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Ïîèñêîâûå ñëîâà: arp 220
Fitting and Comparison of Models of Radio Spectra
Bojan Nikolic
Astrophysics Group, Cavendish Laborator y/Kavli Institute for Cosmology University of Cambridge

1 September 2010 @ Cagliari, Italy
R90

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Introduction

Outline
1 2

Introduction Method Bayesian analysis Implementation Visualisation Simple examples NGC 628 NGC 3627 NGC 7331 Spinning dust Free-free component in a supernova remnant (U)LIRGs Summar y/Fur ther Directions/References
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3

4 5 6 7


Introduction

Introduction

Motivation: Preparation for analysis of for thcoming data from GBT+MUSTANG A bit of a "spare-par ts" project in which I reused various software components I developed for other purposes Method paper : Nikolic (2009) All of the source code available under GPL license from: http://www.mrao.cam.ac.uk/~bn204/galevol/speca/ index.html

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Introduction

Schematic radio spectrum of a star-forming galaxy
1000 500 200 100 50 20 10 1 10 ( GHz )
Schematic & hypothetical (continuum-only) spectrum of NGC 3627: the dashed line is the synchrotron the component; the dotted line is the free-free component; the dash-dot-dash line is the dust component; the solid line is the total emission. B. Nikolic (Cambridge) Fitting of radio spectra 4 / 80

F (mJy)

100

1000


Introduction

Why analyse radio spectra
Energetics
Reconstruct the total energy balance from few/sparse measurements of the spectrum What physical process is the source of the energy?

Inference of proper ties of the source:
Geometr y (e.g., filling factor from the low-frequency turnover) Dynamics (e.g., through electron ageing)

Redshift determination radio "photometric" redshifts
Currently mostly used for sub-millimetre selected ("SCUBA") sources

Physics:
Free-free emission Slope of the dust continuum ­ physics of interstellar dust

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Introduction

Analysis strategy

Model fitting In radio, sub-mm and far-IR, the physics is fairly well understood and candidate models are computational easy. So analysis often consists of "fitting" a set of models to the observations. Synchrotron radiation (analytic or 1-D integral) Thermal free-free (analytic) Modified black-body emission from dust (analytic or 1-D integral) Spinning dust models (analytic)

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Introduction

Requirements for model fitting

1 2

An objective measure of how well the model fits the observed data For all model parameters:
1 2 3 4

Unbiased estimates Error on these estimates Correlations between the errors Full probability distributions if significantly non-Gaussian

3

An objective way of comparing how well different models fit the data A mechanism to incorporate already known constraints on model parameters Visualisation of the fit in comparison to observations

4

5

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Method

Outline
1 2

Introduction Method Bayesian analysis Implementation Visualisation Simple examples NGC 628 NGC 3627 NGC 7331 Spinning dust Free-free component in a supernova remnant (U)LIRGs Summar y/Fur ther Directions/References
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3

4 5 6 7


Method

Bayesian analysis

Bayesian analysis in a nutshell

1

Can handle "nuisance" parameters
1 2

They do not bias estimates of other parameters They are correctly taken into account when calculating significance Even multi-modal distributions (although not ver y efficiently in the present implementation of my program) No fitting into the noise (e.g., "flux-boosting")

2

Fully describes non-Gaussian distributions
1

3

Unbiased
1

4

Objective model (or hypothesis) selection

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Method

Bayesian analysis

Bayes equation & the evidence

p(|D , H ) =

p(D |, H )p(|H ) p(D |H )

D : Obser ved data flux density at several frequencies H : Hypothesis model for emission & priors for parameters p(D |, H ): Likelihood given a model and its parameters, how likely are the obser ved data? p(|D , H ): Posterior given a model, what we know about it's parameters p(D |H ): "Evidence", objective measure of how good the model is
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Method

Bayesian analysis

Bayes equation & the evidence
p(D |, H )p(|H ) p(D |H )

p(|D , H ) =

D : Obser ved data flux density at several frequencies H : Hypothesis model for emission & priors for parameters p(D |, H ): Likelihood given a model and its parameters, how likely are the obser ved data? p(|D , H ): Posterior given a model, what we know about it's parameters p(D |H ): "Evidence", objective measure of how good the model is
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Method

