Line Strengths and Widths

Ca II Fe I, II

He Hd

each line has different strength (quantum mechanics)

Stars &more Elementary ions Astrophysics: --> stronger Introduction line Press F1 for Help 69 Equivalent Width

Measures line strength, NOT line width.

E.W. = width of rectangle with same area as line. Units: nm 1

0 Same width, different equivalent width.

Stars & Elementary Astrophysics: Introduction Press F1 for Help 70 Doppler (1843) Doppler Shift for sound.. l =l 0

l l 0

rest wavelength : l 0 velocity: v

Dl l - l 0 v redshift : z = = » l 0 l 0 c redshifted : z > 0 receding blueshifted : z < 0 approaching

Stars & Elementary Astrophysics: Introduction Press F1 for Help 71 Doppler Shift

-1 • Example: v = 200 km s , l0 = 500 nm v 200 km s-1 Dl = l = ´500 nm = 0.3 nm c 0 3´105 km s-1 • small shift, so no colour changes. • unless v ~ c (near a black hole, or relativistic jet) • Cosmological redshifts can be large:

l =l 0 (1 + z) = (121 nm) (1 + 6) = 848 nm

T0 3000K • Big Bang T = » » 2.7 K 1+ z 1100 Stars & Elementary Astrophysics: Introduction Press F1 for Help 72 Hubble Deep Field

Typical redshift: z ~ 1 High redshift: z > 5, UV light shifts to red wavelengths

Stars & Elementary Astrophysics: Introduction Press F1 for Help 73 Thermal Broadening

m 2 random motions v » kT 2 of atoms

l0 Stars & Elementary Astrophysics: Introduction Press F1 for Help 74 Rotational Broadening

l0 Stars & Elementary Astrophysics: Introduction Press F1 for Help 75 Pressure Broadening Energy levels shift when particles are nearby

high pressure gas

Stars & Elementary Astrophysics: Introduction Press F1 for Help 76 Zeeman Shift Energy levels shift and split in Magnetic field

magnetic field

Stars & Elementary Astrophysics: Introduction Press F1 for Help 77 Quantum Uncertainty “fuzzy” energy levels short visit -> uncertain E

DE Dt » h h = 4.1´10 -15 eV sec

Stars & Elementary Astrophysics: Introduction Press F1 for Help 78 Spectral Types

O Spectral Types M

A

G G A M O B V Stars & Elementary Astrophysics: Introduction Press F1 for Help 79 Why spectra differ

• Line strengths (EW ratios) change mainly due to SURFACE TEMPERATURE (hot-> high ionisation and excitation cool-> neutral atoms and molecules) • Some line widths and ratios change with LUMINOSITY • Very little range of abundances (74% H + 24% He 2% everything else) Stars & Elementary Astrophysics: Introduction Press F1 for Help 80 Spectral Classification – 1890s first photographic spectra – 1918-24 Henry Draper Catalogue "spectral classes" of ~ 225,300 stars !!! (star names HD 35311, HD 209458, etc) – original classification: A,B,… R,S from simple to complex lines – many letters later dropped or merged. – 1920s photometry (colour indices) revealed correct temperature sequence – confirmed by atomic physics – 1940s Morgan & Keenan (MK spectral types) Stars & Elementary Astrophysics: Introduction Press F1 for Help 81 • handout: – spectral classes provide a "short-hand" description of the appearance of a stellar spectrum.

Stars & Elementary Astrophysics: Introduction Press F1 for Help 82 Spectral Types hot cool O B A F G K M Girl ( Oh! Be A Fine Guy, Kiss Me! ) ( "early-type" "late-type" ) – sub-class 0 - 9 e.g. B0, B9, G2

Stars & Elementary Astrophysics: Introduction Press F1 for Help 83 Spectral Types hot cool O B A F G K M Girl ( Oh! Be A Fine Guy, Kiss Me! ) ( "early-type" "late-type" ) – sub-class 0 - 9 e.g. B0, B9, G2

(N R S ( No Romeo, Scram ))

Stars & Elementary Astrophysics: Introduction Press F1 for Help 84 ¬ one example of a luminosity criterion:

• H lines of Balmer series are affected strongly by pressure broadening

• pressure gradient µ surface gravity of star g GM g = R2 (M = mass, R = radius, G = gravitational constant)

• dwarf star, small R, large g Þ broadened H lines • giant star, large R (~100´), small g Þ narrow H lines • (handout: spectra showing luminosity effects)

Stars & Elementary Astrophysics: Introduction Press F1 for Help 85 Luminosity Classes

¬ – main-sequence V most common – subgiants IV – red giants III common ¬ – bright giants II rare – supergiants Ia,b very rare (blue to red) – white dwarfs DA quite common – DB,DO

• Stars & Elementary Astrophysics: Introduction Press F1 for Help 86 MK Spectral Types

– e.g. Sun G2 V Vega A0 V . Betelgeuse M2 Iab Rigel B8 Ia Aldebaran K5 III

Stars & Elementary Astrophysics: Introduction Press F1 for Help 87 Review • Multicolour Photometry – Use filters (e.g. U B V R I )

– measure flux densities : (fB, fV, ...) – apparent magnitudes : (B, V, …) – colour indices :

(B - V ) = - 2.5 log [ f B f V ]+ constant – absolute magnitudes (d from parallax):

M V = V - 5 log( d / 10 pc )

Stars & Elementary Astrophysics: Introduction Press F1 for Help 88 Bolometric Magnitude

Mbol = absolute bolometric magnitude total flux over the entire spectrum.

gives MV

gives Mbol

F

l

Difficult to measure Mbol.

Easy to measure MV .

Stars & Elementary Astrophysics: Introduction Press F1 for Help 89 Spectral Types

O B.C. vs Spectral Type M

A

G G A M O B V Stars & Elementary Astrophysics: Introduction Press F1 for Help 90 Bolometric Corrections

• B.C. = Mbol - MV < 0 to make star brighter.

• Sun: MV = 4.83, B.C. = -0.14 Mbol = 4.69 • F0V B.C. = 0 (most optical) . O5V = -3.8 (mostly UV M8V = -4.0 mostly IR)

L -0.4 çæ M - (sun) ÷ö =10 è bol M bol ø L(sun) æ L ö M bol - M bol (sun) = -2.5 log ç ÷ è L(sun) ø

Stars & Elementary Astrophysics: Introduction Press F1 for Help 91 Calibrations

• Calibrations of colour indices, temperatures,

absolute visual magnitude (MV), and (less precise) spectral types – very well defined for most main-sequence stars (5,000 £ T £ 30,000 K) – less so for hotter O stars (> 40,000 K) – and cooler M stars (< 2,500 K) (handout: example of relevant calibrations)

Stars & Elementary Astrophysics: Introduction Press F1 for Help 92 • The Hertzsprung-Russell (HR) Diagram – first presented independently by H (1911) and R (1913) to show links between spectral types (or colours) of stars and absolute magnitudes – now recognised as one of the most important diagrams for all astronomy, because of its importance for understanding the evolution (ageing) of stars • (handout: HR diagram)

Stars & Elementary Astrophysics: Introduction Press F1 for Help 93 Theory vs Observations • Alternative versions of the H-R diagram: theory observations Luminosity L Mv or

Mbol

colour index (e.g. B-V) Temperature T or Spectral Type

Stars & Elementary Astrophysics: Introduction Press F1 for Help 94