6 Form and Intensity of the Spectral Lines 6.1 The Form of the Spectral Line The chart on the right shows several absorption lines with the same wavelength, showing an ideal Gaussian-l
Trang 1Richard Walker
Version 9.2 12/2013
Trang 2Table of Contents
1 Introduction 7
2 Photons – Messengers from the Universe 8
2.1 Photons – Carriers of Information 8
2.2 The Duality of Waves and Particles 8
2.3 The Quantisation of the Electromagnetic Radiation 8
2.4 Properties of the Photons 9
2.5 Photons – Carriers of Energy 9
3 The Continuum 10
3.1 Black Body Radiation and the Course of the Continuum Level 10
3.2 Plank's Radiation- and Wien's Displacement Law 10
3.3 The Pseudo Continuum 11
4 Spectroscopic Wavelength Domains 13
4.1 The Usable Spectral Range for Amateurs 13
4.2 The Selection of the Spectral Range 13
4.3 Terminology of the Spectroscopic Wavelength Domains 14
5 Typology of the Spectra 15
5.1 Continuous Spectrum 15
5.2 Absorption Spectrum 15
5.3 Emission Spectrum 15
5.4 Absorption Band Spectrum 16
5.5 Band Spectrum with Inversely Running Intensity Gradient 16
5.6 Mixed Emission- and Absorption Spectrum 17
5.7 Composite Spectrum 17
5.8 Reflectance Spectrum 18
5.9 Cometary Spectrum 18
6 Form and Intensity of the Spectral Lines 19
6.1 The Form of the Spectral Line 19
6.2 The Information Content of the Line Shape 19
6.3 Blends 19
6.4 The Saturation of an Absorption Line in the Spectral Diagram 19
6.5 The Oversaturated Emission Line in the Spectral Diagram 20
7 The Measurement of the Spectral Lines 21
7.1 Methods and Reference Values of the Intensity Measurement 21
7.2 Metrological Differences between Absorption and Emission Lines 21
7.3 The Peak Intensity P 22
7.4 Full Width at Half Maximum Height 22
7.5 , Equivalent Width 23
7.6 Normalised Equivalent Width 24
7.7 FWZI Full Width at Zero Intensity 24
7.8 Influence of the Spectrograph Resolution on the FWHM- and EW Values 24
7.9 Practical Consequences for the FWHM and EW Measurements 26
7.10 The Measurement of the Wavelength 26
7.11 Additional Measurement Options 26
Trang 38 Calibration, Normalisation and Radiometric Correction 27
8.1 The Calibration of the Wavelength 27
8.2 The Selective Attenuation of the Continuum Intensity 27
8.3 Relationship Between Original-Continuum and Pseudo-Continuum 28
8.4 Attenuation of Absorption Lines 28
8.5 Attenuation of the Emission Lines 29
8.6 Summary of the consequences: 30
8.7 The Importance of the Pseudo-Continuum 30
8.8 Proportional Radiometric Corrections of the Pseudo-Continuum 30
8.9 Rectification of the Continuum Intensity 31
8.10 Relative Radiometric Flux Calibration by a Synthetic Continuum 32
8.11 Relative Radiometric Profile Correction by Recorded Standard Stars 35
8.12 Absolute Flux Calibration 37
8.13 Intensity Comparison between Different Spectral Lines 37
8.14 Reconstruction of the Original Emission-Line Intensities 37
8.15 Summary – Which Method Fits to Which Task 38
9 Visible Effects of Quantum Mechanics 39
9.1 Textbook Example Hydrogen Atom and Balmer Series 39
9.2 The Balmer Series 40
9.3 Spectral Lines of Other Atoms 41
10 Wavelength and Energy 42
10.1 Planck’s Energy Equation 42
10.2 Units for Energy and Wavelength 42
10.3 The Photon Energy of the Balmer Series 43
10.4 Balmer- Paschen- and Bracket Continuum 44
11 Ionisation Stage and Degree of Ionisation 45
11.1 The Lyman Limit of Hydrogen 45
11.2 Ionisation Stage versus Degree of Ionisation 45
11.3 Astrophysical Form of Notation for the Ionisation Stage 45
12 Forbidden Lines or –Transitions 46
13 The Spectral Classes 47
13.1 Preliminary Remarks 47
13.2 The Fraunhofer Lines 47
13.3 Further Development Steps 48
13.4 The Harvard System 49
13.5 “Early” and “Late” Spectral Types 50
13.6 The MK (Morgan Keenan) or Yerkes System 50
13.7 Further Adaptations up to the Present 50
13.8 The Rough Estimation of the Spectral Class 52
13.9 Diagrams for Estimation of the Spectral Class 53
13.10 Additional Criteria for Estimation of the Spectral Class 54
13.11 Appearance of Elements, Ions and Molecules in the Spectra 55
13.12 Effect of the Luminosity Class on the Line Width 56
13.13 Spectral Class and B-V Colour-Index 56
14 The Hertzsprung - Russell Diagram (HRD) 57
14.1 Introduction to the Basic Version 57
14.2 The Absolute Magnitude and Photospheric Temperature of the Star 58
Trang 414.3 The Evolution of the Sun in the HRD 59
14.4 The Evolution of Massive Stars 60
14.5 The Relation between Stellar Mass and Life Expectancy 60
14.6 Age Estimation of Star Clusters 61
15 The Measurement of the Radial Velocity 62
15.1 The Radial Velocity 62
15.2 The Classical Doppler Effect 62
15.3 The z-Value - A Fundamental Measure of Modern Cosmology 63
15.4 The Relativistic Doppler Effect for Electromagnetic Waves 64
15.5 The Measurement of the Doppler Shift 64
15.6 Radial Velocities of Nearby Stars 65
15.7 Relative Shift within a Spectrum caused by the Doppler Effect 65
15.8 Radial Velocities of Galaxies 65
15.9 The Apparent Dilemma at 66
15.10 Radial Velocity- and Cosmological Spacetime Expansion at Messier-Galaxies 66
15.11 The Redshift of the Quasar 3C273 68
15.12 The Gravitational Redshift 69
15.13 Short Excursus on "Hubble time" t H 69
16 The Measurement of the Rotation Velocity 70
16.1 Terms and Definitions 70
16.2 The Rotation Velocity of the Large Planets 70
16.3 The Rotation Velocity of the Sun 71
16.4 The Rotation Velocity of Galaxies 71
16.5 Calculation of the Value with the Velocity Difference 71
16.6 The Rotation Velocity of the Stars 73
16.7 The Rotation Velocity of the Circumstellar Disks around Be Stars 75
17 The Measurement of the Expansion Velocity 79
17.1 P Cygni Profiles 79
17.2 Inverse P Cygni Profiles 79
17.3 Broadening of the Emission Lines 80
17.4 Splitting of the Emission Lines 80
18 The Measurement of the Stellar Photosphere Temperature 81
18.1 Introduction 81
18.2 Temperature Estimation of the Spectral Class 81
18.3 Temperature Estimation Applying Wien’s Displacement Law 82
18.4 Temperature Determination Based on Individual Lines 85
18.5 The “Balmer-Thermometer“ 85
19 Spectroscopic Binary Stars 87
19.1 Terms and Definitions 87
19.2 Effects of the Binary Orbit on the Spectrum 88
19.3 The Perspectivic Influence from the Spatial Orientation of the Orbit 90
19.4 The Estimation of some Orbital Parameters 91
20 Balmer–Decrement 93
20.1 Introduction 93
20.2 Qualitative Analysis 93
20.3 Quantitative Analysis 94
20.4 Quantitative Definition of the Balmer-Decrement 95
Trang 520.5 Experiments with the Balmer-Decrement 95
21 Spectroscopic Determination of Interstellar Extinction 96
21.1 Spectroscopic Definition of the Interstellar Extinction 96
21.2 Extinction Correction with the Measured Balmer-Decrement 96
21.3 Balmer-Decrement and Color Excess 97
21.4 Balmer-Decrement and Extinction Correction in the Amateur Sector 97
22 Plasma Diagnostics for Emission Nebulae 98
22.1 Preliminary Remarks 98
22.2 Overview of the Phenomenon “Emission Nebulae” 98
22.3 Common Spectral Characteristics of Emission Nebulae 98
22.4 Ionisation Processes in H II Emission Nebulae 98
22.5 Recombination Process 99
22.6 Line Emission by Electron Transition 99
22.7 Line Emission by Collision Excitation 100
22.8 Line Emission by Permitted Transitions (Direct absorption) 100
22.9 Line Emission by Forbidden Transitions 100
22.10 Scheme of the Photon Conversion Process in Emission Nebulae 102
22.11 Practical Aspects of Plasma Diagnostics 103
22.12 Determination of the Excitation Class 104
22.13 The Excitation Class as an Indicator for Plasma Diagnostics 104
22.14 Estimation of Te and Ne with the O III and N II Method 105
22.15 Estimation of the Electron Density from the S II and O II Ratio 106
22.16 Distinguishing Characteristics in the Spectra of Emission Nebulae 106
23 Analysis of the Chemical Composition 108
23.1 Astrophysical Definition of Element Abundance 108
23.2 Astrophysical Definition of Metal Abundance Z (Metallicity) 108
23.3 Quantitative Determination of the Chemical Composition 108
23.4 Relative Abundance-Comparison at Stars of Similar Spectral Class 109
24 Spectroscopic Parallax 110
24.1 Spectroscopic Possibilities of Distance Measurement 110
24.2 Term and Principle of Spectroscopic Parallax 110
24.3 Spectral Class and Absolute Magnitude 110
24.4 Distance Modulus 112
24.5 Calculation of the Distance with the Distance Modulus 112
24.6 Examples for Main Sequence Stars (with Literature Values) 112
25 Identification of Spectral Lines 113
25.1 Task and Requirements 113
25.2 Practical Problems and Solving Strategies 113
25.3 Tools for the Identification of Spectral Lines 114
26 Literature and Internet 115
Trang 6Change log of the Document Versions
Version 8.0:
Sect 5.9: New: “Cometary Spectra“
Sect 6.4: Supplement
Sect 10.4: New: “Balmer- Paschen- and Bracket Continuum”
Sect 18: New: “The Measurement of the Stellar Photosphere Temperature“
Sect 23: New: “Chemical Composition Analysis“
Sect 24: New: “Spectroscopic Parallax”
Versions 8.5 and 8.6:
Sect 8: General revision “Calibration and Normalisation of Spectra” in consideration of
re-cent test results on "correction curves”
Version 8.7:
Sect 15.7: Review and corrections in the table of Messier galaxies and appropriate
ad-justments in the text
Version 9.0:
Sect 8: General revision: Consideration of the different attenuation-behavior of absorption-
