Sensitivity Analysis Applied to Atomic Data Used for X-ray Spectrum Synthesis

(and other topics)

T. KallmanNASA/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

15 16 16 17 17 18 18 19 wavelength (A)

11 12 12 13 13 14 14 15

7 8 8 9 9 10 10 11

3 4 4 5 5 6 6 7

2 Component Fit, log=2.2, 0.1flux/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 1997Chidichimo 2005Landi and Gu 2006Feldman 2000, Brown et al. 2002Fawcett et al. 1987Landi 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. 1998Eissner 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 2003-2006; 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 RaymondBlack=Badnell et al.

Red=Arnaud and RaymondBlack=Badnell et al.

Red=Arnaud and RaymondBlack=Badnell et al.

Arnaud and Raymond

Badnell et al.

Effect of changing dr rate coefficients on the ionization balance of iron

Log()

Log

(ion

fra

ctio

n)

0

0

-2

-2

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 16+ ..• 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 16+ ..• 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?

process status

recombination x

ionization Reciprocal with rec.

Electron impact excitation

linear

Charge transfer N/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+ Fe 16+

Ne 9+Ne 9+ Fe 18+ Fe 17+

Fe 17+

Fe 19+ Fe 18+

(baseline rates)

Fit to HETG Cappella SpectrumFit to HETG Cappella Spectrum

Fe 16+ Fe 16+

Ne 9+Ne 9+ Fe 18+ Fe 17+

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.