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\title{Including All the Lines}
 
\author{Robert L. Kurucz}
 
\address{
Harvard-Smithsonian Center for Astrophysics,
60 Garden Street, Cambridge, MA, USA
\email{rkurucz@cfa.harvard.edu}}
 
 
\begin{abstract}
We present a progress report on including all the lines in the linelists,
including all the lines in the opacities, including all the lines in
the model atmosphere and spectrum synthesis calculations, producing
high-resolution, high-signal-to-noise atlases that show (not quite) all
the lines, so that finally we can determine the properties of stars from
a few of the lines.
\end{abstract}
\maketitle{}
 
 
\section{Atomic and molecular line data}
 
Of the line data on my website, 99 per cent have predicted wavelengths and
can be used only to compute opacities.  One percent have good wavelengths
between known levels and can be used for detailed spectrum calculations for
comparision to observed spectra.  The line data with good wavelengths account for
only one half of the observed lines.  The gf values and damping constants for
most lines must be adjusted to match observed spectra.  We know that the
higher configurations are missing from the line lists.  We know that heavier
elements are missing from the line lists.  We know that isotopic and hyperfine
splittings are missing from the line lists.  We know that many molecules are
missing from the line lists.  Leaving out all these lines systematically
underestimates the opacity, produces energy distributions with systematic
errors, and leads to abundance determinations with large systematic errors.
The most sophisticated 3-D radiation-hydrodynamics calculations for stars
are still wrong if the opacities are wrong.
 
    We need much better laboratory analyses including hyperfine and
isotopic splitting.  We need better calculations that fill in the higher
configurations and the heavier elements.  We need better measurements and
calculations for all the significant diatomic and polyatomic molecules
including all the isotopomers.
 
 
    I am doing as much as I can to fill in the missing data and to make it
available on my web site.
 
 
Half the lines in the solar spectrum
are not identified.  All the features are blended.  Most features have
unidentified components that make it difficult to treat any of the
identified components in the blend.  And even the known lines have hyperfine
and isotopic splittings that have not yet been measured.  Is an asymmetry
produced by a splitting, or by a velocity field, or both?  It is very
difficult to determine abundances, or any property, reliably when you do not
know what you are working with.  Figure 1 illustrates these points.  It shows
one of the emptiest angstroms in the visible in a high-resolution, high-signal-to-noise
solar spectrum taken by James Brault with the FTS at Kitt Peak together with
the spectrum calculated with {\small SYNTHE}.
Figure 2 is
a sample section of the spectrum of Sirius observed by Glenn Wahlgren with the
Goddard High Resolution Spectrograph on the Space Telescope together with the
calculated spectrum.
 
\vspace{10pt}
\ni [Fig. 1 is a large color ledger page on the Kurucz website
{\small KURUCZ.HARVARD.EDU/ PAPERS/NICELINES/FIG1}. It will be
mailed by post on request.]
 
\vspace{5pt}
 
 
\ni {\bf Fig. 1.} A small section of the solar flux spectrum at 599nm
plotted at full scale and at 10-times scale.  The heavy black lines show the
observed spectrum from the Kitt Peak Solar Flux Atlas from 300 to 1000 nm
(Kurucz 2005).  The resolving power is about 300000 and the signal-to-noise
is about 3000.  Higher quality spectra would be helpful because the spectrum
is not resolved and because weaker features would appear at higher
signal-to-noise.
 
The thin lines are the computed spectra: in red for the solar flux,
in blue for the telluric atmospheric transmission, and in purple for their
product which should be compared to the observed heavy black lines.
The computed spectra are broadened to resolving power 0.05666 cm$^{-1}$
to match the observed spectrum.  There are solar lines of Ca I, Ti I, Cr I,
Cr II, Fe I, Fe II, Co I, Yb II, C$_2$, CN, and
telluric lines of H$_2$O.  The first number in each line label is the last
3 digits of the wavelength.   The second number is the species code which is
the atomic number plus 0.01 times the charge. The middle numbers are either the
lower energy level in cm$^{-1}$ for atoms or quantum numbers for molecules.
The 4th number is the per mil line depth if the line were computed in isolation.
Two of the Co I lines have been divided into hyperfine components.  The
hyperfine and isotopic splittings have not yet been determined for the other
lines.  Some splittings may be negligible.  There are many missing lines.
The lines that are present have been adjusted to improve agreement between
the calculated and observed spectra.  That process is continuing.  This sample
will be part of a forthcoming flux atlas with line identifications.
 
\vspace{10pt}
\ni [Fig. 2 is a large color ledger page on the Kurucz website
{\small KURUCZ.HARVARD.EDU/ PAPERS/NICELINES/FIG2}. It will be
mailed by post on request.]
\vspace{5pt}
 
 
\ni {\bf Fig. 2.} A sample section of the spectrum of Sirius at 200 nm observed
by Glenn Wahlgren with the Goddard High Resolution Spectrograph on the Space
Telescope together with a calculated spectrum that has not yet been adjusted
to improve the fit.
 
