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Wednesday, 28 June 2017 20:50

Frédéric Dahringer

"EAAE Summerschools" Working Group

CLEA (France)

Abstract

The aim of this activity is to calculate how old is the Crab Nebula.

Comparing two photographs, at two different dates, of the Nebula, we shall measure the velocity of its expansion.

This velocity is supposed to be constant; so we can calculate the age of the Nebula.

During this workshop we shall give some informations about Supernovae and neutron-stars.

The discovery of the Crab Nebula

The Crab Nebula has been discovered near the star z Tauri, in 1731 by the English astronomer J. Bevis. He was, at that time, making his Stellar Atlas, wich has been published in 1786.

Charles Messier, in France; observed this nebula and gave it the number 1 of his catalogue.

Lord Ross, gave it, 1844, the name of Crab Nebula, according to a drawing that he did, on which the nebula looked like a crab with some filaments.

At the end of the XIX th century, it became clear to the astronomers that this nebula was not a cluster of stars but a mass of gas.

In 1882, the Nebula has been photographed for the first time. From the comparison of two photographs, taken at different dates, would deduct that the Nebula was expanding.

The date of the birth of the Nebula can be estimate, if we suppose that the velocity of expansion is constant.

This calulation gives the year 1054. During that year, Chinese astronomers had observed a very bright star in that part of the sky. This star has been visible with the naked eye, in daylight, during 3 weeks, and disapeared after 600 nights.

In 1942, R. Minkowski and W. Baade, had discovered a star in the middle of the nebula. This can be the remaining of the star which blew up in 1054, ejecting gas all around.

The Crab Nebula, remaining of a Supernova

The last stage of the evolution of a very massive star can be a Supernova.

In these very big stars (more than 3 Solar-mass) the different chimical elements are built from the original hydrogen (H) to the iron (Fe). The iron is the bigest atom which can be synthezised from the other elements, with production of energy.

At the end of the live of a star, the fusion of the different chimical elements are realized in concentric layers, from the center of the star to its periphery. In this case the star is no more stable.

At the end, the star blows out, ejecting violently a lot of gas. It is in the same time visible, with a big brightness during several days.

During this explosion, the energy of the particules are so big that some chimical elements heavier than the iron can be created.

If the mass of the remaining star is big enough, it will have a last evolution, by the action of gravitational forces, to a neutron star. In such a star, with an enormous mass (2 or 3 solar mass) and a very small radius (10 km) all the elements are reduced to neutrons. The pulsars, dicovered in 1967, seem to be neutron stars.

A pulsars with a period of 33 milliseconds, has been found in the center of the Crab Nebula. It can be the remaining of the supernova seen by the Chinese in 1054.

The age of the Crab Nebula.

1. Analysis of the documents

The two photographs of the Crab nebula (fig.2 and 3) have been published in the Americain magazine " Sky and Telescope ". They are available in original size in the booklet " L'age de la Nébuleuse du Crabe " issued in France by the CLEA. (a reproduction on large size will be done, to make the measures).

These two photographs have been taken with a redligth filter, the first one on 19 th january 1942 and the second one on 27 th February 1976.

Figure 2.
Figure 2.
Figure 3.
Figure 3.

We can use the document 4 (positions of some stars visible with the telescope), to locate the center of the nebula.

Looking nearly at the two photographs, we observe some differences caused by the expansion of the nebula. This expansion seems to be more important for the filaments which are far from the center.

This is logical because these filaments are developping themselves perpendicular to the direction of our observation. The filaments which are near the center, are streching themeselves in our direction, they are growing to us and and their developpements seem us, not so large.

We shall only use for the measures the filaments which are on the periphery of the nebula.

2. How to do it!

  • Calculation of the scales.
    First, we shall use the document 4. We can find of the photographs the stars which are on this document and so, find the center of the nebula.
    Then, we can measure the distance between the stars A and B on each document, 2, 3 and 4 and we know that the angular distance between A and B is 576 second of angle.
    We are now able to calculate the scale of each photograph in second of angle per millimeter.
  • The choice of the filament for our study.
    Choice the brillant extremity of 10 filaments which are regularely disposed all along the periphery of the nebula. Give them the numbers 1 and 1'; 2 and 2', n and n' and so on.
    Then, we have to measure very carefully the distances xn (mm) and xn' (mm) of each extremity to the center of the nebula.
  • The calculations.
    We shall use the scales to change the measures xn and xn' in angular distances, Xn and Xn', which are in second of angle.
    Then the differences (Xn' - Xn) will be divided by the difference, in years, between the dates of the two photographs. We shall obtain with this operation, the velocity of the expansion of the nebula in second of angle per year.
    With the hypothesis that this velocity has been the same since the first day, we can calculate the duration of the expansion from the birth of the nebula to the date of the second phtograph.

Conclusion

We shall gather the results of all the participants of the workingshop and calculate the main value and the precision of this result.

We hope a result about 920 years, according to the idea that the Crab Nebula would be the remaining of the supernova seen in 1054.

This activity can take place in the programmes of the secondary school in France:

  • it gives informations about some bodies in the Univers;
  • it proposes calculations of scales and velocities;
  • it permits a statistical analysis of the results.