## Method description

This page describe the tools availables on this web interface. Any details on this methode can be found in (Ducoin et al.).

### Standard galaxies ranking

##### This version of the ranking can be retrieve here

In case of a gravitational wave event, LIGO-Virgo rapidly releases a probability skymap based on the distance and two dimensional localisation of the event allowing to constrain the region of the sky to search for the GW electromagnetic counterpart (Singer & Price 2016). With such skymap we are able to fetch the probability density per unit of volume at a given position. This is used to infer the probability of a given galaxy to be the host of the merger according to its celestial position P_{pos} with the following relation:

P_{pos} = P_{2D} \: N_{dist}\: e^{- \frac{1}{2} \left( \frac{D_{galaxy}-\mu_{dist}}{\sigma_{dist}} \right)^2}

Where P_{2D} is the 2D probability at the position of the galaxy, N_{dist} is the normalisation factor for the given position of the galaxy, \mu_{dist} is the mean distance value at the given position of the galaxy, \sigma_{dist} is the standard deviation at the given position of the galaxy and D_{galaxy} is the luminosity distance of the galaxy fetched from the galaxy catalog. For the selection of the galaxies, we classified as "compatible" with the skymap, a galaxy which fulfills the two following conditions:

• Its 2D position in the sky as to be in the 90% of the 2D skymap probability distribution.
• Its distance has to fall within the 3 sigma distance error localization at the given position of the galaxy.

• With such conditions we ensure that telescopes will not point outside of the 90% skymap probability distribution. Knowing the galaxies compatible we can rank them in decreasingP_{pos} to produce the list.

### Adding galaxies stellar mass for ranking

##### This version of the ranking can be retrieve here

More details on this methode can be found in (Ducoin et al.).

We matched AllWISE catalog to the GLADE catalog to fetch the WISE1 (3.4\mu m) luminosity of the galaxies. From this luminosity, using a constant mass to light ratio \Upsilon_{*}^{3.4\mu m} \sim 0.60 M_{\odot}/L_{\odot,3.4\mu m} we are able to determine trustfully the stellar mass M_{*,galaxy} of the galaxies. From this stellar mass we can define a new factor to use in our selection:

P_{mass} = \frac{M_{*,galaxy}}{\sum{M_{*,galaxy}}}

And the final ranking will use total probability defined as:
P_{tot} = P_{pos} \thinspace (1 + \alpha P_{mass})

Where P_{pos} is defined as above and \alpha is define in such way that in mean the two factor in the addition contribute equally:

\frac{\sum{P_{pos}}}{N} = \frac{\sum{P_{pos}\thinspace \alpha \thinspace P_{mass}}}{N}

\Rightarrow \alpha = \frac{\sum{P_{pos}}}{\sum{P_{pos} \thinspace P_{mass}}}

Again knowing the galaxies compatible we can rank them in decreasing P_{tot} to produce the list.

### Retriev a galaxy list according to your telescope location

You can find here tools to get a galaxy list, ranked according to one of the probabilities described above, that are observable from your telescope location and a the time of your observations. The details of the definition of "observable" can be found here