     The rotation velocity is known from fitting lines in the visible observed
at high resolution.  The spectrum is computed both at 0 km/s rotation
velocity to resolve the blends and at 16 km/s.  The 16 km/s spectrum was then
convolved with the instrumental profile.  The resolution was not high enough
to resolve the actual structure in the spectrum which is on the order of the
zero rotation line width.  Around 201.26 for example the two side bumps are
washed out.  Ideally the measurement should have been made at higher resolution.
 
     The calculations are plotted in residual flux but the continuum level for
the observed spectrum has not been set and its position can be adjusted.  Except
at 201.02 nm it appears that the observed spectrum should be moved up about 3\%.
That would also bring the minima into better agreement.  Either the Mn II line
at 201.0259 is wrong or there is a problem with the reduction at this point
which is near the end of a scan.  Note that the minima in the spectrum at
201.1, 201.22, and 201.42 are not line positions.  Features in spectrum are
blends of many lines.
 
 
     Note the Si II line at 201.5 that is computed very much too strong.
That will be corrected in my next calculation for Si II.  Note the missing
line at 201.11.  That will probably appear when I recompute the Fe group
lines using improved laboratory analyses.  The linelist for this spectrum
has not been updated with new calculations.  It uses the linelist from my
web site.  I am going to update many elements at once to limit the number
of versions of the linelist and also to give me more
time to make comparisons and to check for errors.  Fresh calculations can
be found on the website in the {\small /ATOMS} directory.
\vspace{10pt}
 
For planetary and telluric atmosphere projects the solar irradiance spectrum
is required as the input at the top of the atmosphere.  It has never been
observed.  People ask me to compute it.  I can compute it theoretically using
both known and predicted lines and get agreement averaged over a nanometer
but there is no way to predict the resolved spectrum when only half the lines
are known.  In other stars the situation is worse because the signal-to-noise
and resolution of the observations are worse.  Logically one has to know a
priori what is in the spectrum in order to interpret it; there is not enough
information in the observed spectrum itself.
 
Basically we need a list of all the energy levels of all atoms and molecules
that matter (qualifiers below).  From
that list can be generated all the lines.  With the energy levels
and line positions known, one can measure gf values, lifetimes, damping, or
one can determine a theoretical or semiempirical Hamiltonian whose
eigenvalues and eigenvectors produce a good match to the observed data, and
that can then be used to generate additional radiative and collisional data
for atoms or molecules. Forbidden magnetic dipole and electric quadrupole
lines are required as well.
 
 
For atoms and ions, we need all levels, including hyperfine and isotopic
splittings, for n $\le$ 9 below the lowest ionization limit and as much as
practicable above. Lifetimes and damping constants depend on sums over the levels.
 
Radiative acceleration in stellar envelopes can selectively levitate some
elements.  At the visible surface the enhancement can be as much as a factor
of 10$^{4}$.  The radiative acceleration is computed by integrating
l$_{\nu}$J$_{\nu}$ over the spectrum.  If the diffusion takes place deep in the
envelope, spectra for high stages of ionization are required.  For heavier
elements we need at least the first 5 stages of ionization.
 
In the sun I see unidentified asymmetric triangular features that are
unresolved multiplets of light elements with n $\le$ 20.  Simple spectra
should be analyzed up to n = 20.  Levels that connect to the ground or to
low levels should be measured to high n, say n = 80.  The high levels are
necessary to match line series merging into continua.
 
For molecules, we need all levels below the first dissociation limit and as
much as is practicable above, especially levels of all states that connect
to the ground state.  Except for H$_{2}$(BX,CX), far ultraviolet bands have
been ignored unless they appear as interstellar lines.  We see H$_{2}$ lines
in stars as hot as 8000K when the stars have low metal abundances so that the
lines are not masked.
 
In the sun we see, and have line lists for,
C$_{2}$(AX,ba,da,ea),
CN(AX,BX),
CO(AX,XX),
H$_{2}$(BX,CX),
CH(AX,BX,CX),
NH(AX,ca),
OH(AX,XX),
 
\ni MgH(AX,BX),
SiH(AX),
SiO(AX,EX,XX).
The isotopomers are included.  Some
stellar spectroscopists have more recent linelists than I do.  Mine are based
on old laboratory data and were computed with rotationless RKR potentials.
They all have to be brought up to date, or even further improved, and expanded
to higher V and J levels. In many cases there are new analyses based on FTS
spectra.  Ions and a few minor molecules have to be added to the linelist as
well.  In the sun there are many broad bumpy unidentified features that are
molecular bands that are not in the line lists.  Most of them are probably
just high-V transitions.  It is important that the laboratory analyses include
all the isotopomers.  They are needed to interpret the stellar spectra.  When
they are not measured in the laboratory, we have to make up our own predicted
linelists for them.
 
