Download Searching for Black Holes. Photometry in our Classrooms.

Searching for Black Holes. Photometry in our Classrooms.
Chiotelis Ioannis1, Theodoropoulou Maria2
1
Experimental High School of University of Patras
2
University of Patras
Abstract
Following the main axis of STEM, this module integrates the use of inquiry based learning
methodology and the integration of ICT tools in schools practices. Is devoted to the implementation of
a research based experiment where students can be involved in the identification of stellar mass black
hole candidates and the procedure to “measure” their mass limits. We encourage students to operate
the Salsa-J software, perform some photometry measurements and try to spot a Black Hole candidate
through images captured by telescopes, available on line, or ordered to be taken through a remote
telescope. At the end of this module students should know how to identify black hole candidates and
how to determine the mass limits of a compact object in a binary star system. Thus, Science, Physics
and Astronomy are strongly supported by ICT technology and Mathematics is contributing the data
processing and conclusions outcomes.
Keywords: Photometry, black holes, Salsa-J, binary star systems, full width half maximum.
1. Introduction
1.1 Binary Star Systems
Since 1970 when UHURU satellite was launched by NASA, the study of binary
star systems was rapidly developed [1],[2],[3],[4]. Especially, X-ray radiation
emitting binary systems are of high importance, while in this case one of the
components is a compact object probably a black hole or a neutron star, and the other
component a „normal‟ star (usually a main sequence star or red giant) [5],[6]. The star
usually orbits around the common center of mass gradually losing its mass towards
the black hole or neutron star. Thus, the discovery of a binary X-ray star system can
reveal an out of sight black hole.
While the compact object is pulling matter from its companion due to the intense
gravitational field a disc is forming around the compact object called accretion disc.
Depending on the position of the companion star and the compact object, with its
accretion disc, different amounts of light are coming towards the observer [7].
Actually, we cannot observe the individual components, but only a dot which
brightness changes in time. It is from the study of these changes in the form of a light
curve that we can conclude to some of the binary‟s system characteristics. The image
in Figure 1 shows the infrared light curve of the black hole candidate [8]. Depending
on the position of the companion star and the compact object, with its accretion disc,
we see different amounts of light coming towards the observer. Thus we can assume
whether the compact object is a black hole or a neutron star.
1.2 Photometry
Photometry gained significant importance recently as it is used to discover
exoplanets by measuring fluctuations in the intensity of a star‟s light over time [9].
Generally, photometry is used to generate light curves revealing the variability of
light output over time of objects such as variable stars and supernovae. Photometry is
the measurement of the intensity or brightness of an astronomical object (e.g. star or
galaxy). For example, a star looks like a point of light when you look at it just with
your eyes but the Earth‟s atmosphere smears it out into something that looks like a
round blob when you use a telescope to look at it. In order to measure the total light
coming from the star, we must add up all of the light from the smeared out star.
Figure 1: Infrared light curve of a strong black hole candidate. Credit: Shahbaz et al, 1994.
1.2.1 Aperture radius
One of the most important definitions in photometry is the aperture radius.
Aperture radius defines the radius of the circle that is used to count the pixel values in
the image. The radius of the circle is very important - if the radius is too small, it will
not count all the light coming from the star and if it is too big, it may count too much
background sky or other stars in the image. Therefore we may not get accurate
measurements. In our software (Salsa-J) the radius of aperture is automatically set as
the Full Width Half Maximum (FWHM) of the stars in the image. The FWHM is used
to describe the width of an object in the image. The FWHM is an average measure
that counts the telescope‟s optics, the image recording CCD and the atmosphere
through which the light passes. In order to estimate the FWHM is to cross sect a star
image (Figure 2). The base of the slice is at the value for the background sky, while
the top of the peak represents the counts measured in the brightest pixel along the
slice. The FWHM is the number of pixels across the peak at a point halfway up from
the base.
Figure 2: Estimation of Full Width Half Maximum (FWHM)
2. Experiment
2.1 Calibration
In order to calibrate our photometry measurements we must follow the next steps.
In Salsa-J, we choose Analyse>Photometry Settings. Then we select force Star
Radius and choose the value 6. Next, we go to Analyse>Photometry and another
empty window will then appear entitled „Photometry‟ (Figure 3). Using the mouse,
we click on a star in our image. The intensity of the object is calculated by adding up
all the pixel values within the radius of the aperture. We can clearly see that the
chosen radius is too small. Let‟s increase it a bit to 8. Click on the star again and a
new measurement will appear. Still the radius is too small. Increase the value to 10
and continue until you reach a radius of 40.
