Basic Properties of Stars 3 - PowerPoint PPT Presentation

Loading...

PPT – Basic Properties of Stars 3 PowerPoint presentation | free to download - id: 972f9-ZDc5Z



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Basic Properties of Stars 3

Description:

Magnitude scale later standardized so that mag. = 1 is exactly 100 ... Brightness and the magnitude scale ... (a) What is the absolute magnitude M of the Sun? ... – PowerPoint PPT presentation

Number of Views:109
Avg rating:3.0/5.0
Slides: 17
Provided by: astr91
Learn more at: http://www.astro.ubc.ca
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Basic Properties of Stars 3


1
Basic Properties of Stars - 3
  • Luminosities
  • Fluxes
  • Magnitudes
  • Absolute magnitudes

2
Solid Angle
  • The solid angle, ?, that an object subtends at a
    point is a measure of how big that object appears
    to an observer at that point. For instance, a
    small object nearby could subtend the same solid
    angle as a large object far away. The solid angle
    is proportional to the surface area, S, of a
    projection of that object onto a sphere centered
    at that point, divided by the square of the
    sphere's radius, R. (Symbolically, ? k S/R²,
    where k is the proportionality constant.) A solid
    angle is related to the surface area of a sphere
    in the same way an ordinary angle is related to
    the circumference of a circle.If the
    proportionality constant is chosen to be 1, the
    units of solid angle will be the SI steradian
    (abbreviated sr). Thus the solid angle of a
    sphere measured at its center is 4? sr,

3
For Fun
  • 1) What is the angular size of the Sun as seen
    from Earth?
  • Radius Sun 7.0 x 105 km
  • Distance to Sun 1.5 x 108 km
  • 2) What is the solid angle of the Sun as seen
    from Earth?
  • 3) What fraction of the sky does the disk of the
    Sun then cover?

4
Luminosities and magnitudes of stars
r

5
Luminosities and magnitudes of stars
  • Consider some source of radiation
  • Intensity I? energy emitted at some frequency
    ?, per unit time dt, per unit area of the source
    dA, per unit frequency d?, per unit solid angle
    d? in a given direction (?,?) (see p. 151-152)
  • Units w m-2 Hz-1 ster-1
  • d? da/r2 ? ?d? ?da/r2 4?r2/r2 4?

6
Luminosities and magnitudes of stars 3.2
  • Luminosity is energy passing through closed
    surface encompassing the source (units watts)
  • Luminosity L ???I?dAd?d?
  • If source (star) radiates isotropically, its
    radiation at distance r is evenly distributed on
    a spherical surface of area 4 ? r2
  • Flux is then
    F L /
    4 ? r2 (w m-2)
  • F falls off as 1 / r2
  • Inverse Square Law
  • Solar constant is
    1365 w m-2

7
Brightness, the magnitude scale 4.2-3
  • In 120 BC, Greek astronomer, Hipparchus, ranked
    stars in terms of importance (ie. brightness) ?
    magnitude
  • 1st magnitude were brightest ? 6th magnitude
    faintest visible stars (later extended to 0 and
    -1)
  • Without realizing it, Hipparchus based his scheme
    on the sensitivity of the human eye to flux -
    logarithmic scale, not a linear one.
  • Perceived brightness ? log (actual flux)

8
Rigel Betelgeuse - 0th Magnitude Stars
9
Brightness and the magnitude scale
  • Magnitude scale later standardized so that mag.
    1 is exactly 100 x brighter than mag. 6
  • Difference of 5 mag factor 100 in brightness
  • Difference of 1 mag factor 2.512 in brightness
    i.e. (2.512)5 100
  • Note smaller mag is brighter star
  • We can quantify this definition of magnitude
    scale Ratio of two brightness (flux)
    measurements is related to the corresponding
    magnitudes by b1/b2 100 (m2-m1)/5
  • b1 and b2 are fluxes and m1 and m2 are
    magnitudes
  • NB that it is b1/b2 and m2 - m1

10
Brightness and the magnitude scale
  • This is usually expressed in the form
  • m2 - m1 2.5 log10 (b1/b2)
  • Note that it is m2 - m1 on the left and b1/b2 on
    the right
  • ratio apparent mag.
    difference
            brightness  (b1/b2) m2-m1
  • 1 100
    0
  • 10 101
    2.5
  • 100 102
    5.0
  • 1000 103
    7.5
  • 10,000 104
    10.0
  • 108
    20.0

11
Brightness and the magnitude scale

12
1528 Latin translation of Ptolemys
Almagest based on Hipparchus of 120 BC
13
Brightness and the magnitude scale
  • This is usually expressed in the form
  • m2 - m1 2.5 log10 (b1/b2)
  • Note that it is m2 - m1 on the left and b1/b2 on
    the right
  • ratio apparent mag.
    difference
            brightness  (b1/b2) m2-m1
  • 1 100
    0
  • 10 101
    2.5
  • 100 102
    5.0
  • 1000 103
    7.5
  • 10,000 104
    10.0
  • 108
    20.0

14
Brightness and the magnitude scale
  • Since brightness of a given star depends on its
    distance, we define
  • Apparent magnitude, m (this represents flux)
    magnitude measured from Earth
  • Absolute magnitude, M (this represents
    luminosity) magnitude that would be measured
    from a standard distance of 10 parsecs (chosen
    arbitrarily)
  • m - M 2.5log10 (B/b)
  • Where B is the flux measured at 10 pc and b is
    flux measured at distance d to the star

15
Brightness and the magnitude scale
  • Using inverse square law, B/b (d/10 pc)2 we
    get
  • m - M 2.5 log10 (d/10)2 5 log10 (d/10) 5
    (log10 d - log10 10 )
  • The last term is just 1 so we have
  • m - M 5 log10 d - 5 or m - M 5 log10
    d/10
  • m - M is called the distance modulus and will
    appear often.
  • d is distance to the star in parsecs.

16
Simple problems
  • (a) What is the absolute magnitude M of the Sun?
  • (b) How much brighter or fainter in luminosity
    is the star Proxima Centauri compared to the Sun?
  • Needed data
  • msun -26.7 mproxima 11.05
  • Parallax of proxima 0.77
  • 1 pc 206,265 AU
  • (c) Total magnitude of a triple star is 0.0. Two
    of its components have magnitudes 1.0 and 2.0.
    What is magnitude of the third component?
About PowerShow.com