Measuring the Properties of Stars - PowerPoint PPT Presentation

Measuring the Properties of Stars

© Sierra College Astronomy Department

• Power is the rate at which energy is transferred, or the amount of energy transferred per unit time.
• Luminosity is the rate at which electromagnetic energy is being emitted - the total amount of power emitted by a star over all wavelengths.
• Brightness (or apparent brightness) refers to the luminosity/area of a star as seen at the Earth and is related to the star’s luminosity through the inverse square law.

© Sierra College Astronomy Department

• In the second century B.C., Hipparchus created the first star catalog with corresponding brightnesses determined visually.
• Hipparchus quantified each star’s brightness with a “magnitude”, an integer from 1 (brightest) to 6 (dimmest).
• Ptolemy (second century A.D.) expanded the number of stars with measured magnitudes and popularized this system of measurement.
• Today this magnitude is formally known asapparent magnitude and is designated by the letter m.

© Sierra College Astronomy Department

• The modern apparent magnitude scale is set up so that a 5-magnitude difference (say between two stars) is equal to a brightness change of 100 times (so as to closely match Hipparchus’s original data).
• Consequently, a one-magnitude difference is equal to a brightness change of 2.512 times (2.5125 = 100).
• The magnitude system is useful for its historical connections (for comparisons) and its manageable range (brightness itself covers a much larger range).

© Sierra College Astronomy Department

• Modern measuring devices allow astronomers to determine magnitudes to an accuracy of 0.001 or better.
• Modern, large telescopes equipped with CCD devices can image objects as dim as 25th magnitude or better.
• A few stars (e.g., Sirius) are so bright that they have negative magnitudes. Sirius’s apparent magnitude is –1.47.

© Sierra College Astronomy Department

• Stellar parallaxes were not observed until the mid-1800s.
• Parallax angle is half the maximum angle that a star appears to be displaced due to the Earth’s motion around the Sun.
• The maximum angle of the nearest star is only about 1.52 seconds of arc, but astronomers define the parallax angle as half that value, or 0.76 seconds.

© Sierra College Astronomy Department

• Parallax distance formula (in light-years):
• Distance to star (ly) =
• 3.26 ly/parallax angle in arcsec
• Parallax distance formula (in parsecs):
• Distance to star (pc) =
• 1/parallax angle in arcsec
• A parsec is the distance of a 1 AU object has a parallax angle of one arcsecond. One parsec is equal to 3.26 ly or 206,265 AU.

© Sierra College Astronomy Department

• The satellite Hipparchos (1989-1993) measured parallax angles with very high precision (milli-arcsecond) for over 100,000 stars establishing highly accurate distance measurements out to about 1000 light-years.
• Accurate stellar distances help to determine other quantities about celestial objects.

© Sierra College Astronomy Department

• The intrinsic luminosity of a star is usually given as its absolute magnitudeand designated with a capitalM.
• M is defined as the apparent magnitude a star would have if it were at a distance of 10 parsecs.
• Sirius’s apparent brightness (–1.47) is due to its closeness (2.7 parsecs from Earth). Its absolute magnitude is +1.45 (determined by using inverse square law).

© Sierra College Astronomy Department

• Given the brightness-magnitude relationship:
• And the brightness-luminosity relationship:
• It is possible to show derive the distancemodulus relationship (d is in parsecs):

© Sierra College Astronomy Department

• A star’s color is determined by its temperature.
• An absorption spectrum - the absorption of radiation at various wavelengths - can be used to determine a star’s temperature.
• Harvard astronomers, lead by Edward Pickering and his women “computers” developed the first stellar classification system using letters A-O, in alphabetical order.
• In particular, Williamina Fleming based the system on the strength of the stars’ hydrogen absorption lines (A strong, O weak)

© Sierra College Astronomy Department

• The A-O scheme was eventually found to be inadequate.
• Another “computer”, Annie Jump Cannon, discovered that a reordering and elimination of some of the letters gave a better scheme, which is still used today.
• Cannon’s system was thought to reflect stellar composition, but “computer” Cecilia Payne-Gaposchkin showed that the system was a consequence of the stars’ surface temperatures.

© Sierra College Astronomy Department

• The principal spectral types used today (from hottest to coolest) are designated as O B A F G K M.
• O stars range in temperature from 30,000 K to 60,000 K. M stars have temperatures less than 3,500 K.
• Within each spectral class, stars are subdivided into 10 categories by number (0 to 9).
• For example, the Sun is a G2 star.
• There are also other spectral types which are not quite as well known as the original seven (L and T types are two new ones used to classify very cool stars which form dust grains in their atmospheres).

© Sierra College Astronomy Department

• Hertzsprung-Russell diagram is a plot of absolute magnitude (or luminosity) versus temperature (or spectral class) for stars.
• About 90% of all stars fall into a group running diagonally across the diagram called main-sequence stars.
• Stars on the H-R diagram fall into categories such as main-sequence stars, white dwarfs, red giants, and supergiants.

