snprop

Type Ia supernova underlying population distribution modelling.

Installation

git clone https://github.com/MickaelRigault/snprop.git
cd snprop
python setup.py install

Concept

The package is made to generate random sample realisation of SN sample as they are in nature (i.e. prior selection function). Conceptually, SNe Ia are assumed to be sample mixture of underlying populations that each have their own intrinsic distribution of properties. These may be redshift dependent as well as the mixture composition.

Currently, only the Prompt and Delayed dichotomy has been implemented based on Rigault et al. 2018 and Nicolas et al. 2O20. [dev] implementation of the Survey based asymetric gaussian distribution, a la Scolnic & Kessler 2017.

Underlying distributions of SN properties such as stretch, color or host mass have been modelled for both prompt and delayed populations. Gaussian, Gaussian mixture or asymetric Gaussians are currently used for this modelling and default distribution parameters are provided. One can then draw random sample realisations assuming a fraction of prompt SNeIa. This way the underlying correlation between all the SN properties are accurately handled, assuming they as solely due to their correlation with the age population.

Current limits

The prompt and delayed modeling of the host mass step is not satisfying yet:

It is not redshift dependent while it must
Even at z~0 it is not great yet.

Usage

Loading a PromptDelayModel instance

Load an instance of the prompt and delayed object (PrompDelayModel)

from snprop import age
pdmodel = age.PrompDelayModel()

Draw a random SN sample.

Then to draw a random realisation of a sample of 200 SNeIa, at z=0.4, simply do:

pdmodel.draw_sample(0.4, size=200)

the sample is stored as a pandas datafraom in pdmodel.sample

print(pdmodel.sample)
|     |        color |    stretch |   age |     mass |          hr |   z |,
|----:|-------------:|-----------:|------:|---------:|------------:|----:|,
|   0 | -0.0666667   |  1.20621   |     1 | 10.9329  | -0.125125   | 0.4 |,
|   1 | -0.063964    |  1.54655   |     1 |  9.47548 |  0.0950951  | 0.4 |,
|   2 |  0.0612613   |  0.525526  |     1 |  9.73473 | -0.047047   | 0.4 |,
...
| 197 |  0.0234234   |  1.07608   |     0 | 11.1782  | -0.0710711  | 0.4 |,
| 198 |  0.0342342   |  1.03604   |     0 | 10.2392  |  0.023023   | 0.4 |,
| 199 |  0.0603604   | -0.195195  |     0 | 10.7227  | -0.0830831  | 0.4 |

You can also provide a list of redshift as z and size would be the number of draw per redshift element, i.e.:

pdmodel.draw_sample(z=np.linspace(0.001,0.5, 100), size=2)

pdmodel.sample

|     |        color |     stretch |   age |     mass |          hr |         z |,
|----:|-------------:|------------:|------:|---------:|------------:|----------:|,
|   0 | -0.0513514   | -0.435435   |     0 | 10.6106  | -0.209209   | 0.001     |,
|   1 |  0.0306306   | -0.035035   |     0 | 11.3253  | -0.035035   | 0.001     |,
|   2 | -0.0918919   |  0.385385   |     0 | 11.2272  | -0.127127   | 0.0060404 |,
|   3 |  0.0774775   |  0.895896   |     0 |  9.86086 | -0.189189   | 0.0060404 |,
|   4 |  0.0135135   |  0.365365   |     1 |  9.29329 |  0.037037   | 0.0110808 |,
...
| 195 | -0.0558559   | -0.805806   |     0 | 10.0991  |  0.0530531  | 0.489919  |,
| 196 |  0.0315315   |  0.865866   |     1 |  9.58759 | -0.0510511  | 0.49496   |,
| 197 | -0.0333333   |  0.895896   |     1 | 10.1271  |  0.003003   | 0.49496   |,
| 198 | -0.0351351   |  0.415415   |     1 |  8.93594 | -0.049049   | 0.5       |,
| 199 | -0.0747748   | -1.62663    |     0 | 10.2603  |  0.003003   | 0.5       |

How is the sample built ?

First, the SN ages are randomly drawn following the underlying probability of young (1) and old (0) SNe Ia at a given redshift. Then for each age (1 or 0) the SN parameters are randomly drawn following the underlying distribution associated to this age population.

Fraction of prompt as a function of redshift.

pdmodel has a method deltaz(z) that returns the fraction of prompt at the given z ; z can by a list/array. This is what is used by pdmodel.show_pdf()

Draw a subsample

Let's imagine you only to randomly draw 140 targets from the sample you previously constructed, simply do:

sub_dataframe = pdmodel.get_subsample(140)

Now, if you want to get a subsample that follows a given distribution a parameter, e.g. a mass normally distributed at 10^10 with a dispersion of 0.2 dex:

from scipy import stats
index_pdf = stats.norm.pdf(pdmodel.sample["mass"], loc=10, scale=0.2)
weightedsub_dataframe = pdmodel.get_subsample(140, index_pdf=index_pdf)

Remark about weighted draw

If you parameters used to weight the indexes is non-trivially connected to the age parameters, then the fraction of young/old (1/0) will be changed in the subsample, thus so are the SN properties connected to age, like the stretch.

Parameter distributions

To vizualise the underlying distribution of say, stretch, at z=0.05, z=0.5 and z=1 (the color is the redshift (blue to red) up to, in that case, zmax=1.

fig = pdmodel.show_pdf("stretch", z=[0.05, 0.5, 1], zmax=1)

Change the underlying population properties

The pdmodel install has all the set_distprop_{which} methods where which is any of the SN property. Change that to change the modeling.

Parameter correlations

If two parameters are non-trivially connected to age, they will be correlated. To visualise the correlation between two SN properties, say e.g. stretch and mass:

fig = pdmodel.show_scatter("mass","stretch", colorkey="age")