2010 HRC-I QE Analysis using new HRMA model (N0008), new ACIS contam (N0005), new HRC-S QE (N0010)

1. Redo "low-energy paste"

In 2002 as part of a modification to the HRC-I QE, the HRC-S QE was used as a "shaping factor" below 626 eV. See the memo "A New Flight Model of the HRC-I MCP Quantum Efficiency".
Since the HRC-S QE model has been revised, we need to redo this "low-energy paste".

The figure below shows a comparison of the current QE models - hrciD1999-07-22qeN0007.fits (red dotted line) and hrcsD1999-07-22qeN0010.fits (blue dashed line). Note that the HRC-S QE plotted here is for chip 2, region 203. (This is where the aimpoint is - see figure at bottom of page.) These models include the UVIS transmission efficiency models UVIS-I v4 and UVIS-S1 (a.k.a "center thick section") v4, respectively. The solid lines show the QE models (blue=S, pink=I) with the UVIS efficiencies removed.

The following figure compares the UVIS-I (red) and -S1 (blue) models.

Note that the pasting should be done with the bare MCP QE models, not the ones including UVIS efficiencies.
The following plot shows the HRC-I and S MCP QE models (pink and blue lines), with the dashed green line showing the HRC-S model raised to match the HRC-I model around 626 eV. (The red X shows the point where we will do the paste.)

Model with new paste:

Finally, the UVIS-I efficiency is folded back in, and the QE is saved as hrciD1999-07-22qeN0007prime.fits.

2. Source Models

To get source models for predicting count rates, we fit HRC-S/LETG or ACIS observations, pointing the ardlib to the latest CALDB products when making the ARFs.

Cas A CCO

NOTE: Apparently CCO is not constant in flux or spectral shape, see Nature paper by Ho & Heinke. Also Dan says pileup will be an issue for ACIS.

Absorbed powerlaw model (TBabps*pegpwrlw) joint fit to 14 ACIS-I3 observations, processed with CIAO 4.2, fitting over 1.0 - 5.0 keV:

========================================================================
Model TBabs<1>*pegpwrlw<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp

   1    1   TBabs      nH         10^22    3.10810      +/-  0.335347

   2    2   pegpwrlw   PhoIndex            4.03241      +/-  0.298929

   3    2   pegpwrlw   eMin       keV      1.00000      frozen

   4    2   pegpwrlw   eMax       keV      5.00000      frozen

   5    2   pegpwrlw   norm                3.07990      +/-  0.624229

Chi-Squared = 159.24 using 177 PHA bins.
Reduced chi-squared = 0.91518 for 174 degrees of freedom
Null hypothesis probability = 7.819139e-01
XSPEC12>error 1. 1
Parameter Confidence Range (1)
1 2.77135 3.45868 (-0.336807,0.350529)
XSPEC12>error 1. 2
Parameter Confidence Range (1)
2 3.73706 4.33908 (-0.295395,0.306629)
XSPEC12>error 1. 5
Parameter Confidence Range (1)
5 2.52538 3.81912 (-0.554619,0.739127)

Joint fit to 16 ACIS-S3 spectra, processed with CIAO 4.2, fitting over 1.0 - 5.0 keV:

========================================================================
Model TBabs<1>*pegpwrlw<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp

   1    1   TBabs      nH         10^22    3.31989      +/-  0.479875

  2    2   pegpwrlw   PhoIndex            4.00485      +/-  0.387994

 3    2   pegpwrlw   eMin       keV      1.00000      frozen

  4    2   pegpwrlw   eMax       keV      5.00000      frozen

  5    2   pegpwrlw   norm                2.95970      +/-  0.792795

SNR G21.5-0.9

Absorbed powerlaw model (TBabs*pegpwrlw) from fit to ACIS-S3 subarray observations (not affected by pile-up) in a 43" source region. Using ObsIDs 1553, 1554 and 3693. Fitting over 1-8 keV. Abund=wilm, xsect=vern. Data processed with CIAO 4.2. See /data/hrc/G21.5-0.9/Subarray/.

