Some Useful Astronomical Definitions(Ref: B&M S 2.3, Lena Ch. 2)

• Spectral Energy Distribution

• Flux, Flux Density, & Luminosity

• Magnitudes

• Measuring flux

• Color

• Absolute Magnitude

• Parsec

• An Example

Spectral Energy Distribution

• The energy emitted froma source as a function ofwavelength/frequency

• The whole SED of asource is difficult tomeasure

Transmission of the Atmosphere

• Optical, some infrared (IR), and Radio are easily accessible• Other wavelengths require satellites/planes 1) Absorption scattering 2) Airglow 3) Thermal emission

Flux Density, Flux

• Flux density: fν or fλ, measured in units of W m-2 Hz-1 orW m-2 µm-1 (or the equivalent)

• Flux: measured in units of W m-2 (or the equivalent). Toconvert flux density to flux,

Luminosity

• For a source at a distance R & measured flux f, theluminosity is,

• Luminosity is measured in units of Watts (I.e., J/s) orergs/s, & it is determined for whateverwavelength/frequency the flux is determined at.

• Bolometric Luminosity: the luminosity of an objectmeasured over all wavelengths

Magnitude• The magnitude is the standard unit for measuring the

apparent brightness of astronomical objects• If m1 and m2 = magnitudes of stars with fluxes f1 and f2,

then,

• Alternatively,

Note that 1 mag corresponds to a flux ratio of 2.5 Note that 5 mag corresponds to a flux ratio of 100 The lower the value of the magnitude, the brighter the

object

Measuring flux

• We don’t directly measure the flux that reaches us froma source. We measure:

• Where fν = flux of the astronomical source

• Tν = the transmission of the atmosphere ~ e-a.

• Fν = Transmission of the filter

• Rν = Telescope efficiency

za0

a

Effects of extinction: make standard stars measurements aredifferent z

FilterParameters

• Effective wavelength (λeff) = the central wavelength of thefilter

• The FWHM transmission of the filter: the λ differenceover which fν falls to half its peak value

Photometric System• Johnson & Morgan UBV

system expanded into theinfrared

• These filters arecommonly referred to asbands or wavebands

• Flux density, mag, orluminosity in a particularband X = fX, mX, and LX

Filters (continue)

• fX (mX = 0) = zero pointflux density of X. I.e., theflux density of a zeromagnitude star (the starVega)

• If the flux density ofwavelength X ismeasured, then the magis,

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m = −2.5log fx (source)fx (mx = 0)

Color

• Color: the difference in mags measured in 2 differentwavebands

• Typically, it is written as X-Y

Absolute Magnitude• If the flux F of a source is measured at a distance D,

then the flux f measured from the same source at adistance d is,

• Absolute Magnitude: M is the apparent magnitude asource would have were it at a standard distance D = 10pc. Thus,

where d is measured in parsecs (pc).

Parsec - a commonly used measure ofdistance in extragalactic astronomy

• Method: Parallax – theapparent displacement ofan object caused by themotion of the observer

• A star with a parallax angleof 1” is at a distance of 1 pc= 3.1x1016 m (~ 3.25 lightyears). I.e.,

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θ =Earth−Sun DistanceDistance to Star

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Dstar =D1AUθ

=1AU1"

⋅3600"1° ⋅

180°

π= 3.1×1016m =1pc

An Example• The Sun’s absolute B magnitude is MB = 5.48. At 1

astronomical unit (AU = 4.87x10-6 pc), the sun’s apparentB mag is,

• For galaxies, MB = -7 to -26. I.e., very luminous galaxieshave MB = mB (sun). Comparing solar & luminous galaxyB-band luminosities,

• I.e., it would take 4.2x1012 suns to make up theluminosity of a massive galaxy,

Example (cont)• The flux density of the sun can be calculated using the

zero-point B-band flux density of fB (mB = 0) = 4000x10-26

W m-2 Hz-1. So,

can be rewritten

Example (cont’)• What is the amount of B-band energy the earth receives

per second from the sun?

At B band, the frequency is simply,

Thus, the energy received per second is,

By comparison, the Sun’s B-band & bolometricluminosities are,

Hz