Searching for Black Holes. Photometry in our Classrooms.

Transcription

1 Searching for Black Holes. Photometry in our Classrooms. Abstract Chiotelis Ioannis 1, Theodoropoulou Maria 2 1 Experimental High School of University of Patras 2 University of Patras 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

2 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, 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)

3 Counts 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 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) Aperture Radius Figure 4: Photometry calibration. Counts for Aperture Radius

4 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 The study system-object The object we will study is the black hole candidate XTE J 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 J (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 ( on13/05/2009) and we followed the photometry analysis procedure using Salsa-J 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.

5 Figure 6: The map of stars locating the object and the comparison stars. XTE J 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 (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

6 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 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: Where the MJD is given in the header of each image and T 0 is the MJD of the first image. Scientists already know the period of this object P= 4.08 hrs = 0.17 days. ( ). The results are being shown in Figure Results Using the following formula we tried to determine the mass limit of the compact object [12]. (1)

7 (2) where M 1 and M 2 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 K 2 the radial velocity of the visible star. Εικόνα 9: The orbital period of our system According to scientists ( ) 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 = s and Msolar = 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 J ( )

8 4. References [1] Postnov, K., & Yungelson, L. (2007). The evolution of compact binary star systems. arxiv preprint astro-ph/ [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/ [4] Blanchet, L., & Schafer, G. (1993). Gravitational wave tails and binary star systems. Classical and Quantum Gravity, 10(12), [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), [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), [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), [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 Based 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 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: [11] Doran, R., Lobo, F. S., & Crawford, P. (2008). Interior of a Schwarzschild black hole revisited. Foundations of Physics, 38(2), [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: [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 ).