Archive for the ‘Cosmology’ Category

Allan Sandage and the Globular Cluster M3

In the early fifties Allan Rex Sandage, working on Palomar Observatory investigated the globular cluster M3 for his doctoral dissertation. Together with Martin Schwarzschild, specialized in stellar evolution, he accomplished a project to determine ages and evolution of globular clusters. Global clusters are to be looked upon as some of the oldest objects in universe. They are generally composed of old Population-II-Stars. Stars of Population II are relatively small and cool, so that they are glowing redly. Gas and dust are very scarce, because most of these were turned into stars long ago. In contrast young Population-I-Stars are hot and bluish. They are abundant in the gaseous and dusty spiral-arms of spiral galaxies where new stars are born.

Allan Sandage (born 1926) Source:

The formation of a star begins with a gravitational instability inside a large cloud of gas and dust leading to a collapse under its own gravitational force. The cloud breaks to pieces and every single one of them becomes denser, forming a rotating planetary disc. As the planetary disc becomes smaller under influence of gravitational force, the conservation of angular momentum causes the rotation to increase. The gravitational energy is converted into heat and the temperature of the protoplanetary disk rises, especially in the central region. Finally temperature and density is sufficient for nuclear fusion (hydrogen to helium), converting matter into energy and thus a new star is born. Particles of dust and ice in the disc accrete into planetesimals, the precursors of future planets.

As pointed out stars release energy by nuclear fusion and nuclear fusion in stars is ultimately driven by their own gravitational force. That implies a direct relationship between stellar mass and rate of nuclear fusion. In other words: High-mass stars have a short life, but low-mass stars are long-life, however.

For his dissertation Sandage analysed the Hertzsprung-Russel-Diagram (HRD) of globular cluster M3.

The Hertzsprung-Russel-Diagram shows the relationship between the stars’ brightness (luminosity) and their temperature-dependant colours or spectra.

The ordinary Hertzsprung-Russel-Diagram (HRD) Source: Wikipedia

The prevailing explanation of the diagram at that time, operated in the following way:

The main sequence stars maybe have different relative quantities of nuclear fuel (hydrogen) inside. A fully convective star, mixing fuel (hydrogen) and the product of nuclear fusion (helium) will become gradually denser due to higher molecular weight of the latter. Older stars on the upper bright part of the Main Sequence will move down the sequence if they lose significant mass, caused by intensified nuclear fusion. 

But analysing the Hertzsprung-Russel- Diagram of globular cluster M3 Sandage found a surprising and specific anomaly. There was a sudden break-up in the bottom half of the diagonal curve of main sequence stars and then a turnoff to the Red Giant Branch.


Source: A Study of Globular Cluster M3, Allan Sandage 1953 (left), (right)

Schwarzschild found a convincing solution: Depending on their age the stars move off the Main Sequence, beginning with the bright bluish high-mass stars (swiftly exhausting nuclear fusion) and ending with the faint reddish low-mass stars (enduring nuclear fusion). The more massive short-living stars in M3 had already entered the red giant stage. Only the long-life stars with lower masses still remained on Main Sequence.

The Main Sequence turn-off in the globular cluster M3 for Schwarzschild makes clear the path of stellar evolution:

First and foremost nuclear fusion occurs only in stellar core. Stars are not fully convective. Quite the opposite is true. Energy is transported outwards mainly by radiation. Merely in a layer just below surface transportation of energy goes by convection.

By the time a star exhaust hydrogen fuel at his core, the pressure of radiation balance his own gravitational force not any longer and the core contracts significantly. Through the immense release of gravitational energy the outer layers of the star expand greatly and cool. The star becomes a Red Giant. Due to stellar wind and lower gravity on his surface the star loses a lot of matter. At last all nuclear fusion reactions expire and the star winds up as White Dwarf.

Martin Schwarzschild (1912-1997) Source:

In a red giant with more than two solar masses, the core is compressed enough to start helium fusion (to carbon and oxygen). The hydrogen fusion proceeds in a shell-layer surrounding the core. The star shrinks in radius and surface temperature increases again.   

If the star has exhausted the helium at his core, helium fusion continues in a shell-layer around and the hydrogen fusion in a shell-layer directly above. The star becomes a Red Giant again, but with a higher surface temperature.

A much more massive star continues nuclear fusion in his core up to iron. But if all nuclear fuels are exhausted the core implodes and releases enormous quantities of gravitational energy. All matter in core will be transmuted in neutrons. These neutrons can stop the gravitational collapse, so much that implosion turns into an explosion and the star becomes a supernova. In such a supernova many nuclear fusion reactions occur, creating many new elements, including elements heavier than iron.  

