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# ELAIS-N2: Validation Report (FULL)

ELAIS-N2: Validation Report (FULL)

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Master catalogue used: __master_catalogue_elais-n2_20180201.fits__<br>
Number of rows: 4,026,292
<br>
Surveys included:<br>
| Survey     | Telescope / Instrument      |      Filters (detection band in bold)      | Location                    |
|------------|-----------------------------|:------------------------------------------:|-----------------------------|
| INT/WFC    | Isaac Newton Telescope/Wide Field Camera | ugriz                         | dmu0_INTWFC                 |
| PS1 3PSS   | Pan-STARRS1                 | grizy                                      | dmu0_PanSTARRS1-3SS         |
| RCSLenS    | CFHT/MegaPrime/MegaCam      | grizy                                      | dmu0_RCSLenS                | 
| SpARCS     | CFHT/MegaCam                | ugrzy                                      | dmu0_SpARCS                 | 
| SWIRE      | Spitzer/IRAC MIPS           | IRAC1234                                   | dmu0_DataFusion-Spitzer     | 

Master catalogue used: master_catalogue_elais-n2_20180201.fits
Number of rows: 4,026,292
Surveys included:

Survey Telescope / Instrument Filters (detection band in bold) Location
INT/WFC Isaac Newton Telescope/Wide Field Camera ugriz dmu0_INTWFC
PS1 3PSS Pan-STARRS1 grizy dmu0_PanSTARRS1-3SS
RCSLenS CFHT/MegaPrime/MegaCam grizy dmu0_RCSLenS
SpARCS CFHT/MegaCam ugrzy dmu0_SpARCS
SWIRE Spitzer/IRAC MIPS IRAC1234 dmu0_DataFusion-Spitzer
 
## I. Caveats

I. Caveats

 
### I.a. Magnitude errors 

I.a. Magnitude errors

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At faint magnitudes (mag > 24), some surveys have very large errors on the magnitude. These objects may be unreliable for science puposes.<br>
This includes __CFHT aperture and total__ magnitudes (at mag > 29) and __PanSTARRS aperture and total__ magnitudes (at mag > 24). <br>
<img src="help_plots/ELAIS-N2_magVSmagerr_Megacam_u_mag_total.png" />

At faint magnitudes (mag > 24), some surveys have very large errors on the magnitude. These objects may be unreliable for science puposes.
This includes CFHT aperture and total magnitudes (at mag > 29) and PanSTARRS aperture and total magnitudes (at mag > 24).

 
### I.b. Aperture corrections

I.b. Aperture corrections

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In most of the case when comparing the aperture magnitudes between surveys, we observed a two peak distribution in the difference between the magnitudes ($\Delta_{mag} = mag_{survey1} - mag_{survey2}$). We have one peak around 0 for point-source objects, with a small spread. And a second peak at higher $\Delta_{mag}$ with a larger spread for extended objects; implying a different aperture correction between surveys for these objects.<br>
That means that galaxies will not have the same aperture magnitude in different surveys. <br>
In the ugriz bands, for bright sources, there is a two peaks distribution when comparing CHFT, INT, and Pan-STARRS.
<img src="help_plots/ELAIS-N2_apcorrIssues_WFC_r_aperture_-_GPC1_r_aperture.png" />

In most of the case when comparing the aperture magnitudes between surveys, we observed a two peak distribution in the difference between the magnitudes (Δmag=magsurvey1magsurvey2). We have one peak around 0 for point-source objects, with a small spread. And a second peak at higher Δmag with a larger spread for extended objects; implying a different aperture correction between surveys for these objects.
That means that galaxies will not have the same aperture magnitude in different surveys.

In the ugriz bands, for bright sources, there is a two peaks distribution when comparing CHFT, INT, and Pan-STARRS.

 
## II. Flags

II. Flags

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### II.a. Pan-STARRS aperture magnitude
Few Pan-STARRS sources have exactly the same error (of <font color='blue'>0.0010860000038519502</font>) on the __aperture and total__ magnitudes in all the grizy bands. The corresponding aperture magnitude should not be trusted for these objects.<br>
<img src="help_plots/ELAIS-N2_gpc1Issues_GPC1_g_mag_aperture.png" />

II.a. Pan-STARRS aperture magnitude

Few Pan-STARRS sources have exactly the same error (of 0.0010860000038519502) on the aperture and total magnitudes in all the grizy bands. The corresponding aperture magnitude should not be trusted for these objects.

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### II.c IRAC aperture magnitude
Few IRAC sources have exactly the same aperture magnitude (of <font color='blue'>3.9000000001085695</font>) in the IRAC1 and IRAC2 bands. These magnitudes also have extremely small errors (around 10$^{-8}$-10$^{-9}$). The corresponding magnitudes should not be trusted. <br>
<img src="help_plots/ELAIS-N2_iracIssues_i1_i2.png" />

II.c IRAC aperture magnitude

Few IRAC sources have exactly the same aperture magnitude (of 3.9000000001085695) in the IRAC1 and IRAC2 bands. These magnitudes also have extremely small errors (around 108-109). The corresponding magnitudes should not be trusted.

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### II.b. Outliers
By comparing magnitude in the same band between different surveys, we can see that some magnitudes are significanlty different could not be trusted. <br>
The outliers are identified to have a large weighted magnitude difference (equivalent of the $chi^2$).
$$chi^2 = \frac{(mag_{1}-mag_{2})^2}{magerr_{1}^2 + magerr_{2}^2}$$ 
<br>
We used the 75th and 25th percentile to flagged the objects 5$\sigma$ away on the large values tail of the $chi^2$ ditribution. (__NB:__ bright sources tend to have their errors underestimated with values as low as $10^{-6}$, which is unrealistic. So to avoid high $chi^2$ due to unrealistic small errors, we clip the error to get a minimum value of 0.1% (i.e. all errors smaller then $10^{-3}$ are set to $10^{-3}$).)
<br><br>
$$outliers == [chi^2 >  (75th \;percentile + 3.2\times (75th \;percentile - 25th \;percentile))]$$
<img src="help_plots/ELAIS-N2_outliers_Megacam_g_total_-_GPC1_g_total.png"/>

II.b. Outliers

By comparing magnitude in the same band between different surveys, we can see that some magnitudes are significanlty different could not be trusted.
The outliers are identified to have a large weighted magnitude difference (equivalent of the chi2).

chi2=(mag1mag2)2magerr12+magerr22

We used the 75th and 25th percentile to flagged the objects 5σ away on the large values tail of the chi2 ditribution. (NB: bright sources tend to have their errors underestimated with values as low as 106, which is unrealistic. So to avoid high chi2 due to unrealistic small errors, we clip the error to get a minimum value of 0.1% (i.e. all errors smaller then 103 are set to 103).)

outliers==[chi2>(75thpercentile+3.2×(75thpercentile25thpercentile))]

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