Make a theta-square plot

This tutorial explains how to make such a plot, that is the distribution of event counts as a function of the squared angular distance, to a test position.

Setup

# %matplotlib inline
import matplotlib.pyplot as plt
from astropy.coordinates import SkyCoord
from astropy import units as u
from gammapy.data import DataStore
from gammapy.maps import MapAxis
from gammapy.makers.utils import make_theta_squared_table
from gammapy.visualization import plot_theta_squared_table

Get some data

Some data taken on the Crab by H.E.S.S. are used.

data_store = DataStore.from_dir("$GAMMAPY_DATA/hess-dl3-dr1")
observations = data_store.get_observations([23523, 23526])

Define a test position

Here we define the position of Crab

position = SkyCoord(83.6324, 22.0174, unit="deg")
print(position)

<SkyCoord (ICRS): (ra, dec) in deg
    (83.6324, 22.0174)>

Creation of the theta2 plot

theta2_axis = MapAxis.from_bounds(0, 0.2, nbin=20, interp="lin", unit="deg2")
theta2_table = make_theta_squared_table(
    observations=observations,
    position=position,
    theta_squared_axis=theta2_axis,
)

plt.figure(figsize=(10, 5))
plot_theta_squared_table(theta2_table)
plt.show()

Making a theta2 plot for a given energy range

with the function make_theta_squared_table, one can also select a fixed energy range.

theta2_table_en = make_theta_squared_table(
    observations=observations,
    position=position,
    theta_squared_axis=theta2_axis,
    energy_edges=[1.2, 11] * u.TeV,
)
plt.figure(figsize=(10, 5))
plot_theta_squared_table(theta2_table_en)
plt.show()

Statistical significance of a detection

To get the significance of a signal, the usual method consists of using the reflected background method (see the maker tutorial: Reflected regions background) to compute the WStat statistics (see WStat : Poisson data with background measurement, Fit statistics). This is the well-known method of [LiMa1983] using ON and OFF regions.

The following tutorials show how to get an excess significance:

• Spectral analysis

• Spectral analysis of extended sources