# ph512-11-lec7

```PH512
Professor Michael Smith
MULTIMEDIA ASTRONOMY
School of Physical Sciences
Convenor Prof. Michael Smith
Taught in Spring Term Kent Credits 15 at Level H
1
PH512
ECTS Credits 7.5
A spectrograph is an instrument used to form a spectrum of an object.
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Uses dispersion: the spreading of light into an ordered sequence of
wavelengths.
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A typical spectrograph has the following parts:
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o
Entrance aperture, typically slit-shaped.
o
Optical system to collimate diverging light; make rays parallel so
that all rays approach dispersing device at same angle.
o
Dispersing device (e.g., prism or diffraction grating).
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Camera to focus the image of the dispersed light onto a detector
(photographic plate, CCD).
Spectrograph types are based on what kind of dispersing device is used:
o
Prism spectrograph
Uses a prism to to break up the light from an object into a
spectrum. The lenses focus that spectrum onto a detector.
PH512
Professor Michael Smith
o
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Transmission grating spectrograph
Transmission grating is a piece of transparent glass with etched
grooves in it.
o
Reflection grating spectrograph (e.g., McCormick spectrograph)
Reflection grating is a reflecting surface with etched grooves in it.
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Characterizing the Power of a (Grating) Spectrograph
Resolving power -- defined as
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Professor Michael Smith
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where:
N = # of grooves
m = order of interference
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Increase resolution by increasing N or m.
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Approximately:
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Low resolution: R ~ 102-3.5
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Medium resolution: R ~ 103.5-4
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High resolution: R ~ 104+
By the definition of redshift, we have that v / c = 1 / R.
What this means is we can define the resolution of the spectrograph in terms of
the relative Doppler shifts (in km/s) that the spectrograph can resolve.
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Can achieve higher resolution with gratings:
Rgrating ~ 10 x Rprism
Dispersion
A measurement of the angular separation of different wavelengths of light.
Over what range of output angles, d , is dispersed the range of
wavelength d ?
where W = width of grating (N/W gives the groove density)
SPECTROSCOPY - extracted from
Majewski at Virginia

The presence of gases in the
atmospheres of stars or
surrounding/near any blackbody
perturbs the continuous blackbody
spectrum with the introduction of
lines corresponding to electron
transitions.

Excitation -- When an electron is in
an energy level above the lowest
possible one -- excited state
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Professor Michael Smith
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
Rydberg formula:
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Depending on the relative positions of the gas and the blackbody
(continuous) source, we get either a continuous spectrum, an emission
line (bright line) spectrum, or an absorption line (dark line) spectrum:
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
Professor Michael Smith
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Ionization -- When electron absorbs enough energy to escape from the
atom (atom becomes an ion) -- ionized
Information derived from Spectra
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Chemical composition of the gas
Of course, each chemical element (and ion, isotope and molecule) has a
characteristic ``fingerprint&quot; pattern of emission/absorption lines
corresponding to specific energy levels possible for electrons in that
species.

Physical state of the gas
o
Degree of excitation or ionization
Number of excited or ionized atoms is reflected in the strengths of
lines corresponding to these transitions or ionized species.
o
Temperature of the gas
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Obviously, Wien's Law at most basic level.
But can do better than this by looking at line patterns...
PH512
Professor Michael Smith
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o
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Hotter gas -- greater degree of ionization, molecular
dissociation, and excitation
Density/pressure of the gas
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Higher density/pressure -- greater degree of excitation
Therefore, the strength of an absorption line depends not only on
total abundance of species but in the fraction of those atoms in
the correct state of ionization and excitation to produce the line.
Relative velocity of source
The Doppler effect causes the observed wavelength of lines to be shifted
from their emitted rest wavelength.
where
0
is rest wavelength
Doppler velocity:
From www.astro.ucla.edu/~wright/.
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Professor Michael Smith
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From imagine.gsfc.nasa.gov/.../star_size/ star_velocity.html.
.
