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https://github.com/hw2814/dust-SED-pymc3

Fitting a modified black body spectrum to FIR flux measurements using PyMC3
https://github.com/hw2814/dust-SED-pymc3

astrophysics curve-fitting mcmc physics pymc3

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Fitting a modified black body spectrum to FIR flux measurements using PyMC3

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README 

        
# Deriving the properties of interstellar dust from far-infrared spectral energy distributions

To infer properties of the interstellar dust contained within a galaxy, a modified black body spectrum can be fitted to 

the observed far-infrared (FIR) spectral energy distribution (SED) using a Markov Chain Monte Carlo bayesian sampling 

method with dust temperature, emissivity and dust mass as free parameters.



## Model

A modified black body (also called a 'gray body') has a spectrum given by:



![](figures/equations/mbb.gif)



where ![](figures/equations/F_nu.gif) is the flux density at the frequency ![](figures/equations/nu.gif) in the emitted 

frame, ![](figures/equations/M_dust.gif) the mass of dust, ![](figures/equations/D_L.gif) the luminous distance of the 

source and ![](figures/equations/planck.gif) is the Planck function. ![](figures/equations/kappa.gif) is the emissivity 

cross section per unit dust mass at the frequency 



![](figures/equations/emissivity.gif)



where we have used ![](figures/equations/kappa_0.gif). The index β is the emissivity parameter and thought to vary

between galaxies in the range 1 < β < 2 (where β = 1 would be a pure black body), however values outside of this range

have been observed. [1]

 

For the MCMC implementation we use [PyMC3](https://docs.pymc.io/), modelling each flux measurement as a normal

distribution with the mean given by the MBB function and the standard deviation as the error on the measurement.



## Data Sets

We use 5 sets of galaxies. I have included the data formatted since since the formatting and data cleaning was 

non-trivial and onerous.



- ### Great Observatories All-Sky Survey (GOALS)

GOALS is a comprehensive imaging and spectroscopic survey of over 200 local galaxies (i.e. with a redshift z < 0.088), a

complete subset of the *IRAS* Revised Bright Galaxy Sample which comprises of 629 objects with 60μm fluxes > 5.64Jy [2].

Of these sources, 199 are categorised as Luminous Infrared Galaxies (LIRGs) with

![](figures/equations/log_luminosity.gif) > 11 and 20 as Ultra-Luminous Infrared Galaxies (ULIRGs) with 

![](figures/equations/log_luminosity.gif) > 12.



- ### *Planck* Catalogue of Compact Sources (PCCS)

We include 17 sources from the *Planck* Catalogue of Compact Sources (PCCS) selected at 857GHz with a 90% completeness

level and minimum flux of 0.658Jy [3]. For these sources we were provided with SPIRE 250, 350 and 500 μm measurements,

for which we acquired *IRAS* 60 and 100 μm measurements from the NASA/IPAC Extragalactic Database (NED).



- ### *HERschel* ULIRG Survey (HERUS)

This set contains 43 *IRAS* local (z < 0.3) 60μm selected local ULIRGs from the Herschel ULIRG survey [4]. For these

sources we used the SPIRE flux measurements at 250, 350 and 500μm and *IRAS* 60 and 100μm measurements again retrieved

from NED.



- ### *Herschel* ATLAS (H-ATLAS)

By far the largest catalogue included is that of several hundred thousand sources taken from the *Herschel*

Astrophysical Terahertz Large Area Survey (H-ATLAS) [5], a survey over 600 deg² of the sky in five photometric bands -

100, 160μm (from PACS), 250, 350 and 500μm (from SPIRE).



- ### PACS (Cortese)

323 galaxies from the Herschel Reference Survey (HRS) in Cortese 2014 [6]. The HRS is a volume limited (15Mpc ≤ D ≤ 

25Mpc) K-band selected sample. These sources and Cortese's results are used to validate our method.



## Usage

First, try running `notebooks/model_convergence` to check that the model runs on your machine. All results were produced

with the package versions in `requirements.txt` on python 3.7 and with the default parameters set in `mcmc.create_args`.

To fit the model to the full dataset, run `python mcmc.py` (see `mcmc.create_args` for command line options for changing

the model parameters).



## Notebooks

TODO



## References

[1] [Dupac, X., Bernard, J.P., Boudet, N., Giard, M., Lamarre, J.M., Mény, C., Pajot, F., Ristorcelli, I., Serra, G., 

Stepnik, B. and Torre, J.P., 2003. Inverse temperature dependence of the dust submillimeter spectral index. Astronomy &

Astrophysics, 404(1), pp.L11-L15.](https://www.aanda.org/articles/aa/pdf/2003/22/aafc183.pdf)



[2] [Armus, L., Mazzarella, J.M., Evans, A.S., Surace, J.A., Sanders, D.B., Iwasawa, K., Frayer, D.T., Howell, J.H.,

Chan, B., Petric, A. and Vavilkin, T., 2009. GOALS: The Great Observatories All-Sky LIRG Survey. Publications of the

Astronomical Society of the Pacific, 121(880), p.559.](https://arxiv.org/pdf/0904.4498.pdf)



[3] [Ade, P.A., Aghanim, N., Argüeso, F., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., Aumont, J.,

Baccigalupi, C., Banday, A.J. and Barreiro, R.B., 2014. Planck 2013 results. XXVIII. The Planck catalogue of compact

sources. Astronomy & Astrophysics, 571, p.A28.

](https://www.aanda.org/articles/aa/pdf/2014/11/aa21524-13.pdf)



[4] [Clements, D.L., Pearson, C., Farrah, D., Greenslade, J., Bernard-Salas, J., González-Alfonso, E., Afonso, J.,

Efstathiou, A., Rigopoulou, D., Lebouteiller, V. and Hurley, P.D., 2017. HERUS: the far-IR/submm spectral energy

distributions of local ULIRGs and photometric atlas. Monthly Notices of the Royal Astronomical Society, 475(2),

pp.2097-2121.](https://arxiv.org/pdf/1712.04843)



[5] [Valiante, E., Smith, M.W.L., Eales, S., Maddox, S.J., Ibar, E., Hopwood, R., Dunne, L., Cigan, P.J., Dye, S.,

Pascale, E. and Rigby, E.E., 2016. The Herschel-ATLAS data release 1–I. Maps, catalogues and number counts. Monthly

Notices of the Royal Astronomical Society, 462(3), pp.3146-3179.](https://arxiv.org/pdf/1606.09615)



[6] [Cortese, L., Fritz, J., Bianchi, S., Boselli, A., Ciesla, L., Bendo, G.J., Boquien, M., Roussel, H., Baes, M., 

Buat, V. and Clemens, M., 2014. PACS photometry of the Herschel Reference Survey–far-infrared/submillimetre colours as

tracers of dust properties in nearby galaxies. Monthly Notices of the Royal Astronomical Society, 440(1),

pp.942-956.](https://academic.oup.com/mnras/article/440/1/942/2891848)



## Acknowledgement

This work has made use of the NASA/IPAC Extragalactic Database [(NED)](https://ned.ipac.caltech.edu/) which is operated

by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and

Space Administration.