# X-ray Tutorial Module¶

Lecturer: Dipankar Bhattacharya
Jupyter Notebook Author: Dipankar Bhattacharya & Cameron Hummels

This is a Jupyter notebook lesson taken from the GROWTH Winter School 2018. For other lessons and their accompanying lectures, please see: http://growth.caltech.edu/growth-astro-school-2018-resources.html

## Objective¶

Learn how to analyze x-ray data

## Key steps¶

• Search for gamma-ray bursts in CZTI data

## Required dependencies¶

See GROWTH school webpage for detailed instructions on how to install these modules and packages. Nominally, you should be able to install the python modules with pip install <module>. The external astromatic packages are easiest installed using package managers (e.g., rpm, apt-get).

• python 3
• astropy
• numpy
• scipy
• matplotlib

### External packages¶

None.

In [1]:
from astropy.io import fits
import numpy as np
import matplotlib.pyplot as plt
import math
import scipy as sc
import os


# Load event file with astropy¶

Provide the path to the czti events file in the same format as given in the example below.

In [2]:
filename = os.path.join('data', 'AS1A02_005T01_9000000948_06884cztM0_level2_common_clean.evt')

dataHDU = fits.open(filename)


### Combine data from all quadrants¶

CZTI contains four quadrants, here we obtain the time value for each quadrant and combine the data for them.

In [3]:
times = np.concatenate((dataHDU[1].data['Time'], dataHDU[2].data['Time'],
dataHDU[3].data['Time'], dataHDU[4].data['Time']))


### Make histogram and plot light curve¶

Setting binsize for each interval and accumulate counts in each of them using histogram and plotting it.

In [4]:
# Define timebins
binsize = 5
tbins = np.arange(times.min(), times.max(), binsize)

# Make histogoram
counts, bins = np.histogram(times, bins=tbins)
bins = (bins[1:] + bins[:-1])/2

# Plot
plt.plot(bins, counts/binsize, ls='steps-mid')
plt.xlabel('Time (s)')
plt.ylabel('$counts\ s^{-1}$')

Out[4]:
Text(0,0.5,'$counts\\ s^{-1}$')

# Searching for GRB in Data¶

By zooming in or trimming a portion of the data, we are looking for any possibility of GRB. Here you can play with binsize value and mark the difference.

In [5]:
binsize =0.5 # try binsize=1
tbins = np.arange(221292750.0, 221292870.0, binsize)

counts, bins = np.histogram(times, bins=tbins)
bins = (bins[1:] + bins[:-1])/2

plt.plot(bins, counts/binsize, ls='steps-mid')
plt.xlabel('Time (s)')
plt.ylabel('$counts\ s^{-1}$')

Out[5]:
Text(0,0.5,'$counts\\ s^{-1}$')

The sharp peak observed here accounts for the observed GRB. Change the binsize to 1, to see the shoulder of the GRB.

# Reading event file, gti file,response file¶

We need following files for this tutorial:
1) A LAXPC events file without bary correction.
2) An event file with bary correction.
3) A GTI file (which contains the good time start and stop time values).
4) A response file.
The files can be open in the same format as described in the example below.
GTI = Good Time Interval

In [6]:
fevents=fits.open("data/ObsID406_02741_event.fits")
fevents_bary=fits.open("data/ObsID406_02741_laxpc_bary.fits")
fgti=fits.open('data/ObsID406_02741_laxpc1_bary.gti')
fresponse=fits.open('data/lx10_17aug16.rmf')


# Some information about fits file¶

From the files we can obtain informations like the length, header etc.

In [7]:
#len(fevent_bary)


# Change in time after bary correction¶

Observe the time difference between the data from the event file and bary correction file.

In [8]:
time=fevents[1].data['TIME']
time_bary=fevents_bary[1].data['TIME']
time_diff=time[0]- time_bary[0]
time_diff

Out[8]:
73.24125623703003

# Lightcurve without GTI¶

Plot the light curve without applying gti cuts. This plot will consist of both gti(good time interval) data as well as bti (bad time interval) data. We can compare the two light curves obtained before and after applying gti cuts.

In [9]:
# Define timebins
binsize = 1
tbins = np.arange(time_bary.min(), time_bary.max(), binsize)

# Make histogoram
counts_time, t_bins = np.histogram(time_bary, bins=tbins)
t_bins = (t_bins[1:] + t_bins[:-1])/2

# Plot
plt.plot(t_bins, counts_time/binsize, ls='steps-mid')
plt.xlabel('Time (s)')
plt.ylabel('$counts\ s^{-1}$')

Out[9]:
Text(0,0.5,'$counts\\ s^{-1}$')

# applying GTI¶

Read and filter event file to keep in array only events within the good time interval.

In [10]:
gtidata=fgti[1].data
t_start=gtidata[0][0],gtidata[1][0]
t_stop=gtidata[0][1],gtidata[1][1]
t_start, t_stop

Out[10]:
((197099975.0, 197105810.0), (197103300.0, 197106645.0))

Here we compare the lenght of the event file and the gti file.