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Expansion of a source
o
The expansion of a source, as in the case of rotation, means that
different parts of the source will have different relative velocities
than other parts.
o
Common situations where we see an expanding source is in the
case of a nova (the release of the outer layers of a dying
moderate mass star), a supernova (an explosive, more complete
destruction of a more massive star), or in certain types of
pulsational variable stars, like Cepheids or RR Lyrae (which both
show expansion and contraction).
o
If the source is unresolved, then again we will have a smearing of
the different velocities of the gases that are either absorbing or
emitting lines of radiation, and consequently we will see a
broadening of the lines, similar to the unresolved rotating source
case.
o
However, a very special case sometimes occurs when we have an
unresolved source that includes both absorption and emission line
regions. In this case we can see P Cygni profiles in the spectral
lines, which include an absorption part blueshifted with respect to
a companion emission part.
The geometry of the source that produces a P Cygni profile is
shown in the figure below.
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Strength of magnetic field
PH512
Professor Michael Smith
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Recall that each electron in an atom must have a different
quantum state (Pauli Exclusion Principle).
For a given energy level n, have different orbitals, or angular
momentum quantum number, L (e.g., L=0 is ``s&quot;, L=1 is ``p&quot;, L=2
is ``d&quot;, L=3 is ``f&quot;, etc.).
Each of these orbitals L have 2L+1 sublevels, possible, and these
are expressed in the presence of a magnetic field, which causes
the electrons to precess.
From csep10.phys.utk.edu/astr162/lect/ light/zeemansplit.html.
o
In the presence of a magnetic field, lines corresponding to certain
orbitals will undergo Zeeman splitting , slightly shifting the
energies of the sublevels of the orbitals. Discovered in Sun 1896
by Dutch physicist.
o
Only certain spectral lines have this, those corresponding to levels
that are NOT ``s&quot;, since for ``s&quot; we have L=0 and therefore only
2L+1=1 states.
PH512
Professor Michael Smith
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Zeeman splitting from the intense magnetic fields near a
sunspot. From dilbert.physast.uga.edu/~derek/
ASTR1020/sun.html.

The stronger the external magnetic field, the wider is the split line
separation.
SPECTRAL LINES: CONCEPTS AND TERMS
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One dimensional spectra:
We usually take a spectrum with a detector that yields a two-dimensional
image. One dimension shows wavelength and the other is the distance
along the slit.
Recall that the wavelength dimension is really an infinite set of pictures
of the slit of a spectrograph at each wavelength.
If this concept is confusing to you, here is a picture of the corona of the
Sun after passing through a spectrograph without using a slit (slitless
spectroscopy).
The image of the Sun during an eclipse passed through a
prism shows that the outer parts of the Sun (the corona) -where flares and prominences are made -- emits light in certain
emission lines. Each image here corresponds to a picture of
the Sun in one wavelength. The most prominent image here is
the Halpha (6563 Angstroms) emission line. From
http://www.astrosurf.com/buil/us/eclipse.htm.
To analyze a spectrum with modern methods, we normally look at onedimensional cross-sections showing the relative intensity as a function of
wavelength:
From Abell's Exploration of the Universe, Fourth Edition.
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Line profile:
When we look at the shaped of lines in one-dimensional spectra...
PH512
Professor Michael Smith
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Shape of the line has a core and wings.
o
At any point we have a characteristing line depth, l, and, at the
location of the center of the line, a core line depth, lc.
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10
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Equivalent width:
o
A way of describing the strength of a line.
where S is the line profile area in (counts)x(mm); Ic is the intensity
of the continuum (counts); and d is the dispersion (mm/Angstrom)
W = Area of rectangle of height Ic and width W with same area
as line
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o
W for an element X is function of stellar T, g, [X/H]
o
In practice, the continuum level Ic can be hard to determine if
there are many lines in the spectrum
Terms for closely spaced lines:
In some case you have one transition that has several possible, slightly
different energies possible.
For example, 3p level in sodium has two possible total angular
momentum levels, j=1/2 and j=3/2, induced by the magnetic energy of
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Professor Michael Smith
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the electron spin in the presence of the internal magnetic field caused by
the orbital motion (spin-orbit effect).
Famous NaD doublet at 5890 and 5896 Angstroms. From
hyperphysics.phy-astr.gsu.edu/ hbase/quantum/sodzee.html.
This results in a line doublet corresponding to the transition.
Note that this is not the same as the Zeeman effect, which is additional
splitting induced by outside magnetic field.
