X-Ray Astrophysics
EXOSAT & Chandra Data Analysis
50
A Brief Review: Light Curves, Power Spectra & Energy Spectra
During the Linux Tutorial, you generated light curves, power spectra, and
energy spectra. These are the primary “tools” for examining stellar phenomena
and as such, it’s important that you be able to distinguish between the 3 in terms
of what they are telling you about the source.
The exercises below are intended to help your understanding of these
differences. For each exercise, you’ll be given a description of a source. Your job
is to sketch the energy spectrum, light curve, and power spectrum that represent
the source.
Exercise 1 : The source is a light bulb, which operates using a 60 Hz alternating
current.
energy spectrum
light curve
power spectrum
Exercise 2 : The source is a lighthouse with a d.c. bulb that revolves once every
10 seconds.
energy spectrum
light curve
51
power spectrum
Exercise 3 : The source pulses as it emits only red light.
energy spectrum
light curve
power spectrum
Exercise 4 : The source steadily emits only blue light.
energy spectrum
light curve
52
power spectrum
X-Ray Source 1 : GK Per
EXOSAT Data

At the HEASARC site, click on ARCHIVES, then BROWSE.

Enter GK Per as the Object Name.

Click on EXOSAT under Past X-ray Missions, then scroll to Types of Information
and check the box for Archived Data and Observations. Then click on Start Search.

Scroll to Exosat ME Spectra and Lightcurves, and select the observation that has
quality flag #4.

Under Data Products, check all of the boxes.

Scroll down and click on Preview and Retrieve.

Select the box for Band 3 (these are the GK Per lightcurves…you’ve already
downloaded the energy spectra files, s05865.pha and s05865.rsp, during the
EXOSAT tutorial).
Take note of the names of the .lc files so as not to confuse them with previously downloaded
.lc files from other sources.

Scroll to and click on Tar Selected Products

Download
53

After untarring the files, delete (rm) the tar files.

Concatenate the .lc files

Run lcurve on the concatenated.lc file for both 10s bin times and 90s bin times.

Rescale each concatenated lcurve for the same 1000s sample.

Get a hardcopy for each (the 10s bin and 90s bin)1000s sample concatenated
lcurve.

Use the concatenated 10s bin time .flc output file to get a power spectrum.
54
Chandra Data

Repeat the steps of the Chandra tutorial using GK Per as the object and
seqid 3454. After checking only the Events List under the Data Products, click
on Preview and Retrieve and select the Remote Events List with the file
acisf03454N001evt.2fits.

Once you get the image in ds9, all you’ll see is a dot. To see it better, do the
following:
Frame …tile frames (This will show the x-ray image on the left and the
optical image on the right.)
Color…he
(This will improve the contrast)
Analysis…DSS server (Click in the left box to select the x-ray image.)
Frames…lock crosshairs…WCC
Edit crosshairs

(This will allow you to move around within each image.)
Produce a light curve, power spectrum and energy spectrum using the
Chandra data. Get a hardcopy for each.

Produce an energy spectrum using the EXOSAT data for GK Per.
Get a hardcopy.
55
Analysis
1.
Using the 24000 sec lcurve, determine the period using
(a) the first 4000 sec
(b) the first 24000 sec
2.
What is the frequency based on your power spectrum?
Use this value to determine the period.
3.
Rescale the x-axis of your power spectrum to get a more precise value for
your frequency (i.e., 2.8_ _ x 10-3 Hz)
4.

Use this value to determine the period.