versus emission lines, in relation to the continuum-intensity
Sect 13: New Subtitles, 13.10, 13.11 and 13.13 with new table: Spectral Class and B-V
Colour-Index
Sect 15: General revision: Derivation of the classical and relativistic, spectroscopic
Dop-pler formula Several corrections and supplements, particularly in sect 15.8 dial Velocities of Galaxies New: sect 15.12: Gravitational Redshift
Ra-Sect 16.3: Supplement of the Sun's rotation with spectral profile and measurement results
by SQUES Echelle Spectrograph
Sect 17.1: Supplement of literature reference
Sect 18: Content of former sect 18.6, now integrated in 18.4
Sect 20, 21, 22: Various modifications and additions due to the general revision of sect 8 Literature and Internet: New entries
Trang 71 Introduction
Technological advances like CCD cameras, but also affordable spectrographs on the ket, actually cause a significant upturn of spectroscopy within the community of amateur astronomers Further freeware programs and detailed instructions are available to enable the processing, calibrating and normalising of the spectra Several publications explain the function and even the self-construction of spectrographs and further many papers can be found on specific monitoring projects The numerous possibilities however for analysis and interpretation of the spectral profiles, still suffer from a considerable deficit of suitable lit-erature
mar-This publication is intended as an introduction to practical applications and the appropriate
astrophysical backgrounds Further the Spectroscopic Atlas for Amateur Astronomers [33]
is available, which covers all relevant spectral classes by commenting most of the lines, visible in medium resolved spectral profiles It is primarily intended to be used as a tool for the line identification Each spectral class, relevant for amateurs, is presented with their main characteristics and typical features
Further, Practical Aspects of Astro-Spectroscopy – Instructions and Information for
Ama-teur Astronomers [30], is downloadable It provides detailed instructions for operational
aspects and data reduction of spectral profiles with the Vspec and IRIS software
Spectroscopy is the real key to astrophysics Without them, our current picture of the verse would be unthinkable The photons, which have been several million years “on the road” to our CCD cameras, provide an amazing wealth of information about the origin ob-ject This may be fascinating, even without the ambition to strive for academic laurels Fur-ther there is no need for a degree in physics with, specialisation in mathematics, for a re-warding deal with this matter Required is some basic knowledge in physics, the ability to calculate simple formulas with given numbers on a technical calculator and finally a healthy dose of enthusiasm
uni-Even the necessary chemical knowledge remains very limited In the hot stellar pheres and excited nebulae the individual elements can hardly undergo any chemical com-pounds Only in the outermost layers of relatively "cool" stars, some very simple molecules can survive More complex chemical compounds are found only in really cold dust clouds of the interstellar space and in planetary atmospheres – a typical domain of radio astronomy Moreover in stellar astronomy, all elements, except hydrogen and helium, are simplistically called as "metals"
atmos-The share of hydrogen and helium of the visible matter in the universe is still about 99% The most "metals", have been formed long time after the Big Bang within the first genera-tion of massive stars, which distributed it at the end of their live in to the surrounding space
by Supernova explosions or repelled by Planetary Nebulae
Much more complex, however, is the quantum-mechanically induced behavior of the cited atoms in stellar atmospheres These effects are directly responsible for the formation and shape of the spectral lines Anyway for the practical work of the "average amateur" some basic knowledge is sufficient
ex-Richard Walker, CH 8911-Rifferswil © richiwalker@bluewin.ch
Trang 82 Photons – Messengers from the Universe
2.1 Photons – Carriers of Information
Photons are generated in stars, carrying valuable information over immense periods of time and unimaginable distances, and finally end in the pixel field of our CCD cameras By their
“destruction” they deposit the valuable information, contributing electrons to the selective saturation of individual pixels – in fact trivial, but somehow still fascinating By switching a spectrograph between the telescope and camera the photons will provide a wealth of in-formation which surpasses by far the simple photographic image of the object It is there-fore worthwhile to make some considerations about this absolutely most important link in the chain of transmission
It was on the threshold of the 20th Century, when it caused tremendous "headaches" to the entire community of former top physicists This intellectual "show of strength" finally cul-minated in the development of quantum mechanics The list of participants reads substan-tially like the Who's Who of physics at the beginning of the 20th century: Werner Heisen-berg, Albert Einstein, Erwin Schrödinger, Max Born, Wolfgang Pauli, Niels Bohr, just to name a few Quantum mechanics became, besides the theory of relativity, the second revo-lutionary theory of the 20th Century For the rough understanding about the formation of the photons and finally of the spectra, the necessary knowledge is reduced to some key points of this theory
2.2 The Duality of Waves and Particles
Electromagnetic radiation has both wave and particle nature This principle applies to the
entire spectrum Starting with the long radio waves, it remains valid on the domains of frared radiation, visible light, up to the extremely short-wave ultraviolet, X-rays and gamma rays
in-Source: Wikipedia
For our present technical applications, both properties are indispensable For the entire telecommunications, radio, TV, mobile telephony, as well as the radar and the microwave grill it's the wave character The CCD photography, light meter of cameras, gas discharge lamps (eg energy saving light bulbs and street lighting), and last but not least, the spectros-copy would not work without the particle nature
2.3 The Quantisation of the Electromagnetic Radiation
It was one of the pioneering discoveries of quantum mechanics that electromagnetic tion is not emitted continuously but rather quantised (or quasi "clocked") Simplified ex-
Trang 9radia-plained a minimum "dose" of electromagnetic radiation is generated, called “photon”, which
belongs to the Bosons within the "zoo" of elementary particles
2.4 Properties of the Photons
– Without external influence photons have an infinitely long life
– Their production and “destruction” takes place in a variety of physical processes vant for the spectroscopy are electron transitions between different atomic orbital (de-tails see later)
Rele-– A photon always moves with light speed According to the Special Theory of Relativity (STR) it can therefore possess no rest mass
2.5 Photons – Carriers of Energy
Each photon has a specific frequency (or wavelength), which determines its energy – the higher the frequency, the higher the energy of the photon (details see sect 10.1)
Trang 103 The Continuum
3.1 Black Body Radiation and the Course of the Continuum Level
The red curve, hereafter referred to as continuum level corresponds to the course of the
radiation intensity or flux density, plotted over the wavelength, increasing from left to right
As a fit to the blue continuum it is cleaned by any existing absorption or emission lines
(blue curve) The entire area between the horizontal wavelength axis and the continuum
level is called continuum [5]
Most important physical basis for the origin and course of the continuum is the so-called
black body radiation The blackbody is a theoretical working model which, in that
perfec-tion, doesn’t exist in nature
For most amateurs it is sufficient to know, that:
– The blackbody is an ideal absorber which absorbs broadband electromagnetic radiation, regardless of the wavelength, completely and uniformly
– The ideal black body represents a thermal radiation source, which emits a broad-band
electromagnetic radiation, according to the Planck's radiation law, with an exclusively
temperature-dependent intensity profile
– Stars in most cases may simplified be considered as black-body radiators
3.2 Plank's Radiation- and Wien's Displacement Law
This theory has practical relevance for us because the intensity profile of the spectrum vides information about the temperature of the radiator! The radiation distribution of differ-ent stars shows bell-shaped curves, whose peak intensity shifts to shorter wavelength, re-spectively higher frequency with increasing temperature (Planck Radiation law)
Trang 11With Wien's displacement law (German physicist Wilhelm Wien 1864-1928) and the given wavelength [Å] of the maximum radiation intensity it is theoretically possible to
calculate the atmosphere temperature [K] of a star This is also called “Effective ture” or “Photosphere temperature”
tempera-[Å]: Angström, 1 Å = 10-10m [K]: Kelvin K ≈ °Celsius + 273°
