ROSAT

Data Reduction Using the HEASARC Archive and Ftools

• Open Netscape
• Go to HEASARC web page by typing $\$ http://heasarc.gsfc.nasa.gov
• W3Browse

  On the bottom of the page there are two rows of six links within HEASARC to which you can go. The top left option is the W3Browse location where you can search for observations of various objects.

  • Click on it.
  • Select the Basic option.

• Search for a specific object
  • From the Active Mission Archives section select ROSAT by clicking on the gray button to its left.
  • In the box at the top labeled Object Name or Coordinates enter GK PER.
  • Click on Submit Query.

• Selecting an observation
  • Select the second observation whose instrument is the PSPCB.

  • Slightly below the table of observations there is a box, entitled Categories of data products, containing different types of data collected in each observation. Click on the gray Submit button below. You may receive a security warning message from Netscape, to continue just click on Continue Submission.

  • This page shows all the possible data that can be examined from the observation you chose. At the end of each line the filename of the data you wish to retrieve is printed in the form of file.Z. Select the Basic Science Events file by clicking on the gray button on its left.
  • Scroll down the page and click on Retrieve Data Products

• Downloading TAR files
  • The screen that appears should list the file you chose. Click on Download TAR file which appears right below.

  • The window that appears contains four sections: Filter, Directories, Files, Selection. Make sure that your directory apears in the Selection box. If it does not then you must enter the /temp directory you created to store your files.

    If you had to re-enter your directory then when you finished typing click on Cancel, then Click on Download TAR file again. This time the correct directory should appear in the Selection box.

  • Click on OK

    Netscape will copy the files you have selected into your directory in the form of a w3browse-$\char93$.tar file. It is a compressed file and cannot be used until it is opened up properly.

  • Un-tar your w3browse-$\char93$.tar by typing:

    tar -vxf w3browse-$\char93$.tar < Enter >

    This command produced a subdirectory chain in your directory called rp300217n00/ where youre files are located.

• Organizing and uncompressing the files in your directory
  • You will find the files you downloaded from HEASARC in their new subdirectory by typing:

    cd rp300217n00/

  • File completion.

    If the name of the file (or directory) you are entering reaches a unique string (for example if you had entered rp3 above and there were no other files in your directory with this beginning) you may press the $< Tab >$ key and the filename will be completed. If the string is not unique then the name will complete up to the point where it becomes ambiguous and you must add a character to make it unique - then you can press $< Tab >$ to complete it again.

  • Then type ls < Enter > to list the files.

    rp300217n00_bas.fits.Z should appear.

    Notice the file ends with .Z$\$. This means it is comrpessed further and still cannot be used.

  • Uncompress the files by typing:

    uncompress *.Z < Enter >

    The * is a wildcard character so that your command above says ``uncompress anything in this directory that ends with .Z''.

    Then type ls < Enter > . The .Z should have disappeared from the filename making the file usable.

  • Remove the w3browse-$\char93$.tar file now that you have what you need by returning to the directory to which you downloaded it and typing:

    rm w3browse-$\char93$.tar < Enter > or

    rm w3 < Tab > < Enter > and allow the file completion feature to do its work.

• To see the important information about this observation open up one of the files in the emacs editor. Type:

  emacs rp300217n00_bas.fits $\&$ < Enter >

  The file that comes up contains information such as the date and time of this observation, the telescope and instrument that collected the data, the location of the object as well as its name.

  Close emacs.

• Reading the data into Xselect
  • The program you are using to process and analyze the data from HEASARC, ftools contains a package (i.e. subprogram) named Xselect which contains all the commands you will need to look at the images from your data, and examine lightcurves and power spectra.

  • To use Xselect you must execute its commands. At the prompt type:

    Xselect < Enter >

  • You will be asked to enter a session (so that when you are done you can save all your work into that session or continue where you left off).

    Call your session session1 < Enter >.

  • Notice the information that appears on the screen is specific for ASCA - a different satellite. We want to analyze ROSAT data and we need to tell Xselect to do so. Type:

    read events < Enter >

  • You will be asked in which directory do the event files exist. If you called up Xselect from the directory where youre ROSAT files exist then enter ./ < Enter > (which means this directory).

  • Then enter the name of your file: rp300217n00_bas.fits < Enter > or, again, you may type rp < Tab > < Enter >.