Determine the error (in seconds) using the width of the interval
containing the frequency.
Run efold using the .flc output file for the total observation of the
concatenated .lc files. (This will essentially “blend” your data into one
cycle.)
 You’ll do this twice: once using a 351s period and once using a
356s period.
 Use 20 as the number of phase bins for both.
 Get a hardcopy of each efold.
Which efold exhibits more periodic behavior?
5.
Look at the 10s bin & 90s bin lcurves for the 1000s sample.
 What differences are apparent?
 What is the extent of the error bars for each? What does this imply?
 What is the disadvantage of using longer bin times?
6.
Examine the 10s bin lcurve. You’ll notice negative count rates.
How is this possible?
7.
What does the 0 frequency value on the power spectrum represent?
56
8.
What does the frequency spike to the right of the most prominent spike on
the power spectrum represent?
9.
What does the data show to be GK Per’s most striking aspect?
10.
What can the variability represented by the data mean? List all
possibilities and eliminate those that don’t make sense.
11.
Assume the density of GK Per has the same density as that of a Main
Sequence star like the Sun (~ 1 gm/cm3). Show that this implies a period
of revolution that is inconsistent with the data.
12.
Assume GK per is an M dwarf type star (M = 0.1 Msun & R = 0.8 Rsun).
Does the gravitational field at the surface of this star allow for a rotational
period of 350s ?
13.
Determine whether a white dwarf can support a 350s rotational period.
14.
It has been found that the x-rays coming from GK Per “disappear”every
47h.9 (approximately 2 days). What can this mean about the nature of the
system?
15.
Use the EXOSAT spectral data (s05865.pha and s05865.rsp) to do a model
fit for thermal bremsstrahlung as described in the tutorial.
Get the flux value.
16.
In order to calculate the luminosity of GK Per, we need to know how far
away it is. Parallax can’t be used. However, the distance was found to be
480 pc from the optical nature of its nebulosity. Use this value to calculate
the luminosity of GK Per.
57
17.
Robert Craft found the existence of a spinning accretion disc as part of the
GK Per system. What can this infer about the model of the system?
58
The 24000 sec raggedy lcurve goes here
59
The power spectrum goes here
60
The 10 sec bin lcurve goes here
61
The 90 sec bin lcurve goes here
62
X-Ray Source 2 : Cen X-3
EXOSAT Data

At the HEASARC site, click on ARCHIVES, then BROWSE.

Enter Cen X-3 as the Object Name.

Click on EXOSAT under Past X-ray Missions, then scroll to Types of Information
and check the box for Archived Data and Observations. Then click on Start Search.

Under Exosat ME Spectra and Lightcurves, select the 3 observations marked #1697.

Under Data Products, check all of the boxes.

Scroll down to and click on Preview and Retrieve.

Select the boxes for Band 3 , Spectra, and Response Matrices.

Click on Tar Selected Products

Download

After untarring the files, delete (rm) the tar files.

The mu3 segments will look like :
xxxxx12
xxxxx23
xxxxx32
xxxxx41
xxxxx50
xxxxx59
xxxxx71
xxxxx81
xxxxx90
xxxxx99
Individual groups will be assigned 1 or 2 of these segments to examine.

Run lcurve on your assigned segment (use the minimum bin time…0.5s)

Get a hard copy of the entire segment.

Get a detail of your segment by rescaling x for a 25s interval. Get a hardcopy
of this detail.
63

Run powspec on your segment. Get a detail by rescaling x. Get a hardcopy of
the detail. Record the frequency value to the fifth decimal place.

