  ## VOSA. Help and Documentation

### Version 7.0, July 2021 Help News FAQ Credits Help-Desk
 Stars and brown dwarfs 1. Introduction
2. Input files
 2.1. Upload files 2.2. VOSA file format 2.3. Single object 2.4. Manage files 2.5. Archiving 2.6. Filters
3. Objects
 3.1. Coordinates 3.2. Distances 3.3. Extinction
4. Build SEDs
 4.1. VO photometry 4.2. SED 4.3. Excess
5. Analysis
5.1. Model Fit
5.2. Bayes analysis
5.3. Template Fit
5.4. Templates Bayes
5.5. Binary Fit
 5.5.1. Fit procedure 5.5.2. Extinction 5.5.3. Example
5.6. HR diagram
5.7. Upper Limits
5.8. Statistics
6. Save results
7. VOSA Architecture
8. Phys. Constants
9. FAQ
10. Use Case
11. Quality
 11.1. Stellar libraries 11.2. VO photometry
12. Credits
 12.1. VOSA 12.2. Th. Spectra 12.3. Templates 12.4. Isochrones 12.5. VO Photometry 12.6. Coordinates 12.7. Distances 12.8. Dereddening 12.9. Extinction
13. Helpdesk

Appendixes

## Binary Fit

 Fit procedure Extinction Example

VOSA gives the option to try to fit the observed SED using the linear combination of two theoretical models. That is, assuming that the observed flux is the sum of the fluxes of two different objects. $$F_{\rm obs}(x) \simeq {\rm M}_{\rm d 1} \cdot F_{\rm m 1}(x) + {\rm M}_{\rm d 2} \cdot F_{\rm m 2}(x)$$

where:

 $F_{\rm obs}(x)$ : is the observed flux. $F_{\rm m 1}(x)$ : is the theoretical flux from object 1. ${\rm M}_{\rm d 1}$ : is the Multiplicative dilution factor for object 1. Defined also as: ${\rm M}_{\rm d 1}=(R_1/D)^2$, being $R_1$ the object radius and D the distance between the object and the observer. It is calculated as a result of the fit too. $F_{\rm m 2}(x)$ : is the theoretical flux from object 2. ${\rm M}_{\rm d 2}$ : is the Multiplicative dilution factor for object 2. Defined also as: ${\rm M}_{\rm d 2}=(R_2/D)^2$, being $R_2$ the object radius and D the distance between the object and the observer. It is calculated as a result of the fit too. Most of the explanations given in the chi-square model fit section are also valid for the binary fit.

We will explain here only those aspects that are specific of the binary fit.

### Fit procedure

In the case of the one model chi-square typical fit, VOSA compares the observed SED with the synthetic photometry of all the models in the grid, calculates the best $M_d$ for each case and chooses the model so that chi-square is minimal.

But a binary fit process would involve, in principle, comparing the observed photometry with every linear combination of models from two different grids. This, itself, would already imply a $N^2$ fitting time. But the biggest problem is that, given a couple of models $F_1(x)$ and $F_2(x)$ it is not possible to calculate both the $M_{d1}$ and $M_{d2}$ dilution factors that minimizes $\chi^2$. Given $M_{d1}$ we can calculate the best $M_{d2}$ (or the opposite) but one of them should be estimated in some other way.

Trying a full range of possible values of $r_f \equiv M_{d1}/M_{d1}$ is very difficult too and, in any case, would increase the calculation time as $\sim N^3$, which is not convenient either.

Given that it is not possible to check all the {$F_1(x), F_2(x), r_f$} combinations we need to estimate good initial values for model parameters (and $r_f$) and then explore only the parameter values around these initial ones.

This implies that we cannot guarantee that the binary fit result is the best possible one (we can ensure that in the normal chi-square fit, but not in the binary case) but only a local minimum in the parameter space.

In order to get a good (and faster) estimation of the initial parameter values we do as follows:

• First estimation.
• We first use a special grid of models based in BT-Settl but with only some selected spectra so that $T_{\rm eff}$ is the only fit parameter at this stage.
• We make the assumption that the observed fluxes for the smallest wavelengths are expected to be mostly due to the hotter object and fluxes for the largest wavelengths will be due mostly to the coldest object.
• With this we make a first estimation of the best fit temperatures for the two objects and the propocionality factor $r_f$.
• Estimation refine
• Then we refine this estimation iteratively, checking for parameter values around the previous best ones.
• When we see that the value of $\chi^2$ does not improve much, we stop and go to the next step.
• Final fit loop.
• We start with the parameter values ($T_{\rm eff 1}$, $T_{\rm eff 2}$ and $r_f$) found in the previous step, but now we will use the thoretical models choosen by you.
• In this loop all the model parameters are fitted (not only the effective temperature).
• We iteratively try parameter values around the best ones of the previous step, trying to decrease the $\chi^2$ value.
• The loop ends when a local minimum is reached and $\chi^2$ does not decrease anymore (or the improvement is so small that it is not worth the computation time).

### Extinction.

Please, take into account that, in the binary fit $A_v$ will NOT be considered as a fit parameter by default. That is, the observed SED will be deredenned using the chosen value of $A_v$ for each object (if any) but only that value will be used for the fit. Even if you have set a $A_v$ range for the chi-square one model fit.

So, please, be sure that you have set the value that you want for $A_v$. You can do it (or check it) in the extinction tab. The value under "Final: Av" will be used, no mather what is set in the Av range. That is, for the object in the image $A_v = 1$ will be used to dereden de SED before making the fit. If you really need to fit $A_v$ in the given range, you have the option to do it at the bottom of the form. But take into account that the fit process will be much slower and it could overload VOSA. So, please, use this option only if you really need it and for files with few objects.

### Example.

In preparation. Templates Bayes HR diagram 