  • Type yes < Enter > to reset the mission.

    Now Xselect is configured. Notice the important notes that follow on your screen.

    
    Notes: XSELECT set up for		 ROSAT
    
    
    Keywords for time and pha are		TIME		PI
    
    
    Units of time are		s
    
    
    Default timing binsize=		16.000
    

    This data and that which follows describes how the program is now configured to handle your data. For example, it tells that the units of time in any process will be in seconds. It also prints the directory where your data is located. Finally, the program outputs the information about your object, GK PER, its position in the sky, the livetime (how long the detector was taking data on this object), and the date of observation.

• A few Commands

  Xselect has some general commands that you will be using to create images, light curves, and energy spectra. Here are some of the commands (and their descriptions) that you will be using the most.

  • Read events, which you have already used in the previous section, enters data into the program. If you wish to enter a new set of data, you can do it with this command

  • Filter commands do no work. They merely enter filters selecting a particular region or time interval that will be applied to the next run of the extract command.

  • Extract command produces a product file such as an image, a spectrum, or a lightcurve.

  • Clear command is used to clear any changes you have made to data and restores it to the way it was originally.

  • Another useful command is show data which you can type at any time and you will receive an output of your working directory and the names of the files you are using.

  • Similar to the ls command, to list all the files in your current directory you can type list workdirectory or list datadirectory.

  • The $\$ symbol allows you to exit Xselect temporarily without quitting so that you may move around your directory tree, copy or delete files, and then return to Xselect where you left off by typing exit.

• Image analysis
  • To look at GK PER you need to command Xselect to show it to you. At the prompt type:

    extract image < Enter >

    Once again Xselect prints out information on the screen. The important facts are the seconds and the counts that provide a countrate for the image. This is important because a high countrate means the object was giving off photons at a high rate and will be bright. A very low countrate implies a faint or no image (just noise).

  • The image has been extracted from the data and you must now use an imaging tool to look at it. Type saoimage < Enter > to call up the imaging tool. A new window should pop up with your data displayed upon it.
    SAOIMAGE

    You should take some time to familiarize yourself with this tool. You can change the features of your display by selecting a ``button'' from the top row. If you click on Scale, for example, you have a choice, on the seconds row, of viewing your image in a variety of brightness scales. Notice the grayscale legend at the bottom. A linear scaling would let the brightest thing in your image be the color of the extreme right, the least bright thing in your image be the color of the extreme left, and the values in between would be evenly spaced along the grayscale legend. A square root display would let the square root of the maximum and minimum brightness values be displayed as the leftmost and rightmost grayscale values. Try the logarithmic scaling to see what it does.

    You can also change the color schemes by clicking on Color. The button cmap will add more choices to your display options. You can invert the grayscale legend by clicking on invert. To return to the color options click on cmap again.

    You can mark your object of choice with a cursor and define a region to later observe.

    • The object we are examining is GK PER. It is located at the bottom left of the display. If you want to center your object click on Pan and then click on the object. It should move to the center. Then click on Cursor.

    • Select a circle shaped cursor. With your mouse button choose a circle size that places your object comfortably inside. The left mouse button puts the center of your shape in place, and clicking down on both mouse buttons allows you to drag out the radius of the shape to any size you wish. Make your circle just big enough to enclose the star. Then type s on the keyboard to ``save'' the region.

    • Click on the button labeled region (the rest of the buttons should change) and select write. On the line that appears type a unique filename for your region which saves the region surrounding your object for later use.

    Continue to play with SAOimage until you feel comfotable using it.

  • To look at the data inside your selected region only, return to the window where Xselect is running and type:

    filter region src.reg < Enter >

    When you apply the filter command to an image it is as if you are placing an opaque screen with a hole in it over the data. The hole in the screen is the region you selected.

  • Next you must type extract events < Enter > to select only the data contained in your region. In other words, you are choosing only the points that show through the hole in the screen. The rest are ignored. The output of this command should show a Grand Total of 112910 counts with a much smaller number (around 3 or 4 thousand) of Good counts and the rest are Bad: Region counts. This tells you you have excluded all the points not in your selected region.

  • Now type clear region < Enter >

    This removes the filter from your image since you pulled out the events you wanted and no longer need the filter.

