Principal Component AnalysisRevealing AGN Spectral Variability
Michael Parker
with Andy Fabian, Giorgio Matt, Erin Kara,Andrea Marinucci, Dom Walton, Karri Koljonen,Will Alston, Laura Brenneman and Guido Risaliti
June 16, 2014
M. L. Parker et al. Principal Component Analysis June 16, 2014 1 / 18
A simple example
0
1
2
3Original Functions
y(x
) (A
rbit
rary
unit
s)
−1
0
1
−1
0
1
x/π
1 2 3 4 50
Noisy Data
y(x
)
−0.75
−0.5
−0.25
0
0.25
0.5
0.75
x/π
0 1 2 3 4 5 6
Reconstructed Functions
0
0.05
0.1
y(x
) (A
bit
rary
unit
s)
0
0.1
−0.1
0
0.1
x/π
1 2 3 4 50
PCA isolates and returns the different components of a signal, removingsome of the noise.
When we apply this to AGN spectra, it retrieves the different variable spectralcomponents, in a model-independent way, and we can match these topredictions from simulations.
M. L. Parker et al. Principal Component Analysis June 16, 2014 2 / 18
Applying PCA to spectra
F(E)
0.01
0.1
1
Energy (keV)
0.5 1 2 5 10−1
−0.5
0
0.5
1
1.5
Energy (keV)
0.5 1 2 5 10
To apply this to spectra, we divide the dataset into 10 ks spectra, then calculatenormalised residuals. These residual spectra are then fed into the code. This
removes the effects of the effective area of the detector, and prevents bias fromhigher flux at low energies.
M. L. Parker et al. Principal Component Analysis June 16, 2014 3 / 18
Predictions
We can generate unique predictions for the PCs returned from differentspectral models, by simulating a set of fake spectra and allowing the modelcomponents to vary.
These simulated components can then be compared with the componentsreturned from real data, to identify the cause of spectral variability in aparticular source.
M. L. Parker et al. Principal Component Analysis June 16, 2014 4 / 18
Sample
We have applied this method to a sample of ∼ 30 bright, variable AGN fromthe XMM-Newton archive.
The method is highly dependent on the total number of counts, so we needat least one complete orbit, preferably more. There are now many sources inthe archive with this much time, however!
We plan to extend this to other instruments, as well as looking at binaries. Itis interesting to note that there is no reason data from multiple observatoriescould not be combined, if the instrumental response is properly accounted for.
M. L. Parker et al. Principal Component Analysis June 16, 2014 5 / 18
PCA of a powerlaw: 3C 273Normalised Flux
0
0.1
0.2
−0.2
−0.1
0
0.1
0.2
Energy (keV)
0.5 1 2 5 10
Normalised Flux
0
0.1
0.2
−0.2
0
0.2
Energy (keV)
0.5 1 2 5 10
Left Fig shows the PCs returned from PCA of a simulation of a powerlaw,varying in normalisation and photon index.
Right Fig shows the same thing, but for real data from 3C 273.
M. L. Parker et al. Principal Component Analysis June 16, 2014 6 / 18
PCA of absorption I: NGC 4395
0
0.05
0.1
0.15
Normalised Flux
0
0.1
0.2
Energy (keV)
0.5 1 2 5 10
Norm
alised Flux
93.7 %
NGC 4395
0
0.1
0.2
3.59 %
0
0.1
0.2
Energy (keV)
0.5 1 2 5
Left Fig shows the PCs returned from PCA of a simulation of apartially-covered powerlaw, varying in covering fraction and continuum flux.
Right Fig shows the same thing, but for real data from NGC 4395.
M. L. Parker et al. Principal Component Analysis June 16, 2014 7 / 18
PCA of absorption II: NGC 1365
0
0.05
0.1
0.15
0.2Normalised Flux
−0.2
−0.1
0
0.1
0.2
keV
2 (Photons cm
-2 s
-1 keV
-1)
1
2
5
10
20
50
Energy (keV)
0.5 1 2 5 10
0
0.05
0.1
0.15
0.2
0.25
Normalized Flux
Normalised Flux
−0.2
−0.1
0
0.1
0.2
Energy (keV)
0.5 1 2 5 10
Left Fig shows a simulation of varying column density, with a constant BBcomponent at low energies.
Right Fig shows the PCs from NGC 1365, where the low energy variability isdamped out by diffuse gas around the AGN.
M. L. Parker et al. Principal Component Analysis June 16, 2014 8 / 18
PCA of absorption III: Where are the warm absorbers?
log(ξ)=2
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Normalised Flux
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Energy (keV)
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Many of the AGN in our sample show unambiguous evidence of warmabsorption, but we don’t see any robust signatures of ionized absorptionvariability in our sample.Two explanations for this: 1) PCA is optimised for broad-band spectralvariability, so narrow features get lost; 2) warm absorbers are generally lessrapidly variable than either the intrinsic source spectrum or the absorptioncaused by BLR clouds etc.