In astronomy all elements heavier than helium are called a “metal”. The old stars of Population II have clearly less concentration of metals (metallicity) than the younger stars of Population I. The composition of a star depends on composition of the interstellar cloud from which are formed. Over time interstellar clouds become increasingly enriched in heavier elements. Generations of stars live and die and shed their new created elements.

A very interesting consequence of stellar evolution, Sandage figures out: The absolute magnitude of stars scarcely below the break-up in Main Sequence is directly a function of the age of globular cluster. So Allan Sandage and Martin Schwarzschild succeeded in fixing a lower age-limit of the entire universe.

Jens Christian Heuer

Sources: A study of the globular cluster M3, Allan Sandage (1953); The first 50 years at Palomar: 1949-1999 The Early Years of Stellar Evolution, Cosmology, and High-Energy Astrophysics, Allan Sandage; Lonely Hearts of the Cosmos: The story of the scientific quest for the secret of the Universe, Dennis Overbye


The Expanding Universe

March 17, 2010 1 comment

During the two years 1922 and 1923, astronomer Edwin Hubble, using  world’s largest telescope at that time, the 2,5m Hooker Telescope (Mt. Wilson Observatory), first identified single stars in the famous spiral nebula Andromeda, even visible with the naked eye.

Andromeda Galaxy (M31) Source: Palomar Observatory

Several of these stars were Cepheids, large and bright stars, pulsating and therefore with variable luminosity. Typical Cepheids pulsate with periods of a few days to months. There is a quite relationship between cycle duration and absolute luminosity of these variable stars. As longer the period as higher the luminosity.

That is why cepheids are workable standard candles for cosmic distance measurements. It is merely necesssary to calibrate the distance of the cepheids with other techniques like geometric parallax (difference in the apparent position of an object viewed along two different lines of sight against a much more distant background) and spectroscopic parallax (comparing the luminosity of main sequence stars in Hertzsprung-Russel-Diagrams).


Edwin Hubble (1889-1953) and 2,5m (100 inch) Hooker-Teleskope at Mt.Wilson Observatory Source: Wikipedia,

Using the period-luminosity-relationship of Cepheids in Andromeda, Hubble calculated a distance of nearly one million light years (ly), too much this nebula could be a part of the Milky Way. But Hubble undervalued Andomeda´s distance due to calibration errors. Today`s reading ist about more than two million light years (ly).

Until this point of time the most astronomers thought, that the entire universe only consisted of the Milky Way. But in fact, the Milky Way now was one galaxy among many galaxies in the universe. The world became considerably larger than before.

Hubble also devised a system for classifying galaxies in a diapason diagram, according to their optical appearance, known as the Hubble sequence.

Hubble´s Tune-Fork-Diagram for classification of galaxies. Source: Wikipedia

During the following years Hubble searched out a direct proportionality of the galaxies’ distances with redshifts in their spectra. This redshift is a consequence of the Doppler effect and hence a clear evidence for a recession of galaxies away from the Milky Way. The received frequency of a moving light source is higher during the approach (blueshift), it is identical at the instant of passing by, and it is lower during the recession (redshift). During approach the electromagnetical waves are compressed, during recession they are stretched. From there the direct proportionality of the galaxies’ distances with redshifts also means a direct proportionality of the galaxies’ distances with the galaxies’ escape velocity.

Hubble´s Law Source: Edwin Hubble (

But the redshift of  almost galaxies does not mean that the Milky Way is centre of universe. It´s rather as in the raising yeast dough of  a plum cake. From the viewpoint of every raisin all the other raisins are going away as faster as longer the distance between raisins. That´s because the dough itself is expanding.

In almost the same manner the space between galaxies increases, leading to an expansion of the entire universe. This discovery was a complete surprise at that time. Universe was not stable and eternal. Instead universe evolved and had to narrate it´s own history, leading to big bang theory.

All along the following years Hubble wanted to know, if universe is open or closed. In other words: Contained the entire universe matter and energy in sufficient amounts to stop its expansion by gravitational force,warping space  to a closed (four-dimensional) space-time bubble, or not?

Hubble tried to count the galaxies as a function of their distance. He assumed in average a relationship between luminosity and distance of galaxies. If the nummber of galaxies increased more than proportional with their distance, the space should have a positive curvature, leading to a closed universe. 

For a better understanding: a two-dimensional analogy: A spherical surface has a positive, a riding saddle (hyperboloide) has a negative curvature but a flagstone is flat.

Jens Christian Heuer

Jens Christian Heuer

Sources: Lonely Hearts of the Cosmos: The Story of the Scientific Quest for the Secret of the Universe, Dennis Overbye, Wikipedia

Categories: Cosmology