lecture 1 - summary - qubrk/l2/handouts/lecture2...lecture 1 - summary: 1 au = 1.49 x 1011 m = mean...

PHY2083Lecture 1 - Summary:

1 AU = 1.49 x 1011 m = mean Earth-Sun distance1 pc = 206265 AU ~ 3.26 lydistance (pc) = 1 / parallax (arcsecs)

PHY2083ASTRONOMY

Lecture 2 - Magnitudes and photon fluxes

Flux and luminosityThe “brightness” of a star is measured in terms of the flux received from it.

Flux: amount of energy received per unit time per unit area i.e., Watts / m2

Flux depends on intrinsic luminosity (energy / time) and distance

Flux and luminosityImagine a star of luminosity L surrounded by a huge spherical shell of radius d (see fig.) Assuming that no light is absorbed during its journey out to the shell, the flux is given by:

F = L / (4πd2)

radius of a sphere

F ∝ 1 / d2inverse square law

Flux and luminosityKey point:

Luminosity does NOT depend on distance, but flux does.

If a star appears faint, is it because it is really (i.e. intrinsically) faint, or because it is very far away [or both] ?

N.B. For stars at the same distance, the ratio of their fluxes = ratio of their luminosities

Flux and luminosityKey point:

Luminosity does NOT depend on distance, but flux does.

F ∝ 1 / d2

Example:The luminosity of the sun is 3.839 x 1026 W.

Calculate the flux received at Earth.

Solution:

Earth is 1 AU from the Sun = 1.49 x 1011m

F = L / (4πr2) = 1365 W / m2

This value of the solar flux is known as the “solar irradiance” or “solar constant”

The magnitude systemIn theory: measure the brightness of astronomical objects in an absolute way by measuring the energy emitted in a specific wavelength region.

In practice: difficult due to absorption by atmosphere, instrument calibration etc.

Solution: perform relative measurements with respect to standard stars which have been calibrated in an absolute way

The magnitude system• The Greek astronomer Hipparchus catalogued 850 stars that he saw, and invented a numerical scale corresponding to how bright each star was.

• He divided the stars into 6 groups or “magnitudes” with m = 1 being the brightest stars, and m = 6 being those that were faintest

Larger (positive) magnitudes => fainter objects

The magnitude system

Stars brighter than 1st magnitude were assigned negative magnitudes.

Larger (positive) magnitudes => fainter objects

It was thought the response of the human eye was logarithmic (and not linear) => quantify the scale so that a difference of 1 magnitude => constant ratio in brightness.

Pogson’s Law (1895): 5 magnitudes = factor of 100 in brightness

Blackboard derivations + notes

The magnitude equation

m = −2.5 log f + C

Apparent and absolute magnitudes

The magnitudes of standard stars are corrected for absorption by the Earth’s atmosphere. The magnitude of any object determined by comparison is therefore a measure of its flux at Earth. This is called the APPARENT MAGNITUDE (m)

In order to make comparisons more meaningful, define a measure of intrinsic brightness, which is a function of its distance and apparent magnitude.

The ABSOLUTE MAGNITUDE (M) is the magnitude a star would have if it were located at a distance of 10pc

Example:

The apparent magnitude of the Sun is -26.83. Calculate its absolute magnitude. Calculate the flux received from the Sun if it were at 10pc

Solution:The apparent magnitude of the Sun is -26.83. i) Calculate its absolute magnitude. ii) Calculate the flux received from the Sun if it were at 10pc

i) Msun = msun - 5 lg (d) + 5 d = 1 AU = 4.848 x 10-6 pc => Msun = -26.83 - 5 lg (4.848 x 10-6) + 5 => Msun = +4.74

ii) F = L / 4πr2 c.f. previous example at 1 AU now 10 pc = 2.063 x 106 AUInverse square law => flux will be 1 / (2.063 x 106)2 times lower => Flux at 10pc = 3.21 x 10-10 W / m2

Filter systems

Magnitudes should be quoted for a specific wavelength range since real detectors are not sensitive to the entire EM spectrum, and the Earth’s atmosphere transmits radiation only over certain wavelength regions.

Johnson UBV filter system

In practice, magnitudes are quoted for well-defined wavelength regions using filters e.g.

Vega: magnitude 0 by definition

What can we do with light from stars / galaxies?

I. We can take images e.g in different filters. Stars emit different amounts of energy at different wavelengths

What can we do with light from stars / galaxies?

II. We can take disperse the light and measure the amount of flux as a function of wavelength i.e. obtain a spectrum of the object

If the spectrum can be approximated by a blackbody, then we can estimate its temperature

absorption lines

emission lines

Recall basic atomic physics:

Emission lines: arise from energy state transitions of electrons in gas atoms / ions / molecules. Excited electrons decay back down to equilibrium level, releasing photons of a characteristic energy.

Absorption lines: Produced by a continuous source with cooler gas in front. The cooler gas preferentially absorbs at characteristic wavelengths, causing dark lines.

We can use spectra to

i) estimate the composition of the star

ii) estimate the physical conditions (e.g. Teff)

iii) measure its radial velocity (i.e. the velocity in the line-of-sight to the observer) using the Doppler shift of spectral lines:

∆λ / λ = vradial / c where ∆λ = λ - λ0

Astronomical measurements summary:

• Astrometry (Position, sky-plane velocity)

• Photometry (Brightness of objects)

• Spectroscopy (Flux as a function of wavelength)

• Spectroscopy (Doppler shift gives radial velocity)

Optical Telescopes

© G. Bertini

Galileo Galilei

“The Starry Messenger”

28-inch Refractor

Greenwich Observatory

London

2.5-m Isaac

Newton Telescope

4x8.2m

Very Large Telescope

Paranal, Chile

Sensitivity

Photons/secnλ =NλD2

16 d2

Sensitivity

Photons/secnλ =LλD2

16 d2

nλ =AλCD2Lλ

64πR2h∆2

photons/sec

20-m Giant Magellan Telescope

(~2021?)

Thirty-Metre Telescope

(~2020)

42-m European Extremely Large Telescope

(2021?)