Bayesian analysis

Calculating the evidence
Evidence is an integral over the likelihood surface p(D |H ) = dp(D |, H )p(|H )

Evidence is not available from standard Markov Chain Monte Carlo calculations I use a new implementation of the nested sampling algorithm by Skilling (2006). Compared to MCMC, this algorithm is:
Efficient (fewer likelihood function evaluations) Reliable (less chance of getting stuck in local maxima) The output is both the evidence and the posterior distribution

The algorithm is available under GPL

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Method

Implementation

Inputs/outputs
Inputs
1 2 3

The model (as a routine/class) Priors: only flat, independent priors suppor ted. I.e., a "prior box" Observed data and errors (for the moment assumed Gaussian)

Outputs
1 2 3 4 5

The evidence value Histograms of marginalised distributions of each model parameter Two-dimensional histograms of par tially marginalised distributions Fan-diagram of flux vs frequency Maximum likelihood plot of flux vs frequency

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Method

Implementation

Inputs/outputs
Inputs
1 2 3

The model (as a routine/class) Priors: only flat, independent priors suppor ted. I.e., a "prior box" Observed data and errors (for the moment assumed Gaussian)

Outputs
1 2 3 4 5

The evidence value Histograms of marginalised distributions of each model parameter Two-dimensional histograms of par tially marginalised distributions Fan-diagram of flux vs frequency Maximum likelihood plot of flux vs frequency

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Method

Visualisation

NGC 628 observations
10

1 F (Jy) 0.1 0.01 101 102 (MHz)
Obser vations at five frequencies of the near-by galaxy NGC 628 collected by Paladino et al. (2009)
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103

10

4


Method

Visualisation

NGC 628 ­ max. likelihood line fit
10

1 F (Jy) 0.1 0.01 101 102 (MHz)
Obser vations at five frequencies of the near-by galaxy NGC 628 collected by Paladino et al. (2009)
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103

10

4


Method

Visualisation

NGC 628 ­ doubled errors & max. likelihood line fit
10

1 F (Jy) 0.1 0.01 101 102 (MHz)
I have scaled up the error estimates by a factor of two
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103

10

4


Method

Visualisation

NGC 628 ­ original errors & fan-diagram
40 2

1 0.5 F (Jy)

30

20 0.2 0.1 0.05 0 101 102 (MHz)
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10

103

10

4


Method

Visualisation

NGC 628 ­ doubled errors & fan-diagram
2 6 1 0.5 F (Jy) 4 0.2 0.1 0.05 0 101 102 (MHz)
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2

103

10

4


Simple examples

Outline
1 2

Introduction Method Bayesian analysis Implementation Visualisation Simple examples NGC 628 NGC 3627 NGC 7331 Spinning dust Free-free component in a supernova remnant (U)LIRGs Summar y/Fur ther Directions/References
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3

4 5 6 7


Simple examples

Four simple models for synchrotron emission
Underlying synchrotron spectrum Power law 0 F ( ) = F ·
1 GHz

Continuous injection of electrons ver y approximately broken power law
1 GHz " " ,, « 0 F · 1 GHz br 0 F ·

Low-frequency optical depth effects None



Synchrotron self-absorption x = /pk As = x
-+5/2 -5/2

"

"

br
-1/2

> br .

â 1 - exp 1 - x

(1)
For the pur poses of these examples, I've taken the models from Paladino et al. (2009) to go with their data ­ both more complex and more physical models could be used
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Simple examples

NGC 628

Model fits for NGC 628 I

Power-law (Z = 185.874)
40 2 2 1 0.5 F (Jy) 20 0.2 0.1 0.05 0 101 102 (MHz) 103 10
4

Power-law + SSA (Z = 76.3034)
15 12.5 10 7.5 5 2.5 0 101 102 (MHz) 103 10
4

30

1 0.5 F (Jy) 0.2 0.1 0.05

10

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Simple examples

NGC 628

Model fits for NGC 628 II
CI (Z = 83.4132)
2 15 12.5 10 7.5 5 2.5 0 101 102 (MHz) 103 10
4

