Astronomy with SalsaJ Print

A black hole lurked at the center of our Galaxy !?

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! 

The VLT laser points to the Milky WayBlack 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.


Introduction

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.

Picture of what our Galaxy looks like. Click to download.
Credit: R. Hurt (SSC), JPL-Caltech, NASA

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.
 
Centre of the Milky Way
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

These images are infrared photos of stars rotating around the center of our galaxy, where the "supermassive" black hole is hidden. The latter is represented by a cross in the center of the images. One of the stars of the picture shows almost a complete rotation around the black hole. We will call later this star "the reference star".

We will now specifically address the coordinates of the reference star to determine its trajectory. Mark my position thereof on each image.

Complete the following table with the positions of the moving star:
 Year 1992 1993 1994
1995
1996
1997
1998
1999
2000 2001
2002 2002,9
 x pixels
                       
 y pixels
                       

 




Measurement of semi-major axis

Use Excel or any other similar Spreadsheet program

2 * a = ......... pixels

We must now convert the pixels into a distance.

10 light-days = ........... pixels

2 * a = ........ light-days
 

a = ........ light-days

 

Calculation of the black hole mass

The third law of Kepler

T2 / a3 = 4 π2 / GM

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

T = ....... s
a = ............. meters
Mblack hole = .......... kg
Mblack hole = ................ Msun

 


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?

Images
Download the images to analyse: 12 images in FITS format, compressed in zip (348 Kbyte)  



Authors Translation to english & adaptation: Olivier Marco
Original idea: Pachomius Delva & Jean-Christophe Mauduit