Examples: Alnitak = ca 25‘000 K = 1‘160 Å (Ultraviolet)
Sun = ca 5‘800 K = 4‘996 Å (Green) Betelgeuse = ca 3‘450 K = 8‘400 Å (Infrared)
3.3 The Pseudo Continuum
By all stellar spectra, the course of the unprocessed continuum differs strongly from the theoretical shape of reference curves, regardless if recorded with professional or amateur equipments The reasons are primarily interstellar, atmospheric and instrument-specific at-tenuation effects (telescope, spectrograph, camera), which distort the original intensity
course of the spectral profile to a so called pseudo continuum (details see sect.8.2)
Therefore, the Wien’s displacement law, on the basis of the maximum profile intensity, can
qualitatively only be observed The following chart shows a superimposed montage of
spec-tral profiles (pseudo continua) of all bright Orion stars, obtained with a simple transmission grating (200L/mm), a Canon compact camera (Powershot S 60) and processed with the
Vspec software Denoted are here the spectral classes, as well as some identified
Theoretically and according to sect 3.2, the maximum intensities of the O and B stars
should be located far left, outside of the diagram in the UV range On the other hand the
maximum for the cold Betelgeuse should be also moved, but here to the IR range, on the
Trang 12right side, also outside of the diagram Main causes for this error are the spectral selectivity
of the CCD chip and the IR filter in the compact camera, pretending that all the peaks would
be located within the diagram Here is also clearly visible, that the absorption lines (sect 5.2) are quasi "imprinted" on the continuum profile, similar to the modulation on a carrier
wave These lines carry the information about the object, the course of the continuum veals only the temperature of the radiator The profile of Betelgeuse shows impressively, that the spectra of cool stars are dominated by broad molecular titanium oxide (TiO) bands
re-(sect 5.4) The example also shows the dramatic influence of the spectral characteristics of the camera In the blue wavelength range, the sensitivity of most cameras drops quickly Astronomical cameras usually have easy removable/upgradable IR filters, exclusively used for the astrophotography and without them spectra can be recorded well in to the IR range
Trang 134 Spectroscopic Wavelength Domains
4.1 The Usable Spectral Range for Amateurs
The professional astronomers nowadays study the objects in nearly the entire magnetic spectrum – including also Radio Astronomy Also space telescopes are used, which are increasingly optimised for the infrared region in order to record the extremely red-shifted spectra of objects from the early days of the universe (sect 15.8–15.11) For the ground-based amateur, equipped with standard telescopes and spectrographs only a modest fraction of this domain is available The usable range for us is, in addition to the specific design features of the spectrograph, limited mainly by the spectral characteristics
electro-of the camera including any filters The Meade DSI III or Atik 314L+ e.g achieves with the DADOS spectrograph useful results in the range of approximately 3800 – 8000 Å, i.e throughout the visible domain and the near infrared part of the spectrum Here also the best known and best documented lines are located, such as the hydrogen lines of H-Balmer series and the Fraunhofer lines (see later)
4.2 The Selection of the Spectral Range
For high-resolution spectra, the choice of the range is normally determined by a specific monitoring project or the interest in particular lines Perhaps also the calibration lamp emission lines have to be considered in the planning of the recorded section
For low-resolution, broadband spectra mostly the range of the H-Balmer series is preferred (sect 9) Hot O- and B- stars can be taken rather in the short-wave part, because their maximum radiation lies in the UV range It usually makes little sense to record the area on the red side of Hα, except the emission lines of P Cygni, Be stars, as well as from emission line nebulae (sect 22) Between approximately 6,200 – 7,700Å (see picture below), it lit-erally swarms of atmospheric related (telluric) H2O and O2 absorption bands
Apart from their undeniable aesthetics they are interesting only for atmospheric physicist For astronomers, they are usually only a hindrance, unless the fine water vapour lines are used to calibrate the spectra! They can partly be extracted with the Vspec software or
nearly completely with the freeware program SpectroTools by Peter Schlatter [413]
By the late spectral types of K, and the entire M-Class (sect 13), however, it makes sense
to record this range, since the radiation intensity of these stars is very strong in the IR range and shows here particularly interesting molecular absorption bands Also, the reflec-tion spectra (sect 5.8) of the large gas planets show mainly here the impressive molecular gaps in the continuum
Useful guidance for setting the wavelength range of the spectrograph are eg the ter scale, the calibration lamp spectrum or the daylight (solar) spectrum, respectively At night the reflected solar spectrum is available from the moon and the planets A good marker on the blue side of the spectrum is the impressive double line of the Fraunhofer H- and K-Absorption (sect 13.2.)
microme-Fraunhofer
A Band O2
B Band O2
Trang 144.3 Terminology of the Spectroscopic Wavelength Domains
Terminology for wavelength domains is used inconsistently in astrophysics [4] and depends
on the context Furthermore many fields of astronomy, various satellite projects etc often use different definitions
Here follows a summary according to [4] and Wikipedia (Infrared Astronomy) Given are
ei-ther the center wavelength λ of the corresponding photometric band filters, or their proximate passband
ap-Optical range UBVRI λλ 3,300 – 10,000 (Johnson/Bessel/Cousins)
Center wavelength Astrophysical wavelength
Infrared range according to Wikipedia (Infrared Astronomy)
Center wavelength Astrophysical
2.20 22,000 K – Band
3.45 34,500 L – Band Some optical- and dedicated
infrared telescopes 4.7 47,000 M – Band
10 100,000 N – Band
20 200,000 Q – Band
200 2,000,000 Submilimeter Submilimeter telescopes
For ground based telescopes mostly the following terminology is in use [Å]:
– Far Ultraviolet (FUV): λ <3000
– Near Ultra Violet (NUV): λ 3000 – 3900
– Optical (VIS): λ 3900 – 7000
– Near Infrared (NIR): λ 6563 (Hα) – 10,000
– Infrared or Mid-Infrared: λ 10,000 – 40,000 (J, H, K, L – Band 1 – 4 μm)
– Thermal Infrared: λ 40,000 – 200,000 (M, N, Q – Band 4 - 20μm)
– Submilimeter: λ >200,000 (200 μm)
Trang 155 Typology of the Spectra
5.1 Continuous Spectrum
Incandescent solid or liquid light sources emit, similar to a black body radiator, a ous spectrum, eg Bulbs The maximum intensity and the course of the continuum obey the Plank's radiation law
continu-5.2 Absorption Spectrum
An absorption spectrum is produced when radiated broadband light has to pass a low sure and rather cool gas layer on its way to the observer Astronomically, the radiation source is in the majority of cases a star and the comparatively "cooler" gas layer to be trav-ersed, its own atmosphere Depending on the chemical composition of the gas it will ab-sorb photons of specific wavelengths by exciting the atoms, ie single electrons are momen-tarily lifted to a higher level The absorbed photons are ultimately lacking at these wave-lengths, leaving characteristic dark gaps in the spectrum, the so-called absorption lines This process is described in more detail in sect 9.1 The example shows absorption lines in the green region of the solar spectrum (DADOS 900L/mm)
Hβ Fe Fe Fe Mg Fe
5.3 Emission Spectrum
An emission spectrum is generated when the atoms of a thin gas are heated or excited so that photons with certain discrete wavelengths are emitted, eg neon glow lamps, energy saving lamps, sodium vapor lamps of the street lighting, etc Depending on the chemical composition of the gas, the electrons are first raised to a higher level by thermal excitation
or photons of exactly matching wavelengths – or even completely released, where the atom becomes ionised The emission takes place after the recombination or when the ex-cited electron falls back from higher to lower levels, while a photon of specific wavelength
is emitted (sect 9.1) Astronomically, this type of spectral line comes mostly from ionised nebulae (sect 22) in the vicinity of very hot stars, planetary nebulae, or extremely hot stars, pushing off their gaseous envelops (eg, P Cygni) The following picture (DADOS 200L/mm) shows the emission spectrum (Hα, Hβ, Hγ, He, [O III]), of the Planetary Nebula NGC6210, which is ionised by the very hot central star (some 58‘000K), [33]
Hγ Hβ [O III] He Hα
Trang 165.4 Absorption Band Spectrum
Band spectra are generated by highly complex rotational and vibrational processes, caused
by heated molecules This takes place in the relatively cool atmospheres of red giants The
following spectrum originates from Betelgeuse (DADOS 200L/mm) At this resolution it
