the highest s/n spectra in the X-ray band – Many line wavelengths fit adequately – Effects of rydberg series, Fe M shell UTAs – Ionization balance is ~OK – Recent improvement due to inclusion of data from Chianti v.5 and Fe L shell data from Landi and Gu (2006) and experimental and IP references (too numerous to mention here, but indispensable) ● There are still many lines (eg. Al, inner shells of medium-Z elements) missing from the database (I use), and some wavelengths may need reexamination ● Data needed for spectrum synthesis (wavelengths, ids, etc.) is (are?) crucial to deriving astrophysical results owing to detector limitations, blending, counting statistics.

● Procedure: – We perturb the DR rates coefficients by a constant factor in the log, and examine the effects on the ionization balance and on the results of spectral fits such as those shown in the previous section – We also examine the effects of 2x changes in Auger rates ● Past work: – Gianetti Landi and Landini (2000) examine 3 different ionization balances on abundance determinations. Compare Shull and VanSteenburg, Arnaud and Rothenflug and Mazzotta effects on line ratios of high vs. low FIP lines. Compare with observed Soho CDS data. ● Find that DEM is very different among the 3 curves, factors ~several. ● Inferred abundances also differ by ~2x. – Savin and Laming (2002) discussed the effects of uncertainties in DR rates on inferred solar abundances. In this case the observed line emission may be from temperatures different from the temperature of peak abundance ● They show that inferred solar abundances can differ by factors as much as 5 given their estimates of the DR rate coefficients How sensitive are the spectral fits to rates affecting ionization balance?

Dielectronic rate coefficients ● Existing rates: Arnaud and Raymond; Culled from various theoretical works, mostly DW: ● Fe 24+: Chen (1986a) ● Fe 23+: Romanik (1988) ● Fe 22+, Badnell (1986) ● Fe 21+, Badnell (1986) ● Fe 20+ Roszman (1987, 1990) ● Fe 19+ Roszman (1987, 1990) ● Fe 18+ Roszman (1987, 1990) ● Fe 17+ Dasgupta and Whitney (1990) ● Fe 16+ Smith et al (1995) ● Fe 15+ Jacobs (1977) ● Experiments suggest ~20% accuracy for the best calculations (eg. Savin et al. 2002…)

Iron Recombination rate coefficients vs. temperature Perturbed DR rates: log(Rate’) =  log(Rate) 0.9 <  <1.1 Baseline dielectronic recombination (DR) rate (including radiative cascades from n>5) based on Arnaud and Raymond (1992); cf. Also work by Nahar and Pradhan

Photoionization equilibrium  =4  Flux/density baseline Perturbed DR -->  log(  )=0.2 or greater

Photoionization equilibrium  =4  Flux/density baseline Auger enhanced 2x -->  log(  )=0.1

Fe XXII baseline What’s the effect on the spectrum?

Fe XXI baseline What’s the effect on the spectrum?

Perturbed DR What’s the effect on the spectrum?

Perturbed DR What’s the effect on the spectrum?

Photoionized Fitting results For baseline model:  2 =11105/3400 Log(  )=2.2,0.1 (similar to Krongold et al.) Abundances:[Ne/O]=1, [Si/O]=1, [S/O]=2, [Fe/O]=0.4 With perturbed DR, no iterations  2 =17660/3400 With perturbed DR, iteratively fit  2 =13072/3400 (worse!) Log(  )=2.9,0.1 (Significantly different!)

Sensitivity analysis Summary photoionized:  log(DR rate coefficients) <0.1 -->  log(  peak ) ~0.2 or greater Detailed abundances of minority ions change by factors ~several Results of fitting to Chandra spectrum detectable,  (DEM)~0.5 in log(  ) Smaller effects are associated with 100% changes in Auger This represents statistically significant effects on the spectrum, which affect quantititative results.

We can also test other calculations… Recent work (Badnell and coworkers ; Gu 2003, 2004) has resulted in dr rates which are likely to be more reliable, due to: Experimental validation of resonance structure Efficient computational algorithms Allowing inclusion of many channels for dr and autoionization Treatment of fine structure at high (>10) Z Importance of forbidden autoionization rates Allow for treatment of level-resolved DR (but we have not adopted these yet) We consider the effects of introducing these into model calculations

Red=Arnaud and Raymond Black=Badnell et al.

Red=Arnaud and Raymond Black=Badnell et al.

Red=Arnaud and Raymond Black=Badnell et al.

Arnaud and Raymond Badnell et al. Effect of changing dr rate coefficients on the ionization balance of iron Log(  ) Log(ion fraction)

Ratio of Fe ion fractions new/old vs. 

So what happens to spectral fitting? From sensitivity experiment: If DR rates change enough to move ion fractions by  log(  ) >0.1, then fitting results reflect this change But the new DR rates have a smaller effect for many ions Exceptions: Fe 15+, Fe Fitting results for NGC 3783 find similar  2, with the exception that the fit using the newer DR rates is slightly improved,  2 ~30. Perhaps DR is not a major contributor to model uncertainty, for photoionized models

 (A) Arnaud and Raymond Badnell et al.

So what happens to spectral fitting? From sensitivity experiment: If DR rates change enough to move ion fractions by  log(  ) >0.1, then fitting results reflect this change But the new DR rates have a smaller effect for many ions Exceptions: Fe 15+, Fe Fitting results for NGC 3783 find similar  2, with the exception that the fit using the newer DR rates is slightly improved,  2 ~30. Perhaps DR is not a major contributor to model uncertainty, for photoionized models

conclusions ● Spectrum synthesis ● Propogation of errors in rates affecting ionization balance ● Importance of new DR rates

Supplementary slides

What atomic data goes into models? processstatus recombinationx ionizationReciprocal with rec. Electron impact excitation linear Charge transferN/a Inner shell fluorescence/auger x In this talk I will discuss the effects of changes in recombination and Auger on model results

Coronal ionization balance baseline Perturbed DR -->  log(T)=0.1

Fit to HETG Cappella Spectrum Fe 16+ Ne 9+ Fe 18+ Fe 17+ Fe 19+Fe 18+ (baseline rates)

Fit to HETG Cappella Spectrum Fe 16+ Ne 9+ Fe 18+ Fe 17+ Fe 19+Fe 18+ (Perturbed rates)

Coronal Fitting results ● For baseline model: –  2 =3267/1602 (NOT acceptable, ~OK for discussion) – Log(  )=6.9,7.1 (simple DEM) – Abundances:[Ne/Fe]=2.1, [O/Fe]=1 ● With perturbed DR, no iterations –  2 =3610/1602 ● With perturbed DR, iteratively fit –  2 =3522/1602 (worse!) – Log(  )=6.9,7.2 --> Fit results change by ~0.1 in log(T)

Fitting results ● For baseline model: –  2 =11105/3400 – Log(  )=2.25,0.125 – Abundances: [Fe/O]=0.4,[Fe/S]=0.2,[Fe/Si]=0.4 ● With perturbed DR, no iterations –  2 =17695/3400 ● With perturbed DR, interatively fit –  2 =13072/3400 – Log(  )=2.95,0.125

outline ● challenges of modeling photoionization – 2 paradigms in astrophysics: coronal and photoinized – Photoionized applies to compact sources with intense source of continuum radiation – Turns out that these are the most feasible targets for current high resolution (grating) detectors -> this is the frontier for high resolution X-ray obs.