BLACK HOLES IN MY SCHOOL Observing Stellar Mass Black Hole Candidates
This module integrates an online training course introducing participants to the use of the inquiry methodology and the integration of ICT tools in schools practices. This module 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.
Learning outcomes At the end of this module participants should know the procedure used to identify black hole candidates and how to determine the mass limits of a compact object in a binary system.
Rationale This module introduces participants to the technique used to determine the mass limits of a compact companion to a visible star.
Resources Set of images of black hole candidates Salsa J Excel Images and parts of the text credited to Fraser Lewis (Faulkes Telescope Educational Team) BHIMS is developed in the framework of the SoNetTE project
Eclipsing Binary Stars The most common stellar mass black hole candidates live in binary systems where one of the components is a compact object (a black hole or neutron star) and the other a ‘normal’ star. The light curve of a binary system can allow us to study the different components. Take for instance the example below: In the case where one of the components is a compact object we only see the ‘normal’ star (usually a main sequence star or anevolved red giant). In the case of Low Mass X-ray Binaries (LMXBs), these stars fill their Roche Lobes and therefore acquire a pear (or teardrop) shape. As the two objects orbit their common centre of mass, different parts of the system are visible to us. Depending on the inclination of the system (where 0° is a face-on orbit and 90° is an edge-on orbit) a limit on the mass of the compact object can be established. Figure 1 Light curve of binary star Kepler-16 (Credit: NASA)
The image in Figure 2 shows the infrared light curve of the black hole candidate A0620-00. Depending on the position of the companion star and the compact object, with its accretion disc (see fig.4), we see different amounts of light coming towards the observer. Remember that we don’t see the individual components; we only observe a dot whose brightness changes in time. It is from the study of these changes in the form of a light curve that we can start to infer some of its characteristics. Figure 2 Infrared light curve of A0620-00 (a binary system where the compact object is a strong black hole candidate). Credit: Shahbaz et al, 1994.
Images and parts of the text credited to Fraser Lewis (Faulkes Telescope Educational Team) BHIMS is developed in the framework of the SoNetTE project
Finding the minimum mass for the black hole candidate XTE J1118+480 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 6 000 light-years away in the constellation of Ursa Major.
The system is composed of a compact object and a low mass star (less than 2 solar masses). The compact object is pulling matter from its companion and the intense, time-variable heating of this material in the accretion disc helped astronomers discover this object. This heating means that the disc emits copious amounts of Xrays. Figure 3 Location of the black hole candidate XTE J1118+480 (Credit: Black Hole Encyclopedia)
The optical component of this system (the star; KV UMa) already appeared in images (some over 40 years old) and it appears to be following a looping path that takes in out of the disc of our Galaxy (see Figure 5). Studies of this trajectory indicate that the object might have been inside a globular cluster and was probably kicked out after the supernova explosion of the massive progenitor star that gave birth to the compact object. The estimated mass of this black hole candidate is around 7 solar masses. This is precisely what we want to confirm with this exercise.
Figure 4 Here we find an artist impression of the binary system XTE J1118+480 composed by a low mass star and a compact object. The material of the companion star is attracted by the intense gravitational field of the compact object forming an accretion disc. Credit: Hynes
Figure 5 Artist impression of the path of the XTEJ1118+480 through the disc of our Galaxy. Credit: STScI
Images and parts of the text credited to Fraser Lewis (Faulkes Telescope Educational Team) BHIMS is developed in the framework of the SoNetTE project
The data we will analyse are a sequence of 62 images obtained by Faulkes Telescope North taken on 13/05/2009. We will analyse this images using Salsa J and Excel. The images show several stars surrounding the object we wish to study. We will select some of these stars to be comparison stars in our study. The procedure is to make photometry measurements of all the comparison stars and the black hole candidate for all the images. If we are fortunate, the brightness (or intensity) of the comparison stars should remain constant (although there are variations in the images based on weather) as a function of time while the brightness of the binary system containing the black hole candidate should vary. By plotting the intensity against time we should see variability and can use this to estimate the mass of the non-visible compact object.
Figure 6 The finding chart (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)
First, we need to determine the best aperture radius before proceeding with the photometry.
Figure 7 Evaluating the best aperture with Salsa J, as explained in the photometry lesson
Images and parts of the text credited to Fraser Lewis (Faulkes Telescope Educational Team) BHIMS is developed in the framework of the SoNetTE project
Previous studies show show that average star in this image has a FWHM of 4 pixeis In practice, a good choice for the radius of an aperture is about 1.5 or 2.0 times the FWHM. In the examples below the value used was 6 for the aperture radius. Now you can start to measure the intensity for the 3 comparison stars and for the black hole candidate. Make the measurements in each image for all 4 objects. Since the images are 2 Mb each, it is best to process no more than 20 images at a time. Alternatively, you can distribute the images amongst a group of students and collate the group’s results later, ensuring that each group use the same aperture radius and the same comparison stars. You can choose to ‘tile’ them (in Salsa J, ‘Tile’ is under ‘Window’) which will make it easier to perform the procedure. It is important to process the images in order which is easy if you follow their number.