shows only a few discrete lines The majority is dominated by absorption bands, which are here mainly caused by titanium oxide (TiO) and to a lesser extent by magnesium hydride (MgH) In this case, these asymmetric structures reach the greatest intensity on the left,
short-wave band end (called bandhead), and then slowly weaken to the right The
wave-length of absorption bands always refers to the point of greatest intensity ("most distinct edge")
But also several of the prominent Fraunhofer lines in the solar spectrum are caused by lecular absorption The following picture, taken with the SQUES Echelle spectrograph [400], shows a high-resolution O2 band spectrum of the Fraunhofer A line (sect 4.2 and 13.2)
mo-5.5 Band Spectrum with Inversely Running Intensity Gradient
The following picture (DADOS 200L/mm) shows C2 carbon molecular absorption bands in
the blue-green region of the spectrum of the carbon star Z Piscium [33] Generally at some
carbon molecules (eg CO, C2), the intensity gradient of the absorption bands runs in the posite direction as with titanium oxide (TiO) or O2
op-Already in the middle of the 19th Century this effect has been recognised by Father Angelo Secchi (Sect 13.3) For such spectra, he introduced the “Spectral type IV”
Trang 175.6 Mixed Emission- and Absorption Spectrum
There are many cases where absorption and emission lines appear together in the same spectrum The best known example is P Cygni, a textbook object for amateurs To this un-stable and variable supergiant of the spectral type B2 Ia numerous publications exist In the 17th Century, it appeared for 6 years as a star of the third magnitude, and then "disap-peared" again In the 18th Century it gained again luminosity until it reached its current, slightly variable value of approximately +4.7m to +4.9m The distance of P Cygni is esti-mated to ca 5000 – 7000 ly (Karkoschka 5000 ly)
The picture below shows the expanding shell, taken with the Hubble Space Telescope (HST) The star in the center is fully covered The diagram right shows the typical formation
of the so-called P Cygni profiles, which are shown here in the violet region of the spectrum (DADOS 900L/mm)
In the area of the blue arrow a small section of the shell, consisting of thin gas, is moving exactly toward Earth and generating blue-shifted absorption lines (Doppler Effect) The red arrows symbolise the light, emitted by sections of the shell, expanding sideward, producing emission lines In the combination results a broad emission line and a generally less intense blue-shifted absorption line P Cygni profiles are present in almost all spectral types and are
a reliable sign of a massive radial motion of matter ejected from the star
Based on the wavelength difference between the absorption and emission part of the line, the expansion velocity of the envelope can be estimated using the Doppler formula (sect 15) This object is further described in sect 17, where also the estimation of the expansion velocity is demonstrated
5.7 Composite Spectrum
Superimposed spectra of several light sources are also called “composite”- sometimes also
“integrated spectra” The English term “composite” was coined in 1891 by Pickering for
composite spectra in binary systems Today it is often used also for integrated spectra of stellar clusters, galaxies and quasars, which consist from hundreds of thousands up to sev-eral hundred billions superposed individual spectra
Direction towardearth
Trang 185.8 Reflectance Spectrum
The objects of our solar system are not self-luminous, but only visible thanks to reflected sunlight Therefore, these spectra always contain the absorption lines of the solar spec-trum The continuum course is however coined, because certain molecules in the atmos-pheres of the large gas planets, eg CH4 (methane), absorb and/or reflect the light differ-ently strong at specific wavelengths
The following chart shows the reflection spectrum of Jupiter (red), recorded with the DOS spectrograph and the 200L/mm grating Superimposed (green) is generated by dawn light, previously captured in the daylight- (solar) spectrum Before rectifying, both profiles have been normalised on the same continuum section [30] In this wavelength range, the most striking intensity differences are observed between 6100 and 7400 Å
DA-5.9 Cometary Spectrum
Such can be considered as a special case of the reflectance spectra Comets, like all other objects in the solar system, reflect the sunlight However on its course into the inner solar system core material increasingly evaporates, flowing out into the coma, and subsequently into the mostly separated plasma- and dust tails The increasing solar wind, containing highly ionised particles (mainly protons and helium cores), excites the molecules of the comet Thus the reflected solar spectrum gets more or less strongly overprinted with mo-lecular emission bands, chiefly due to vaporised carbon compounds of the cometary’s ma-terial The most striking features are the C2 Swan bands Further frequently occurring emis-sions are CN (cyan), NH2 (Amidogen Radicals), and C3 Sometimes also Na I lines can be detected Only slightly modified appears the solar spectrum, recorded from sunlight, which
has exclusively been reflected by the dust tail All these facts and the associated effects,
create complex composite spectra The influence of the possible components depends marily on the current intensity of the core eruptions, as well as on our specific perspective, regarding the coma, as well as the plasma- and dust tail Further details see [33]
Trang 196 Form and Intensity of the Spectral Lines
6.1 The Form of the Spectral Line
The chart on the right shows several
absorption lines with the same wavelength,
showing an ideal Gaussian-like intensity
dis-tribution but with different width and
inten-sity According to their degree of saturation,
they penetrate differently deep into the
con-tinuum, maximally down to the wavelength
axis The red profiles are both unsaturated
The green one, which just touches the
deep-est point on the wavelength axis, is saturated
and the blue one even oversaturated [5] The
lower part of the profile is called "Core",
which passes in the upper part over the
"Wings" in to the continuum level The
short-wavelength wing is called "Blue Wing", the
long-wave- "Red Wing" [5]
Emission line profiles, in contrast to the presented absorption lines, always rise upwards
from the continuum level
6.2 The Information Content of the Line Shape
There hardly exists any stellar spectral line, which shows this ideal shape But in the tion from this form a wealth of information is hidden about the object Here are some ex-amples of physical processes which have a characteristic influence on the profile shape and become therefore measurable:
devia-– The rotational speed of a star, caused by the Doppler Effect, flattens and broadens the line (rotational broadening), see sect 16
– The temperature and density/pressure of the stellar atmosphere broaden the line
(tem-perature/pressure-/collision broadening), see sect 13.12
– Macro turbulences in the Stellar Atmosphere, caused by the Doppler Effect, broaden the
line, see sect 16.6
– Instrumental responses broaden the line (instrumental broadening)
– In strong magnetic fields (eg sunspots) a splitting and shifting of the spectral line occurs due to the so-called Zeeman Effect
– Electric fields produce a similar phenomenon, the so-called Stark Effect
The combined effects of pressure- and Doppler broadening result in the so-called Voigt
pro-files
6.3 Blends
Stellar spectral lines are usually more or less strongly deformed by closely neighbouring lines - causing this way so-called "blends" The lower the resolution of the spectrograph, the more lines appearing combined into blends
6.4 The Saturation of an Absorption Line in the Spectral Diagram
The following spectral profile is generated with Vspec, based on the course of an 11-step gray-scale chart, running parallel to the wavelength axis The maximum possible range from
Trang 20black to white, covered by Vspec, comprises 256 gray levels [411] The Profile section in the black area is here, as expected, saturated to 100% and runs therefore on the lowest level, ie congruent with the wavelength axis The saturation of the remaining gray values decreases staircase-like upward, until on the continuum level, it finally becomes white If an underexposed spectral stripe was prepared in advance with IRIS [410] [30], the gray scale
is stretched, so that the highest point on the chart becomes white Thus, a maximum trast is achieved
con-So far remains the theory, covering the electronic recording and the data reduction level
According to [11] however, in astronomical spectra, an absorption line reaches already full saturation before it touches the wavelength axis In fact the "Wings" in the upper part of an
oversaturated line profile, appear massively broadened, without penetrating much further
into the continuum (sketch according to [11])
6.5 The Oversaturated Emission Line in the Spectral Diagram
No tricks are required for the presentation
of an oversaturated emission line This
just needs to overexpose the calibration
lamp spectrum Such oversaturated Neon
lines appear flattened on the top Such an
unsuccessful neon spectrum must never
be used for calibration purposes!
