- Introduction
- Updating the model shape at low energies
- Checking the model normalization
- Renormalizing the model
- Summary
- Appendix: Checking cross-calibration with E0102
*(added July 2012)*

The figure below shows a comparison of the current HRC-S and old HRC-I 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 (where the HRC-S aimpoint is located.) 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 "low-energy paste" will be done with the bare MCP QE models, not 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:

After redoing this low-energy paste, the UVIS-I efficiency is folded back in, and the resulting QE is saved as hrciD1999-07-22qeN0007prime.fits.

Count rates from the first several observations are depressed for reasons we do not yet understand. For the purposes of cross-calibration to renormalize the HRC-I QE model, we do a linear fit to the points shown in red, beginning around t=40 months. The best-fit line has a slope that is consistent with zero (-3.205e-05 +/- 8.270e-05 cts/s/month) and y-intercept of 0.543 +/- 0.006 cts/s (errors are 1 sigma). The mean rate is 0.541 cts/s with standard deviation 0.006. The mean of the errors is 0.006.

We obtain best-fit parameters of nH = 3.23466 x 10^22 cm^-2 [3.20203, 3.26783], PhoIndex = 1.79686 [1.78078, 1.81308] and norm = 54.9971 x 10^-12 erg cm^-2 s^-1 [54.7394, 55.2557] (90% confidence intervals indicated in brackets), with chi-squared = 969.97 using 924 PHA bins (reduced chi-squared = 1.0532 for 921 degrees of freedom).

Combined HRC-S/LETG spectrum:

The "model" (ie spectrum/ARF):

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

The mean rate is 3.88 cts/s with standard deviation 0.05. The mean of errors is 0.04.

To compensate for the HRC-S QE decline, we multiply the ARF for each
observation by a corrective factor based on the linear fit to 0th
order count rates (`norm=[yint + tnrm*slope]/[yint
+ obs_date*slope]` where `tnrm` corresponds to July 2008)
when constructing the HZ 43 "model".

The combined HRC-S/LETG spectrum:

The "model" (ie spectrum/ARF):