If time permits, concatenate all of the .lc files (the mu3 segments) and run
lcurve.
Analysis
1.
What is the frequency of this source, based on the power spectra found by
the individual groups? Do the 25s light curves support this value?
2.
What is happening during the 7th through 9th segments? How much time
elapses during these intervals?
3.
Compared to our analysis of GK Per, what might the smaller periodicity
of Cen X-3 represent?
4.
Can Cen X-3 be a rotating white dwarf? Provide a reason for your answer.
5.
Can Cen X-3 possibly be a neutron star (Mns ~ 2Msun & Rns ~ 10 km)?
Provide a reason for your answer.
6.
List the possible causes of the 40,000s “drop-out” during the 7th through
9th intervals. Eliminate those that don’t make sense.
7.
What would you expect to happen to the high energy versus the low
energy x-ray photons as Cen X-3 enters the eclipse phase?
8.
What will happen to the frequency with which the x-ray source emits
photons as it approaches us? Recedes from us?
9.
The eclipse was found to repeat every 2d.09 (about 180,000s). Using (a)
this information, (b) the frequency values we’ve determine for the 10
intervals of the observation, (c) the fact that each interval lasts for about
64
12,000s, and (d) the eclipse time, draw a picture showing where Cen X-3 is
in its orbit relative to earth for each of the ten intervals.
10.
How much of the radiation received from the x-ray source is in the optical
part of the spectrum?
11.
Our hypothesis is that we have an optical object orbiting a neutron star.
What might we expect to observe optically in such a system?
12.
Krzeminski found that the optical star was a blue supergiant (B0Ia) that
produced the opposite effect of what is expected in #11. Account for how
this unexpected result can happen.
13.
How can a neutron star (which is old) co-exist with a blue supergiant
(which is young)?
14.
Use the Doppler Effect to determine the speed of the neutron star in its
orbit. Assume the maximum and minimum frequencies are 0.20745 Hz
and 0.20685 Hz, respectively.
15.
Use the speed of the neutron star to determine the radius of its orbit.
How does this value compare to the distance from the earth to the sun?
16.
Using the eclipse time, estimate the radius of the supergiant.
Where is the error in making this determination?
17.
Use Kepler’s 3rd law to determine the sum of the masses in this system.
18.
For the supergiant B0Ia, m = 13 and M = -7. Use these values to determine
the distance to the system.
19.
Based on the actual (estimated) size of our galaxy, does your answer to
#18 make sense?
65
20.
Use the model fitting procedure for EXOSAT to determine the flux.
(See next page for a quick review of the procedure for model fitting)
66
Fitting Spectral Model swith EXOSAT data

Go to the directory where the .pha and .rsp files have been downloaded.
There will be 3 sets of each of these files. Choose any one of the .pha files

% xspec

XSPEC : >data sxxxxx.pha

XSPEC : >cpd /xw

XSPEC : >plot data
An energy spectrum will appear with “CHANNEL” on the x axis.

XSPEC : >setplot energy

XSPEC : >plot data
This will generate an energy spectrum in terms of keV on the x axis. We’ll
now try to “fit” a spectral model to this spectrum. The best fit indicates the
method of x-ray production: thermal bremsstrahlung, blackbody radiation, or
power law. We’ll only do a blackbody (bb) fit here. You can do the other 2 on
your own…see the Tutorial.

XSPEC : >mo phabs(bb)
Hit return until you see a 2 value that is >> 1 (and Null Hypothesis = 0).

XSPEC : >renorm
Continue renorming until the 2 value doesn’t get any lower.

XSPEC : >fit
Hit return until the 2 value doesn’t change anymore.

