Intro to AstrophysicsNIS Grade 11 Physics

By Mr. MartyVisible Brightness = Apparent magnitude ‘m’, Absolute

Magnitude ‘M’, Luminosity and Star classification

Objectives:• Understand that stars are classified by luminosity

which relates to their brightness and measured in terms of apparent magnitude

• define apparent and absolute magnitude in terms of “m”

• define absolute magnitude “M” of a star as the apparent magnitude ‘m” it would have if the star is at 10 parsecs

Apparent Magnitude

• Introduced by the Greek astronomer Hipparchus– Based on naked eye observations– Hipparchus used 6 levels of brightness that he called

magnitudes.

• Brightest stars – first magnitude

• Half as bright – second magnitude

• Dimmest stars – sixth magnitude

• Apparent magnitude decreases as brightness increases!

The Apparent Magnitude Scale “m”• The Apparent Magnitude was formalized in 1856 with

exact numerical basis of how bright a star “appears” to a person on Earth. It is an extension of Hipparchus’ original magnitude scale.

• This magnitude scale is backwards, larger number in magnitude means the star is dimmer.

• Our Sun has m = -26, the dimmest star seen by the unaided eye has m = 6 and the faintest objects observable in visible light have m = 36

Apparent Magnitude “m”, a measure of brightness as seen from Earth

• The scale is logarithmic, because first magnitude stars are 100 times brighter than sixth magnitude stars, a magnitude difference of ‘1’ corresponds to brightness difference factor of 2.512 = (5√100)

• The brightness of a star is defined as the amount of energy per second (power) striking a unit area at the Earth’s surface.

• Also called the ‘Intensity’ of light hitting the Earth.• Sometimes it is called the flux (flow per unit area), in

astronomy the it is the flow of radiant energy coming to the Earth’s surface per meter squared per second.

Absolute Magnitude, “M”• Absolute Magnitude “M”: the magnitude a star

would appear to have if it is placed at a distance of 10 parsecs from Earth.

• m-M = 5 log(d) – 5 where d = distance to the star in parsecThis formula does not need to be known by learners, although they should know:

stars closer than 10 pc, M is less bright and has a larger number absolute magnitude than apparent magnitude, M > m

stars further than 10 pc, M is more bright and has smaller number absolute magnitude than apparent magnitude, M < m

stars at 10 parsecs have absolute magnitude equal to apparent magnitude, M = m

Absolute Magnitude of our SunOur Sun would have a magnitude of 4.8 if it were at

10 pc, so its absolute magnitude is 4.8!Apparent magnitude = -26 Absolute Magnitude = 4.8

Image comparison is estimated

Brightness of a Star Depends on1. Distance and 2. Power or Luminosity of the star

The Inverse Square LawThe brightness of a star depends on both its luminosity and its distance. The farther away a star is, the dimmer it will appear.

The brightness decreases as the square of the distance, the same principal as Newton’s Law of Universal Gravitation.

Luminosity• The luminosity of a star represents the Power of the

star (amount of energy a star emits per second).• Astronomers specify luminosity using the same

magnitude scale that they use for brightness.

Luminosity = Power OutputThe apparent brightness of a star is inversely

proportional to the square of its distance and its Power is equal to Sigma x Area x Temperature4(Kelvin).

b = L /(4d2) and B = σ T4 , because b=B when d=r L = 4π r2σT4 → P = σA T4 → Stefan’s lawwhere: b=apparent brightness , B=absolute brightness, L=luminosity,

P=Power , d=distance to star, r=radius of star, T=temperature in Kelvin and σ = 5.67 x 10-8 Wm-2K-4 , is Stefan’s constant

Most stars have low luminosity

How do Astronomers measure distances to stars and galaxies?

Stellar Parallax• Stellar parallax is a direct trigonometric technique for

measuring distance by taking observations from 2 locations.

• Definition: A parallax angle is the shift, relative to the background, caused by a shift in the observer’s position.

Other Units for Stellar Distances• One unit frequently used for stellar distances is the

light year (ly), the distance light travels in one year (about 10 trillion kilometers).

• Astronomers use the parsec (pc), the distance from which the size of Earth’s orbit around the Sun would appear to be 1 arcsecond. A parsec is 3.26 light years.

• Parallax is denoted by ‘p’.

• Distance (d) is measured in parsec.

• d = 1 parsec = the distance at which a star has a

parallax (p) of 1 arc second.