  • Now you must extract the image from those points you selected by typing:

    extract image < Enter >

  • Call up SAOimage again to display your new image. (You may close your old SAOimage window by clicking on etc and then on QUIT or leave it up for comparison with your new display.)

  • Getting a Filtered Image

    The following is a list of the commands you just used with no comment so that you may refer to it quickly beginning after read events:

    extract image < Enter >

    saoimage < Enter > (select a region with the cursor)

    filter region src.reg < Enter >

    extract events < Enter >

    clear region < Enter >

    extract image < Enter >

    saoimage < Enter > (To see the final image)

    You may now proceed to manipulate the image of GK PER

• Image manipulations in Xselect

  The following instructions are optional exercises that demonstrate how you can smooth and average the images using the tools in Xselect. If you choose to try these exercises make sure you return the data to its original form before proceeding to lightcurves and energy spectra. Instructions for restoring the data are part of this exercise, so if you begin these instructions you must follow them through.

  1. Binning up pixels.
     1. The image you originally displayed (before the filtering) is made up of 1024 $\times$ 1024 pixels. When you chose the region you simply selected a particular set of pixels to be displayed. Sometimes, however, it is helpful to group pixels together into one block to get a smoother appearence of the data. This technique is called block-averaging. If you tell Xselect to take every 8 pixels and replace them with 1 pixel whose grayscale value is the average of those eight, you have binned up your image into 128 $\times$ 128 pixels. To see this type:

        set xybinsize < Enter >

     2. You will be asked for a rebinning factor (this would be the value 8 mentioned above) select 8 < Enter > to see a 128 $\times$ 128 pixel image.

        Then continue to process the image by commanding:

        extract image < Enter > and

        saoimage < Enter >

        You should see your region selected image in a binned up fashion. The pixels should now be larger sized squares.

     3. Try to rebin with different values such as 32. To do this you simply need to type:

        set xybinsize < Enter > and input the binning you desire.

        extract image < Enter >

        saoimage < Enter >

        The default xybinsize is 15; this means the first image you looked at had an xybinsize of 15. When you are done exploring this function, set it back to 15.

  2. Smoothing images.
     1. Smoothing images often allows you to concentrate on the general features of the image and not worry about individual pixels.

        Type: smooth image < Enter >

        You will be asked for a smoothing method. Your options are Boxcar, Gaussian, or Lorentzian. Type Gaussian < Enter > to select this method. You will be asked for a sigma for image smoothing. The default is 1.5 you may accept that value to see what happens.

        Again display your result with saoimage < Enter >.

     2. Notice your object is now smoothed. Try different color schemes on the smoothed data and pan in on it so you can see it clearer. Notice the top left part of the image is now bright and there is a dark ``hole'' in the middle. The value 1.5 is the $\sigma$ in a gaussian curve which you are applying to the image, a larger $\sigma$ means a smoother image.

     3. An image will be smoothed differently depending on the binning factor of the image. You can explore different possibilities by following these steps:

        set xybinsize < Enter > and input the binning you desire.

        extract image < Enter >

        smooth image < Enter > then choose Gaussian < Enter > with a $\sigma$ of 2 or any value you wish to explore.

        Then view it with saoimage < Enter >.

        Try a $\sigma$ of 3 or 4 to see what happens when you smooth too much!

     4. To return the original pixel data set xybinsize 15 < Enter >.

        Then type extract image < Enter >. You should saoimage < Enter > just to be sure that your original filtered pixel image is there.

• Examining lightcurves
  • You will now use the extract command to make a lightcurve of your observation.

    extract curve

  • Next you must set a program device upon which your lightcurve can be plotted.

    set device /XW < Enter >

    and now plot it plot curve < Enter >

  • You will notice that all of your data is in the center of the plot and a curve or spectrum is hard to make out. Also, notice that at the top of your plot you are told that the binsize is 16.000s. This means that the total livetime has been divided into 16s intervals and plotted accordingly.

    Notice on your Xselect screen that the prompt has changed from session1:ROSAT-PSPC> to PLT>. This means you are in an interactive mode with the plot window and commands you give the screen will be received by the plot window.

    The most important command is exit; type it if things get really crazy. In this case you can clear events and start the lightcurve extraction all over.