© Sierra College Astronomy Department

• In the 1880s Antonia Maury and Ejnar Hertzsprung discovered that the width of a star’s absorption lines was directly related to the star’s luminosity (which in turn is related to a star’s surface density).
• Luminosity classes are one of several groups into which stars can be classified according to the characteristic widths of their spectra.
• The luminosity classes are: Ia (supergiants), Ib (dimmer supergiants), II (bright giants), III (ordinary giants), IV (subgiants), and V (main-sequence).
• Complete Stellar Classification: A star is fully classified if its spectral class and luminosity class are specified (e.g., the Sun is designated as a G2 V star)

© Sierra College Astronomy Department

Spectroscopic Parallax

• Knowing a star’s luminosity class and temperature (spectral class) gives its absolute magnitude.
• Knowing a star’s absolute magnitude and apparent magnitude gives its distance.
• The distances to stars too far away for parallax measurements can be determined using this procedure.
• Spectroscopic parallax represents the second rung (geometric parallax being the first) in the distance ladder created and used to scale the Universe.

© Sierra College Astronomy Department

The Sizes of Stars

• The sizes of a few very large stars have been measured directly by interferometry.
• Knowing the temperature of a star gives its energy emitted per square meter.
• Knowing the total energy emitted (from the absolute magnitude) one can then calculate the surface area of the star.
• From that the diameter of the star can be determined.

© Sierra College Astronomy Department

Multiple Star Systems and Binaries

• More than half of what appear as single stars are in fact multiple star systems.
• Optical doubles are two stars that have small angular separation as seen from Earth but are not gravitationally linked.
• Binary star system is a system of two stars that are gravitationally linked so that they orbit one another.

© Sierra College Astronomy Department

• A visual binary is an orbiting pair of stars that can be resolved (normally with a telescope) as two stars.
• If one uses large telescopes, about 10% of the stars in the sky are visual binaries.
• Binaries can be confirmed by observing the system over time and looking for signs of revolution.
• Spectroscopic binary is an orbiting pair of stars that can be distinguished as two due to the changing Doppler shifts in their spectra.

© Sierra College Astronomy Department

• Algol, discovered by Goodricke in 1783, is an eclipsing binary in which one star moves in front of the other as viewed from Earth.
• Algol’s light curve - a graph of the numerical measure of the light received from a star versus time - shows peaks and dips that indicate an unseen companion.

© Sierra College Astronomy Department

• Binary stars are important because they allow one to measure masses of stars using Newton’s version of Kepler’s laws.
• Knowledge of the size of one of the star’s ellipses, along with knowledge of the period of its motion, permits calculation of the total mass of the two stars.
• To determine how the system’s total mass is distributed between the two stars, one need only consider the ratio of the two stars’ distances to the center of mass.

© Sierra College Astronomy Department

• Because the inclination of spectroscopic binary orbits are usually not known, exact mass calculations cannot be done.
• However, assuming an average inclination can provide information about average masses of spectroscopic binary stars.
• Eclipsing binaries that are also spectroscopic binaries provide us with a way of measuring not only the masses of the two stars but also their sizes.
• We derive this information using measurements of their Doppler shifts.

© Sierra College Astronomy Department

• Mass-luminosity diagram plots the mass versus the luminosity of a number of stars.
• More massive stars are more luminous.
• The mass-luminosity relationship holds only for main-sequence stars.

where p has a value between 3.5 and 3.9

• The mass-luminosity relationship is valuable in investigating less accessible stars and in constructing and evaluating hypotheses on the life cycle of stars.

© Sierra College Astronomy Department

• The lifetime on the main-sequence depends on how much fuel (hydrogen) the star has and how fast the star is consuming it.
• This lifetime can be expressed as:
• Using the main-sequence mass-luminosity relation, we have:
• where t⊙ is for the Sun and is ~ 10 billion years
• Examples: A 10 M⊙ will last about 10 million years, whereas a 0.3 M⊙ star will last 300 billion years

© Sierra College Astronomy Department

• Open (galactic) cluster is a group of stars that share a common origin and are located relatively close to one another.
• Globular cluster is a spherical group of up to hundreds of thousands of stars found primarily in the halo of the Galaxy.
• Clusters are important for two reasons:
• All stars in a cluster are at about the same distance from us, so their apparent magnitude is a direct indication of their absolute magnitude.
• All the stars within a cluster formed at about the same time (more or less).
• Age of cluster determined from main-sequence turnoff
• Much of our knowledge of star formation has come from examination of clusters

© Sierra College Astronomy Department

• Not all stars shine steadily like the Sun.
• Stars that vary significantly over time are called variable stars.
• A certain sub-class of variable stars are called pulsating variable stars (based on how the star is pulsates in size)
• Most pulsating variable stars occupy the instability strip on the H-R diagram.
• A special class of very luminous pulsating variable stars called Cepheid variable stars have a well established period-luminosity relation that provides a powerful means for determining cosmic distances.

© Sierra College Astronomy Department