Continuum Level = white
oversaturated
Trang 217 The Measurement of the Spectral Lines
7.1 Methods and Reference Values of the Intensity Measurement
Depending on the specific task, the line intensity is determined either by simple relative measurement, or quite complexly and time consuming, with absolutely calibrated dimen-sions Here we focus exclusively on the relative measurement which is sufficient for most amateur purposes, and is supported by the analysis software (eg Vspec) As a reference or
unit usually serves the local or normalised continuum level (sect 8) but possibly also ues of a linear, but otherwise arbitrary scaling of the intensity axis
val-7.2 Metrological Differences between Absorption and Emission Lines
For measurements of spectral lines the following differences must be noted
The absorption lines can simplified be considered as the product of
a "filtering process" The photons of a specific wavelength λ, which, in
most of the cases are absorbed in a stellar photosphere, cause a gap
in the continuum of defined area, shape and penetration depth
Therefore, the parameters of the absorption remain always
propor-tionally connected to the continuum-intensity
The emission lines are generated independently of the continuum
by recombination and/or electron transitions (sect 9) Because this
process is mostly also excited by the stellar radiation, it results a
cer-tain strongly object-dependent, time related degree of coupling to the
continuum radiation For instance at P Cygni these lines are generated
directly in the turbulent expanding gas envelope – at the Be stars
(sect 16) mostly in the relatively nearby circumstellar gas disk – and
in the cases of the H II regions or Planetary Nebulae PN, even up to
some ly away, where almost regular laboratory conditions exist!
The combination of emission lines and continuum radiation results in
a superposition of the two intensities:
Due to the physically, and often even locally, different generation,
as well as may fluctuate independently of each other The
continuum-level is dependent on the specific radiation density,
which the star generates at the wavelength To this level, the
emis-sion intensity is adding up independently
The combination of emission lines and absorption lines results also in
a superposition of the two intensities
At Be-stars, the slim hydrogen emission line is produced in the
cir-cumstellar disk or -shell, and appears superimposed to the rotation-
and pressure-broadened H-absorption of the stellar photosphere The
resulting spectral feature is therefore called “Shell Core” [4] The
H-absorption of such a spectral feature may also originate from the
pho-tosphere of a hot O-star and the emission line from the surrounding H II region, see eg the
Trang 22½ Imax
Imax
I = 0
7.3 The Peak Intensity P
The Line Intensity
The intensity offers the easiest way to measure a spectral
line in a linear but otherwise arbitrarily scaled intensity axis
However this measure is only significant in a radiometrically
corrected or absolutely calibrated profile as described in
section 8.10 - 8.12
The Peak intensity
In a pseudo-continuum, but also in a just rectified profile
ac-cording to sect 8.9, the intensity gets only comparable
with other lines if related to its local continuum level This
is expressed as the dimensionless Peak intensity
The Peak intensity at absorption lines
is here also called for “Line Depth” Related to the continuum level , the peak sity of the absorption line, corresponds to the maximum intensity or flux density , which is removed from the continuum radiation by the absorption process This further cor-
inten-responds to the photon energy per time, area, the considered wavelength interval and
re-lated on the level (units see sect 8.12) In addition, it qualitatively shows the degree of
absorption, or the share of photons, which is absorbed in the peak of the absorption line
with the penetration depth
The Peak intensity at emission lines
If the upwards striving and independently generated emission lines appear superimposed
on a continuum {3}, they are, just as a pure makeshift, sometimes also related to the
inde-pendent continuum-level {4}, eg for investigations of individual lines Related to the
maximum intensity or flux density This further corresponds to the photon energy per
7.4 Full Width at Half Maximum Height
The FWHM value is the line width in [Å] at half height of
the maximum intensity It can be correctly measured even
in non-normalised spectral profiles The width of a
spec-tral line is inter alia depending on temperature, pressure,
density, and turbulence effects in stellar atmospheres It
allows therefore important conclusions and is often used
as a variable in equations, eg to determine the rotational
velocity of stars (sect 16.6)
This line width is specified in most cases as
wavelength-difference For the measurement of rotational and
ex-pansion velocities, is also expressed as a velocity
value according to the Doppler principle For this purpose
[Å] is converted with the Doppler formula {16}
to a speed value [km/s] (sect 15)
The FWHM value, obtained from the spectrum [30] has now to be corrected from the strumental broadening
Ic I
P=I/Ic
Trang 23corresponds to the theoretical maximum resolution [Å] of the
spectrograph, ie the smallest dimension of a line detail, which can be resolved
The resolution is limited on one side by the optical design of the spectrograph (dispersion
of the grating, collimator optics, slit width, etc.) It can normally be found in the manual of the spectrograph as so-called -Value which is valid for a defined wavelength range ( = considered wavelength) [302]
This value is determined by measurements at thinnest possible spectral lines, eg atmospheric H2O absorptions or somewhat less accurate, at emission lines of calibration light sources [11], [123], [302] In the laboratories for example emissionlines, generated by
microwave excited mercury lamps are used, in order to minimise temperature broadening
Such profiles are called "instrumental profile" or "δ-function response" [11] The resolution may further be limited by the pixel grid of the connected camera [Å/pixel], if this value is greater than of the spectrograph For a wavelength-calibrated profile, this value is
shown in the head panel of the Vspec screen Compared to monochrome-, with color CCD
cameras, a significant loss of resolution must be accepted
7.5 , Equivalent Width
The EW-value or Equivalent Width is always based on the continuum level and is a
relative measure for the area of a spectral line
Definition
The profile area between the continuum level and
the profile of the spectral line has the same size as
the rectangular area with the fully saturated depth
(here ) and the equivalent width [Å]
The -value must therefore be measured in a spec-
trum, normalised to ([30], sect 10) This is the
mathematically correct expression for :
In simple terms the red area above the spectral
curve is calculated by summing up an infinite
number of vertical, infinitely narrow rectangular
strips with the width and the variable heights
, within the entire range from to To get
finally the equivalent width , these values are still
to divide by the entire height of the continuum-,
resp of the saturated square
The integral sign ∫ is derived from the letter S, and
stands here for "sum" is the continuum intensity,
the variable intensity of the spectral line
depending on (or a function of) the wavelength
Trang 24The EW value at absorption lines
As sketched above and related to the continuum-level , corresponds to the measure
of the total radiation flux , which the entire absorption line removes from the
continuum radiation This further corresponds to the photon energy per time, area and
absorp-tion lines an absolute measure, because they are inseparably and proporabsorp-tionally linked to
the continuum level
The EW value at emission lines
The value of the just relatively to the independent continuum level related emission
lines, corresponds to the measure of their entire radiation flux This further
corre-sponds to the photon energy per time, area, and relatively related on the independent
level In contrast to the absorptions the EW value is for the emission lines not an absolute
measure, because the relation to the independently generated continuum is always relative,
just by makeshift, but never absolute
Measurement and signs of the EW values
values of absorption lines are by definition always positive (+), those of emission lines
negative ( )
Since the value is always measured at a continuum level, normalised to , it is
neither influenced by the course of the continuum, nor by the absolute radiation flux
Should be measured in a non rectified profile, the continuum must be normalised
immediately at the base of the spectral line to !