  • One useful thing you can do is reset the x and y axes to zoom into some interesting part of the lightcurve.

    rescale x 4e5 6e5 < Enter >

    This displays the chosen datapoints across the entire screen. You can zoom in even more by typing rescale x 4.8e5 5.5e5

    One notable feature of the PLT$>$ environment is that you may an abbreviation of a command, so long as it is unique instead of the entire string. In this case you can type r x X$_{min}$ X$_{max}$ to get the same results.

    Type exit to return to Xselect now.

  • It is useful to define a region of interest from your image and extract the events from that region. Since you already extracted the lightcurve you can define a time interval through which you can filter the data.

    Type: filter time cursor < Enter >

    Again you will be in the PLT> mode. The first thing to do is to enter quit as you are told to do on the screen. Then in the plot itself click to the right of the curve (around x=5.5e5) and to the left (around x=4.8e5). A horizontal line should have connected your clicks.

    Then type x in the plot window to exit this mode. NOTE: You can get tangled up very quickly while in this mode. Do not attempt to try the other commands that appear unless you have plenty of time and motivation! The instructions above will be sufficient for your purposes.

  • Type show status < Enter > to see that file of the time selections was added to the filters. It also shows what you have done so far under PRODUCTS.

  • Type extract curve < Enter > since now there has been a filter applied to it.

    And plot curve < Enter >.

  • You now have a light curve. You can rescale this curve as you did before. Typing rescale < Enter > with no argument will return the original curve.

  • Finally, you might want to make a hardcopy (printout) of your lightcurve. to create a postscript file that can be printed, type at the PLT> prompt:

    filename.ps/PS (make sure there are no spaces in this command) this will make a ps file in your main directory that you can later print out.

  • Save your light curve by typing save curve < Enter > and enter a name for your light curve such as gkper_curve < Enter > which will be save by the program under the name gkper_curve.lc

• Extracting an Energy Spectrum from the Lightcurve
  • You will want to make an energy spectrum of the data we have on GKPER. An energy spectrum contains vital data on the photons that we have collected from our source - and therefore the photons produced in our source. You will see that by analyzing and fitting this spectrum to theoretical curves you can find the temperature of the source, its luminosity, and information about its chemical composition as well as its distance.

    Type extract spectrum < Enter >

    Followed by plot spectrum < Enter >.

    You will get a plot of COUNTS vs. CHANNEL

  • Look at your plot. The data at the end of your spectrum is not useful and will affect your analysis later on. You will want to cut out this data by applying a filter to your spectrum. You should eliminate data below channel 10 and above cahnnel 300, for example.

    filter pha_cutoff < Enter > then enter 10 for the lower cutoff and 300 for the upper cutoff.

    Then you must extract spectrum < Enter > and plot spectrum < Enter >.

  • Again you will want to save your spectrum by typing save spectrum < Enter > and entering a name like gkper_spec < Enter >. The program will ask you if you want to rebin the data. Enter yes < Enter >.

    Xselect has now saved your extracted energy spectrum under the name gkper_spec.pha. You should plot spectrum one more time to see what the rebinning did.

• When you are done using Xselect you may type exit < Enter > at the prompt and save the session so that all the images, curves and spectra remain in your directory as independent files. You are now able to take these data and manupilate them to produce power spectra, as well as fit the spectral data to learn more about the properties of this star!

• You shold be back at the regular prompt and out of Xselect. Type ls < Enter > to see a list of the files your session created. They should begin with session1 followed by suffixes that indicate the type of file they are. For example session1_fits_curve.xsl is the file containg the lightcurve you produced.

• Creating a power spectrum

  To better analyze the light curve you extracted, it is useful to make a power spectrum, which is the Fourier transform of the light curve so that you may see the major features of the curve.

  • At the prompt type powspec < Enter >. You will be asked to input a lightcurve file.

    You may enter session1_fits_curve.xsl or gkper_curve.lc which is your lightcurve that you saved manually.

  • You will be asked for the 'window file'. This is a mask that allows you to choose various subsets of the data. Choose the default.

  • When asked to select newbin time, the program is asking how much time can it group together into one bin. At first, type in the default values given. This will bin all the data into one plot or frame (which allows you to select 1 < Enter > when asked for the number of intervals/frame).

  • Respond to Rebin Results? with 0 < Enter >.
  • Select a name for the output file such as gkper.fps < Enter >

  • Type yes< Enter > to plot the results.