XSPEC : >plot data

XSPEC : >flux
Record the flux value you obtain for each of the 3 model fitting procedures.
67
21.
What do you notice about the 3 flux values?
22.
The actual distance to the system is about 10 kpc. Find the luminosity of
the system.
23.
If the neutron star is “feeding” off the material from the supergiant, what
might be happening to it over time?
24.
Using the Chandra obsid 1943 and the Chandra tutorial, extract a light
curve and power spectrum to help in answering #23. You will be selecting
the Remote Events List with file acisf01943N001_evt2.fits.gz
(Remember that you must start by reading the data into xselect and you
should get the TIMEDEL value as described in the Chandra tutorial)
On your power spectrum, rescale x and y to show a detail of the frequency
to 5 decimal places. Compare this value to the EXOSAT value for
frequency.
25.
What might be happening to cause the neutron star to increase its spin
frequency?
26.
How much mass does Cen X-3 accrete in 20 years?
27.
Would you expect to see the accretion disc spinning in the same sense as
the neutron star?
28.
Using the graph of period vs time for Cen X-3 shown below, what value
for the frequency does the graph predict for the Chandra observation
(which was done on 12/30/2000)?
What frequency do you observe from the Chandra power spectrum?
period vs time for Cen X-3 goes here
68
29.
The period vs time data for the x-ray binary systems GX 301-2 and
4U0900-40 is shown in the graphs below. Provide a model for how this
may be happening.
period vs time graphs go here
30.
What is radiation pressure? How can light exert pressure? What role does
radiation pressure play in modulating the production of x-rays?
69
Concatenated lcurve goes here
70
12000 segment goes here
71
25 second segment goes here
72
Power spectrum goes here
73
pow spec segment 1 goes here
74
pow spec segment 2 goes here
75
pow spec segment 3 goes here
76
pow spec segment 4 goes here
77
pow spec segment 5 goes here
78
pow spec segment 6 goes here
79
pow spec segment 7 goes here
80
pow spec segment 8 goes here
81
pow spec segment 9 goes here
82
pow spec segment 10 goes here
83
Chandra pow spec goes here
84
X-Ray Source 3 : Cas A
ds9 & Virtual Observatory

Use vncviewer to get into the basho environment

% ds9

Analysis…Virtual Observatory…click on the Rutgers box
(will bring you into the ds9 window)
You should now be in a Netscape window at http://basho.rutgers.edu

Click on Load Cas A Image
This will bring up the image of Cas A in ds9.

Select “he” for the color map: Color…contrast/bias (play with this tool)
85
Analysis
1.
How can you get the distance to Cas A? (What do you need?)
2.
When did Cas A explode? (What do you need?)
3.
What is the diameter of Cas A? Investigate the possible ways to make this
determination by using the image and information provided in the
ds9 window.
4.
Extract a Light Curve: under Analysis, select FTOOLS Light Curve. (You
may have to wait a minute before the light curve appears)
You can rescale the axes in Virtual Observatory by going to View
and then selecting Axis Range. You will have to uncheck the box at
the right so that you can enter the desired range of values.
5.
Extract a Power Spectrum: under Analysis, select FTOOLS Power Spectrum.
6.
Compare and contrast the energy spectra corresponding to different
regions of Cas A.
To do this, go to Edit and click on Pointer. Move your cursor until the
physical pixel position has coordinates (4050, 4100). Then right click the
mouse to lock on that location. Under Analysis, select Quick Energy
Spectrum. Get a hardcopy.
Repeat the above procedure for coordinates (4530, 4170).
Note : you can identify the element corresponding to particular
absorption lines in your energy spectrum by going to any of the following
sites:
http://www.csrri.iit.edu/periodic-table.html
http://www-structure.llnl.gov/Xray/elements.html
http://www.bmsc.washington.edu/scatter/periodic-table.html
http://ie.lbl.gov/xray/mainpage.htm
86
7.
Based on the light curve and power spectrum, what can be said about the
variability of Cas A?
87
X-Ray Source 4 : MXB1728-34
EXOSAT Data

Go to HEASARC, ARCHIVES, BROWSE.

Enter MXB1728-34 as the Object Name

Click on EXOSAT under Past X-ray Missions, then scroll to Types of Information
and check the box for Archived Data and Observations. Then click on Start Search.

Scroll to Exosat ME Spectra and Lightcurves and select only the first observation
#1039

Check all of the boxes under Data Products.

Scroll down and click on Preview and Retrieve.

Select the boxes for Band 1, Band 2, and Band 3 files.

Click on Tar Selected Products and then Download.

After untarring the files, delete (rm) the tar files.

Move all the files into a single directory

Run lcurve with Number of Time Series [2]
First series is axxxxx.lc
Second series is bxxxxx.lc

PGPLOT default command [2]

Get a hardcopy 100s detail of the “spike” in the plot.
Next, we’re going to generate a plot of the “hardness”:

Go to the PGPLOT command and enter [1] (for Hardness) &
[2] for Number of Time Series

Your plot should look like that shown on page 87. (Do not make a hardcopy!)