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

Source | Instrument | ObsID | Date | Exposure (s) |
---|---|---|---|---|

G21.5-0.9 | ACIS-S3 | 1553 | 2001-03-18 | 9741.1 |

1554 | 2001-07-21 | 9060.7 | ||

3693 | 2003-05-16 | 9783.6 | ||

HRC-I | 2867 | 2002-03-12 | 18438.0 | |

2874 | 2002-07-15 | 19762.4 | ||

3694 | 2003-05-15 | 17055.9 | ||

3701 | 2003-11-09 | 12846.9 | ||

5167 | 2004-03-25 | 18984.0 | ||

6072 | 2005-02-26 | 19018.7 | ||

6742 | 2006-02-21 | 19134.6 | ||

8373 | 2007-05-25 | 19983.5 | ||

10648 | 2009-02-17 | 10054.2 | ||

PKS 2155-304 | HRC-S/LETG | 3709 | 2002-11-30 | 13741.8 |

4406 | 2002-11-30 | 13762.8 | ||

HRC-I/LETG | 3716 | 2002-11-30 | 7328.6 | |

HZ 43 | HRC-S/LETG | 1011 | 2001-03-18 | 18774.9 |

1012 | 2001-08-18 | 20807.7 | ||

2584 | 2002-01-01 | 19004.0 | ||

2585 | 2002-07-23 | 19989.8 | ||

3676 | 2002-12-04 | 20716.5 | ||

3677 | 2003-07-24 | 20008.8 | ||

5042 | 2003-12-20 | 21377.1 | ||

5044 | 2004-07-19 | 19693.1 | ||

5957 | 2005-02-02 | 21371.7 | ||

5959 | 2005-07-29 | 18180.1 | ||

6473 | 2006-03-13 | 20901.2 | ||

6475 | 2006-08-07 | 21771.7 | ||

8274 | 2007-03-14 | 20189.3 | ||

10622 | 2009-03-18 | 20292.0 | ||

11933 | 2010-03-15 | 20365.9 | ||

HRC-I/LETG | 1514 | 2000-02-03 | 2159.6 | |

1000 | 2001-01-12 | 3891.8 | ||

1001 | 2001-07-25 | 4955.0 | ||

2600 | 2002-01-02 | 1893.4 | ||

2602 | 2002-07-23 | 1893.3 | ||

3714 | 2003-01-24 | 1868.7 | ||

3715 | 2003-07-24 | 1894.1 | ||

5043 | 2003-12-20 | 1980.8 | ||

5045 | 2004-07-19 | 2145.3 | ||

5958 | 2005-02-20 | 2171.4 | ||

5960 | 2005-08-08 | 1758.9 | ||

6474 | 2006-01-25 | 2154.1 | ||

6476 | 2006-07-24 | 2177.8 | ||

8275 | 2007-03-19 | 2173.7 | ||

9619 | 2008-03-14 | 2164.9 | ||

10623 | 2009-03-11 | 2177.4 | ||

11934 | 2010-03-20 | 2176.0 |

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 uncertainty sqrt((0.25/4.03)^2+(0.07/3.88)^2)*(4.03/3.88) = 0.0671025.

For PKS 2155-304 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.

(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.

The error-weighted mean of the I:S ARF-corrected spectrum ratios is ~1.027. 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 Table 2.

New paste:

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

With this new model (N0007prime_renorm) the ratio of I to S ARF-corrected spectra for PKS 2155-304 has mean 1.01 and standard deviation 0.267 in the 20-31 Angstrom range.

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, PKS 2155-304 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.

**Figure 20:** Ratio of new (N0008) and intermediate QE models to
old (N0007) QE model.

Source | Observed Count Rate | Predicted Count Rate | |||
---|---|---|---|---|---|

with N0007 | with N0007prime | with N0007prime_renorm | with N0008 | ||

G21.5-0.9 | 0.541+/- 0.008 | 0.601 +/- 0.018 (+9.98% +/- 3.00%) | 0.601 +/- 0.018 (+9.98% +/- 3.00%) | 0.601 +/- 0.018 (+9.98% +/- 3.00%) | 0.541 +/- 0.016 (0% +/- 2.96%) |

PKS 2155-304 | 1.537 +/- 0.014 | 1.639 +/-
0.052 (+6.22% +/- 3.17%) | 1.669 +/- 0.054 (+7.91% +/- 3.24%) | 1.644 +/- 0.052 (+6.51% +/- 3.16%) | 1.535 +/-
0.052 (-0.13% +/- 3.39%) |

HZ 43 | 3.88 +/- 0.07 | 3.46 +/- 0.21 (-12.50% +/- 6.07%) | 4.03
+/- 0.25 (+3.72% +/- 6.20%) | 3.92 +/- 0.24 (+1.02% +/- 6.12%) | 3.91 +/- 0.24 (+0.77% +/- 6.14%) |

MSE | 0.243 | 0.114 | 0.087 | 0.066 |

From the two HRC-I observations, we get background-subtracted source count rates of 3.22 +/- 0.01 cts/s (ObsID 1410, 1999-10-25) and 3.20 +/- 0.01 cts/s (ObsID 11093, 2010-03-04). The errors given are 1 sigma.

To calculate a predicted count rate for the HRC-I, we use as a source model a joint fit to two ACIS-S3 subarray observations (ObsIDs 3545 and 6765) with the IACHEC E0102 model. (See the Plucinsky et al 2008 SPIE paper for more information about this model.) The ACIS data are fit between 0.3 - 2 keV and the ACIS ARF includes contamination model N0007. The ACIS spectra and HRC-I counts are extracted from a circular region with radius 25.3" centered at J2000 coordinates (R.A., Dec.) = (01:04:01.996, -72:01:53.44).

From this source model and an HRC-I ARF (using HRC-I QE model N0008),
we get a predicted count rate of 3.16 +/- 0.01 cts/s. The
uncertainty on the predicted rate is taken from the standard deviation
of 5000 MCMC iterations, sampling among the errors on the free
parameters in the ACIS fit.

Last modified: 05/23/18