========================================================================
Model TBabs<1>*pegpwrlw<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp

   1    1   TBabs      nH         10^22    3.23466      +/-  3.22915E-02

   2    2   pegpwrlw   PhoIndex            1.79686      +/-  1.60639E-02

   3    2   pegpwrlw   eMin       keV      2.00000      frozen

   4    2   pegpwrlw   eMax       keV      8.00000      frozen

   5    2   pegpwrlw   norm                54.9971      +/-  0.257131

Chi-Squared = 969.97 using 924 PHA bins.
Reduced chi-squared = 1.0532 for 921 degrees of freedom
Null hypothesis probability = 1.278098e-01
XSPEC12>error 1. 1
Parameter Confidence Range (1)
1 3.20203 3.26783 (-0.0326274,0.0331677)
XSPEC12>error 1. 2
Parameter Confidence Range (1)
2 1.78078 1.81308 (-0.0160794,0.0162158)
XSPEC12>error 1. 5
Parameter Confidence Range (1)
5 54.7394 55.2557 (-0.257731,0.258575)

white dwarf HZ 43

HRC-S/LETG 0th Order Count Rates

The red line marks July 2008 -- this is the time that the current HRC-S QE model is pinned to. The blue dashed line shows a linear fit to the count rates. When making the model we multiply each ARF by norm=(yint + tnrm*slope)/(yint + obs_date*slope) where tnrm corresponds to July 2008.

Combined HRC-S/LETG Spectrum

The "model":

The predicted HRC-I spectrum (model * HRC-I ARF):

We sum over 0.06 - 0.3 keV to get the predicted count rate.

blazar PKS 2155-304

Combined HRC-S/LETG Spectrum

The "model":

The predicted HRC-I spectrum (model * HRC-I 0th order ARF):

We sum over 0.1 - 5.6 keV to get the predicted 0th order count rate.

To check the shape of the HRC-I N0007prime QE model around the point where the "paste" was done (~0.62 keV / 20 Ang) we compare the HRC-S/LETG and HRC-I/LETG spectra, after correcting by the respective ARFs.

HRC-I spectrum:

HRC-I grating ARFs:

HRC-I spectrum/ARF:

(HRC-I spectrum/ARF) / (HRC-S combined spectra / ARF):

Close-up of range softwards of the pasting point:

The mean value of the ratio in this range (20-31 Angstroms) is 0.983 with standard deviation 0.260.

3. Predicted Fluxes

To get the predicted HRC-I count rates for Cas A and G21.5-0.9, we read the HRC-I ARF (made with given HRC-I QE model) into XSPEC, define the source model with parameters set to best-fit ACIS values, and check the model predicted rate.

For HZ43 and PKS 2155 we create a source model by dividing the HRC-S spectra by the HRC-S grating ARF, as described above. We then fold in the HRC-I ARF (made with QE model N0007 or prime) and sum over a defined energy range to the get total predicted count rate.

Predicted rates are shown in the first two columns of the table in Section 5.

4. Observed Count Rates

HZ 43

Cas A

G21.5-0.9

5. Comparing Observed and Predicted Rates

6. Renormalize N0007prime to get new QE, N0008.

a) Below 0.62 keV

First we renormalize the "re-pasted" section of model N0007prime, i.e. below 0.62 keV, based on predicted and observed HZ 43 count rates and on the PKS2155 spectra/ARF ratios for this energy range.

The observed rate for HZ 43 is 3.88 +/- 0.07 cts/s and the predicted rate with N0007prime is 4.03 +/- 0.25, giving a ratio of 1.03866 with uncertainity sqrt((0.25/4.03)^2+(0.07/3.88)^2)*(4.03/3.88) = 0.0671025.

For PKS2155 the ratio of (HRC-I spectrum / HRC-Iprime ARF) to (HRC-S combined spectrum / HRC-S ARF) has mean 0.983 with standard deviation 0.260 in the 20-31 Angstrom range.

The error-weighted mean is ~1.02:
IDL> ss=[0.26,0.067] & mm=[0.98,1.03866]
IDL> print, total(mm/ss)/total(1/ss)

1. 1. 02664
      

So we divide the HRC-S shifted QE by 1.027 below 0.62 keV, then redo the paste to get model N0007prime_renorm. Predicted counts with this model are shown in the third column of the table in Section 5. Now the ratio of (HRC-I spectrum / HRC-Iprime ARF) to (HRC-S combined spectrum / HRC-S ARF) for PKS2155 has mean 1.01 and standard deviation 0.267 in the 20-31 Angstrom range.

New paste:

Closeup: (The pasting point is just below 0.63 keV)

b) Large-scale correction

Finally, we do a large-scale, energy-dependent correction to model N0007prime_renorm to get the new HRC-I QE model N0008. For the correction function, we use a step function convolved with a Gaussian:

f(E)= (K/2) * (1 - Erf[ (E - E_s) / (sqrt(2) * sigma) ] + constant

where

K = amplitude of step function
E_s = energy where step is located
sigma = Gaussian sigma
constant = constant offset

We chose this function since it has the simplicity of a step function but is continuous to avoid introducing any artificial edges in the QE model.

We fix sigma to a narrow value of 0.1 keV and constrain the value of the constant so that f(0)=1.