For the cooler stars we
need all the diatomics among all the abundant elements, and, essentially,
the hydrides and oxides for all elements (such as ScO. TiO, VO, YO, ZrO,
LaO, etc.).  Ca appears as CaOH and CaH, not CaO.  I use the TiO linelist
from Schwenke (1998) with 38 million lines.
 
Stars that are
evolved and have high C abundances from nuclear burning can bind all the
O into CO so that there are no other oxides, just C-bearing molecules.  CN and
C$_{2}$ bands are everywhere.
 
For M stars cooler than 3500K triatomics also become important.  Much more
laboratory and computational work is needed for H$_{2}$O.  I currently use the
linelist from Partridge and Schwenke (1997) with 66 million lines.
 
In the brown dwarfs and ``planets" methane is important and it needs more
laboratory and computational work.
 
Some of this is described in more detail in my paper ``Atomic and molecular
data needs for astrophysics" (Kurucz 2002).
 
 
\subsection {Isotopic and hyperfine splitting}
%
\begin{figure}[]
\rotatebox{90}{\includegraphics[0,0][192,177]{nicelinesfig3.eps}}
 
\ni {\bf Fig. 3.} Examples of isotopic splitting in Fe II and Ni II after
Rosberg, Litz\'en, and Johansson (1993).  The indications for $^{61}$Ni
and $^{57}$Fe are guesses.
 
\end{figure}
%
\vskip 5pt
 
%
\begin{figure}[]
\resizebox{\hsize}{!}{\rotatebox{90}{\includegraphics[0,0][279,375]{nicelinesfig4.eps}}}
 
\ni {\bf Fig. 4.} Asymmetries in the Ca II infrared triplet arise from isotopic and
hyperfine splittings, not from velocity or non-LTE effects.  The splitting
data are listed in Table 1.  Two \AA \ around each line are  plotted twice,
centered on the centroid wavelength, with splitting, and, offset, without
splitting.  The calculation uses model C by Fontenla, Avrett, and Loeser 1993
which has a chromosphere.  In lieu of a real non-LTE calculation, the line
opacity was smoothly changed to scattering for $\tau$$_{Ross}$ $<$ 0.04.  The
number was chosen by experimenting until the emission from the chromosphere
was eliminated.    Note that the splitting also changes the
line wings.  The heavy lines are the observed spectrum from the Kitt Peak Solar
Flux Atlas from 300 to 1000 nm (Kurucz 2005).
 
\end{figure}
%
%
\begin{figure}[]
\includegraphics[0,0][360,400]{nicelinestable1.eps}
\end{figure}
 
 
There are two papers on isotopic and hyperfine splitting on my website
(Kurucz 1992; 1993).  In the second is a table that lists all the stable
isotopes, their fractional abundances, nuclear spin, dipole moment, and
quadrupole moment.  The only element that does not have isotopic or
hyperfine splitting is thorium. ``Lines" are normally asymmetric because
of the splitting.   Figure 3 from Rosberg, Litzen, and Johansson (1992)
show the isotopic splitting of an Fe II line and a Ni II line.  If the
splitting is not taken into account many kinds of errors are possible:
the use of bisectors to determine velocity fields is incorrect; Fourier
analysis of line profiles to determine rotational, microturbulent, and
macroturbulent velocities is incorrect; damping constants are over-estimated.
When stronger components become saturated, the weak components are still on
the linear part of the curve of growth.  They make a larger contribution to
the total feature than their fractional abundances might suggest.  This
introduces the additional systematic errors: wavelengths of saturated lines
are shifted relative to the isotopic abundance weighted position; abundances
determined from equivalent widths are wrong unless the curve of growth is
computed from the real line profile with components.  In addition, the
Doppler width and Voigt profile differ significantly from the lightest to
the heaviest isotope.
 
I was recently asked about the Ca II infrared triplet so I collected the data
from the literature.  Figure 4 shows the solar flux spectra for the cores of
the Ca II infrared triplet lines for two \AA \ around their centroid wavelengths
and with the LTE computed profiles including hyperfine and isotopic splitting.
In non-LTE the cores become weaker as observed.  The components are listed
in Table 1.
 
 
Molecular lines can also have hyperfine splitting, but I have not yet had to
deal with it.
 