  • Enter your PGPLOT device to be /xw < Enter >.

  • Behold the power spectrum!

    The axis on you plot should be labeled Power vs. Frequency (Hz) and have the bintime printed at the top right corner. The power spectrum does not show any dominant frequency in the lightcurve. It is mostly noise. This is because our source is weak and because the ROSAT PSPC is only sensitive up to an energy of 1keV. There should be a peak at or around 2.864$\times$10$^{-3}$Hz which is a period of 349 seconds.

    With a different detector the noisy frequencies would not be present and there would be an obvious peak at the frequency of the source.

• The ROSAT PSPC response matrices

  Since the detector spans 256 pixels on each axis there are certain factors arising from the detector itself that must be accounted for before further analyzing our data. For each position in the detector there is a certain probability that a photon of a certain energy will be recorded as an event. This probability function (independent of the source we are pointing at) is located in a file that has been created for the ROSAT PSPC named: pspcb_gain2_256.rmf.

  The energy spectrum you extracted was plotted in Counts vs. Channel. Each channel on the detector corresponds to an energy. In order to analyze the data properly Xspec must convert the spectrum from Counts vs. Channel to Counts vs. Energy and for this you will need a file named pspcb_v2.spec_resp.

  • To retrieve these files you must go back into your Netscape window. Enter the URL:

    http://xray.rutgers.edu/$\sim$matilsky/documents/

  • At the top of the netscape screen. A page entitled Index of $\sim$matilsky/documents should appear with a column of links to various files. With the right mouse button click on pspcb_gain2_256.rmf and select the option Save Link As...

    In the dialog window that appears, make sure the correct directory to which you want to save these files appears in the Selection box (the same directory with all your GK PER files).

  • Click on OK.

  • Repeat this for pspcb_v2.spec_resp.

• Preparing the energy spectrum for analysis in Xspec.

  The energy spectrum you extracted in the last step of our Xselect session can be model-fit in a program called Xspec to determine the characteristics of our source. First, however, we must prepare our data to be used in Xspec.

  • The task pcarf will make the necessary channel to energy corrections to your gkper_spec.pha file.

    Type pcarf < Enter > and input gkper_spec.pha < Enter > as your PHA file.

  • Next you will be asked for the RMF file explained above. Input pspcb_gain2_256.rmf < Enter > .

  • Name the ARF file (which is what this program outputs) gkper.arf< Enter > .

  • Enter pspcb_v2.spec_resp < Enter > for the SPECRESP file.

• Entering your spectrum into Xspec

  You have now created all the necessary data files to run an Xspec analysis on GKPER. The next step is to open the Xspec package and fit our data to some spectral models.

  • Type xspec < Enter > to call up the package.

  • The first thing to do is enter the data into the program. Type data gkper_spec.pha < Enter > .

  • Command the program to ignore glaringly bad data points that may be problematic to a good fit by typing ignore bad < Enter > .

  • Next, you should tell the program which plotting device to use to plot your spectrum.

    Type cpd /xw < Enter > (change plotting device).

  • Now you must give the program the data it needs regarding the channel to energy conversion and the ancillary response function we created using pcarf

    Type resp pspcb_gain2_256.rmf < Enter > .

    Followed by arf gkper.arf < Enter > .

  • To plot your spectrum type plot data < Enter >.

    If you type plot ? < Enter > you will get a list off all the things besides your data that you can plot.

  • Notice that the plot that appeared is in Counts vs. Channels and it is similar in shape to the spectrum you extraced from Xselect. To convert from channels to energy, type setplot energy < Enter > followed by plot data < Enter >.

    It is also possible to use the command plot ldata < Enter > which plots the data with a logarithmic scale on the y-axis.

• Fitting the data to spectral models.

  We will attempt to fit our data to three spectral models:

  1. Powerlaw spectrum

     This model represents a spectrum that arises from a source whose radiating electrons are moving within a magnetic field and therefore experience a force perpendicular to their motion. This torque accelerates the electrons and causes them to radiate in a characteristic way. The spectrum produced by this effect has the mathematical form of a powerlaw where the intensity of the radiation energy is proportional to the energy raised to a power.

     I(E)=AE$^\alpha$

     Where:

     $\alpha$ is a spectral index, and

     A is a constant.

