1B11 Foundations of Astronomy

Star names and magnitudes

Liz Puchnarewiczemp@mssl.ucl.ac.ukwww.ucl.ac.uk/webctwww.mssl.ucl.ac.uk/

1B11 Our night sky

Our Sun is one of approximately 200 billion stars in our Galaxy, the Milky Way. It lies in one of the spiral arms, about two-thirds of the way out from the centre, which is called Sagittarius A*

On a clear dark night in the UK, we can see ~3000 distinct stars, plus the fuzzy glow from the plane of the Milky Way.

From the very earliest times, humans have grouped patterns of stars into constellations, often animals and characters from myths and legends. There are now 88 official constellations.

1B11 Star positions

Astronomical co-ordinates

The most important parameter you can know about any astronomical source is its position on the sky.

Why?

1. Isolate, identify and re-visit the source

2. Check for transient sources, supernovae etc.

3. Associate sources at different wavelengths

By grouping stars into constellations, our ancestors developed the first system for unambiguously identifying celestial sources. Now, we use co-ordinate systems based on angular distance scales.

1B11 Constellation names

Constellations, their names and boundaries were defined by the International Astronomical Union (IAC) in 1930.

The brightest stars have their own names, eg Orion, Vega, Aldebaran, Polaris, Betelgeuse.

Many “naked-eye” objects are identified by their constellation name abbreviated to an IAU 3-letter standard, followed by a letter from the Greek alphabet in order of decreasing brightness (eg, Sirius,the brightest star in Canis Majoris, is also known as CMa). This was devised by Bayer in 1603.

If there are more than 24 stars in a constellation, then the remainder are numbered in order of Right Ascension (Flamsteed, 1925).

Fainter stars

Some stars which are too faint to be seen with the naked eye are identified by a catalogue number, eg

HD = “Harvard Revised”

HR = “Henry Draper”

eg Sirius = CMa = HR2491 = HD48915

These catalogues give information on the position, colour, brightness and type of stars.

There are now many, many different types of astronomical catalogue. VizieR is a web service run by the CDS which is effectively a catalogue of catalogues.

1B11 Faint stars and catalogues

1B11 Multiple and variable stars

Multiple stars

Most stars in the Galaxy (at least a half) are in binary and multiple systems. In these cases, components are labelled A, B, C…. etc. in order of decreasing brightness. Eg. 61Cyg is a double star – the brighter component is 61CygA, the fainter one is 61CygB.

Variable stars

Many stars are variable, which complicates labelling based on brightness! If they have a Bayer designation (eg Cep), they keep these. Otherwise, their constellation name is prefixed by one or two letters, depending on the time of discovery. 334 combinations of letters are available – after that they are prefixed by Vnnn where nnn is >334.

Non-stellar objects

In the late 18th Century, Charles Messier compiled a list of about 100 diffuse objects, to distinguish these from comets.

This has become known as a collection of beautiful deep sky objects, including galaxies, nebulae and clusters of stars. All 110 Messier objects can be seen at the SEDS Messier Database.

Another catalogue of fuzzy objects, the New General Catalogue, was compiled in 1888 and contains 7840 objects including galaxies, star clusters, planetary nebulae and supernova remnants.

1B11 Nebulae and galaxies

1B11 Example of a constellation

Constellation of Asterix

Ast

Ast

AstAAst

Ast

AstB

RRAst

M25

NGC1234

1B11 The magnitude scale

this star this staris 100 times brighter than

[Pogson (1856)]

Hipparchus (120BC) and Ptolemy (180AD) devised the magnitude scale for measuring stellar brightness, based on the response of the eye, which is logarithmic.

brightest stars are 1st magnitude

faintest stars are 6th magnitude

A difference in 1 magnitude = a factor of 2.512 in brightness

1B11 Defining magnitudes

Thus Pogson defined the magnitude scale for brightness.

This is the brightness that a star appears to have on the sky,

thus it is referred to as apparent magnitude.

Also – this is the brightness as it appears in our eyes. Our eyes have their own response to light, ie they act as a kind of filter, sensitive over a certain wavelength range. This filter is called the visual band and is centred on ~5500 Angstroms.