Run lcurve with Number of Time Series [3]
First series is axxxxx.lc
88
Second series is bxxxxx.lc
Third series is cxxxxx.lc

PGPLOT default command [3]

Get a hardcopy 100s detail of the “spike” in the plot.
Analysis
1.
Based on the light curves, what is the most prominent aspect of this
source?
2.
How often does the phenomenon cited in #1 occur?
3.
Describe your light curve. What is happening?
4.
What does series a represent? series b?
5.
What does the ratio of series b to series a indicate about the temperature?
6.
What does the hardness plot (page 87) indicate about what is happening
to the temperature during the outburst interval?
7.
The flux at the peak of each burst has been found to be 7 x 10-8
ergs/s/cm2.
The distance to this source has been determined to be approximately
10 kpc (like most x-ray sources, it is located in the galactic bulge).
Determine the peak luminosity.
8.
The temperature during the peak outburst has been found to be 30 x 106 K.
Determine the radius of the source. Based on this value, what type of star
is it?
9.
Calculate the gravitational energy (in MeV) that is converted into x-ray
energy for each hydrogen that is accreted onto the source.
89
10.
Describe the model of the complete process that occurs, starting with the
“quiet” intervals and continuing through the burst intervals.
90
Series 1 & 2 light curve goes here
91
Hardness plot goes here
92
Series 1, 2, 3 light curve goes here
93
X-Ray Source 5 : The Rapid Burster
Illustration of original lcurve goes here
94
Analysis
1.
Examine the plot on the previous page. (Please note that each subsequent
line is NOT a continuation of the previous line!) Make a list of any
distinctive characteristics of this plot.
2.
What is the relationship between the intensity of the bursts and the
interval of time that occurs between the bursts?
3.
Can you think of any processes on earth that are analogous to what is
happening (based on the light curve observation) on the Rapid Burster?
4.
Compare the signature characteristics of a standard burster (like
MXB1728-34) to those of the Rapid Burster.
5.
When analyzing bursters, it can be helpful to observe the optical emissions
in the bursts. How can x-ray photons from the burst be converted into
optical photons? What is this process called?
6.
What component of the physical system containing the burster enables the
generation of optical photons from the x-ray photons? Describe what is
happening.
7.
How does the generation of photons from the accretion disc provide
information about the accretion disc?
8.
Why are there no x-rays between the bursts on the Rapid Burster?
9.
How can hydrogen be prevented from being accreted onto the neutron
star (which would produce x-rays) during the intervals of time between
the bursts?
10.
On the 6th line of the light curve observations, a helium flash occurs
(i.e., triple helium fusies into carbon) at the peak indicated by the arrow.
Develop a model to account for this event.
11.
What distinguishes the helium flash burst from the other bursts?
12.
Thus far we’ve examined 2 bursters…MXB1728-34 and the Rapid Burster.
As with the pulsar model, the burster model represents a neutron star.
Is it possible for a pulsar to also be a burster? Why or why not?
95
X-Ray Source 6 : Exo0748-676
EXOSAT Data

At the HEASARC site, click on ARCHIVES, then BROWSE.

Enter Exo0748-676 as the Object Name.

Click on EXOSAT under Past X-ray Missions, then scroll to Types of Information
and check the box for Archived Data and Observations. Then click on Start Search.

Scroll to Exosat ME Spectra and Lightcurves, and check both sequences #1405
(These observations will contain a total of seven segments)

Check all the boxes under Data Products.

Scroll down and click on Preview and Retrieve.

Select the box for Band 3 only.

Scroll to and click on Tar Selected Products

Download

After untarring the files, delete (rm) the tar files.

Concatenate the seven .lc files. Remember to list them in chronological order.

Do lightcurves for both 1s and 60s bins.

