# Galaxy-classified Supernovae in the SDSS-II Supernova Sample

## Description of the sample

### * Galaxy data

We will use four different host galaxy observables as parameters in the galsnid method: morphology, the $$B_{0}-K$$ color, $$K$$-band magnitude, and the dimensionless offset of SN relative to the nucleus $$R$$.

Given its host galaxy property, the posterior probability that a supernova is of type Ia is:

$$P(Ia|\vec{D})=k^{-1}P(Ia)\prod_{i\in O}P(D_{i}|Ia)\\$$

where k is defined as:

$$k=P(Ia)\prod_{i\in O}P(D_{i}|Ia)+\big{(}1-P(Ia)\big{)}\prod_{i\in O}P(D_{i}|CC)\\$$

and $$O$$ is a set of observables we wish to consider in the model. We will use $$O=\big{\{}morphology,\ (B_{0}-K)\ color,K\ band\ magnitude,distance\ modulus\big{\}}$$.

$$P(x|Ia)$$ is the probability density for a particular value of observable x for the host galaxy, given Supernova type, and $$P(Ia)$$ is the probability density of type Ia supernova for the an unbiased set of sample(also referred to as the prior probability).

(1) & (2) yields

$$P(Ia|D)=\bigg{[}1+\frac{1-P(Ia)}{P(Ia)}\Omega(D)\bigg{]}^{-1}\\$$

where $$\Omega(D)=\prod_{i\in O}\frac{P(D_{i}|Ia)}{P(D_{i}|CC)}$$ encodes information of observable $$i$$ could provide for calculating the posterior probability.

Among the 4 galaxy properties, we obtained the effective offset $$R$$ from the SDSS DR12 database, color($$B_{0}-K$$) and $$K$$-band magnitude using SED fitting to the Photometric data in the SDSS DR12 database. To acquire the morphology data for host galaxies, we needed to scrutinize SDSS images available in the SDSS DR12 database.

## Galaxy Morphology Classification

Among the 4 host galaxy properties we will be using to test galsnid, morphology provides the most discriminating information. To acquire such data, the most straight forward way is to examine each of these galaxies and assign a morphology class to it.

### Web interface

A webpage that functions very much alike that of the Galaxy Zoo project was built to fulfill such purpose. Image of individual galaxy would be presented for people to classify, and the classifications made by different people was stored in the database.

Images of galaxies on the webpage are drawn directly from the SDSS Data Release 12 using the ImgCutout service, and presented in gray-scale to avoid the possible bias due to the well-known correlation between the color of the galaxy and its Hubble type.

The complete set of galaxies being classified consists of three sub-samples: (1) the sample of interest (3800 host galaxies in the SN sample), (2) the control sample that contains all of the galaxies in galaxy zoo sample within stripe 82 region(2835 galaxies) and (3) all galaxies from the KAIT sample that lie in the Data Release 12 footstep. These three samples make up the complete sample with 7224 galaxies.