Figure 3: Calibrating the photometry measurements
Counts
Then in Excel we create two columns one for Radius and one for Intensity adding the
radius and intensity values from Salsa-J. Then we plot a graph of this data (Figure 4).
450000
400000
350000
300000
250000
200000
150000
100000
50000
0
0
5
10
15
Aperture Radius
Figure 4: Photometry calibration. Counts for Aperture Radius
20
We can see the rapid rise of intensity as the radius of the aperture increases. This
is because more of the star is included in the increasing radii of the apertures. The
graph begins to flatten out when we have the entire star within the aperture, but keeps
rising gradually as more and more of the background sky is included. From this graph,
we can see that the best radius to use is around 20. Once we have chosen the best
aperture radius, this can be set for our photometry analysis. It is advisable to carry out
this exercise every time we come to work with a new set of images. These steps are
the main steps of photometry calibration and photometry measurements.
2.2 Finding a black hole candidate
2.2.1 The study system-object
The object we will study is the black hole candidate XTE J1118+480. It was
discovered in March 2000 by the Rossi X-ray Timing Explorer satellite. It is
approximately 6000 light-years away in the constellation of Ursa Major (Figure 5).
Figure 5: Location of the black hole candidate XTE J1118+480 (Credit: Stellarium)
The system is composed of a compact object and a less than 2 solar masses star. The
optical component of this system is a star (KV UMa), while the estimated mass of the
black hole candidate is around 7 solar masses. This is precisely what we want to
confirm with this exercise. The data we analyzed were obtained by Faulkes Telescope
(https://archive.lco.global/ on13/05/2009) and we followed the photometry analysis
procedure using Salsa-J.
2.2.2 The experimental procedure
As we can see on Figure 6 several stars are surrounding the object we wish to
study. We will select some of these stars as reference stars in our study. The
procedure is to make photometry measurements of all these stars and the black hole
candidate in as many as possible images [10]. We are looking for differences in the
brightness (intensity) of the comparison stars. These variations probably reveal that
these stars are orbiting around the accretion disc of the black hole candidate. In any
case we must be careful while these variations can often be attributed to weather
conditions during the observation.
Figure 6: The map of stars locating the object and the comparison stars. XTE J1118+480 is denoted by
the two black lines – the comparison stars are shown as 1, 2, 3. (Image from Faulkes Telescope North)
Ensuring that the variations are due to orbital reasons we can then plot the
intensity against time. Thus we should trace the variability and use this to estimate the
mass of the non-visible compact object. According to the procedure described in
paragraph 1.2.1 (Figure 2) we are determining the best aperture radius before
proceeding with the photometry. In practice, a good choice for the radius of an
aperture is about 1.5 or 2.0 times the FWHM (Figure 7).
Figure 7: Evaluating the best aperture with Salsa J
Then we must measure the intensity for the 3 comparison stars and for the black
hole candidate in as many as possible different images. During our school project we
distribute the images amongst a group of students, ensuring that each group uses the
same aperture radius and the same comparison stars. Furthermore, we adjust the
brightness and contrast in all images in order to be able to see all three objects. If we
can‟t see all of them we decide not to use the particular image.
2.2.3 Data processing
Since we are working with relative magnitudes, we don‟t have to worry about
absolute magnitudes and standard stars. We are not looking for the absolute value of
the magnitude of the object but the variations to its intensity relative to other stars in
the same image. We also used the Modified Julian Date (MJD) for each image. We
found this information in the header of FTS images. In Salsa J we selected the “Show
Info” under the Image menu and in the header we found the value for MJD. This is
the value to be used on the x-axis of our graph. Thus, we plotted the following graph
(Figure 8):
Figure 8: Plot of counts vs. time
From this graph we can clearly see that our target (xte J1118) varies far more than
the comparison stars (stars 1, 2, 3). We already know that the orbit of the visible star
and compact object around each other is periodic. Finding the orbital period is
complicated and time demanding [11]. But we can make a rough estimate from the
values plotted on Figure 8. The formula that transforms the Julian dates in Phase is the
following:
(1)
Where the MJD is given in the header of each image and T0 is the MJD of the first
image. Scientists already know the period of this object P= 4.08 hrs = 0.17 days.
