Astronomy with SalsaJ
Tracking the movement of stars around the centre of our Galaxy, the Milky Way, you can unveil the hidden monster: a black hole, four million times more massive than our Sun!
Black holes are objects whose gravity is so great that nothing - including light - can escape them. Black Holes can not directly be seen, one can infer its presence by searching for the gravitational influence it imposes on nearby objects, namely stars. Observations have been done during almost 20 years, with the most powerful telescopes, including a laser shooting star in a very "star wars" style...
This exercise offers, through the analysis of images of the galactic centre, measure the mass of the supermassive black hole. By following the movement of a star, thanks to Kepler's laws, the pupils will get very recent scientific results with a very good approximation. They will come to appreciate the limitations of the method and results.
An history of invisible holes
By 1796, the idea of "black hole" was put forward by John Michell and Pierre-Simon Laplace. The latter wrote in his Exposition of the World System:
"A luminous star, of the same density as Earth, whose diameter is 250 times larger than the Sun, would not, by virtue of its attraction, any of its rays from reaching us. It is therefore possible that the greatest luminaries of the world can, through this cause, be invisible. "
This idea was not taken seriously by astronomers of the time because they do not have satisfactory theory to describe these new stars. With general relativity, a theory invented by A. Einstein in the early twentieth century, astronomers have adequately describe what a black hole, but it took almost another century before most experts agree on their existence. Today, while black holes have never been observed directly, several indirect observations corroborate their existence.
Recently, new techniques for observing the sky in the infrared region were allowed to see the center of our galaxy, which is buried in the dust. Astrophysicists have discovered, so existence of a black hole "supermassive." The study of motion of stars near the galactic center can measure the mass of this black hole. This is about those Hands.
Morphology of Our Galaxy
The Milky Way, the white band that you can see the starry night sky is our galaxy. It consists of approximately 100 billion stars and many gas clouds. Its shape is a disk about 80,000 light years in diameter with a central bulge, the nucleus of the galaxy, as shown in the illustration below.
The Solar System, where the Earth is located, revolves on the outskirts of the galaxy around the nucleus. Many clouds of gas and dust between us and the nucleus have long prevented its direct observation. Recently, with high resolution infrared cameras, one could directly observe the motion of stars near the galactic center, as shown in the picture below.
Photo of the galactic center taken by the VLT, ESO, Chile.
In space we do not usually measure distances in meters but in light year. A light year is the distance light travels in one year, or 9.45*1015 meters! This explains why we can not measure the galaxy in meters ... Another unit of distance in practice for us is the day-light, which is the distance light travels in one day, or 2.59*1013 meters. On the picture, the stars closest to the center are less than a light year from the galactic center.
The Kepler's laws
Johannes Kepler (1571-1630) was a German astronomer known for having confirmed the heliocentric hypothesis (the planets orbit the Sun) by Nicolas Copernicus. By compiling and studying numerous observations made by Tycho Brahe, he postulated three laws that characterize the orbit of a planet around the Sun. The first law states that the trajectories of planets are not circles but ellipses. An ellipse is drawn on the diagram below:
It is characterized by a length of its semi-major axis, the length b of its semi-minor axis, the two foci S and S', and its center C. The third law states that when the square of the period T of a planet (the time it takes for a ride around the sun) is directly proportional to the cube of the semi-major axis a of the elliptical orbit of the planet:
a3 / T2 = constant
These laws stay true for the trajectory of a star rotating around a black hole "supermassive" property which we will leverage to calculate the mass of the central black hole.
Measuring the trajectory of a star
First, start SalsaJ and download the images
- Select the 12 FITS images (download the zip archive): tn000.fts, tn010.fts, tn020.fts, tn030.fts, tn040.fts, tn050.fts, tn060.fts, tn070.fts, tn080.fts, tn090.fts, tn100.fts & tn110.fts (Hold down the Shift key while clicking to open them all at once) and press "Open".
- Click on «Upload images in stack" in the menu "Stacks" menu "Images". Click "Start animation" in the same menu.
- What do you observe?
- Also in the menu "Stacks" menu "Images", press "Stop Animation". Back to the top of the animation repeatedly pressing the left arrow at the bottom of the window stack. Locate the reference star with the image below (note it is a bit confused by another star):
- Follow his progress on the other images by pressing the right arrow at the bottom of the window.
Does it make a full turn round? For how many years do the images tracked its progress (the date of the photo is written in the top left of the image) ?
- Back to individual images by clicking on "Convert Stack to Images" menu "Stack" menu "Images". Click on "cascade" in the menu "Window".
- Select the tool "Selections point" (a cross superimposed on a square in the main menu icon). Click with this tool at the center of the reference star and record the precise pixel coordinates of the star that appear in the "Results." Repeat for each image (if you have lost the reference star, start from the second stage or locate it looking at the images above).
| x pixels
| y pixels
Measurement of semi-major axis
- Report line X in column A and line Y in column B.
- Press tool "Chart" menu "Insert". Click on "scatter" in the left column. Click "Next." Select the input values remaining pressed the left click of the mouse. Verify that the Opton "Series in Columns" is checked. Click "Done". The graph is created.
- Stretch the graph vertically so that the scales on the abscissa and ordinate have approximately the same length. The major axis is along the X or Y?
- Select the tool "Ellipse" in the toolbar at the bottom (if it is not there, go to the View menu, "Toolbars" and click on "Drawing" for the show) .
- Draw an ellipse on the graph (if the ellipse is filled, double click, and in the color menu, select "no fill"). To convey the best possible ellipse at every point by varying the width and height, and its position.
- Measure the length of the major axis, denoted by "2 * a". It will help the tool "line" in the menu below to see the ends of the ellipse axis (to be more precise coordinates , double click on the axis and select "Outside" in the box "Minor tick").
2 * a = ......... pixels
We must now convert the pixels into a distance.
- Back in SalsaJ and select an image. Top right scale is given.
- Select Tool Selection rectilinear "in the main bar. Measured with this tool the standard of length in the upper right pixel:
10 light-days = ........... pixels
- Convert the position of the major axis of the ellipse is in day-light:
- Give then the value of the semi-major axis "a":
a = ........ light-days
Calculation of the black hole mass
The third law of Kepler
- The general form of Kepler's third law is:
G is the gravitational constant G = 6.67 * 10-11 N.m2. Kg-2 and M is the mass of the central body, π=3.14
- Knowing that the total period of revolution T of the reference star is 14 years, convert the period in seconds:
- Calculate the semi-major axis "a" in meters, knowing that one day-light is the distance that light travels in one day (at a velocity of 38 m.s-1):
- Deduce the black hole mass in kilograms by the third Kepler law:
- Compare the mass of the Black Hole to the mass of our Sun: is it greater? (Msun = 2 * 1030 kg)
- Give the black hole mass in units of solar mass Msun (that is, calculate how much solar mass it takes to get the mass of the black hole):
Study of a scientific article
Open the PDF file of the scientific article "stellar proper motions in the central 0.1pc of the galaxy" and read the "Abstract", which is the summary of the article.
What is the value of the mass found by researchers? Compare with your result.
Limit of the method and results
Projection effects: while the motion of the star is not necessarily in the image plane, actually the trajectory is measured within the projected path (see diagram below). Thus, what can we deduct about the estimated mass of the black hole we have calculated?
Download the images to analyse: 12 images in FITS format, compressed in zip (348 Kbyte)
Translation to english & adaptation: Olivier Marco
Original idea: Pachomius Delva & Jean-Christophe Mauduit