  2. Blackbody spectrum

     A blackbody spectrum is one that is only dependent on the temperature of the radiating source. This model assumes that the radiating photons get their energy solely from the temperature of the object.

     I(E)=2E$^3$/h$^2$c$^2$(e$^{E \over kT}$-1)

     Where:

     h is Planck's constant, and

     c is speed of light.

  3. Thermal Bremsstrahlung

     This radiation spectrum is caused by the thermal motions of electrons in gasses hot enough to be ionized. The presence of charges from the ions exert electromagnetic forces on the electrons that 'bend' their motion and cause them to radiate. The distribution of the energy emitted from such 'bending' depends on the densities of both electrons and ions as well as the temperature of the gas, and it has the form:

     A(E)=C$\times$G(E,T) Z$^2$n$_e$n$_i$(kT)$^{-1/2}$e $^{-E \over kT}$

     Where:

     C is a constant, G(E,T) is a function that varies with temperature and energy, Z is the charge of positive ions in the gas, n$_e$ and n$_i$ are electron density and positive ion density, respectively, and T is the temperature.

  • We will enter a powerlaw spectrum first. Type model phabs(powerlaw) < Enter > or for the abbreviated command (Xspec accepts truncated commands as long as they are unambiguous) type mo pha(po) < Enter >.

    You will receive a list of parameters that this particular model requires. These parameters are default and we can change them to fit our data with the fit command later. We will accept the default values by pressing < Enter > three times.

    The output that follows includes a $\chi$$^2$ (Chi-Squared) and a reduced $\chi$$^2$ (the original $\chi$$^2$ divided by the number of degrees of freedom). If the reduced $\chi$$^2$ is near 1 then the fit should be good. The null hypothesis probability is the probability of getting a value of $\chi$$^2$ as large or larger than observed if the model is correct. If this probability is small then the model is not a good fit.

  • plot data < Enter >

    Your fit should be very bad. This is because the model is constructed using the initial default values that do not correspond to your data. Notice that the null hypothesis probability is 0 and that the reduced $\chi$$^2$ is tens of thousands large. Both of these facts indicate a poor fit.

  • You can help the fit by renormalizing your data, you are basically scaling the model down by multiplying the entire curve by a single factor determined by your data. Just type renorm < Enter > and plot data $\$< Enter > to see the results.

    Notice that the right side of the model is attempting to match the slope of the data. Also notice the dramatic reduction in $\chi$$^2$ (but still not close to 1).

  • We will now fit our data. The fit command will attempt to match the parameters of the model to the data. The algorithm goes through ten iterations at a time attempting to find a minimum $\chi$$^2$ and prints out the results of the fit.

    Type fit < Enter > and after ten iterations, when prompted to continue fitting type y < Enter >.

  • When the fitting is done plot data < Enter > to see the results.

    The model does converge to the data though not exactly. To see where the model departs from the data type plot data residuals < Enter >. At the bottom of the screen, the model is represented by the straight line and the data oscillates above and below. It is only toward the higher energies that the residuals shrink and stop oscillating.

    Now look at the tabulated results. The reduced $\chi$$^2$ should be around 6 or 7, which is better than our previous results, but not close to 1. The null hypothesis probability is tiny as well. This indicates that our model is not good enough to describe this source very well.

    In the table (your results may not exactly match but should be close):

    ---------------------------------------------------------------------------
    ---------------------------------------------------------------------------
    mo = phabs[1]( powerlaw[2] )
    Model Fit Model Component  Parameter  Unit     Value
    par   par comp
      1    1    1   phabs      nH       10^22     0.1122     +/-  0.4740E-02
      2    2    2   powerlaw   PhoIndex            4.015     +/-  0.1184
      3    3    2   powerlaw   norm               2.0524E-02 +/-  0.5383E-03
    ---------------------------------------------------------------------------
    ---------------------------------------------------------------------------
    

    Recall that the EXOSAT powerlaw fit gave a column density (nH) of 2.32$\times$10$^{23}$ and here we have a column density 1.12$\times$10$^{21}$ . Two orders of magnitude smaller!

    How would you account for this inconsistency?

    The reduced $\chi$$^2$ from this analysis is also closer to 1 than the EXOSAT analysis. This implies that the fit is somewhat better. Are these signs actual or are they a result of fewer data points (20 vs 57) that give the illusion of a better fit?