In scientific publications is also designated with the capital designates the equivalent width of the Hα Line
Somewhat confusing: In some publications I have also found the FWHM value expressed as The conclusion: One must always simply check which value is really meant
7.6 Normalised Equivalent Width
Rather rarely the normalised value is used [128]:
This allows the comparison of -values of different lines at different wavelengths ,
tak-ing into consideration the linearly increastak-ing photon energy towards decreastak-ing
wave-length λ, according to formula {8} Anyway, in astrophysics this is not applied by most of the
mainly empirical formulas and procedures
7.7 FWZI Full Width at Zero Intensity
Rather rarely the FWZI value of a spectral line is applied The Full With at Zero Intensity responds to the integration range of the definite integral according to formula and chart {6a}:
7.8 Influence of the Spectrograph Resolution on the FWHM- and EW Values
The above outlined theories about FWHM- and must realistically be relativated This
need is dramatically illustrated by the following spectral profiles of the Sun, taken with different highly resolving spectrographs (M Huwiler/R Walker) The R-values are here within a range of approximately 800 – 80,000
Trang 25The comparison of these graphs shows the following:
If the resolution (R) is increased it becomes clearly evident that in stellar spectra cally no "pure" lines exist Apparent single lines almost turn out as a "blend" of several sub lines, if considered at higher resolutions
practi-Sun Spectrum λ 5256 – 5287 Å
Comparison Prototype Echelle- with Cerny Turner Spectrograph
Echelle R ≈ 20‘000 Cerny Turner R ≈ 80‘000
Sun Spectrum λ 5160 – 5270 Å
Comparison Prototyp Echelle- with DADOS Spectrograph 900- and 200 L mm-1
Echelle R ≈ 20‘000 DADOS 900L mm -1 R ≈ 4‘000 DADOS 200L mm -1 R ≈ 800
Magnesium Triplet: λ 5167, 5173, 5183 Å
Richard Walker 2011/03
Trang 26 Striking is also the so-called "Instrumental Broadening" effect Even relatively
well-insulated seeming lines broaden dramatically with decreasing resolution (R), due to the
instrumental influences This affects the measured FWHM or the half-width of a line
The value, related to the profile area, remains theoretically independent of the
reso-lution At higher resolutions, the area of the slimmer line profile is compensated by a higher peak-value
7.9 Practical Consequences for the FWHM and EW Measurements
FWHM values must always be corrected in respect of the "Instrumental Broadening",
applying the formulas {5} to {5b}
The comparability of the values, obtained with different resolutions, remains purely
theoretical and is limited to discrete and well isolated single lines Assuming the case of
a blended absorption line, a high-resolution spectrograph measures, in an ideal case, the value of only one, well-defined single line However, at low resolution and the same
wavelength, a substantially larger value is measured due to a blend of several ble lines In this case, only -values are seriously comparable, if they have been ob-tained from profiles with similar resolution This necessarily requires a declaration of the R-value
insepara- According to formula {6a}, the -value is clearly defined However to determine this value e.g for strongly deformed, broad emission lines, possibly even with a double peak, remains a serious problem With Gaussian fits in such cases reasonably reproducible, al-
beit relatively imprecise results may result The profile fit with Spline filter, or similar
al-gorithms is perhaps more accurate, but the result is subjectively influenced by the tigator
inves- For amateur monitoring projects it is important, that all participants work with similarly high resolutions and the recording and processing of the spectra is clearly standardised
A problem with the values poses the standardisation of the integration area
(FWZI) of formula {6a}, since the width of the line base may change significantly with
varying intensity Further the section of the continuum must be specified, on which the profile is to normalise This is unavoidable at least for the later spectral classes, which exhibit a rather diffuse continuum When monitoring emission lines one must always keep in mind that the measured values are related to a possibly independently fluc-tuating continuum level (sect 7.2)
7.10 The Measurement of the Wavelength
The wavelength of a spectral line (Nanometer [nm] or Angström [Å]) can be obtained in a wavelength calibrated spectrum directly via Gaussian fit (Vspec) or by positioning of the
cursor at the peak of the line Which method is better, depends upon whether a strongly asymmetric blend or an isolated single-line is present
7.11 Additional Measurement Options
Depending on the applied analysis software, further information can be obtained from the calibrated spectral profile In Vspec these are, among other, e.g the signal to noise ratio SNR and the dispersion in Å/pixel, etc For details see the respective manuals
Trang 278 Calibration, Normalisation and Radiometric Correction
8.1 The Calibration of the Wavelength
Usually spectra are plotted as course of the radiation intensity over the wavelength In ciple, both dimensions can be calibrated For most applications, only the calibration of the wavelength is required This can be done relatively easy with lines of known wavelength within the spectrum, or absolutely with appropriate spectral calibration lamps These pro-cedures are well documented in literature eg [30], [411]
prin-8.2 The Selective Attenuation of the Continuum Intensity
The intensity profile of the undisturbed stellar original spectrum is determined mainly
by the black body radiation characteristics of the star and its effective temperature (sect 3.2) On the long way to the unprocessed raw spectrum the continuum of be- comes deformed by the following damping influences into a so called pseudo-continuum
(sect 3.3)
1 The Attenuation by the Interstellar Matter is mainly caused by scattering effects
of dust grains and gas Thereby the intensity is selectively much stronger dampened in the
blue short wave part of the spectrum Thus the maximum of the continuum radiation is
shifted in to the red, long-wavelength range, which is called "Interstellar Reddening" (sect 21) The extent of this effect depends on the object-distance, the direction of the line of
sight and is, as expected, most intensive within the galactic plane It can roughly be
esti-mated with a corresponding 3D model by F Arenou et al [209], [201]
2 The Attenuation in the Earth's Atmosphere acts similarly Well known effects are the reddish sunsets The modelling of the atmospheric transmission is mainly applied in the professional sector It is rather complex and depends inter alia on the zenith-distance (or the complementary elevation angle) of the observed object, the altitude of the observa-tion site and the meteorological conditions [303]
3 The Attenuation by Instrumental Influences of the system
telescope-spectrograph-camera follows at the very end of the transmission chain This can be
deter-mined quite precisely, eg by comparison with the exactly known radiation distribution of a continuum light source (eg special calibration lamps) [11], [300], [313], [315], [316], [480]
The resulting attenuating effect does:
The empirical function provides to any wavelength the correction factor between the continuum-intensity of and
This empirical scaling- or "correction function" can be determined as a rough ap-proximation only The intensity profile of the original stellar spectrum can be simulated just
on a theoretical basis and the individual factors can just very roughly be estimated Similar
approaches with empirical functions can be found in [300] and [303] The practical
calcula-tion with profiles is normally enabled – including all basic operacalcula-tions – by the software of
the analysis tools At Vspec this feature is to find under Operations/Divide-, /Multiply,-
/Add-, or /Subtract profiles by a profile
Trang 288.3 Relationship Between Original-Continuum and Pseudo-Continuum
The following diagram shows two identical sections of the same spectrum: on the left the undisturbed original profile and on the right the recorded raw spectrum with the pseudo-continuum It shows each an absorption and an emission line Within this fic-tional spectral section, the course of , and is assumed to run horizon-tally
The following relationships and its consequences can be derived:
Due to the selective attenuation, at a certain wavelength , the continuum-intensity of the recorded profile appears to be reduced by , compared with the original-spectrum
8.4 Attenuation of Absorption Lines
The continuum intensity and the penetration depth of the absorption line , are tenuated equally proportional
As an example the following graph shows the Sirius spectrum with the virtual original
pro-file and the recorded pseudo-continuum The absorption lines always remain
proportionally and inseparably connected to the continuum Therefore the -related
measurement categories – Peak Intensity , and Equivalent width – cannot be
changed by a simple division or multiplication by
Trang 29
Anyway the example of the Hγ line also shows that the relative line intensity of , which
is measured independently of the continuum-level, appears strongly attenuated,
com-pared with At , corresponds to the intensity of the original profile
Further in the original profile of Sirius, spectral class A2V, it gets clearly evident,
that the absolute energy flux ,(sect 8.12) which is absorbed by the Hγ – line and is not related to the continuum-level , is much higher, compared to the Hα – Absorption
8.5 Attenuation of the Emission Lines
Completely different is the behaviour of the emission lines, which appear superimposed on the continuum, but are otherwise extensively independent of Therefore, in contrast to
the absorptions, also the continuum related peak intensities as well as the equivalent
width are affected here by the attenuation process, and both appear selectively
damp-ened, dependent on their specific wavelength Thus, these values significantly differ from
the undampened so-called Balmer-Decrement according to sect 20 This becomes clearly
evident in the recorded spectra of objects with intense hydrogen emission (eg P Cygni)
This effect totally excludes an attenuation, which acts proportional to the continuum-level , and therefore would never change this way the or values However, as a rough
approximation, even in the professional practice, for emission-lines quite often – and for accordingly non-critical applications – an attenuation, acting proportional to , is assumed Analogously to the absorption , , for emission lines:
Due to the wavelength-dependent- and therefore differently strong attenuation, the tensity ratio of two arbitrary emission - or absorption-lines , measured in the original profile , appears as changed in the recorded pseudo-continuum :
, therefore it follows
Hγ
Trang 308.6 Summary of the consequences:
For absorption lines, absolutely connected with the continuum, the -related
measure-ments – peak intensity and equivalent width – remain untouched by the
attenua-tion due to The original ratio of remains the same also in the continuum
pseudo- The emission lines, superimposed to the pseudo continuum , stay independent of
the continuum level In contrast to the absorption lines, their values appear here
to be attenuated, depending on the specific wavelength This effect excludes an
attenua-tion, acting proportional to the dampened continuum-level , and shows up by the called Balmer-Decrement of the hydrogen emissions according to sect 20 Nevertheless
so-as a rough approximation, sometimes an attenuation is so-assumed, which acts tional to
propor- The intensity values and , which are measured in arbitrary measuring units, and dependently from the continuum-level, appear to be attenuated in the pseudo-continuum ,
