Fitting your SED

On mmdc.am you can fit the SSC, EIC or hadronic model (Blazar SED modeling) to your own SED. The fit runs in the background with MultiNest (Feroz et al. 2009), which gives the posterior distribution of every parameter; the result is sent to you by email.

Open Theoretical Modeling on mmdc.am

In short

1. Upload SED (CSV) in the Data card and set the Redshift z (and EBL absorption).
2. Choose the model: SSC, EIC or Hadronic.
3. Press Fit (email)…, check the summary, fix any parameter you know, enter your email.
4. Press Submit fit. A fit runs for at most 15 minutes, plus any wait in the queue; the email links to the result.

The data file

A comma-separated file with a header row and three columns:

Column	Content	Unit
frequency	frequency	Hz
flux	νF(ν)	erg cm⁻² s⁻¹
flux_err	error on νF(ν)	erg cm⁻² s⁻¹

frequency,flux,flux_err
1.4000e+09,2.5100e-14,3.0000e-15
4.5300e+14,1.1200e-11,5.6000e-13
2.4200e+17,3.8000e-12,4.1000e-13
2.4200e+23,2.0400e-11,3.9000e-12

Exactly these three columns, in this order, with these names in lowercase; the file name must end in .csv. Once uploaded, the data appear on the plot and the Data card shows the number of points and the frequency range.

Before a fit starts, the file is checked:

• Rows with an empty or zero flux_err are dropped.
• Only the data above 10¹¹ Hz are fitted: fitting lower frequencies makes the model converge very slowly. The points below are still drawn.
• The SED should be from one period (quasi-simultaneous data). Between 10¹¹ and 10²⁸ Hz the data are grouped in frequency bins 0.1 dex wide; if the fluxes differ by more than a factor of 3 within a bin, in three or more bins, the file is refused as too variable. Remove the outliers, or use averaged or binned data.

Start a fit

With data uploaded, the redshift set and a model chosen, press Fit (email)….

The dialog sums up what will be fitted (the file, the number of points and their frequency range, z, EBL and the model) and asks for:

• Source (optional): names the result. Pick a source from the list to also record its coordinates.
• Parameters: the fit samples every free parameter from its prior (below), so the values in the Model panel are not used. Tick Fix for a parameter you know to hold it at a value. The parameters that can be fixed are log γ_min (all models) and, for EIC, log L_d and log M_BH. The EIC dialog also lists log ν_BLR and log ν_DT; they are fixed in the model whatever is ticked.
• Email: where the result is sent.

The priors

The priors are uniform, over ranges close to the form's, except for the Doppler factor δ of the SSC and EIC models:

Parameter	SSC	EIC	Hadronic
δ	Gaussian, mean 30, σ ≈ 7.1, within 3–100	Gaussian, mean 35, σ ≈ 8.4, within 3–100	3.5 – 100
log R [cm]	15.2 – 17.8	14.5 – 18.5	14.5 – 18
log B [G]	−2.95 – 1.98	−3 – 2.5	−3 – 3.5
p (pe)	1.8 – 4.9	1.8 – 5	1.75 – 5
log γmin	1.5 – 5	1.5 – 5	1.5 – 2
log γmax (γe,max)	2.2 – 7.8	2 – 7.5	2 – 8
log Le [erg s⁻¹]	42.1 – 47.8	42 – 48.5	42.5 – 48.5
log Ld [erg s⁻¹]		43.5 – 47.5
log MBH [M⊙]		7 – 10
pp			1.65 – 3.45
log γp,max			3 – 11
log Lp [erg s⁻¹]			42 – 52

Hadronic fits: the neutrino likelihood

For the hadronic model the fit can also use neutrino information. Choose one:

Option	You give	What the fit compares
Spectral information (χ²)	E₁ [TeV] (1–1000) and E₂ [TeV] (100–10000), the band's edges; log flux, the neutrino flux [erg cm⁻² s⁻¹] (−16 to −9)	The model's neutrino flux at E₁ and E₂ with the given flux (10 % error assumed)
Number of neutrinos (Poisson)	N, the number of neutrinos (1–100); Δt, the observation time [months] (1–120)	N with the number the model predicts over Δt (its neutrino spectrum folded with the IceCube effective area)

The result

You receive an email when the fit starts (and, if it has to wait, one with its place in the queue), and another when it is ready. If the fit fails, an email tells you. The last one has a View Results link that opens the fit on mmdc.am, with:

• the plot of your data, the best fit and the posterior samples;
• the best-fit parameters, each with its 1σ error (or "fixed"), also loaded into the Model panel so you can run the model from them;
• three downloads: Corner plot (the posterior distributions, PDF), Parameters (the best-fit parameters, CSV) and Model (the best-fit SED, CSV).

Up to five fits from one network address can be queued or running at a time; a sixth is refused until one of them finishes.

Your data

Uploaded data are used only to perform the fit you asked for. The data and the results are deleted automatically 15 days after the fit is submitted; until then the View Results link works. The email address you give is also added to the MMDC updates list.

Need more?

To fit many SEDs, set constraints such as linked parameters, or get more advanced data products, write to us:

• Damien Bégué: begueda@biu.ac.il
• Narek Sahakyan: narek.sahakyan@icranet.org
• MMDC: mailtommdc@gmail.com

To fit from Python, including many SEDs at once, see the SDK guide Blazar emission modeling.