Showing spectral variability in AGN by principal component analysis (PCA)

(1)

Showing spectral variability in AGN

by principal component analysis (PCA)

G. Miniutti and G. Risalitti

Beatriz Agís González

(2)

• INTRODUCTION

1.1- What is PCA?

1.2- Example

1.3- Simulations

• NGC4051

2.1- Previous analaysis with PCA

2.2- Another observation

2.3- Further analysis: greatest flux

2.4- Furhter analysis: lowest flux

• CONCLUSIONS AND FUTURE WORK

(3)

•

1. INTRODUCTION

LINEAR TRANSFORMATION METHOD

n variables

correlate amog

each other

• WHAT IS PCA?

p < n

uncorrelated

variables

INITIAL DATA SET

_{NEW DATA SET}

that yields the directions

that maximizethe variance of the data

ANALYSING SPECTRA :

Set of

spectra

Individually

variant spectral

componets in a model

independent way

PCA

(4)

y3(x)=sin(2x)

•

1. INTRODUCTION

• EXAMPLE

y

2

(x)=sin(x)

y

1

(x) = 0.3 +x/8

y

i

(x) = 0.6

a

1

y

1

(x)+0.2

a

2

y

2

(x)+0.1

a

3

y

3

(x)+0.1

a

4

Parker et al. (2015)

(5)

DIFFICULT INTERPRETATION

•

1. INTRODUCTION

• SIMULATIONS

Number of variable components of the initial spectrum contributing

to the variability in a

model independent way

SIMULATIONS

Baseline Model :

POWER LAW

Varying

photon index

and

normalization

Timesliced spectra binned in energy

(6)

•

1. INTRODUCTION

• SIMULATIONS

POWER LAW

+

SOFT EXCESS

Parker et al. (2015)

_{Parker et al. (2015)}

-PP:

varying

photon

index

varying

normalization

-BB:

constant

-PP:

varying

normalization

-BB:

varying

normalization

-PP:

varying

photon

index

varying

normalization

-BB

: varying

normalization

(stronger BB variations)

-PP:

varying

photon

index

varying

normalization

-BB:

varying

normalization

(stronger PP variations)

(7)

•

1. INTRODUCTION

• SIMULATIONS

RELATIVISTIC REFLECTION COMPONENT

Parker et al. (2015)

-PP:

varying

photon index

varying

normalization

-RR:

constant

(8)

• PREVIOUS PCA ANALYSIS

=

•

2. NGC 4051

Parker et al. (2015)

14 OBSERVATIONS

~40ks

(9)

• PREVIOUS PCA ANALYSIS

=

•

2. NGC 4051

Parker et al. (2015)

(10)

• PREVIOUS PCA ANALYSIS

=

•

2. NGC 4051

Parker et al. (2015)

POWER LAW

Varying

photon index

and

normalization

CONSTANT REFLECTION COMPONENT

(11)

• PREVIOUS PCA ANALYSIS

=

•

2. NGC 4051

Parker et al. (2015)

POWER LAW

Varying

photon index

and

normalization

&

RELATIVISTIC REFLECTION

CONSTANT REFLECTION COMPONENT

(12)

• PREVIOUS PCA ANALYSIS

=

•

2. NGC 4051

Parker et al. (2015)

POWER LAW

Varying

photon index

and

normalization

&

RELATIVISTIC REFLECTION

CONSTANT REFECTION COMPONENT

(13)

• PREVIOUS PCA ANALYSIS

=

•

2. NGC 4051

Parker et al. (2015)

VARYING POWER LAW

&

RELATIVISTIC REFLECTION

(14)

• PREVIOUS PCA ANALYSIS

=

•

2. NGC 4051

Parker et al. (2015)

VARYING POWER LAW

&

RELATIVISTIC REFLECTION

CONSTANT REFLECTION COMPONENT

PARTIALLY COVERED

POWER LAW

(15)

• PREVIOUS PCA ANALYSIS

=

•

2. NGC 4051

Parker et al. (2015)

VARYING POWER LAW

&

RELATIVISTIC REFLECTION

CONSTANT REFLECTION COMPONENT

PARTIALLY COVERED

POWER LAW

(16)

• ANOTHER OBSERVATION: Same PCs

•

2. NGC 4051

(17)

• ANOTHER OBSERVATION: Same PCs

•

2. NGC 4051

(18)

• Further analysis: GREATEST FLUX

(19)

• Further analysis: GREATEST FLUX

(20)

• Further analysis: GREATEST FLUX

•

2. NGC 4051

Parker et al. (2015)

Simulation

Data

Power law varying in normalization

+

(21)

• Further analysis: LOWEST FLUX

•

2. NGC 4051

(22)

• Further analysis: LOWEST FLUX

•

2. NGC 4051

(23)

Power law varying in normalization

+

constant relativistic reflection component

+

Soft Excess

• Further analysis: LOWEST FLUX

•

2. NGC 4051

(24)

• Further analysis: LOWEST FLUX

•

2. NGC 4051

Data

Simulation

Vaughan et al. (2011)

Power law varying in normalization

+

constant relativistic reflection component

+

(25)

• Check previuos Parker et al (2015)

• Corroborate

constant soft excess

Vaughan et al (2011)

• EVOLUTION

of the PCs with

FLUX

• Check and simulated intermediate flux states

• Check this evolution in other sources

• CONCLUSIONS