CI + SSA (Z = 27.65)
2 5 1 0.5 F (Jy) 3 0.2 0.1 1 0.05 0 101 102 (MHz) 103 10
4

1 0.5 F (Jy)

4

0.2 0.1 0.05

2

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Simple examples

NGC 3627

Model fits for NGC 3627 I

Power-law (Z = 9.7 â 10-15 )
2 4 · 10 1 0.5 F (Jy) 3 · 10
- 15 - 15

Power-law + SSA (Z = 3.9 â 10-15 )
2 2 · 10-
15

1 0.5 F (Jy)

1.5 · 10-

15

1 · 10- 0.2 0.1 0.05 5 · 10-

15

0.2 0.1 0.05

2 · 10-

15

1 · 10-

16

15

0 101 102 (MHz) 103 10
4

0 101 102 (MHz) 103 10
4

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Simple examples

NGC 3627

Model fits for NGC 3627 II
CI (Z = 1.3 â 10
2 5 · 10- 1 4 · 10- 0.5 F (Jy) F (Jy) 3 · 10- 0.2 2 · 10- 0.1 1 · 10- 0.05 0 101 102 (MHz) 103 10
4 10 10 10 10 10

-09

)
6 · 10-
10

CI + SSA (Z = 2.6 â 10
2 1

-10

)
1 · 10- 8 · 10-
10

11

0.5 6 · 10- 0.2 0.1 2 · 10- 0.05 0 101 102 (MHz) 103 10
4 11 11

4 · 10-

11

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Simple examples

NGC 7331

Model fits for NGC 7331 I

Power-law (Z = 2.9 â 10-17 )
2 2.5 · 10-
17

Power-law + SSA (Z = 0.5)
2 0.4
17

1 0.5 F (Jy)

2 · 10-

1 0.5 0.3

17

F (Jy)

1.5 · 10- 0.2 0.1 5 · 10- 0.05

1 · 10-

17

0.2 0.1

0.2

18

0.1

0.05 0 101 102 (MHz) 103 10
4

0 101 102 (MHz) 103 10
4

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Simple examples

NGC 7331

Model fits for NGC 7331 II
CI (Z = 70)
2 60 2 4 · 104 1 0.5 F (Jy) 50 1 0.5 F (Jy) 3 · 104

CI + SSA (Z = 5.0 â 105 )

40

30 0.2 20 0.1 10 0.05 0 101 102 (MHz) 103 10
4

0.2 0.1 0.05

2 · 104

1 · 104

0 101 102 (MHz) 103 10
4

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Spinning dust

Outline
1 2

Introduction Method Bayesian analysis Implementation Visualisation Simple examples NGC 628 NGC 3627 NGC 7331 Spinning dust Free-free component in a supernova remnant (U)LIRGs Summar y/Fur ther Directions/References
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3

4 5 6 7


Spinning dust

Introduction I
See Scaife et al. (2010) for details

Original obser vation Centimetre-wave emission correlated with galactic dust foregrounds (e.g., de Oliveira-Costa et al., 1997) in excess to what is expected from simple models Draine & Lazarian (1998) suggest it could be due to spinning dust Vigorous debate about the nature the emission... First detection in an external galaxy Mur phy et al. (2010) ­ but is it due to spinning dust or a very compact HI I region?

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Spinning dust

Introduction II
See Scaife et al. (2010) for details

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Spinning dust

Results
"Region 4" ­ the anomalous region

High-opacity HI I region model
0.01 2.5 · 103
5

Spinning dust model
0.01 8 · 103
6

0.005

2 · 103

5

0.005

6 · 103

6

F (Jy)

F (Jy)