Thus, strictly speaking, these are apparent visual magnitudes, mv.

1B11 More on the magnitude scale

For example, if star A has mv=1 and star B has mv=6

1 6

1

100

apparent visual magnitude, mv

flux

(arb

itrar

y un

its)

Their flux ratio,

fA/fB = 2.512 mv(A)-mv(B)

= 2.5125

= 100

1B11 Converting from fluxes to magnitudes

So if you know the magnitudes of two stars, you can calculate the ratio of their fluxes using fA/fB = 2.512 mv(A)-mv(B)

Conversely, if you know their flux ratio, you can calculate the difference in magnitudes since:

mB-mA = mv = 2.5log10(fA/fB).

To calculate the apparent visual magnitude itself, you need to know the apparent visual flux for an object at mv=0, then:

mS-m0 = mS = 2.5log10(fm=0) - 2.5log10(fS)

=> mS = - 2.5log10(fS) + C

where C is a constant, ie C = 2.5log10(fm=0)

1B11 Magnitudes of different sources

-12.0 Full Moon

-5.0 Venus

-1.5 Sirius

0.0 Vega

4.5 Andromeda Galaxy

6.0 Naked eye limit

7.0 Neptune

14 Pluto

25 4m ground-based telescope limit

29 Hubble Space Telescope limit

1B11 How low can we go?

We can see stars as faint as mv=6.

The Hubble Space Telescope can reach mv=29.

How much fainter is this?

FHST/Feye = 100(mHST-meye)/5 = 10(mHST-meye)/2.5

= 109.2

In other words, HST can see stars which are over a billion

times fainter than we can see with the naked eye.

1B11 Magnitude systems

Every star has a different temperature => a different “colour”

4400 5500 7000

Flu

x (a

rbitr

ary

units

)

Wavelength (Angstroms)

Measurements in different colour bands give different magnitudes for different stars.

Curves are spectra for 3 stars, hot, Sun-like and cool.

1B11 UBV Johnson System

Different types of stars emit strongly at different wavelengths, thus will have different strengths depending on the filter used to observe them.

Harold Johnson (1921-1980) pioneered the standard UBV system of filters for measuring magnitudes in various colours.

tra

nsm

issi

on

(arb

itra

ry u

nits

)

3000 4000 5000 6000

Wavelength (Angstroms)

U 3600A

B 4400A

V 5500A

1B11 UBV Johnson System

In the Johnston UBV system, each filter is about 1000A wide.

Filter name band Apparent magnitude

Central wavelength

ultraviolet U mu3600

blue B mb4400

visible V mv5500

red R mr7000

infra-red I mi8000

The system was extended to R and I, then J,H,K in the IR.

(other colour filter systems are available!)

1B11 Colour index

Every star has a different temperature => a different “colour”

B V R4400 5500 7000

Flu

x (a

rbitr

ary

units

)

Wavelength (Angstroms)

Star B-V V-R

blue -ve -ve

yellow +ve -ve

red +ve +veV

-R

B-V

1B11 Colour index

You can use many different combinations of colour index, depending on the type of objects you’re looking at the science you’re interested in.

eg., (U-B), (B-V) for hot stars is useful

(V-R), (R-I) for red stars or for red properties of source population

For example:

Spica (Vir) B=0.73 V=0.96 => (B-V) = -0.23

Betelgeuse (Ori) B=2.66 V=0.96 => (B-V) = +1.86

So Spica is brighter in the blue, Betelgeuse is brighter in V.

1B11 Temperatures, colours and classification

Spectral class

Colour Surface temp (K)

B-V example

O Blue-white 30000-35000 -0.4 Naos

B Blue-white 11000-30000 -0.2 Rigel, Spica

A Blue-white 7500-11000 0.0 Sirius, Vega

F Blue-white to white

6000-7500 +0.3 Canopus, Procyon

G White to yellow-white

5000-6000 +0.5 Sun, Capella

K Yellow-orange 3500-5000 +0.8 Arcturus, Aldebaran

M Red <3500 +1.3 Betelgeuse, Antares

1B11 Temperatures, colours and classification

And thereafter, stars are further subclassified using the numbers 0-9:

O B A F G K M R N S

0,1,2,3,4,5,6,7,8,9

For example, our Sun is a G2 type star and has a temperature of 5800K.