From hyperphysics.phy-astr.gsu.edu/
hbase/quantum/sodzee.html.
Thus, we often see very closely placed lines in a spectrum
PH512
Professor Michael Smith
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doublets, triplets, etc. are as described above splitting in same
energy transition in same element, e.g., NaD doublet (5890, 5896
A) and Mgb triplet (5167, 5173, 5184 A).
Highly magnified view of Mg triplet region shown in the
spectrum of an F star. The triplet is marked. Other lines
shown are unrelated. From
http://www.edpsciences.com/articles/astro/full/1998/06/d
s1424/node3.html.
Highly magnified view of Na doublet region shown in the
spectrum of an F star. The doublet is marked D1 and D2.
Other lines shown are unrelated. From
http://www.edpsciences.com/articles/astro/full/1998/06/d
s1424/node3.html.
o
blends are chance near coincidences of lines from different
transitions/different atoms. Undesirable usually. A famous set is
the N II lines at 6548, 6583 Angstroms which always make
measuring the H Balmer line at 6563 Angstroms difficult (see
Seyfert 2 spectrum below).
o
bands are large numbers of lines near one another from
molecular vibrational, rotational modes (as discussed in an earlier
lecture). A famous example is the MgH band starting at 5211
Angstroms.
o
a continuum of lines is created at wavelengths corresponding to
many successive electron transitions with nearly similar energies,
which occurs between low numbered energy levels (n1=1,2,...)
and high energy levels (n2 approaching infinity).
As can be seen from Rydberg formula, when n 2 gets large, the
change in 1/n2 is small, and the corresponding energy absorbed
approaches a limit (corresponding to the ionization energy of the
atom from the n1 level). Thus, the lines get ever closer together,
until they pile up at nearly the same wavelength and we have a
dramatic drop in the flux level of a star at that point. Photons more
energetic than the continuum wavelength ionize the atom.
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Professor Michael Smith
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Example: Note the increased bunching of lines and the Balmer
continuum or Balmer jump (n1=2 transitions) near 4000 Angstroms
in the spectrum of this A type star (spectrum is shown from 3500
to 5000 Angstoms).
The Lyman continuum (n1=1 transitions) occurs at 912 Angstroms.
NOTE: Astronomers uses the simple expression ``continuum&quot; to
mean two things -- don't confuse the ``continuum&quot; of lines with the
``continuum&quot; of the spectrum, which means the level of flux from
the blackbody emission part of the spectrum of the star.
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Line naming convention for ions in astronomy
For an element X:
o
Line from a neutral element X I
e.g. H I, Fe I, Na I
o
Line from a once-ionized species X II
e.g. Ca II H+K lines, N II
o
Line from a twice-ionized species X III
e.g. Si III
Note that the ionized forms of an atom have different locations for the
energy level transitions in the outermost remaining electron.
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Isotopes
The isotopes of atoms have slightly different line locations
For example, the spectrum of neutral deuterium (D I) lines is
nearly the same as, but shifted by 0.027% with respect to, neutral
hydrogen (H I) lines.
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``Forbidden Lines&quot;
These are line transitions seen in emission in certain hot nebulae that
are not seen on Earth -- thus ``forbidden&quot;.
o
Normally, atoms can be excited by collisions or by absorption of
photons. De-excitation / emission occurs rapidly ~ 10-8 - 10-7
seconds
o
However, some ionized atoms have metastable levels that they
can remain in for several seconds to hours
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Normally probability for emission is so low that low
emission rate is not seen in laboratory
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But in a nebula around a hot star -- many electrons free to
excite at right energy, and so many ionized atoms, get lots
of emission -- strong lines. Famous ones:
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[O II] -- 3727
PH512
Professor Michael Smith
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o
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[O III] -- 4959, 5007
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[N II] -- 6584, 6548
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[Ne III] -- 3867, 3968
We indicate a forbidden line transition by putting square
braces around the name, as above.
Until 1927, lines were unidentified because not seen under normal
Earth conditions (gas density) -- &quot;Nebulium&quot; -- &quot;new element in
nebulae&quot; only
EXAMPLES OF EMISSION LINE OBJECTS
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Emission Nebula (Orion)
For M57:
http://www.astrosurf.com/~buil/us/spe6/planet.htm
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Professor Michael Smith
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