in- The original intensity ratios between two different absorptions , or emissions , which are measured within the original profile in arbitrary measuring units, ap-pears to be modified in the pseudo-continuum ,
8.7 The Importance of the Pseudo-Continuum
If the attenuation-function is approximately known, the pseudo continuum
contains the information, to enable the approximate reconstruction of the original profile
, applying formula Further, according to sect 3.2 and 3.3, the wavelength of the maximum intensity is, even in the strongly dampened pseudo-continuum, a very rough indi-cator at least for the order of magnitude of the effective temperature
Apart from these effects the course of the recorded pseudo-continuum , is useless
Depending on the wavelength, just shows the amount of electrons, which has been read out of the individual pixels, amplified by the camera electronics and finally averaged by the spectral processing software over a defined height of the vertical pixel rows Thus it re-
flects roughly proportional the recorded photon flux which however is loaded with all the
mentioned attenuating influences As intensity unit for raw profiles therefore often [ADU] (Analog – Digital Units) is used
8.8 Proportional Radiometric Corrections of the Pseudo-Continuum
In the following sections 8.9 – 8.12 several proportional-radiometric correction processes are presented, which transform the recorded pseudo-continuum for different applica-
tions to appropriate forms All are based on the division of by empirical
correction-functions Thus , the intensities of the embedded absorption lines and also the perimposed appearing emission lines , are scaled proportionally to a new value
su-Important:
The -related measurements – peak intensity and equivalent width – remain
un-touched by the division Just the intensity values and , which are measured in trary measuring units, and independently from the continuum-level, are concerned
arbi-These effects are appropriate only for the absorption lines
For the emission lines, however, only a rough approximation is achieved this way cause, related to , the original equivalent widths can't be reconstructed by a
Be-simple division, and the original -values can just very roughly be approximated The
original intensity ratios of the emission lines can only be determined by individual,
ar-ithmetical scaling, proportional to the values of the theoretical Balmer-Decrement of the
Trang 31hydrogen lines, according to sect 20 and 21 Practical example are the strongly ated hydrogen lines of P Cygni
attenu-8.9 Rectification of the Continuum Intensity
The most simple correction process is the rectification of the recorded profile by dividing of
the pseudo-continuum by its own “smoothed” or fitted intensity course cording to [11], this method is appropriate even for most professional applications This way the continuum-intensity is unified or "normalised" through the entire range, and set
Ac-to The resulting profile is called „Residual Intensity“
Due to this division, the profile runs now horizontally and the intensity of the emissions - and absorptions is related to the unified continuum intensity This process proportionally scales by the intensities of all spectral lines from their individual -values in the pseudo-continuum, up to the level This corresponds now to the origi-
nal, not attenuated profile of a virtual star which shows a horizontally running, but
physi-cally impossible radiation characteristic For the intensity of the emission lines this tion process is just a rough approximation (see sect 8.8)
correc-Consequences and benefits of Rectifying the Pseudo-Continuum
Useful for certain applications – the profile normalisation allows the elimination, of the often irrelevant, or even hindering, wavelength-dependent distribution, of the stellar
radiation intensity It generates a "quasi neutralisation", but never a real correction of the
attenuating effects
Between individual absorption lines, enables the direct comparison of the peak
in-tensities between individual absorption lines, according to The scaling effect of
a rectified profile is impressively demonstrated at the absorptions in the solar spectrum
by the two Fraunhofer H- and K- lines of ionised calcium (Ca II) The blue profile of the pseudo-continuum shows these lines only stunted at the short wavelength end of the spectrum (blue arrow) After rectifying of the continuum (red profile), the H- and K- lines appear now obviously as the strongest absorptions, which the sun generates itself (red arrow)
The original ratio of the individual emission lines is maintained just as a rough
approximation {7h}
, with the unified and normalised radiation-intensity , enables for the
re-corded emission lines the intensity comparison with those of the original, unattenuated
Balmer-Decrement (sect 20)
Trang 32 Like in the recorded pseudo-continuum , also in changes the intensity ratio of any two emissions or absorptions , measured in the original profile {7i}, {7j}
The rectified profile, normalised to , enables the determination of the -values
and facilitates the measurement of the , the Doppler-shift , as well as the termination of the spectral class
de- By the rectification of the profile, by the information gets lost, which allows, by
means of the known attenuation function , to approximately reconstruct the original profile (according to formula )
Anyway, even for most professional applications – with just a few exceptions –, the file normalisation is clearly the best and easiest option [11]
pro-8.10 Relative Radiometric Flux Calibration by a Synthetic Continuum
The goal of this procedure is a rough approximation of the recorded profile with the
pseudo-continuum , to the original- and therefore not reddened continuum This
procedure is described in the manual of the Vspec software With dividing by correction
curves, the spectral lines of the pseudo-continuum are directly transferred to the
syn-thetically produced and fitted continuum course of a virtual model star with the
same spectral class and unreddened by any interstellar dust Similar to sect 8.9, this
proc-ess proportionally scales the intensities of all spectral lines from their individual -values in the pseudo-continuum, up to the level of For specific applications this procedure
is also applied in the professional field [301]
In the following chart the blue spectrum is the recorded profile with the pseudo-continuum
of Sirius The red profile is the aimed, fitted continuum course of the thetic model star of the same spectral type, from the Vspec library (CDS Database) It ap-pears cleaned from all spectral lines and thus roughly corresponds to the black body radia-tion characteristics of this star:
Trang 33In a rough approximation corresponds here to the attenuation-function , cording to
Finally the division of the blue recorded raw profile , by the green correction-function , results in the radiometrically corrected profile (black) It shows now the same
with the accordingly scaled lines of the recorded profile
Remarks to the „Instrumental Response“
For a correction function , obtained according to , the term "instrumental
re-sponse" is misleading and possibly just acceptable if the spectrum was recorded with a
space telescope In professional fields, this term is used as "Instrumental System
Re-sponse", which is clearly restricted to the erroneous recording characteristic of ,
considering just the system telescope – spectrograph – camera [305] In contrast, the
cor-rection curve , generated according to , is additionally loaded by the wavelength
dependent damping effects of the Interstellar Matter and of the earth's
phere
Experiments have shown that such correction curves , which are generated just with
an unreddened virtual model spectrum of the same spectral class, are not universally cable They can generally not be applied to any other raw profiles of different spectral
appli-classes, which have been recorded at different atmospheric conditions as well as different zenith distances and observation sites
Deviation between and
The following figure shows for the spectral classes B, A, F, G, the ranges of the smallest viation between (pink) and (blue), valid for the setup C8/DADOS/Atik 314L+ This information may be useful to estimate the rough size of error, when intensity ratios, for applications as described in sect 20 – 22, are measured approximately, ie without any ra-diometric corrections This applies also for the detailed analysis of the Hα line!
Trang 34Consequences and benefits of a radiometric profile correction with a synthetic continuum
This procedure provides not a true correction of the attenuation influences
, , With the direct transformation of the intensity profile from
to , the pseudo continuum is just scaled up to the level of the synthetic and therefore unreddened model star, and not to the original profile of the observed
ject Thus, the attenuating effects are simply bypassed here and just a “synthetic”,
rough approximation to the original profile is reached this way Therefore
fluctua-tions of the continuum radiation cannot be measured in such a profile
Since complies now very roughly to the original profile , also the relative
in-tensities of the absorption lines correspond approximately with those in the original
profile For emission lines , generated independently from the continuum, this applies
just as a rough approximation (sect 8.8)
The original relative relationship between two absorption-intensities and ,
which are measured directly and independently of the continuum level, can be estimated here {7i}, {7j} For emission line intensities and this applies just as a rough
approximation
However it must generally be kept in mind that between different stars, even of the very
same spectral class, considerable differences in the continuum course may occur This
effect can be significantly enhanced by a strongly different metallicity and/or rotation locity ( s ) This method does not yet allow any calibration of the intensity axis in physical units!
ε Ori, Alnilam B0 Iab
α Cma, Sirius A1V
ζ Leo, Adhafera F0 III
Sun G2V
Trang 358.11 Relative Radiometric Profile Correction by Recorded Standard Stars
Correction methods in amateur fields
With this somewhat time consuming procedure the recorded profile is corrected,
similarly to section 8.10, with a correction function However is obtained here, analogously to formula , by a recorded and real existing standard star , mostly of the spectral type A0V The continuum course of is very well known and corresponds
to the profile, just reddened by interstellar dust, as it would have been recorded outside the Earth's atmosphere and without any instrument influences [300] Such flux-calibrated spec-tra can eg be found in the ISIS software [410], containing profiles from the MILES-, ELODIE, UVES and Pickles databases [104], [105], [106], [107]
Standard stars must be recorded with a minimum of time difference and as close as ble to the object under investigation Subsequently, the obtained raw profile is divided by
possi-the specific reference spectrum of possi-the very same star from possi-the catalogue Thus, possi-the
atmos-pheric and instrumental influences can be corrected in a good tion Anyway the resulting spectrum remains here – star-dependent differently strong – reddened by the interstellar matter , however in the "close range" of a few dozen light years, just very slightly [209] [11] In contrast to and the correction function
is determined here only by and , which corresponds also
to common practice in professional astronomy
In contrast to sect 8.10 such real standard star correction curves, recorded very promptly
and with similar elevation angle to the investigated object, can be applied to any spectral classes With the graphic below, Robin Leadbeater [481] shows, that for different spectral
classes, very similar correction curves are obtained this way (many thanks Robin!)