1B11 Absolute magnitudes

Knowing how bright a star is on the sky is very useful – but the stars all lie at very different distances from the Earth. Scientifically, we want to know a star’s intrinsic flux – ie its luminosity.

Astronomers have two ways of quantifying this –

Absolute magnitudes and Luminosities

10pc

The absolute magnitude is the magnitude a star

would have if it were placed 10 parsecs away

from the Earth.

1B11 Absolute magnitudes

Definition of magnitudes

The flux from any source falls off as the inverse square of the distance,

ie

Example: a star lies at distance d with apparent magnitude m and flux Fm. If this star was 10 parsecs away so that the flux

was FM, then (because of the inverse square law):

But from the

definition of

magnitudes,

2distance

flux intrinsicflux observed

2M

m

d

pc10

F

F

B

A10VAB f

flog5.2mmm

1B11 Distance modulus

Definition of magnitudes

B

AVAB f

fmmm 10log5.2

2

1010log5.2

d )10(log5log5 1010 d

5log5 10 dMm

So since

m

M

F

FMm 10log5.2Then

where m-M is known as the distance modulus

The absolute (V band) magnitude of the Sun is +4.6.

1B11 Absolute bolometric magnitude

Definition of magnitudes

So CFm bolbol 10log2.5

Similarly, we can define an absolute bolometric magnitude, Mbol (ie mbol at 10 pc). Visual magnitudes can be converted to bolometric magnitudes via the bolometric correction, BC:

)()( VbolVbol MMmmBC

bol

V

F

F10log5.2

BCMM Vbol BC is always negative and is determined empirically.

1B11 Reddening and extinction

extinctionreddening

Any dust which lies between an observer and a source will absorb light from the source and use it to heat the dust. This is extinction. Dust will also scatter the light and blue light is scattered more than red, which makes the source look more red (although strictly speaking, “less blue”) and this is called reddening. This effect makes sunsets and sunrises red.

1B11 Reddening and colour excess

Colour index

Extinction is hard to measure because it is monochromatic, but scattering is easier because its effect is wavelength-dependent so will manifest itself as a colour change.

Observed colour = (B – V)

Intrinsic colour = (B – V)0

Reddening is measured by the colour excess which is defined as:

E(B – V) = (B – V) – (B – V)0

It’s measured in magnitudes – and it’s always positive! (why?)

1B11 Correcting for reddening and extinction

Spectral features (absorption and emission lines, red continuum)

Spectral type

Intrinsic continuum shape

Calculate (B – V)0Generally, extinction is given by:

A = m – m0

Where m0 would be the apparent

magnitude if there was no extinction.

In the V band:

AV = V – V0 ~ 3.1E(B – V)

Strictly speaking, m in this equation has been assumed to be unaffected by dust, so it should read:

From A = m – m0,

=> m0 = m – A

1B11 Including extinction in distance modulus

Distance modulus

m – M = 5log10d –5

Remember the distance modulus equation:

m0 – M = 5log10d –5

(m – M) = 5log10d – 5 + A

1B11 Bolometric luminosity

V Wavelength, (Angstroms)F

lux

f (

erg

cm-2 s

-1 A

-1)

Filter band magnitudes (eg U, B, V) will only

give the flux at particular wavelengths (shaded). For the total bolometric

luminosity, need to integrate over all

wavelengths (pink).

Stellar spectrum

Fbol = integ(0-inf)Flambda dl

where F is the flux at each wavelength () in the spectrum.

1B11 Bolometric magnitudes

Converting fluxes to magnitudes

Alternatively, the total intrinsic emission of a star integrated over all wavelengths may be expressed as a bolometric magnitude, Mbol.

Since mB-mA = mv = 2.5log10(fA/fB)

Mbol(Sun) – Mbol(star) = 2.5log10(Lstar/LSun)

Mbol(Sun) = +4.75

Log10(Lstar/LSun) = 1.90 – 0.4Mbol(star)