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.)
Finally, the UVIS-I efficiency is folded back in, and the QE is saved as hrciD1999-07-22qeN0007prime.fits.
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.
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
Chi-Squared = 74.97 using 74 PHA bins.
Reduced chi-squared = 1.056 for 71 degrees of freedom
Null hypothesis probability = 3.510163e-01
XSPEC12>error 1. 1
Parameter Confidence Range (1)
1 2.84391 3.81973 (-0.476007,0.499813)
XSPEC12>error 1. 2
Parameter Confidence Range (1)
2 3.62323 4.4075 (-0.381645,0.402625)
XSPEC12>error 1. 5
Parameter Confidence Range (1)
5 2.29047 3.94488 (-0.669294,0.985121)
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)
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.
The predicted HRC-I spectrum (model * HRC-I ARF):
We sum over 0.06 - 0.3 keV to get the predicted count rate.
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/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.
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.
Source | Predicted cts/s w/ N0007 (current CALDB) | Predicted cts/s w/ N0007prime | Predicted cts/s w/ N0007prime_renorm | Observed cts/s | Notes |
---|---|---|---|---|---|
Cas A | 2.67E-02 (I3), 2.31E-02 (S3) | 2.67E-02 (I3), 2.31E-02 (S3) | 3.12e-2 +/- 0.36e-2 | observed rate excluding obsid 02878, 1 sigma error on ACIS fluxes are ~ 20% (I3) and 20-30% (S3). If nH is set to 2.83e22, within the 90% confidence interval from the I3 fit, the predicted rate based on I3 is 3.12e-2. For the S3 prediction, if nH=2.85e22 and norm=3.1 (both in 90% confidence intervals from S3 fit), the predicted rate is 3.12e-2. | |
G21.5-0.9 | 6.01e-01 (S3 subarray) | 6.01e-01 (S3 subarray) (+11.09%) | 6.01e-01 (S3 subarray) (+11.09%) | 5.41e-1+/- 0.08e-1 | Observed rate from observations after time=40 months. 1 sigma error on ACIS flux is < 1% (jointly fit) though scatter among individual fluxes is ~ 3%. |
PKS 2155-304 | 1.639 +/- 0.052 | 1.669 +/- 0.054 (+8.59%) | 1.644 +/- 0.052 (+6.96%) | 1.537 +/- 0.014 | Obs. from obsid 3716 0th order. Pred. from HRC-S obsids 3709 & 4406 (0.1-5.6 keV band) |
HZ 43 | 3.46 +/- 0.21 | 4.03 +/- 0.25 (+3.87%) | 3.92 +/- 0.24 (1.03%) | 3.88 +/- 0.07 | Predicted counts are from 0.06-0.3 keV band. Error on predicted counts is stddev of predictions from individual HRC-S obs. |
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)
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.
Closeup: (The pasting point is just below 0.63 keV)
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.
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% |
HRC-I QE Memos:
To Do:
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.
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.
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 |
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 |
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 |