Characterizing the Spatial Distribution of Elements in Groups and Clusters

Estimate Total Count Rate

Use COLDEN to estimate the galactic line-of-sight NH to SS2b153. Here we use the coordinates RA=10 50 26.9, Dec=-12 50 26.0 (J2000). The resulting nH returned by COLDEN is 4.50E20.

SS2b153 has a ROSAT PSPC count rate of about 0.28 counts/sec. We assume an optically thin plasma model, temperature 1keV=1.16E7K. To get the predicted ACIS-S count-rate, run PIMMS with the following inputs.

Input Count Rate
Input Mission -- ROSAT
Input Detector/Grating/Filter -- PSPC/None/OPEN
Energy Input -- default
Output Count Rate
Output Mission -- Chandra Cycle 10
Output Detector/Grating/Filter -- ACIS-S/None/None
Output Energy -- default
Model -- Raymond Smith
NH -- 4.5E20
Abundance -- 0.2
Log T -- 7.05
Count Rate -- 0.28

PIMMS gives an estimated ACIS-S count rate of 0.846 counts/sec.

Repeat the command with ``Output Detector/Grating/Filter'' set to ``ACIS-I/None/None'' to get an estimated ACIS-I count rate of 0.491 counts/sec.

ACIS-S Simulations

• Defines a response ``aciss'' consisting of the redistribution matrix aciss_2am_cy10.rmf and the area response file aciss_2am_cy10.arf.
• Defines the instrument response for dataset 1 to be aciss.
• Defines a model ``gabs'' for galactic line-of-sight absorption.
• Defines a model ``vmek'' for the target. The source for this model is the XSPEC model ``vmekal'', or variable mekal (the plasma code is based on the calculations of Mewe, Kaastra and Liedahl). This version of the model allows individual abundances to be set. Here we initially set all abundances to 30% of solar.
• Sets the model for dataset 1 to be galactic absorption x mekal plasma.
• Sets the exposure time to be 7 ks and runs fakeit to generate a fake spectrum. Note that 7 ks is a guess at this point. We may need to refine the exposure time to obtain enough counts to measure the Fe abundance to 10%.

sherpa> rsp[aciss](aciss_2am_cy10.rmf,aciss_2am_cy10.arf)
The inferred file type is ARF.  If this is not what you want, please 
specify the type explicitly in the data command.
sherpa> instrument 1 = aciss
sherpa> xswabs[gabs]
gabs.nH parameter value [0.1] 0.045
sherpa> xsvmekal[vmek]
vmek.kT parameter value [1] 
vmek.nH parameter value [1] 0.001
vmek.He parameter value [1] 0.3
vmek.C parameter value [1] 0.3
vmek.N parameter value [1] 0.3
vmek.O parameter value [1] 0.3
vmek.Ne parameter value [1] 0.3
vmek.Na parameter value [1] 0.3
vmek.Mg parameter value [1] 0.3
vmek.Al parameter value [1] 0.3
vmek.Si parameter value [1] 0.3
vmek.S parameter value [1] 0.3
vmek.Ar parameter value [1] 0.3
vmek.Ca parameter value [1] 0.3
vmek.Fe parameter value [1] 0.3
vmek.Ni parameter value [1] 0.3
vmek.redshift parameter value [0] 0.0153
vmek.Switch parameter value [1] 
vmek.norm parameter value [1] 
sherpa> source 1=gabs*vmek
sherpa> fakeit time=7000
sherpa> fakeit

Now we need to adjust the normalization so that the count rate in the fake spectrum is the observed count rate for SS2b153. To do this, we need the count rate in the fake spectrum:

sherpa> show

Optimization Method: Levenberg-Marquardt
Statistic:           Chi-Squared Gehrels

-----------------
Input data files:
-----------------
Data 1: fake pha.
Total Size: 1024 bins (or pixels)
Dimensions: 1
Total counts (or values):    1.391507e+06
Exposure: 7000 sec
Count rate: 198.787 cts/sec


---- output truncated ----

The count rate in the fake spectrum is 198.787 counts/sec. The predicted ACIS-S count rate is 0.846 counts/sec. We therefore need to set the normalization for model ``vmek'' to be 0.846/198.787=0.00426, and run fakeit again.

sherpa> vmek.norm=0.00426
sherpa> fakeit
sherpa> show
-----------------
Input data files:
-----------------

Data 1: fake pha.
Total Size: 1024 bins (or pixels)
Dimensions: 1
Total counts (or values): 5807
Exposure: 7000 sec
Count rate: 0.830 cts/sec

---- output truncated ----

This observation will yield 7000*0.830, or ~5810 counts.