Trang 36Consequences and benefits of the Radiometric Correction with recorded standard stars
The achievable accuracy of this rather delicate method is highly dependent on the quality of
execution By amateurs it tends to be rather overestimated Numerous are the potential sources of errors and in addition, some of the reference profiles of the various databases show significant differences in their continuum courses
Anyway, if applied appropriately and accurately, this fairly time consuming method vides a reasonable approximation to the original theoretical spectral profile , which
pro-still appears individually reddened by the interstellar matter
This way, at least theoretically, also greater fluctuations in the continuum radiation are detectable
The effective temperature according to sect 18.3 can roughly be estimated
This time consuming correction procedure is required if spectra must be obtained for
certain scientific databases For the intensities of emission lines , even this correction
procedure applies just as a rough approximation (see sect 8.8)
Correction methods in professional fields
Anyway the professional astronomy applies significantly higher sophisticated and more curate methods For most of the large professional telescopes is well known
is usually determined separately by observations of standard stars with different zenith distances This way not a correction curve is generated, but instead a model of the atmospheric extinction becomes parameterised, like MODTRAN [314] Thus, finally the pro-file of the examined object will be corrected in function of the zenith distance [305] Fur-ther methods are presented in [300] and [303]
The recording of standard stars consumes valuable telescope time To relieve the main strument of this "annoying" task, the separate determination of with smaller
in-“Photometric Monitoring Telescopes” was already proposed [314] Further possibilities are based on the measurement of atmospheric Cherenkov radiation as well as on LIDAR [314]
In the infrared range the spectral class A0 shows just few and very faint stellar lines fore, these more or less purely telluric influenced profiles are generally used to extract the atmospheric H20 and O2 lines in any stellar spectra [300]
Trang 37There-8.12 Absolute Flux Calibration
As a final step of the radiometric correction, the intensity axis
could be absolutely calibrated in physical units for the spectral
flux density – normally [erg s-1 cm-2 Å-1] This calibration is very
challenging, time consuming and just needed by some special
sectors of the professional astronomy It is relatively common for
spectra, recorded by space telescopes, which of course at least
remain clean of any atmospheric influences [301]
For amateur applications an acceptable accuracy of the results
is usually prevented already by the inadequate quality of the
ob-servation site Thus even in the professional sector, such
abso-lutely flux-calibrated spectra can be found rather rarely
The total flux of an emission line, here in a simplified form
di-rectly drawn on the wavelength axis, corresponds to their area,
[302] The unit for the total flux of the line is [erg s-1 cm-2]
If the emission line is superimposed on a continuum, the continuum flux must
be subtracted from formula However, there exists no easy way to determine the real original undamped flux of an emission line (sect 8.14)
This process is based on the comparison of the absolute calibrated radiation flux of a dard star However, many additional data are required here, such as the exposure time of the spectral recordings Further, the recording usually requires a large slit width to measure
stan-really the total flux of the object
8.13 Intensity Comparison between Different Spectral Lines
The intensities of two different lines can be compared in normalised profiles with their equivalent widths However if the widths of the lines are not too different, a rough
8.14 Reconstruction of the Original Emission-Line Intensities
Most of the emission nebulae (sect 22), don’t show any evaluable continuum But even in spectra with existing continuum (eg P Cygni), the original values of the emission lines
in , can never be reconstructed with the already presented, proportional-radiometric procedures according to sect 8.10 to 8.12 At least for amateurs here just remains the ar-ithmetical scaling of the individual, attenuated emissions, proportionally up to the known
line ratios of the undampened Balmer-Decrement for the hydrogen emissions (sect 20 and
21) These corrected intensitiy ratios allow now to perform the appropriate procedures, eg for plasma diagnostics (sect 22), with higher accuracy Anyway with the extinction at
, according to sect 21.1, formula , the original, absolute values of the
-emissions could roughly be estimated
Trang 388.15 Summary – Which Method Fits to Which Task
The following table provides an overview of which calibration-, normalisation- or ric correction methods are appropriate, or even required for the following tasks
radiomet-Legend: R = Requirement B = Best option, P = possible option
Methods of bration, Normali-sation or Radio-metric correction
Absolute calibration of the profile to
Measurement of the relative
Optical intensity comparison of the
Measurement of the reddened
Estimation of the original IE- and IA-
values in the unreddened original
profile
Comparison of the absorbed fluxes
Evaluation of the emission
Estimation of the effective
Fluctuations of the continuum
Trang 399 Visible Effects of Quantum Mechanics
9.1 Textbook Example Hydrogen Atom and Balmer Series
The following energy level diagram shows for the simplest possible example, the hydrogen
atom, the fixed grid of the energy levels (or "terms") , which a single electron can occupy
in its orbit around the atomic nucleus They are identical with the shells of the famous
Bohr's atomic model and are also called principal quantum numbers Which level the tron currently occupies depends on its state of excitation A stay between the orbits is ex- tremely unlikely The lowest level is It is closest to the nucleus and also called the
elec-ground state
With increasing number (here from bottom to top):
– increases the distance to the nucleus
– increases the total energy difference, in relation to
– the distances between the levels and thus the required energy values to reach the next higher level, are getting smaller and smaller, and finally tend to zero on the Level (or )
The energy level E on the level is physically defined as [5] and also called
Ionisation Limit The level number is to consider as "theoretical", as a limited number
of about 200 is expected, which a hydrogen atom in the interstellar space can really occupy
[6] By definition, with decreasing number the energy becomes increasingly negative Above , ie outside of the atom, it becomes positive
Absorption occurs only when the atom is hit by a photon whose energy matches exactly to
a level difference by which the electron is then briefly raised at the higher level (resonance absorption)
Emission occurs when the electron falls back to a lower level and though a photon is
emit-ted, which corresponds exactly to the energy level difference
Hydrogene Series
Lyman
(Ultra violet)
Balmer (visible)
Paschen (Infrared)
Trang 40Ionisation of an atom occurs when the excitation energy is high enough so the negative
electron is lifted over the level and leaves the atom This can be triggered by a high-energy photon (photo ionisation), by heating (thermal ionisation) or a collision with ex-
ternal electrons or ions (collision ionisation)
Recombination occurs if an ionised atom recaptures a free electron from the surrounding
area and becomes "neutral” again
9.2 The Balmer Series
A group of electron transitions between a fixed energy level and all
higher levels is called “Transition Series” For amateurs primarily the
Balmer series (red arrow group) is important, because only their
spec-tral lines are in the visible range of the spectrum It contains the
fa-mous H-lines and includes all the electron transitions, which start
up-ward from the second-lowest energy level (absorption) or end
here, “falling” down from an upper level (emission) The Balmer series
was discovered and described by the Swiss mathematician and
archi-tect (!) Johann Jakob Balmer (1825-1898) The lines of the adjacent
Paschen series lie in the infrared, those of the Lyman series in the
ul-traviolet range
This sounds very theoretical, but has high practical relevance and can virtually be made
"visible" using even the simplest slitless spectrograph! For this purpose the easiest way is
to record the classical beginner object, a stellar spectrum of the class A (sect 13.4) Most suitable is Sirius (A1) or Vega (A0) These stars have a surface temperature of about
10,000 K, which is best suited to generate impressively strong H-Balmer absorptions The reason for this: Due to thermal excitation at this temperature, the portion of electrons reaches the maximum which occupy already the basic level of the Balmer series With further increasing temperature, this portion decreases again, because it is shifted to even higher levels (Paschen series) and will finally be completely released, which results in the ionisation of the H atoms
In the following Sirius spectrum six of the H-Balmer lines appear, labelled with the relevant electron transitions These absorption lines are labelled consecutively with lowercase Greek letters, starting with Hα in the red region of the spectrum, which is generated by the lowest transition From Hε upwards often the respective level number is used, eg
Hζ = H8 Here is nice to see how the line spacing in the Blue area gets more and more closer – a direct reflection of the decreasing amounts of energy, which are required to reach the next higher level In my feeling this is the aesthetically most pleasing, which the spectroscopy has optically to offer!
Hγ Hδ
Hε
Hζ
Triggering electron transitions
Denotation of the lines