1.5 · 10

35

4 · 103 0.002

6

1 · 103 0.002 5 · 103

5

4

2 · 103

6

0.001 1 2 5 10 (GHz) 20 50 100

0

0.001 1 2 5 10 (GHz) 20 50 100

0

Z=2.4 â 10

36

Z=7.2 â 1037 Clearly should prefer this model

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Spinning dust

Results
"Region 8" ­ a normal region

Simple thermal + synchrotron
0.01 5 · 103
9

Spinning dust model
0.01 4 · 103
9

0.005

4 · 10

39

0.005 3 · 103
9 9

F (Jy)

F (Jy)

3 · 103

2 · 103 0.002

9

2 · 103 0.002 1 · 103

9

9

1 · 103

9

0.001 1 2 5 10 (GHz) 20 50 100

0

0.001 1 2 5 10 (GHz) 20 50 100

0

Z=4.8 â 1040 Simpler model preferred!

Z=4.3 â 10

40

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Free-free component in a supernova remnant

Outline
1 2

Introduction Method Bayesian analysis Implementation Visualisation Simple examples NGC 628 NGC 3627 NGC 7331 Spinning dust Free-free component in a supernova remnant (U)LIRGs Summar y/Fur ther Directions/References
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3

4 5 6 7


Free-free component in a supernova remnant

Introduction
Data cour tesy of D. A. Green in Cambridge

Analysis of spectrum of supernova remnant HB3 Is there evidence for flattening of the spectrum?
Could be inter preted as a thermal free-free component due to interaction of shock with the molecular cloud

´ ´ ´ See Urosevic et al. (2007), Green (2007), Onic & Urosevic (2008)

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Free-free component in a supernova remnant

Condon model

Single power-law synchrotron with slope () as a free parameter Free-free emission component (H is the thermal fraction at 1 GHz) Thermal free-free absorption at low frequencies ( is the optical depth at 1 GHz) 1 GHz
2

A( ; ) = 1 - exp -10 F ( ; H , ) =



-2.1

A( ) A(1 GHz) 1 GHz

H + (1 - H )

1 GHz

0.1+

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Free-free component in a supernova remnant

Maximum likelihood model fits for HB3

Power-law
1000 500 200 F (Jy) 100 50 20 10 101 102 (MHz) 103 10
4

Condon
1000 500 200 F (Jy) 100 50 20 10 101 102 (MHz) 103 10
4

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Free-free component in a supernova remnant

Fan diagrams of the Bayesian analysis of HB3

Power-law Z = 9 â 10-
1000 500

25
1000 1.25 · 10-
25

Condon Z = 1.9 â 10
500 1 · 10-
25

-24
2.5 · 10-
25

2 · 10- 200 F (Jy)

25

200 F (Jy) 7.5 · 10- 100 5 · 10-
26 26

100

1.5 · 10-

25

50

50

1 · 10-

25

20

2.5 · 10-

26

20

5 · 10-

26

10 101 102 (MHz) 103 10
4

0

10 101 102 (MHz) 103 10
4

0

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Free-free component in a supernova remnant

Marginalised distribution of

Power-law Z = 9 â 10-
8 · 10- 6 · 10
26 - 26

25
1 · 10
- 25

Condon Z = 1.9 â 10
7.5 · 10- 5 · 10- 2.5 · 10-
26

-24

4 · 10- 2 · 10-

f

26

26

f

26

26

0 -0.8 -0.6 -0.4

0 -0.8 -0.6 -0.4

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Free-free component in a supernova remnant

(Par tially-)Marginalised distribution of H
PD of thermal fraction at 1 GHz Correlation between thermal fraction and synchrotron slope
0.6 1.5 · 10-
26

6 · 10-

26

0.5 1.25 · 10- 0.4 1 · 10 0.3 0.2 0.1 H
26

4 · 10- f

- 26

26

7.5 · 10- 5 · 10- 2.5 · 10-

27

2 · 10-

26

27

27

0 0.1 0.2 0.3 H 0.4 0.5

0 -1 -0.8 -0.6 -0.4

0

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Free-free component in a supernova remnant

New prior: constrain to 0.1 range around -0.7

Power-law Z = 1.2 â 10-
1000 500

25
1000 1.5 · 10- 1.25 · 10-
26

Condon Z = 5.4 â 10
500
26

-24
8 · 10-
25

6 · 10- 200 F (Jy)