In [11]:
eventsdata=fevents_bary[1].data
for i in range(len(t_start)) :
time_gti = time_bary[np.where((time_bary>=t_start[i]) & (time_bary<=t_stop[i]))]
len(time_bary), len(time_gti)

Out[11]:
(13614384, 2550273)

# lightcurve after applying GTI¶

Here we plot the light curve only taking time values falling in the gti range. We can compare this plot with the plot before applying gti cuts.

In [12]:
# Define timebins
binsize = 1
tbins = np.arange(time_gti.min(), time_gti.max(), binsize)

# Make histogoram
counts_time, t_bins = np.histogram(time_gti, bins=tbins)
t_bins = (t_bins[1:] + t_bins[:-1])/2

# Plot
plt.plot(t_bins, counts_time/binsize, ls='steps-mid')
plt.xlabel('Time (s)')
plt.ylabel('$counts\ s^{-1}$')

Out[12]:
Text(0,0.5,'$counts\\ s^{-1}$')

# Calculating Phase and folding¶

1) From filtered events calculate the phase array using the expression and constants provided.
2) Create the histogram of array.
3) Obtain the pulse profile.
We can see that the pulse profile matches with that of Crab Nebula.

In [13]:
tref=fevents_bary[1].header['MJDREFI']
tref=tref*86400
time_current =time_gti + tref
T0=57480.5635028439*86400 # Reference Epoch for which nu is known
t_phase=time_current-T0

# freq and its derivatives
nu,nudot,nuddot = 29.6553306828504,-3.69261197216621e-10,-3.9353064617231e-20

#calculating phase
phi=t_phase*(nu+0.5*t_phase*(nudot+t_phase*nuddot/3.0))
phi_int=np.zeros(len(phi))
for i in range(len(phi)):
phi_int[i]= int(phi[i])
phase=phi - phi_int
phase=phase+1
min(phase),max(phase)

#folding phase
no_bins=250
pbins=np.linspace(0.,1.,no_bins+1)
phase_counts, pbin_edges = np.histogram(phase,bins=pbins)
pbin_edges = (pbin_edges[1:] + pbin_edges[:-1])/2
phase_counts=[float(i) for i in phase_counts]
phase_counts=np.array(phase_counts)
pcounts=phase_counts/max(phase_counts) # normalising
plt.plot(pbin_edges, pcounts) # plotting pulse profile
plt.xlabel('Phase')
plt.ylabel('norm ')

Out[13]:
Text(0,0.5,'norm ')

# Making energy spectrum¶

1) Bin in energy (You can play around with binsize).
2) Show apparent spectrum in log scale.
3) Plot log N vs log E.

In [14]:
for i in range(len(t_start)) :
energy_gti = eventsdata['Energy'][np.where((time_bary>=t_start[i]) & (time_bary<=t_stop[i]) & (eventsdata['Energy']<=80))]

#energy_gti, len(energy_gti)
binsize = 0.5 #change as required
ebins = np.arange(energy_gti.min(), energy_gti.max(), binsize)
counts_energy, ebin_edges =np.histogram(energy_gti,bins=ebins)
ebin_edges = (ebin_edges[1:] + ebin_edges[:-1])/2
log_counts=np.log(counts_energy)
log_ebins=np.log(ebin_edges)
plt.plot(log_ebins, log_counts)

Out[14]:
[<matplotlib.lines.Line2D at 0x7fe7cf279ac8>]

# Making PHA spectrum¶

1) Bin in channel.
2) Show apparent spectrum in log scale.
3) Plot log N vs log 'channel'

In [15]:
for i in range(len(t_start)) :
channel_gti = eventsdata['Channel'][np.where((time_bary>=t_start[i]) & (time_bary<=t_stop[i]) & (eventsdata['Channel']<=512) )]

binsize = 1 # change as required
cbins = np.arange(channel_gti.min(), channel_gti.max(), binsize)
counts_channel, cbin_edges =np.histogram(channel_gti,bins=cbins)
cbin_edges = (cbin_edges[1:] + cbin_edges[:-1])/2
log_counts_channel=np.log(counts_channel)
log_cbins=np.log(cbin_edges)
plt.plot(log_cbins,log_counts_channel)

Out[15]:
[<matplotlib.lines.Line2D at 0x7fe7cf1d69b0>]

# Making contour plots for response matrix¶

2) Make 2D plot/ contour for the MATRIX.

In [16]:
resp_data = fresponse[2].data
mat = np.zeros((len(resp_data), len(resp_data[0]['matrix'])))
for i in range(338): mat[i,:] = resp_data[i]['matrix']

# plotting contour and 2d-array of response matrix
plt.imshow(mat)

Out[16]:
<matplotlib.image.AxesImage at 0x7fe7cf1c5da0>
In [17]:
plt.contour(mat)

Out[17]:
<matplotlib.contour.QuadContourSet at 0x7fe7cf06fb38>