Die Eichkerzen der Kosmologie

The Brightest Stars in the Sky Common Name Luminosity Solar Units Distance LY Spectral Type Proper Motion arcsec / year R. A. hours min Declination deg min Rigel 80,000 815 B8Ia 0.00 05 12.1 -08 12 Betelgeuse 100,000 500 M2Iab 0.03 05 55.2 +07 24 Deneb 80,000 1400 A2Ia 0.00 20 41.4 +45 17 Source: Fraknoi, Morrison, and Wolff Die hellsten Sterne liegen im Sternbild Orion, sind aber nicht mit der Wolke assoziiert.

Eta Carinae

Mit L » dex(6.7)L = 2× 10⁴⁰ erg/s und einer Masse von M » 100 M übertrifft h Car die Eddington Leuchtkraft, L_Edd = 4p Gm_HM/s_Th = dex(40)(M/100M ) erg s^-1.

In unserer Galaxie gehören zu den hellsten Sternen:

• HD 97950, ein Stern mit M_V = - 7^m,9; vom SpTyp O3, Masse » 80 M in NGC 3603.
• Eta Carinae, ein Stern vom SpTyp O3 (M_V = -7^m), L » dex(6.7)L = 2× 10⁴⁰ erg/s, Masse » 100 M .
• z Pup und c Vel ein Doppelsternsystem mit M_V = - 7^m,3; SpTyp O5.

• Mk42, ein Stern mit SpTyp O3, Masse » 110 M , T = 42 000 K, L = 2.3× 10⁶L (M_V = -7^m,1).
• R136a1, ein Stern mit SpTyp O3, Masse » 100 M im Sternhaufen R136 im Zentrum des 30-Doradus-Nebels.
• R127 = HDE 269858, ein variabler Stern mit SpTyp OIafpe und mit bipolarem Ausfluß (im Zentrum des 30-Doradus-Nebels).

Harlow Shapley

Es ist allerdings fraglich, ob diese Sterne wirklich als Eichstandards zu gebrauchen sind. Sie sind nicht mehr im hydrostatischen Gleichgewicht, sie pulsieren und verlieren Masse mit einer Rate von bis zu dM/dt = 3× 10^-4 M yr^-1. Die Massenverlust-Rate ist hier so groß, daß die Entwicklungszeit von 1 Myr für solche Sterne deutlich unterschritten wird, die Leuchtkraft wird damit eine Funktion der Zeit. Der Stern R127 = HDE 269858 war 1989 der hellste in LMC.

The Astronomical Distance Scale

Cepheid Variable Stars: Delta Cephei

Light Curve of Delta Cephei

The pulsations of Cepheids are very regular; Cephei has a period of pulsation (time between maxima or minima) of 5.366341 days. Furthermore the period is directly related to the luminosity of the star as shown from the Period-Luminosity Relation.

This relationship was first discovered by Henrietta Leavitt at Harvard who noticed that Cepheids in the Magellanic Clouds have a relationship between apparent brightness and period in the sense that brighter Cepheids have longer pulsation periods.

Period-Luminosity Relation

Period-Luminosity Relation W Virginis.

The fainter Cepheids in the Magellanic Clouds have shorter periods. Because all the Cepheids in a Magellanic Cloud are at the same distance from us, Leavitt reasoned that the more luminous Cepheids pulsated more slowly. This is the period-luminosity relation. Leavitt did not know the distances to the Magellanic Clouds, so she could not tell what the actual value of the luminosity part of the relation was.

Astronomers had to wait a few years for Harlow Shapley to calibrate Leavitt's relation using Cepheids in our galaxy for which the distances could be determined. In the calibration process Shapley put actual values to the luminosity part of the period-luminosity relation. With a calibrated period-luminosity relation astronomers could use Cepheid variables as standard candles to determine the distances to distant clusters and even other galaxies.

Cepheids have pulsation periods of 1 to 50 days. In the 1950's astronomers found that there are two types of Cepheids:

• Type I:
  classical Cepheids are from young high-metallicity stars and are about 4 times more luminous than Type II Cepheids. Above is the light curve (the plot of brightness vs. time) of a classical Cepheid from the Hipparcos database of variable stars.
• Type II:
  W Virginis Cepheids are from older low-metallicity stars and are about 4 times less luminous than Type I. Above is the light curve of a W Virginis Cepheid from the Hipparcos database of variable stars. Note the differences in the shape of the light curve. The two types of Cepheids are distinguished from each other by the shape of the light curve profile. In order to compare the shapes without having to worry about the pulsation periods, the time axis is divided by the total pulation period to get the ``phase'': one pulsation period = one ``phase''.