To find values of K and E_s, we do a grid search, computing the predicted count rates for G21.5-0.9, PKS2155-304 and HZ 43 for each pair of values by multiplying f(E) with the source model and ARF (made with HRC-I QE model N0007prime_renorm). The values yielding the minimum chi-square (0.25) are E_s = 0.35 keV and K=0.099.

The correction function:

We multiply this function with model N0007prime_renorm to get the new HRC-I QE model N0008.

Predicted count rates with model N0008:

Source	Predicted Rate	(predicted - observed)/observed
G21.5-0.9	0.541 +/- 0.016	0.087%
PKS2155-304	1.535 +/- 0.052	-0.101%
HZ43	3.913 +/- 0.239	0.862%

Dec 2008 - Jan 2009 Analysis (new HRMA model, old ACIS contam, old HRC-S QE)

Jump to Section:

• History of HRC-I QE model and links to memos
• Modeling our calibration sources
• Predicted fluxes for our calibration sources
• Observed count rates
• Summary table comparing observed and predicted rates

  ---

  Current QE Model:

  • (i) first there were lab measurements
  • (ii) modified with quadratics by Patnaude et al 1998 to match XRCF
  • (iii) then the quadratics were scaled over 3 distinct passbands to match flight observations of HZ 43, G21.5 and Cas A
  • (iv) then the HRC-S QE was tacked on below ~0.6 keV (scaled to have the same normalization as the original HRC-I QE)
  • (v) and an additional quadratic modification was applied to match PKS2155 (Posson-Brown et al 2003)

  HRC-I QE Memos:

  • Patnaude 1998 SPIE paper
  • 2002 cal memo - normalization w/ flight data; HRC-S shape @ low energies
  • 2003 cal memo - renorm w/ PKS2155

  To Do:

  1. transform PKS2155 HRC-S LETG spectrum to HRC-I LETG to make sure that (iv) is still OK, and that the only change that needs to be applied is the global HRMA EA factoring out.
  2. divide by old HRMA CALDB EA and multiply by model F
  3. measure fluxes for HZ 43, PKS2155, Cas A, G21.5
  4. compute predicted fluxes for all of the above, using the observed HRC-S+LETG spectrum (divided by appropriate gARF) as the model and the usual suspects for the rest
  5. if necessary, back out the 2003 correction and reapply as either a quadratic or a spline

  ---

  Source Models

  To get source models for predicting count rates, we fit HRC-S/LETG or ACIS observations, pointing the ardlib to either the new HRMA effective area (model F) or the current CALDB model when making the ARFs.

  SNR Cas A

  I tried fitting the central point source in the ACIS-I calibration observations with an absorbed powerlaw model over 0.5-4 keV, but the fits are all over the place. Below is one of the better fits:
  nH=1.49894e22; gamma=3.22547; norm=1.90391E-03 with model F. fitting this obsid with the caldb hrma model we get nH=1.52879e22; gamma=3.23948; norm=1.80222E-03

  To do: Try freezing nH? Fitting the whole SNR? And should probably use S3 instead of ACIS-I.

  Dan Patnaude is working on fitting Cas A using HRMA model F and will send us his results by next week.

  SNR G21.5-0.9

  From fits to ACIS S3 observations, we have an absorbed (TBabs) powerlaw model with parameters: nH=2.19e22, gamma= 1.83, and norm=1.93e-2 for model F and parameters: nH=2.15e22 , gamma= 1.73, and norm=0.0162 for the current caldb hrma model.

  white dwarf HZ 43

  We don't fit the HRC-S/LETG observations of this source as there is a known QE problem at low energies. (See 2007 CCW poster Figure 1.) We use a blackbody model with kT=4 eV, nH=1e17 cm^-2, and norm (L_39/D_10) = ?? for computing predicted flux.

  blazar PKS 2155-304

  This source is variable, so for the QE analysis we use two HRC-S/LETG observations (obsids 3709 and 4406) which bracket an HRC-I/LETG observation (obsid 3716). We fit the HRC-S/LETG observations with an absorbed powerlaw over 0.2 - 2.5 keV. We freeze the absorption at nH=1.36e20 cm^-2 (Lockman & Savage 1995). We do not add the +/- orders, but we do fit them together.
  
  Note: Need to include higher orders in RMF!

  We also try fitting ACIS-S/LETG obsid 3703, which was done on the same day as the HRC-S/LETG and HRC-I/LETG observations. We fit over 0.5-5 keV.
  We freeze the absorption at nH=1.36e20 cm^-2 and find best-fit parameters of gamma=2.75492 and normalization=5.04673E-03.