25

200 F (Jy)

1 · 10

- 26

100

7.5 · 10- 5 · 10- 2.5 · 10-

27

100

4 · 10-

25

50

27

50 2 · 10-
25

20

27

20

10 101 102 (MHz) 103 10
4

0

10 101 102 (MHz) 103 10
4

0

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Free-free component in a supernova remnant

New prior: distribution of H
PD of thermal fraction at 1 GHz Correlation between thermal fraction and synchrotron slope
0.6 0.5 0.4 0.3 0.2 2.5 · 10-
26

0.04 0.03 0.02 0.01
H

2 · 10-

26

1.5 · 10-

26

f

1 · 10-

26

0.1

5 · 10-

27

0 0.1 0.2 0.3 H 0.4 0.5
0 -0.75 0 -0.725 -0.7 -0.675 -0.65

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(U)LIRGs

Outline
1 2

Introduction Method Bayesian analysis Implementation Visualisation Simple examples NGC 628 NGC 3627 NGC 7331 Spinning dust Free-free component in a supernova remnant (U)LIRGs Summar y/Fur ther Directions/References
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3

4 5 6 7


(U)LIRGs

A physically based analysis of (U)LIRG spectra
In-progress work in collaboration with Marcel Clemens from U. of Padua Data are based on Clemens et al. (2010) Model:
Parametrise in terms of supernova rates, star-formation rates, filling factors Not in terms of: flux densities, opacities, electron densities, etc. Two components: one with 0.5kpc scale, the other with 0.05kpc Each component consists of star-formation driven thermal opacity and supernova-driven synchrotron component Prior :
0.5 kpc comp: -1 < < -1/2, 10-1 yr-1 < SN rate < 101 1 M yr-1 < SFR < 103 M yr-1 , 10-3 < areal filling factor 0.05 kpc comp: -1 < < -1/2, 10-1 yr-1 < SN rate < 10 1 M yr-1 < SFR < 103 M yr-1 , 10-5 < areal filling factor yr-1 , <1 1 yr-1 , < 10-2

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(U)LIRGs

Gallery of fan char ts I
Arp 148 0.5 kpc comp + 0.05 kpc comp
1 3 · 101 2.5 · 101 2 · 101 1.5 · 10
0

One 0.5kpc comp
1 0.5 0.2 0.1 F (Jy) 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100

0.5 0.2 0.1 F (Jy)

5 · 109

0

4 · 109

0

3 · 109 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) 2 · 109

10

1 · 101

0

5 · 109

1 · 109

(GHz)

Z this model is preferred

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(U)LIRGs

Gallery of fan char ts II
Arp 220 0.5 kpc comp + 0.05 kpc comp
600 1 0.5 500 0.2 400 0.1 F (Jy) 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz) 300 F (Jy) 0.1 0.05 0.02 0.01 0.005 0 7.5 · 103 0.2 1 · 104 1.25 · 104

One 0.5kpc comp
1 0.5

200

5 · 103

100

2.5 · 103

Z this model is preferred

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(U)LIRGs

Gallery of fan char ts III
Arp299 0.5 kpc comp + 0.05 kpc comp
1 1.5 · 10- 0.5 0.2 1 · 10
- 60 60

One 0.5kpc comp
1 0.5 0.2 0.1 F (Jy) 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100

1.25 · 10- 1 · 10- 7.5 · 10- 5 · 10- 2.5 · 10-

40

40

0.1 F (Jy) 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz)
41

41

5 · 10-

61

41

(GHz)

Z this model is preferred

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(U)LIRGs

Gallery of fan char ts IV
CGCG436-30 0.5 kpc comp + 0.05 kpc comp
8 · 104 1 0.5 3000 0.2 0.1 F (Jy) F (Jy) 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz) 2 · 104 4 · 104 6 · 104 0.2 0.1 0.05 0.02 1000 0.01 0.005 0 2000