Next, we need to determine whether 5810 counts is enough to measure the Fe abundance to 10%. Freeze the galactic absorption, thaw the Fe abundance, fit the fake spectrum, and obtain the 1-sigma uncertainties:

sherpa> freeze gabs.nh
sherpa> thaw vmek.Fe
sherpa> fit
sherpa> sherpa.cov.sigma=1
sherpa> set_verbose(2)
sherpa> covariance
Information Matrix (Second Derivatives of Fit Statistic): 

   vmek.kT         vmek.Fe         vmek.norm    
          9642.5        -7793.91         -843170
        -7793.91         14683.5     1.83807e+06
         -843170     1.83807e+06     2.91155e+08

Eigenvectors (Principal Axes) of the Covariance Matrix: 

   vmek.kT         vmek.Fe         vmek.norm    
         0.90566        0.423995     -0.00289601
       -0.423972        0.905653      0.00631297
      0.00529945     -0.00448958        0.999976

Eigenvalues of the Covariance Matrix: 

     0.000119656     0.000520068     3.43444e-09

Covariance Matrix (Inverse of Information Matrix): 

   vmek.kT         vmek.Fe         vmek.norm    
     0.000191638     0.000153758    -4.15703e-07
     0.000153758     0.000448072    -2.38342e-06
    -4.15703e-07    -2.38342e-06     1.72774e-08

Covariance Matrix Determinant (Product of Eigenvalues): 2.13722e-16


Computed for sherpa.cov.sigma = 1
        --------------------------------------------------------
        Parameter Name      Best-Fit Lower Bound     Upper Bound
        --------------------------------------------------------
          vmek.kT           0.988668  -0.0138433      +0.0138433    
          vmek.Fe           0.335748  -0.0211677      +0.0211677    
          vmek.norm       0.00384965  -0.000131443    +0.000131443  

The measured Fe abundances will be 0.336 +/- 0.021 solar. This simulation shows that with about 5810 counts, it is possible with ACIS-S to constrain the Fe abundance within 10%.

ACIS-I Simulations

• Defines a new set of responses called ``acisi''.
• Sets the responses for dataset 2 to ``acisi''.
• Resets the values of Fe, vmek normalization, and temperature to their original values.
• Sets the model for dataset 2 to be ``vmek'' convolved with galactic absorption.
• Defines the exposure time for the second dataset to be 7 ks and runs fakeit to generate a fake spectrum.

sherpa> rsp[acisi](acisi_2am_cy10.rmf,acisi_2am_cy10.arf)
The inferred file type is ARF.  If this is not what you want, please 
specify the type explicitly in the data command.
sherpa> instrument 2=acisi
sherpa> vmek.Fe=0.3
sherpa> vmek.norm=1.0
sherpa> vmek.kT=1.0
sherpa> source 2=gabs*vmek
sherpa> fakeit 2 time=7000
sherpa> fakeit 2
sherpa> show

----output truncated----

Data 2: fake pha.
Total Size: 1024 bins (or pixels)
Dimensions: 1
Total counts (or values): 829576
Exposure: 7000 sec
Count rate: 118.511 cts/sec

----output truncated----

Next, adjust the normalization of vmek so that the count rate in fake data file 2 becomes 0.491 counts/sec (which was obtained from PIMMS). Then fit the fake spectrum and obtain the uncertainties:

sherpa> vmek.norm=0.00414
sherpa> fakeit 2 
sherpa> show

----output truncated----

Data 2: fake pha.
Total Size: 1024 bins (or pixels)
Dimensions: 1
Total counts (or values): 3352
Exposure: 7000 sec
Count rate: 0.479 cts/sec

----output truncated----

sherpa> fit 2 
sherpa> covariance 2 

----output truncated----
Computed for sherpa.cov.sigma = 1
        --------------------------------------------------------
        Parameter Name      Best-Fit Lower Bound     Upper Bound
        --------------------------------------------------------
          vmek.kT            1.00599  -0.0199983      +0.0199983    
          vmek.Fe           0.329407  -0.0334598      +0.0334598    
          vmek.norm       0.00374149  -0.000207821    +0.000207821  

 

We find that the constraints on the Fe abundance obtained with ACIS-S are slightly better than with ACIS-I, for the same exposure time. However, it is possible to show that the constraints on the Fe abundance can be improved by increasing the exposure time for ACIS-I so that the total number of counts is the same as for ACIS-S. This is not demonstrated explicitly here, but is left as an exercise for the reader.

Determine Total Exposure Time

From the above simulations we know that we need about 5810 counts to get the required constraint on the Fe abundance in a single region. Our goal is to measure abundances in 6 regions, which can be of varying size. Since the spatial distribution isn't well known, we assume that each region will produce the same count rate and that we will need a total of 34860 counts from the entire group to determine the Fe abundances in the 6 regions. This implies a total ACIS-S exposure time of approximately 42 ks and an ACIS-I exposure time of approximately 73 ks.

