## VOSA. Help and Documentation

### Version 7.5, July 2022

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 5.6. 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 11.3. Binary Fit Quality
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

## Total flux calculation example

We want to to calculate the total "observed flux" using the photometric values corresponding to different filters.

But we have observed photometric values corresponding to filters covering wavelength ranges that, often, overlap with each other.

We want to:

• First, discover what filters are overlaping with each other.
• Define wavelength regions with apreciable overlaping.
• Estimate the amount of overlaping in each of those regions.
• Estimate the total observed flux, suming up the contribution of each observation but weighted by the amount of overlaping in the corresponding region.

With this purpose:

1. we use the filter effective width as an estimation of the wavelength range covered by each filter.

 lambda width start end flux error 3447 372 3261 3633 1.87e-12 2.33e-14 3570 657 3242 3899 5.98e-12 8.15e-13 4110 223 3998 4222 8.70e-12 5.40e-14 4280 708 3925 4634 9.48e-12 8.44e-14 4297 843 3875 4718 1.00e-11 7.33e-13 4378 972 3891 4864 9.77e-12 1.50e-12 4640 1158 4061 5219 9.60e-12 4.78e-14 4663 202 4562 4764 1.06e-11 2.50e-14 5340 1005 4837 5842 9.38e-12 6.66e-14 5394 870 4959 5829 7.31e-12 1.50e-13 5466 889 5021 5910 8.30e-12 1.44e-12 5472 253 5345 5599 8.63e-12 1.57e-14 5857 4203 3755 7959 6.89e-12 1.23e-12 6122 1111 5566 6677 5.79e-12 1.99e-13 7439 1044 6917 7961 4.60e-12 6.02e-13 12350 1624 11537 13162 1.51e-12 2.45e-14 16620 2509 15365 17874 6.85e-13 1.34e-14 21590 2618 20280 22899 2.66e-13 4.19e-15 33526 6626 30212 36839 4.73e-14 5.03e-15 46028 10422 40816 51239 1.66e-14 8.67e-16 82283 41027 61769 102797 1.50e-15 2.92e-17 101464 60670 71129 131799 7.88e-16 9.19e-17 115608 55055 88080 143135 3.91e-16 5.28e-18 217265 100173 167178 267352 6.24e-17 1.48e-17 220883 41016 200374 241391 3.25e-17 1.19e-18 519887 305160 367307 672467 1.29e-17 2.96e-18 952971 332639 786651 1119290 4.52e-17 1.04e-17

2. Using this, we find the regions where we have continuous filter coverage.

To do this, we define different regions when the last filter in one region ends before the starting point of the first filter in the following region.

In this case, we find 10 different regions:

• 7 of them contain only one filter and they can be considered "simple regions" with no overlaping.
• 3 of them contain 2 or more overlaping filters.

We see, with more detail, the three complex regions containing more than one overlaping filters:

 lambda width start end flux error 3447 372 3261 3633 1.87e-12 2.33e-14 3570 657 3242 3899 5.98e-12 8.15e-13 4110 223 3998 4222 8.70e-12 5.40e-14 4280 708 3925 4634 9.48e-12 8.44e-14 4297 843 3875 4718 1.00e-11 7.33e-13 4378 972 3891 4864 9.77e-12 1.50e-12 4640 1158 4061 5219 9.60e-12 4.78e-14 4663 202 4562 4764 1.06e-11 2.50e-14 5340 1005 4837 5842 9.38e-12 6.66e-14 5394 870 4959 5829 7.31e-12 1.50e-13 5466 889 5021 5910 8.30e-12 1.44e-12 5472 253 5345 5599 8.63e-12 1.57e-14 5857 4203 3755 7959 6.89e-12 1.23e-12 6122 1111 5566 6677 5.79e-12 1.99e-13 7439 1044 6917 7961 4.60e-12 6.02e-13

 lambda width start end flux error 82283 41027 61769 102797 1.50e-15 2.92e-17 101464 60670 71129 131799 7.88e-16 9.19e-17 115608 55055 88080 143135 3.91e-16 5.28e-18

 lambda width start end flux error 217265 100173 167178 267352 6.24e-17 1.48e-17 220883 41016 200374 241391 3.25e-17 1.19e-18
3. For each region, we define the amount of overlaping as the ratio between the sum of lengths of the filters in the region and the lenght of the region. $${\rm over} = \frac{\sum {\rm W}_i}{\rm (\lambda_{\rm max} - \lambda_{\rm min})}$$