One 0.5kpc comp
1 0.5

Z this model is preferred

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(U)LIRGs

Gallery of fan char ts V
I0136-1042 0.5 kpc comp + 0.05 kpc comp
15 1 4 · 106 0.5 0.2 10 0.1 F (Jy) 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz) 7.5 F (Jy) 0.1 0.05 0.02 0.01 0.005 0 1 · 106 2 · 106 12.5 0.5 0.2

One 0.5kpc comp
1

3 · 106

5

2.5

Z this model is preferred

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(U)LIRGs

Gallery of fan char ts VI
I03359+1523 0.5 kpc comp + 0.05 kpc comp
1 400 0.5 0.2 0.1 F (Jy) 200 0.05 0.02 100 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz) 0 1 · 105 2 · 105 4 · 105

One 0.5kpc comp
1 0.5 0.2 0.1 F (Jy) 0.05 0.02 0.01 0.005

300

3 · 105

Z this model is preferred

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(U)LIRGs

Gallery of fan char ts VII
I05189-2524 0.5 kpc comp + 0.05 kpc comp
1 4 · 106 2.5 · 106 0.5 0.2 0.1 F (Jy) 2 · 106 0.05 0.02 1 · 10
6

One 0.5kpc comp
1 0.5 0.2 0.1 F (Jy) 0.05 0.02 0.01 0.005

2 · 106

3 · 106

1.5 · 106

1 · 106

0.01 0.005

5 · 105

0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz)

0

Evidence about the same

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(U)LIRGs

Gallery of fan char ts VIII
I10173+0828 0.5 kpc comp + 0.05 kpc comp
1 5 · 10
9

One 0.5kpc comp
1 0.5 0.2 0.1 F (Jy)

0.5 3 · 101
0

4 · 109 F (Jy)

0.2 0.1

0.05 0.02 0.01 0.005

3 · 109

0.05 0.02

2 · 101

0

2 · 109

1 · 101 1 · 109 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz)

0

0

Z this model is preferred

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(U)LIRGs

Gallery of fan char ts IX
I10565+2448 0.5 kpc comp + 0.05 kpc comp
1 5 · 106 0.5 0.2 0.1 F (Jy) 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz) 0 2 · 105 4 · 105 6 · 105

One 0.5kpc comp
1 0.5 0.2 0.1 F (Jy) 0.05 0.02 0.01 0.005

4 · 106

3 · 106

2 · 106

1 · 10

6

Z this model is preferred

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(U)LIRGs

Gallery of fan char ts X
I12112+0305 0.5 kpc comp + 0.05 kpc comp
8 · 10
-9

One 0.5kpc comp
1 0.5 0.2 0.1 F (Jy) 0.05 0.02 0.01 0.005

1 0.5 6 · 107

6 · 10

-9

0.2 0.1 4 · 107

4 · 10

-9

F (Jy)

0.05 0.02

2 · 10

-9

2 · 107

0.01 0.005 0 0 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz)

0.1

0.2

0.5

1

2

5

10

20

50

100

(GHz)

Z this model is preferred

B. Nikolic (Cambridge)

Fitting of radio spectra

51 / 80


(U)LIRGs

Gallery of fan char ts XI
I14348-1447 0.5 kpc comp + 0.05 kpc comp
5 · 105 1 0.5 4 · 105 0.2 0.1 F (Jy) 0.05 2 · 10 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz) 1 · 10
5 5

One 0.5kpc comp
1 0.5

2.5 · 105

0.2 3 · 105 F (Jy) 0.1 0.05 0.02 0.01 0.005

2 · 105

1.5 · 105

1 · 105

5 · 104

0

Z this model is preferred

B. Nikolic (Cambridge)

Fitting of radio spectra

52 / 80


(U)LIRGs

Gallery of fan char ts XII
I15250+3609 0.5 kpc comp + 0.05 kpc comp
1 0.5 0.5 0.2 0.1 F (Jy) 0.3 0.05 0.02 0.01 0.005 0 0.1 0.2 0.5 1 2 5 10 20 50 100 0.1 0.2 0.5 1 2 5 10 20 50 100 (GHz) (GHz) 0.2 0.05 0.02 0.01 0.005 0 5 · 105 1 · 106 2 · 106