Figure 8 Selection of 20 images, tiled and then reordered
Make sure you adjust the brightness and contrast in all images in order to be able to see all the objects. If you can’t see all of them don’t use the particular image. Sometimes if you close and reopen the image the brightness and contrast appear better. Since we will be working with relative magnitudes, where we are comparing intensities of the comparison stars and the black hole candidate we don’t have to worry about absolute magnitudes and standard stars etc. 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. You will also need the Modified Julian Date (MJD) for each image. You find this information in the header of FTS images. In Salsa J you select the “Show Info” under the Image menu and in the header you will find the value for MJD. This is the value to be used on the x-axis of your graph.
Images and parts of the text credited to Fraser Lewis (Faulkes Telescope Educational Team) BHIMS is developed in the framework of the SoNetTE project
After removing a couple of images, your results should look like this:
star 1
54964.40339
54964.39307
54964.38534
54964.37761
54964.36671
54964.35897
54964.35124
54964.3435
54964.33576
54964.32451
54964.31678
54964.30905
54964.30037
54964.29263
54964.28377
54964.27603
54964.26829
54964.26055
54964.2528
star 2 54964.24506
counts
10000 9000 8000 7000 6000 5000 4000 3000
star 3 xte J1118
Julian Date Figure 9 Plot of counts over time
From this graph we can clearly see that our target varies far more than the comparison stars. 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. But we can make a rough estimate from the graph above since it is showing evidence that the whole period is in the set of images. We can try to adapt the value of the period that best fit our purposes. You students can play a bit with the value of the period and try to find the best fit. Scientists already know the period of this object P= 4.08 hrs = 0.17 days. (http://adsabs.harvard.edu/abs/2001ApJ...556...42W) A nice tutorial on the calculation of periodicity and determination of phase in variable systems can be found here: http://www.aavso.org/files/Chapter12.pdf The formula to transform the Julian dates in Phase is the following đ?‘ƒâ„Žđ?‘Žđ?‘ đ?‘’ =
đ?‘€đ??˝đ??ˇ − đ?‘‡0 đ?‘ƒđ?‘’đ?‘&#x;đ?‘–đ?‘œđ?‘‘
Where the MJD is given in the header of each image, T 0 is the MJD of the first image and the period is 0.17 days. The result should look like this.
Images and parts of the text credited to Fraser Lewis (Faulkes Telescope Educational Team) BHIMS is developed in the framework of the SoNetTE project
9900
8900
7900
xte J1118
6900
Average star
Counts
5900
4900
3900 0
0.2
0.4
0.6
0.8
1
Phase Using the formula to determine the mass limit of the compact object đ?‘€1 3 sin đ?‘– 3 đ?‘ƒđ??ž2 3 đ?‘“ (đ?‘€) = = (đ?‘€2 + đ?‘€1 )2 2đ?œ‹đ??ş
where M1 and M2 are the masses of the compact object and the companion star respectively, P the orbital period, i.e., the time it takes for the star to complete an orbit, 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 We can use the radial velocity of the visible component of this system was determined to be ~ 700 km s-1 , the mass of the companion is ~ 6.1 Solar Masses (http://adsabs.harvard.edu/abs/2001ApJ...556...42W) Both of these are determined using spectrocopy – the companion mass is inferred once we know its spectral class and several spectra can be taken to determine the object’s radial velocity. Images and parts of the text credited to Fraser Lewis (Faulkes Telescope Educational Team) BHIMS is developed in the framework of the SoNetTE project
P = 0.17 * 24 * 60 * 60 = 14 688 s Msolar = 1.9891 Ă— 1030 kg Assuming all the above values we end up with the following value for the mass limit of this black hole candidate: đ?‘“(đ?‘€) =
đ?‘€1 3 sin đ?‘– 3 14 688 đ?‘ ∗ (700đ?‘˜đ?‘š đ?‘ −1 ) 3 = (đ?‘€2 + đ?‘€1 )2 2đ?œ‹ đ?‘Ľ 6.67384 ∗ 10−11 m3 kg −1 s−2
đ?‘“ (đ?‘€) =
đ?‘€1 3 sin đ?‘– 3 = 1.2 ∗ 1031 đ?‘˜đ?‘” ~ 6.3 đ?‘€đ?‘ đ?‘œđ?‘™đ?‘Žđ?‘&#x; (đ?‘€2 + đ?‘€1 )2
These calculations used approximate values but reached a very good guess for the mass of the stellar black hole candidate XTE J1118+480. The assumed value for the mass function (the minimum mass) is of the order of 6.1 Msolar (http://arxiv.org/pdf/astro-ph/0104032.pdf)
Images and parts of the text credited to Fraser Lewis (Faulkes Telescope Educational Team) BHIMS is developed in the framework of the SoNetTE project