Regions:

 nreg tot $\lambda_{min}$ $\lambda_{max}$ len $\sum W_i$ over 0 15 3242 7961 4719 14516 3.076 1 1 11537 13162 1624 1624 1.000 2 1 15365 17874 2509 2509 1.000 3 1 20280 22899 2618 2618 1.000 4 1 30212 36839 6626 6626 1.000 5 1 40816 51239 10422 10422 1.000 6 3 61769 143135 81365 156753 1.927 7 2 167178 267352 100173 141190 1.409 8 1 367307 672467 305160 305160 1.000 9 1 786651 1119290 332639 332639 1.000

4. Then, to calculate the total observed flux, we have to weight the contribution from each observed photometric point, dividing it by the amount of overlaping in the correponding region. $${\rm Fobs} = \frac{\sum {\rm F_{o,i}} \cdot {\rm W_{eff,i}}}{ {\rm Over_i}}$$

We also do the equivalent calculation for the model fluxes corresponding to the observations: $${\rm Fmod} = \frac{\sum {\rm Md \cdot F_{M,i}} \cdot {\rm W_{eff,i}}}{ {\rm Over_i}}$$

The total flux is the total flux of the model plus the estimated observed flux minus the estimated model flux corresponding to the observations: $${\rm Ftot} = \int{\rm Md \cdot mod(\lambda) \ d\lambda} \ + {\rm Fobs} - {\rm Fmod}$$

In this particular case, we have:

• Kurucz model
• Teff = 6250 K
• logg = 0.50
• meta = 0.50
• Md=6.239e-18
$$\int{\rm Md \cdot mod(\lambda) \ d\lambda} = 5.22 \ 10^{-8}$$
5. If we make the calculations filter by filter, we get very different results if we take into account the overlaping.

The partial numbers for each filter are:

 lambda width start end reg over flux error mod*md w*flx w*flx/over w*mod*md w*mod*md/over 3447 372 3261 3633 0 3.076 1.87e-12 2.33e-14 2.20e-12 6.98e-10 2.27e-10 8.20e-10 2.67e-10 3570 657 3242 3899 0 3.076 5.98e-12 8.15e-13 3.07e-12 3.93e-9 1.28e-9 2.02e-9 6.56e-10 4110 223 3998 4222 0 3.076 8.70e-12 5.40e-14 8.84e-12 1.95e-9 6.33e-10 1.98e-9 6.44e-10 4280 708 3925 4634 0 3.076 9.48e-12 8.44e-14 8.59e-12 6.72e-9 2.18e-9 6.08e-9 1.98e-9 4297 843 3875 4718 0 3.076 1.00e-11 7.33e-13 9.11e-12 8.45e-9 2.75e-9 7.68e-9 2.50e-9 4378 972 3891 4864 0 3.076 9.77e-12 1.50e-12 9.24e-12 9.50e-9 3.09e-9 8.99e-9 2.92e-9 4640 1158 4061 5219 0 3.076 9.60e-12 4.78e-14 9.58e-12 1.11e-8 3.62e-9 1.11e-8 3.61e-9 4663 202 4562 4764 0 3.076 1.06e-11 2.50e-14 1.05e-11 2.15e-9 6.98e-10 2.12e-9 6.90e-10 5340 1005 4837 5842 0 3.076 9.38e-12 6.66e-14 8.96e-12 9.43e-9 3.07e-9 9.01e-9 2.93e-9 5394 870 4959 5829 0 3.076 7.31e-12 1.50e-13 8.68e-12 6.37e-9 2.07e-9 7.56e-9 2.46e-9 5466 889 5021 5910 0 3.076 8.30e-12 1.44e-12 8.51e-12 7.38e-9 2.40e-9 7.58e-9 2.46e-9 5472 253 5345 5599 0 3.076 8.63e-12 1.57e-14 8.65e-12 2.19e-9 7.11e-10 2.19e-9 7.13e-10 5857 4203 3755 7959 0 3.076 6.89e-12 1.23e-12 6.40e-12 2.90e-8 9.42e-9 2.69e-8 8.75e-9 6122 1111 5566 6677 0 3.076 5.79e-12 1.99e-13 7.29e-12 6.43e-9 2.09e-9 8.10e-9 2.63e-9 7439 1044 6917 7961 0 3.076 4.60e-12 6.02e-13 4.98e-12 4.80e-9 1.56e-9 5.20e-9 1.69e-9 12350 1624 11537 13162 1 1.000 1.51e-12 2.45e-14 1.57e-12 2.45e-9 2.45e-9 2.55e-9 2.55e-9 16620 2509 15365 17874 2 1.000 6.85e-13 1.34e-14 6.74e-13 1.72e-9 1.72e-9 1.69e-9 1.69e-9 21590 2618 20280 22899 3 1.000 2.66e-13 4.19e-15 2.63e-13 6.98e-10 6.98e-10 6.90e-10 6.90e-10 33526 6626 30212 36839 4 1.000 4.73e-14 5.03e-15 5.26e-14 3.13e-10 3.13e-10 3.48e-10 3.48e-10 46028 10422 40816 51239 5 1.000 1.66e-14 8.67e-16 1.57e-14 1.73e-10 1.73e-10 1.64e-10 1.64e-10 82283 41027 61769 102797 6 1.927 1.50e-15 2.92e-17 1.37e-15 6.17e-11 3.20e-11 5.64e-11 2.93e-11 101464 60670 71129 131799 6 1.927 7.88e-16 9.19e-17 5.85e-16 4.78e-11 2.48e-11 3.55e-11 1.84e-11 115608 55055 88080 143135 6 1.927 3.91e-16 5.28e-18 4.25e-16 2.15e-11 1.12e-11 2.34e-11 1.21e-11 217265 100173 167178 267352 7 1.409 6.24e-17 1.48e-17 2.96e-17 6.25e-12 4.43e-12 2.96e-12 2.10e-12 220883 41016 200374 241391 7 1.409 3.25e-17 1.19e-18 3.20e-17 1.33e-12 9.47e-13 1.31e-12 9.31e-13 519887 305160 367307 672467 8 1.000 1.29e-17 2.96e-18 8.03e-19 3.93e-12 3.93e-12 2.45e-13 2.45e-13 952971 332639 786651 1119290 9 1.000 4.52e-17 1.04e-17 8.50e-20 1.51e-11 1.51e-11 2.83e-14 2.83e-14

And the corresponding sums, region by region are:

 reg Σ w*flx Σ w*mod*md Σ w*flx/over Σ w*mod*md/over 0 1.1e-7 1.07e-7 3.58e-8 3.49e-8 1 2.45e-9 2.55e-9 2.45e-9 2.55e-9 2 1.72e-9 1.69e-9 1.72e-9 1.69e-9 3 6.98e-10 6.9e-10 6.98e-10 6.9e-10 4 3.13e-10 3.48e-10 3.13e-10 3.48e-10 5 1.73e-10 1.64e-10 1.73e-10 1.64e-10 6 1.31e-10 1.15e-10 6.8e-11 5.98e-11 7 7.58e-12 4.27e-12 5.38e-12 3.03e-12 8 3.93e-12 2.45e-13 3.93e-12 2.45e-13 9 1.51e-11 2.83e-14 1.51e-11 2.83e-14 Σ 1.16e-7 1.13e-7 4.12e-8 4.04e-8 Ftot 5.49e-8 5.3e-8 Fobs 1.16e-7 4.12e-8 Fobs/Ftot 2.11 0.778

In the last lines we see the final results, first without taking overlaping into account and then considering it.

We see that Ftot (the total flux) is not very dependent of the method because the effect of the overlapping is similar in the observed and model contributions and they, mostly, cancel each other.

But the total observed flux (and thus the Fobs/Ftot ratio) changes dramatically.

Actually, the value obtained when we don't take overlaping into account (2.11) is clearly incorrect.

The value obtained estimating the overlaping with this method, 0.778, is much more trustable.