Get a hardcopy of the 60s lightcurve.

Run powspec on the .flc file for the 60s bin lightcurve.

Use your power spectrum to determine the period for this source.

Using the period & the efsearch procedure, run an efold using the .flc file for
the 1s lightcurve. (For help, refer to the EXOSAT tutorial.)
96

Get a hardcopy of this efold.
Analysis
1.
Give a description of the data.
2.
What does the light curve show about the source?
3.
If a certain feature occurs on the efold plot, does that mean that that
feature is periodic?
4.
Do the bursts exhibit “classic” burst shapes? (Look at a detail)
5.
Look at both the light curve and the efold. Is there anything else present
(not mentioned in #2) that persists over the period?
6.
See if you can develop a model that includes all of the following:
 period of ~13, 720s
 3 spikes (bursts)
 periodic rapid dips
 600s interval (as can be shown by a detail) for each of these rapid dips
7.
How can the eclipse dip period be so short (600s) as opposed to that of
Cen X-3 (40,000s)? Develop a visual model for what happens as seen from
our point of view.
8.
Does the 13,720s period infer a period of rotation or a period of
revolution?
Why?
9.
Why is the companion star a dwarf star (M0V) instead of a
giant/supergiant?
10.
Can the compact object be a white dwarf? Why or why not?
11.
What other component of the system must be present?
12.
Develop a model that explains the presence of the “wide” dips.
13.
The system exhibits both a large amount of variability in the wide dips
and a gradual variability in the eclipse dips. Make a list of possible
97
mechanisms for these characteristics & eliminate those that don’t make
sense.
98
60s light curve goes here
99
efold of 1s light curve goes here
100
X-Ray Source 7 : 3c273
ds9 & Virtual Observatory

Use vncviewer to get into the basho environment

% ds9

Analysis…Virtual Observatory…click on the Rutgers box
(will bring you into the ds9 window)
You should now be in a Netscape window at http://basho.rutgers.edu

Click on Load 3C273 Image
This will bring up the image of 3c273 in ds9.
Analysis
1.
What do you need to know in order to determine the length of the jet?
2.
What are you able to determine about the jet?
3.
If you were to plot # of observations versus angle of the jet in the sky,
what would it look like?
4.
What can affect the values used in #3?
5.
Use the spectral record of 3c273 shown on the following page to
determine the value of . (This value is also known as Z, and refers to
the Doppler shift). The laboratory values for the lines shown are:
H = 4861 Å, H = 4340 Å, H = 4102 Å
101
6.
Hubble’s Law can be used to determine the distance to the source.
Hubble’s Law states that: v = Hr
where H ~ 100 km/s/Mpc
and
r = distance to the source.
Using this information along with that of #5, determine the distance to
this source.
Spectrum of 3c273 goes here
102
7.
How many light years away is this source?
8.
Determine the length of the jet.
9.
Find the flux for the source by doing the following in the ds9 window:

Select a region to encircle the source, or the jet, or both.

In the Analysis column, select CIAO Energy Spectral Fit.
A window will appear containing, among other information, the value for
the flux.
10.
Find the luminosity of this source. How many “suns” is this equivalent
to? What type of object has a luminosity of this magniitude?
11.
Why is the jet so straight?
12.
How big is this type of object? To determine this value, use the data
shown on the following page (for a total of 100 photons, and analyzed in
part by none other than T. Matilsky) for the source 1525 +227, an object
which is similar to 3c273

Divide the photons in 800s bins, 400s bins, 200s bins, and 100s bins.

For each bin size, make a bar chart of counts/bin versus # of bins.
Be sure to include error bars on your chart.
13.
Is this source variable on these time scales?
14.
What would the power spectrum look like? (qualitatively)
15.
If this source varies on a time scale of 100s, how big can the emitting
region be?
103
16.
How big is100 light-seconds? (The Sun is 480 light-seconds from earth.)
104
Terry’s data goes here
105