What About Background?

The above simulations do not include the effect of background which, in this case, is dominated by the diffuse X-ray background. The POG Table 6.9 gives background rates for ACIS-S positioned at the aimpoint. Assuming we are using chip S3 with an exposure time of 42 ks and the default energy range of 0.3-10 keV, the number of background counts is 1.18 counts/sec/chip * 42,000 sec = 49560 counts. The total background depends on the size of the region that the counts are extracted from. The chip is 1024*1024 pixels. If our smallest region is 100x100 pixels, then the total number of background counts inthis region 100^2/1024^2 * 49560, or about 473 counts.

The background counts must be subtracted from the source counts; the uncertainty in the background is only 17 counts. If we extract counts from a region 10 times larger, then the uncertainly in the background rises to about 53 counts. This is still small compared to our 5810 source counts. These are ``worst case'' estimates, since (1) the S3 chip has a high background relative to other chips and (2) if we use VF telemetry format we can further reduce the background by using the "clean55" algorithm developed by Alexey Vikhlinin to eliminate charged particles; this is now incorporated into the CIAO tool acis_process_events (see http://cxc.harvard.edu/ciao/threads/aciscleanvf for more information). The POG (Section 6.13.1) provides a detailed description of ACIS telemetry formats. For this observation, we do not expect background to be a problem in our analysis.

Summary of Simulations

We have performed a simple simulation to determine the number of counts required to constrain the Fe abundance to better than 10%. We find that about 5810 counts are required to do this in both the ACIS-I and ACIS-S detectors. We therefore conclude that for the purpose of measuring Fe abundance either array will do. If we choose ACIS-I we will need a higher total exposure time. The cosmic X-ray background will not impact our analysis if we have a minimum of 5810 extracted counts.

ACIS-I or ACIS-S?

Both arrays have advantages and disadvantages for this observation. As described above, ACIS-I or ACIS-S could be used to constrain the Fe abundance within our goal, although the exposure time for ACIS-I will be longer. ACIS-I has a larger field of view and lower background than ACIS-S, but suffers from the disadvantage of degraded CTI (see the POG Section 6.7). The main result of degraded CTI is that the spectral resolution is position dependent, which can complicate analysis. Since the higher background in S3 should not impact our analysis, we choose ACIS-S to avoid CTI complications.

Exposure Mode, Telemetry Format, Choice of Chips and Optional Chips

There are only two ACIS modes available: Timed Exposure (TE) and Continuous Clocking (CC). TE mode is appropriate for imaging observations. There are three telemetry formats available for TE mode; Faint, Graded, and Very Faint. Very Faint format provides pixel values in a 5x5 island around the event position; less information is telemetered in the other two formats. The extra information provided by the Very Faint format can be used to reduce the number of background photons by using a screening algorithm. Since we are extracting spectra from large areas of the chip, Very Faint format is our best choice.

The chips most commonly used for ACIS-S imaging are S1-S4, I2, and I3. In order to reduce the probability of telemetry saturation, we choose to turn off chip S4. The telemetry saturation limit is less for Very Faint than for the Faint and Graded formats. As long as we do not exceed the telemetry limit, we would prefer to use Very Faint format because of the detailed information provided for each event.

The telemetry saturation limit for Very Faint mode is 68.8 cts/sec. From the POG Table 6.10, the background rates for the on chips are: S2: 9.7 cts/s and S3: 13.5 cts/s. So the total background rate is 23.2 cts/s. If we add the source count rate of 0.83 cts/s to the background rate, a good estimate for the maximum total count rate is 24.03 cts/sec. This is significantly less than the saturation limit, so we can safely choose VF format.

For Cycle 10, observers are being asked to identify "optional" chips. These chips can be turned off (without warning!) should the ACIS Power Supply and Mechanism Controller be in danger of overheating (see the ACIS chapter of the POG). We have already turned off chip S4 to avoid telemetry saturation. We now choose to designate I and I2 as optional because these are farthest from the aimpoint and have the worst PSF. I2 is designated O1 (first chip to be turned off) and I3 is designated O2 (second chip to be turned off).

Offset Pointing

The default ACIS-S aimpoint is close to the boundary between chips S3 and S2. This will put the peak of the group X-ray emission at the point of highest spatial resolution. This is shown here . However, it will also put the outer edges of the group emission onto S2. We choose to move the peak X-ray emission into the CENTER of S3, thus minimizing overlap onto other chips. For SS2b153 this corresponds to a Y offset of -2 arcmin. This is shown here . This has the slight disadvantage that the X-ray core will be moved away from the area of highest spatial resolution. Since we will be extracting spectra from a number of resolution elements, this is not a major concern.