    Clearly with EXOSAT's wider energy band we are able to show a spectrum with features that the ROSAT data could not reveal - given the 1keV threshold of the PSPC detector.

  • Lets try fitting a blackbody spectrum to our data. Type model phabs(bbody) < Enter> (or mo pha(bb)) and again accept the default parameters by pressing < Enter > three times.

  • plot data < Enter >

    Again this is not a good fit and $\chi$$^2$ is in the thousands.

  • renorm < Enter > and plot data to scale down the model.

  • You must now fit < Enter > the model to the data and continue to fit the data by entering y when prompted. When fitting is done, plot data residuals < Enter > to see the deviation from the curve.

    This fit is not as good as the power law fit resulting in a reduced $\chi$$^2$ around 14 and an even smaller null hypothesis probability. The temperature (in units of keV) from the output in kT is 0.1550 or 1.8E6 Kelvin. This is much lower than the EXOSAT temperature of 3.6$\times$10$^7$ Kelvin.

    Also, note the column density (nH) in this output. The rising function on the left which indicates absorbtion and complicates the fit.

    The deviation in column density between models is greater with the ROSAT than with EXOSAT implying a better consitency among the EXOSAT fits. This is probably due to more datapoints from the broader energy range in EXOSAT's detector. The column density here should be around 3.4E20 which is lower than that calculated by the power law model by an order of magnitude.

    The presence of the rising function on the left indicates absorbtion and complicates the fit.

  • Finally, let's try a thermal bremsstrahlung radiation model. Type mod pha(bre) < Enter > and accept the initial parameters as before.

  • plot data < Enter >

  • renorm < Enter > and plot data < Enter > again.

  • fit < Enter > until the fitting is complete. Then plot data residuals < Enter >.

    The results give a better reduced $\chi$$^2$ (round 10) and a less tiny null hypothesis probability, but it seems that the powerlaw fit was the best one. We can calculate a temperature from here too, and compare it to the blackbody temperature we calculated earlier. With an output of 0.3700keV (or something around that value) the temperature comes out to be 4.3E6 Kelvin. This value agrees at least to the same order of magnitude, showing that our analysis is consistent.

    This temperature and that extracted from the blackbody analysis are lower than the EXOSAT temperature, but there we got completely inconsistent results.

    Again the column density changed. This time it increased slightly to about 6.9E20.

    None of these fits were good enough, however to provide confident results.

• Fitting the data while neglecting absorbtion

  It would be useful to examine how well our data fits the model spectra without the leftmost points indicating absorbtion. This way the fitting process will be 'interacting' with the data points representing photons produced by the processes inside the source and not by the interstellar medium.

  • First we must remove any model from our data. Type model none < Enter > then plot data < Enter >.

  • The data is in counts vs. energy. We would like to edit our data to remove points, it is easiest to do this by converting back to channels. Type setplot channel < Enter > and plot data < Enter >.

  • To neglect the absorbed points use the ignore command and type ignore 0-15 < Enter >. This commands the program to ignore channles 0 to 15 in the data. plot data < Enter > again to see the new dataset. The leftmost point is still sloping down but it is not certain that it is due to absorbtion, so we will allow it to remain.

  • Now switch back to energy units by typing setplot energy < Enter > and plot data < Enter >.

  • Select a powerlaw model, renormalize, fit, and plot the data.

    Did your reduced $\chi$$^2$ improve from the original powerlaw fit?

    What is the column density for this data set?

  • Repeat the process for blackbody and thermal bremsstrahlung models.

    What about these reduced $\chi$$^2$'s and column densities?

    Did the temperature output change and if so did it go up or down? why?

    Was the change in temperature as significant as that of the column density?

  • Now that you have done the analysis for each model, twice, and have looked at the data with and without absorbtion, which model fit your data best?

• Remove all models from your data by typing model none < Enter >. Switch back to channel mode again. This time you will notice 0-15 < Enter > and plot data < Enter >.

• Now select the model that fit your data best. Using all the points, fit the model to the data and plot it.

  Type flux < Enter >. You will receive an output showing the flux of the star in photons/cm$^2$/s and in ergs/cm$^2$/s. Once you know the flux and the distance to the source, you can know its luminosity.

  How did the flux here compare with EXOSAT? Why?