  

Period-Luminosity Relation.

Since all the stars in the Magellanic clouds are about the same distance, this relationship must be a relationship between luminosity and period as well. Cepheids exemplify the desirable characteristics of standard candles:

• Their luminosities may be determined from the P-L relationship which has very little scatter.
• They are giant stars so they are pretty luminous and can be seen out to relatively large distances. With HST Cepheids are being studied in galaxies in the Virgo Cluster. about 50 million light-years away.
• The variability of Cepheids makes them easy to pick out. Photographs (now digital images) are obtained of galaxies over several nights. When the images are compared, most stars don't change, but the Cepheids blink brighter and fainter and are easily distinguished from the billions of other "normal" stars.

RR Lyrae

They pulsate with a period between 5 and 15 hours (Cepheid pulsation periods are greater than 24 hours). Low-mass stars will go through a RR Lyrae pulsation stage while the high-mass stars will go through a Cepheid stage. Because low-mass stars live longer than high-mass stars, the Cepheid stars as a group are younger than the RR Lyrae stars.

RR Lyrae are found in old star clusters called globular clusters and in the stellar halo part of our galaxy. All of the RR Lyrae stars in a cluster have the same average apparent magnitude. In different clusters, the average apparent magnitude was different.
This is because all RR Lyrae have about the same average absolute magnitude (M_v = +0.6, or L = 49 L ). If the cluster is more distant from us, the RR Lyrae in it will have greater apparent magnitudes.

HST: Cepheid Variables in M100

Cepheid Variable in M100

The more luminous Cepheid variables can be used to measure distances out to 40 Mpc. These distances are many thousands of times greater than the distances to the nearest stars found with the trigonometric parallax method.

One of the prime goals of the Hubble Space Telescope has been the detection of Cepheid variable stars in distant galaxies. Before HST Cepheids had only been detected in very nearby galaxies, out to about 4 Mpc.

A team led by Dr. Wendy Freedman of the Carnegie Observatories has detected the furthest Cepheids yet in the Virgo Cluster spiral M100 at a distance of about 18 Mpc.

Our Location

  

Lupe: NGC 891 mit IR Spektrum (ISO) The galaxy NGC 891 (AAO)

Our galaxy probably closely resembles the galaxy NGC 891 as seen edge-on. Note the prominent dust lanes going through the disk mid-plane and how flat the galaxy is.

From above our galaxy may resemble NGC 2997 = AAT 17 in Antila (at a distance of 10 Mpc, z = 0.003626) or the galaxy Messier 83 (VLT).

In 1918 Harlow Shapley used his calibrated variable star period-luminosity relation to find distances to 93 globular clusters. Globular clusters are spherical clusters of 100,000's to several million stars (looking like a glob of stars) in very elliptical orbits around the center of the galaxy. Two globular clusters are shown below:

Messier 5 (in Serpens Caput constellation) and 47 Tucanae (in the southern constellation Tucana).

In this side view picture of the Galaxy the globular clusters are represented by the small circles congregating around the bulge of the Galaxy (they have been enlarged over a 100 times to make them visible).

Shapley found a strong concentration of globular clusters in the direction of the constellation Sagittarius.

Supernova Überreste

Supernovae

  

Supernovae

Probably the most promising new distance determination technique involves the use of Type Ia Supernovae as "Standard Candles".

Type Ia Supernovae are white dwarf stars in binary systems in which mass is being transferred from an evolving companion onto the white dwarf. If the amount of matter transferred is enough to push the white dwarf over the 1.4 M "Chandrasekhar limit" for electron-degeneracy support, the white dwarf will begin to collapse under gravity. Unlike massive stars with iron cores, the white dwarf will have a C/O core which can undergo further nuclear reactions. The collapse of the white dwarf liberates enough heat that nuclear reactions ignite and blow the remnant apart in a thermonuclear deflagration.

These SNIa explosions have all the right characteristics for Standard Candles; they are:

• extremely bright, outshining the entire galaxy of stars in which they reside.
• easily detected, but very rare, occurring only about once every 100 years in our galaxy.
• very uniform in brightness at maximum light.

Hubble Constant

Hubble's (1929) Velocity-Distance Relation for Nearby Galaxies

The data from Hubble's original velocity-distance relationship. Hubble's distance scale was in error by a factor of several, but his result was a most important one, demonstrating that the Universe is expanding and providing a means of estimating the distances to galaxies at the "edge of the Universe. Hubble's "law" is