M. L. Parker et al. Principal Component Analysis June 16, 2014 9 / 18
PCA of reflection I
0
0.05
0.1
0.15
0.2Normalised Flux
0
−0.2
−0.1
0.1
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−0.2
0.2
Energy (keV)
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0.1
0.15
Normalised Flux
0
−0.2
0.2
0
−0.2
0.2
Energy (keV)
0.5 1 2 5 10
Left Fig shows the PCs returned from PCA of a simulation of a powerlaw,varying in normalisation and photon index AND a blurred reflectioncomponent, which is less variable than the powerlaw.
Right Fig (from Parker et al. 2014) shows the same thing, but for real datafrom MCG–6-30-15...
M. L. Parker et al. Principal Component Analysis June 16, 2014 10 / 18
PCA of reflection II
0
0.05
0.1
0.15
0.2
Normalised Flux
0
−0.2
−0.1
0.1
0.2
0
−0.2
0.2
Energy (keV)
0.5 1 2 5 10
Normalised Flux
1H 0707-495
0
0.1
0.2
0
−0.2
0.2
Energy (keV)
0.5 1 2 5 10
0
−0.2
0.2
0.4
...and 1H 0707-495...
M. L. Parker et al. Principal Component Analysis June 16, 2014 11 / 18
PCA of reflection III
0
0.05
0.1
0.15
0.2
Normalised Flux
0
−0.2
−0.1
0.1
0.2
0
−0.2
0.2
Energy (keV)
0.5 1 2 5 10
Normalised Flux
Mrk 766
0
0.1
0
−0.2
0.2
Energy (keV)
0.5 1 2 5 10
0
−0.2
0.2
...and Mrk 766...
M. L. Parker et al. Principal Component Analysis June 16, 2014 12 / 18
PCA of reflection IV
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0.05
0.1
0.15
0.2
Normalised Flux
0
−0.2
−0.1
0.1
0.2
0
−0.2
0.2
Energy (keV)
0.5 1 2 5 10
Nor
mal
ised
Flu
x
NGC 3516
0
0.1
0.2
0
−0.2
0.2
Energy (keV)
0.5 1 2 5 10
0
−0.2
0.2
...and NGC 3516...
M. L. Parker et al. Principal Component Analysis June 16, 2014 13 / 18
PCA of reflection V
0
0.05
0.1
0.15
0.2
Normalised Flux
0
−0.2
−0.1
0.1
0.2
0
−0.2
0.2
Energy (keV)
0.5 1 2 5 10
NGC 4051
0
0.1
0.2
Normalised Flux
0
−0.2
0.2
0.2
−0.2
0
Energy (keV)
0.5 1 2 5 10
...and NGC 4051!
M. L. Parker et al. Principal Component Analysis June 16, 2014 14 / 18
PCA of reflection
All five of these sources are dominated by the same variability mechanism.
The method shows, in a completely model independent way, that there has tobe a spectral component responsible for both the soft excess and broad ironline in these sources.
In all these sources (and several others) there is a strong pivoting term, whichcan be well modelled with changes in the photon index.
In all cases, the soft excess and iron line is less variable than the continuum.
M. L. Parker et al. Principal Component Analysis June 16, 2014 15 / 18
Conclusions
PCA is a powerful tool for examining AGN variability. It returns completelyunbiased, model-independent spectral components, and can be used toexamine and quantify their variability.
An analysis of a large sample of bright, variable AGN has revealed a largenumber of different variability patterns. These patterns can be matched tothe predictions from simulations to unambiguously determine the nature ofthe variability in each source.
M. L. Parker et al. Principal Component Analysis June 16, 2014 16 / 18
Mrk 335
DataSimulation
Norm
alized Flux
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Simulation
Norm
alized Flux
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E (keV)
1 2 5 10
Gallo et al., in prep.
M. L. Parker et al. Principal Component Analysis June 16, 2014 17 / 18
Normalised Flux
64.2 %
IRAS 13349
−0.2
0
0.2
75.6 %NGC 3227
−0.1
0
0.1
0.2
82.2 %
PDS 456
0
0.1
0.2
92.5 %
RE 1034
0
0.2
0.4
66.2 %
1ES 1028
0
0.2
0.4
73.0 %
PG 1116
0
0.2
0.4
68.2 %
3C 273
0
0.1
0.2
98.6 %
Ark 120
0
0.1
0.2
98.2 %
Mrk 509
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0.1
0.2
Energy (keV)
0.5 1 2 5
19.4 %−0.2
0
0.2
12.8 %−0.2
0
0.2
9.06 %
−0.2
0
0.2
2.94 %−0.2
0
0.2
16.1 %−0.2
0
0.2
19.4 %−0.2
0
0.2
30.3 %−0.2
0
0.2
0.62 %−0.2
0
0.2
1.28 %−0.2
0
0.2
Energy (keV)
0.5 1 2 5
2.59 %−0.2
0
0.2
1.91 %−0.2
0
0.2
0.55 %−0.2
0
0.2
0.11 %−0.2
0
0.2
Energy (keV)
0.5 1 2 5