1 parsec = 3.26 light years.

Also d = 1/p

Closest star, Proxima centauri, p = 0.772 arc seconds. Hence distance ‘d’ in parsec is

d = 1/p = 1/0.772 = 1.3 parsec = 4.2 light years

The Limits for Measuring the Distance to Stars by Parallax

• The nearest star is 4.2 ly (1.29 pc) away. Thus its parallax is less than 1 arcsecond.

• The smallest parallax which can be accurately measured is about 0.01 arcseconds. This corresponds to a distance of 100 pc or 326 ly.

• Our Milky Way galaxy is about 100,000 ly across, so stellar parallax can be accurately measured for only the nearest stars.

Distances to farther away starsCalculation techniques require the use of

• Apparent Magnitude (m)

• Absolute Magnitude (M)

• Luminosity (L)

• Inverse Square Law

The Surface Temperatures of Stars•A star’s color reveals the surface temperature. Blue

stars are hotter than white stars and white stars are hotter than red stars.

• The Wien's Displacement Law state that the wavelength carrying the maximum energy is inversely proportional to the absolute

temperature of a black body. λmax T = b λmax  =  Wavelength of maximum intensity ( meters )

T  =  Temperature of the blackbody ( kelvins ) b  =  Wien's displacement constant  =  2.8977685 ± 51 × 10-3 meters·kelvins

Reference: http://www.physicshandbook.com/laws/wienlaw.htm

• A star’s spectrum reveals the surface temperature, and additionally the chemical composition, atmospheric pressure, and rotation rate.

Thermal Radiation: Temperature and color of radiation

Hot……. Hotter…... Hottest!

Must Watch video for Homework:• Our simulation Lab on Mon/Tue will give you

an experience with Wien’s Displacement Law which relates the Wavelength emitted by a blackbody to its temperature.

• The temperature and composition of stars:

• http://www.youtube.com/watch?v=01U7ZUKVW8o

Black Body Radiation and Wien’s Lawhttp://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

Black Body Radiation and Wien’s Lawhttp://hyperphysics.phy-astr.gsu.edu/hbase/wien.html#c2

Surface Temperature and Apparent Color of Stars

Vocabulary Terms of AstrophysicsAstronomy Term Definition Russian Kazakh

Absolute Magnitude “M”

The apparent magnitude a star would have at 10 parsecs (32.6 light years)

Абсолютная величина "М"

Apparent Magnitude brightness “m”

Each division is 2.51 times brighter than the next magnitude, sun has m= -26

Кажущаяся яркость Магнитуда "м"

Apparent Magnitude scale

A modern version of Hipparchus scale Полная шкала Магнитуда

Intensity Power per unit area at the observer: I=P/4πr2

интенсивность

Luminosity Total power radiated by a star (joules/sec=watts), depends on the temperature and distance between the star and the observer. L≈ d2T4

светимость

Parallax Angle The shift, relative to the background, caused by a shift in the observer’s position.

Параллакс Угол

Parsec The distance at which one AU subtends an angle of one arc second (1/3600th of a degree), 1 pc = 3.26 light years

парсек

Relative Brightness scale

A scale created by in 120 BC where 1 is the brightest star and 6 is the dimmest star

Относительная шкала Яркость

Spectral Class A classification of a star based on features of its spectrum which also indicate its surface temperature and chemical composition

Спектральный класс

Wein’s Displacement Law

Defines a relationship between the peak radiation emitted by a star and its temperature.

Объем Закон Wein в

References:• Wien’s Law from Physics Handbook:• http://www.physicshandbook.com/laws/wienlaw.htm• Astronomy General Topics Page with links to specific topics:

http://www.astro.cornell.edu/academics/courses/astro201/topics.html

• Windows to the Universe from National Association of Earth Science Teachers:

• http://www.windows2universe.org/the_universe/Stars/magnitude_scale.html

• Spectral Classes of Stars:• http://hyperphysics.phy-astr.gsu.edu/hbase/starlog/staspe.html • Wien’s and Stefan-Boltzman Laws explained:• http://csep10.phys.utk.edu/astr162/lect/light/radiation.html

References 2:• Brightness, Luminosity and Radius:

• http://science.howstuffworks.com/star3.htm

• Luminosity and how far away things are:

• http://zebu.uoregon.edu/~soper/Light/luminosity.html

• Properties and Classification of Stars:

• http://www2.astro.psu.edu/~mce/A001/lect13.html