  Fit results for ACIS-S/LETG obsid 3707 with statistic=chi:

  HRMA	Orders	Grouped?	nH	Gamma	Normalization	Chi-Sq / DOF	Notes
  F	+/- 1,2,3	50 cts/bin	1.36e20 (frz)	2.76	2.01e-2	385.07 / 755	see plot above
  F	+/- 1	50 cts/bin	1.36e20 (frz)	2.75	2.01e-2	374.67 / 663
  F	+/- 1,2,3	no	1.36e20 (frz)	2.73	1.88e-2	2918.73 / 21416
  F	+/- 1	no	1.36e20 (frz)	2.72	1.89e-2	2004.87 / 3566
  CALDB	+/- 1,2,3	no	1.36e20 (frz)	2.71	1.72e-2	2907.48 / 21416
  CALDB	+/- 1	no	1.36e20 (frz)	2.71	1.73e-2	1992.44 / 3566
  CALDB	+/- 1,2,3	50 cts/bin	1.36e20 (frz)	2.74	1.84e-2	380.77 / 755	see plot below

  Fit results for ACIS-S/LETG obsid 3707 with statistic=cstat:

  HRMA	Orders	Grouped?	nH	Gamma	Normalization	Cstat / DOF
  F	+/- 1,2,3	50 cts/bin	1.36e20 (frz)	2.76	2.03e-2	762.66 / 755
  F	+/- 1	50 cts/bin	1.36e20 (frz)	2.75	2.04e-2	657.80 / 663
  F	+/- 1,2,3	no	1.36e20 (frz)	2.75	2.01e-2	15899.64 / 21416
  F	+/- 1	no	1.36e20 (frz)	2.75	2.04e-2	3770.40 / 3566
  CALDB	+/- 1,2,3	no	1.36e20 (frz)	2.74	1.84e-2	15889.01 / 21416
  CALDB	+/- 1	no	1.36e20 (frz)	2.74	1.86e-2	3762.65 / 3566
  CALDB	+/- 1,2,3	50 cts/bin	1.36e20 (frz)	2.75	1.85e-2	755.34 / 755

  
  
  

  Predicted Fluxes

  In the plots below, the blue, pink, and yellow regions represent the energy ranges where 50, 70, and 90% of the predicted flux is coming from. The red dashed line is the ratio of the HRC-I ARFs made using either the CALDB or model F HRMA effective area. The blue dot-dashed line is the ratio of source models (see section above). The solid black line is the ratio of predicted fluxes.

  
  

  
  

  
  

  Observed Count Rates

  HZ 43

  
  these are 0th order count rates. best fit line is y= (-4.24e-4 +/- 4.15e-4) t + (3.65 +/- 0.03)
  mean rate is 3.62 with standard deviation 0.04. mean of errors is 0.05.
  Note that the best fit slope is consistent with zero.

  Cas A

  Extraction region=1.5"
  
  best fit line is y= (3.27e-5 +/- 3.57e-5) t + (0.028 +/- 0.003)
  mean rate is 0.031 with standard deviation 0.003. mean of errors is 0.003.
  Note that the best fit slope is consistent with zero.

  G21.5-0.9

  Extraction region=43"
  
  best fit line is y= (-2.58e-5 +/- 1.68e-4) t + (0.54 +/- 0.01)
  mean rate is 0.541 with standard deviation 0.005. mean of errors is 0.009.
  Note that the best fit slope is consistent with zero.

  Comparing Observed and Predicted Rates

  Source	Predicted cts/s w/ CALDB	Predicted cts/s w/ model F	Observed cts/s	Notes
  Cas A	0.032 (+3.2%)	0.032 (+3.2%)	0.031 +/- 0.003	avg from several obs, see plot
  G21.5-0.9	0.59 (+9.2%)	0.59 (+9.2%)	0.54 +/- 0.01	avg from several obs, see plot
  HZ 43			3.62 +/- 0.05	avg of 0th order from several obs, see plot
  PKS 2155-304	1.55 (+1.3%)	1.57 (+2.6%)	1.53 +/- 0.01	0th order from obsid 3716

  ---

  ---

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  HRC-S HZ 43 Observations

  N	Obsid	Date	Predicted Count Rate
  0	1011	2001-03-18	4.298
  1	1012	2001-08-18	4.339
  2	2584	2002-01-01	4.279
  3	2585	2002-07-23	4.257
  4	3676	2002-12-04	4.110
  5	3677	2003-07-24	4.262
  6	5042	2003-12-20	4.097
  7	5044	2004-07-19	4.338
  8	5957	2005-02-02	4.263
  9	5959	2005-07-29	4.296
  10	6473	2006-03-13	4.347
  11	6475	2006-08-07	4.476
  12	8274	2007-03-14	4.433