One 0.5kpc comp
1 0.5 0.2 0.1 F (Jy)

0.4

1.5 · 106

0.1

Z this model is preferred

B. Nikolic (Cambridge)

Fitting of radio spectra

53 / 80


(U)LIRGs

Star-formation as evidenced by the free-free emission I
Arp 148 0.5 kpc comp + 0.05 kpc comp
0.08 0.06 0.04 0.02 0 0.5 1 1.5 log10 2 2.5 0.5 1 1.5 log10 2 2.5

One 0.5kpc comp
0.15

0.1 f f 0.05 0

Z this model is preferred

B. Nikolic (Cambridge)

Fitting of radio spectra

54 / 80


(U)LIRGs

Star-formation as evidenced by the free-free emission II
Arp 220 0.5 kpc comp + 0.05 kpc comp
0.04 0.03 0.02 0.01 0 0.5 1 1.5 log10 2 2.5 0.5 1 1.5 log10 2 2.5

One 0.5kpc comp
0.15

0.1 f f 0.05 0
B. Nikolic (Cambridge)

Z this model is preferred

Fitting of radio spectra

55 / 80


(U)LIRGs

Star-formation as evidenced by the free-free emission III
Ar p 299 = IC 694 + NGC 3690 One 0.5kpc comp 0.5 kpc comp + 0.05 kpc comp
0.15 0.2 0.15 0.1 0.05 0 0 0.5 1 1.5 log10 2 2.5 0.5 1 1.5 log10 2 2.5

0.1 f f 0.05 0
B. Nikolic (Cambridge)

Z this model is preferred
Comment: good upper limits on thermal emission. Normally classified as star-forming but does also have an AGN
Fitting of radio spectra 56 / 80


(U)LIRGs

Star-formation as evidenced by the free-free emission IV
One 0.5kpc comp
0.4 0.3 0.2 0.1 0 0.5 1 1.5 log10 2 2.5

CGCG436-30 0.5 kpc comp + 0.05 kpc comp
0.1 0.075 0.05 0.025 0 0.5 1 1.5 log10 2 2.5

f

Z this model is preferred
Comment: nice clear detection of the thermal emission, with SFR roughly consistent with the IR luminosity
B. Nikolic (Cambridge) Fitting of radio spectra 57 / 80

f


(U)LIRGs

Star-formation as evidenced by the free-free emission V
I0136-1042 0.5 kpc comp + 0.05 kpc comp
0.075

One 0.5kpc comp
0.075

0.05 f f 0.025

0.05

0.025

0 0 0.5 1 1.5 log10 2 2.5

0 0.5 1 1.5 log10 2 2.5

Z this model is preferred

B. Nikolic (Cambridge)

Fitting of radio spectra

58 / 80


(U)LIRGs

Star-formation as evidenced by the free-free emission VI
I03359+1523 0.5 kpc comp + 0.05 kpc comp
0.08 0.06
0.05

One 0.5kpc comp
0.075

0.04 0.02 0

f

0.025

0 0 0.5 1 1.5 log10 2 2.5

f

0.5

1

1.5 log10

2

2.5

Z this model is preferred

B. Nikolic (Cambridge)

Fitting of radio spectra

59 / 80


(U)LIRGs

Star-formation as evidenced by the free-free emission VII
I05189-2524 0.5 kpc comp + 0.05 kpc comp
0.04 0.03
0.05

One 0.5kpc comp
0.075

0.02 0.01 0

f

0.025

0 0.5 1 1.5 log10 2 2.5

f

0.5

1

1.5 log10

2

2.5

Evidence about the same

B. Nikolic (Cambridge)

Fitting of radio spectra

60 / 80


(U)LIRGs

Star-formation as evidenced by the free-free emission VIII
I10173+0828 0.5 kpc comp + 0.05 kpc comp
0.06

One 0.5kpc comp
0.15

0.1 f f 0.05

0.04

0.02

0 0.5 1 1.5 log10 2 2.5

0 0.5 1 1.5 log10 2 2.5

Z this model is preferred
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