(http://adsabs.harvard.edu/abs/2001ApJ...556...42W ). The results are being shown in
Figure 9.
3. Results
Using the following formula we tried to determine the mass limit of the compact
object [12].
( )
(
(2)
)
where M1 and M2 are the masses of the compact object and the companion star
respectively, P the orbital period, G is the universal gravitational constant, i is the
inclination of the orbital plane of the system with the line of sight of the observer and
K2 the radial velocity of the visible star.
Εικόνα 9: The orbital period of our system
According to scientists (http://adsabs.harvard.edu/abs/2001ApJ...556...42W ) the
radial velocity of the visible component of this system was determined to be ~700
km/s and the mass of the companion is ~6.1 Solar Masses. We tried to confirm these
values from our measurements. Calculating that P = 0.17 * 24 * 60 * 60 = 14 688 s
and Msolar = 1.9891 × 1030 kg we have [13]:
( )
( )
(
(
)
(
)
)
Although we used approximate values, we can mention that our calculations reached a
very good value for the mass of the stellar black hole candidate XTE J1118+480.
(http://arxiv.org/pdf/astro-ph/0104032.pdf )
4. References
[1] Postnov, K., & Yungelson, L. (2007). The evolution of compact binary star
systems. arXiv preprint astro-ph/0701059.
[2] Belczynski, K., Kalogera, V., & Bulik, T. (2002). A comprehensive study of
binary compact objects as gravitational wave sources: evolutionary channels,
rates, and physical properties. The Astrophysical Journal, 572(1), 407.
[3] Thorsett, S. E., Arzoumanian, Z., McKinnon, M. M., & Taylor, J. H. (1993).
The masses of two binary neutron star systems. arXiv preprint astroph/9303002.
[4] Blanchet, L., & Schafer, G. (1993). Gravitational wave tails and binary star
systems. Classical and Quantum Gravity, 10(12), 2699.
[5] Aharonian, F., Akhperjanian, A. G., Aye, K. M., Bazer-Bachi, A. R., Beilicke,
M., Benbow, W., ... & Bolz, O. (2005). Discovery of very high energy gamma
rays associated with an X-ray binary. Science, 309(5735), 746-749.
[6] Gallo, E., Fender, R. P., & Pooley, G. G. (2003). A universal radio–X-ray
correlation in low/hard state black hole binaries. Monthly Notices of the Royal
Astronomical Society, 344(1), 60-72.
[7] Fabian, A. C., Rees, M. J., Stella, L., & White, N. E. (1989). X-ray
fluorescence from the inner disc in Cygnus X-1. Monthly Notices of the Royal
Astronomical Society, 238(3), 729-736.
[8] Shahbaz, T., Ringwald, F. A., Bunn, J. C., Naylor, T., Charles, P. A., &
Casares, J. (1994). The mass of the black hole in V404 Cygni. Monthly
Notices of the Royal Astronomical Society, 271(1), L10-L14.
[9] Brown, T. M., Charbonneau, D., Gilliland, R. L., Noyes, R. W., & Burrows,
A. (2001). Hubble Space Telescope Time-Series Photometry of the Transiting
Planet of HD 209458Based on observations with the NASA/ESA Hubble
Space Telescope, obtained at the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.
under NASA contract NAS 5-26555. The Astrophysical Journal, 552(2), 699.
[10]
Doran, R., Melchior, A. L., Boudier, T., Ferlet, R., Almeida, M. L.,
Barbosa, D., & Roberts, S. (2012). Astrophysics data mining in the classroom:
exploring real data with new software tools and robotic telescopes. arXiv
preprint arXiv:1202.2764.
[11]
Doran, R., Lobo, F. S., & Crawford, P. (2008). Interior of a
Schwarzschild black hole revisited. Foundations of Physics, 38(2), 160-187.
[12]
Lewis, F., Russell, D. M., Fender, R. P., Roche, P., & Clark, J. S.
(2008). Continued monitoring of LMXBs with the Faulkes Telescopes. arXiv
preprint arXiv:0811.2336.
[13]
Roberts, S., Roche, P., & Lewis, F. (2013, August). Educational
projects with the Faulkes Telescopes. In Proc. Discover the Cosmos
Conference: e-Infrastructure for an Engaging Science Classroom, Volos,
Greece (pp. 25-32).