 
\subsection{Adding atomic and molecular data}
 
     The basic rule seems to be that if you need data you have to produce it
yourself.  My workstation and my website have a directory for each ion of
all the atoms up through Zn, and the first five ions of heavier elements, and
for all the diatomic molecules that I should work on.  Here are a few examples:
 
 
 
{\bf Fe II}. The semiempirical calculation for n$\le$9 was
based on Johansson (1978) and on more recent published and unpublished data.
Johansson has data for more than 100 energy levels that I do not yet have.
There were 46 even configurations: d$^{7}$, d$^{6}$ns, nd, ng, ni, nl,
d$^{5}$4sns, nd, ng, ni, nl, d$^{4}$4s$^{2}$4d, d$^{4}$4s$^{2}$5s, d$^{5}$4p$^{2}$
which produce 19771 levels of which 403 are known.  There are 39 odd configurations:
d$^{6}$np, nf, nh, nk, d$^{5}$4snp, nf, nh, nk, d$^{4}$4s$^{2}$4p, d$^{4}$4s$^{2}$5p,
d$^{5}$4s$^{2}$4f, which produce 19652 levels of which 492 are known.  These
produced 7,719,963 E1 lines and 28 million M1 and E2 lines.  Only 81225 E1 lines
have good wavelengths.  Only 2884 of the forbidden lines are from metastable levels.
The previous calculation (Kurucz 1988) produced 1,264,969 lines
with 45815 good wavelengths.  There are four stable isotopes:
 
\vspace{5pt}
\ni Isotopes \ \ \ $^{54}$Fe \ \ \ \ \ $^{56}$Fe \ \ \ \ \ $^{57}$Fe \ \ \ \ \ $^{58}$Fe
 
\ni Fraction \ \ \ \ .059 \ \ \ \ \ .9172 \ \ \ \ .021 \ \ \ \ .0028
 
\vspace{5pt}
\ni Only a few lines have been measured by Rosberg, Litz\'en, and Johansson (1993)
so I put in the splittings by hand.
 
 
 
The {\bf Ni I} calculation was mostly based on the analysis by Litz\'en, Brault, and
Thorne (1993) which includes isotopic splitting.  There were 46 even configuations
with 3203 levels of which 120 are known.  There were 48 odd configurations
with 4800 levels of which 153 are known.  These produced 529632 E1 lines
compared to 149926 from Kurucz (1988).  Only 9637 lines have good wavelengths.
There were 1.5 million M1 and E2 lines of which 65 were from metastable levels.
There are 5 stable isotopes,
 
\vspace{5pt}
\ni Isotope  \ \ \ \ $^{58}$Ni \ \ \  $^{60}$Ni \ \ \  $^{61}$Ni \ \ \ $^{62}$Ni \ \ \ $^{64}$Ni
 
\ni Fraction  \ \   .6827 \ \  .2790 \ \   .0113 \ \  .0359 \ \   .0091
 
\vspace{5pt}
\ni   There are measured splittings for 326 lines
from which I determined 131 energy levels relative to the ground.  These
levels are connected by 11670 isotopic lines.  Hyperfine splitting was
included for $^{61}$Ni but only 6 levels have been measured which produce 4
lines with 38 components.  A pure isotope analysis is needed.
 
Ni I lines are asymmetric from the splitting.  When the isotopic calculation
was first checked against the solar spectrum it did not look right.  Subsequently,
I found a program error and recomputed the splittings.  Now the profiles match the
observed.  Observed stellar spectra are generally not high enough quality to show
that there are such errors.
 
 
The {\bf Co I} calculation was based on Pickering and Thorne (1996) and on Pickering
(1996) with hyperfine splitting.  This calculation was made before my programs
were expanded.  I will rerun this with twice as many configurations.
This calculation had 32 even configurations with 3546 levels of which 139 were
known.  There were 32 odd configurations with 5870 levels of which 223 were known.
These produced 1729299 E1 lines of which 15481 were between known levels.
The old calculation (Kurucz 1988) produced 546130 lines.  There were 4.7 million
forbidden lines of which 696 were from metastable levels, $^{59}$Co is the only
stable isotope.  Hyperfine constants have been
measured in 297 levels which produce 244264 component E1 lines.  I have
not yet computed the M1 or E2 components.  The new calculation greatly
improves the appearance of the Co I lines in the solar spectrum.
 
 
{\bf C I}.  The lower levels of C I were computed as in the previous examples and higher
levels up to n = 20 were added from Ritz extrapolation for low l or from the
polarization formula for high l.
There were 136 even configurations: s$^{2}$p$^{2}$, s$^{2}$pnp, nf, nh, nk, nm,
no, nr, nv, nw, ny, with 2382 levels.  There were 139 odd configurations:
s$^{2}$pns, nd, ng, ni, nl, nn, nq, nt, nv, nx, sp$^{2}$np, p$^{3}$ns, p$^{3}$nd,
with 1962 levels.  They produced 469918 E1 lines of which 182979 have good wavelengths.
The low levels produced 652897 forbidden lines of which 10 were from metastable levels.
The series were extrapolated to n = 99 to produce 36182 lines that merge into
low continua.  I have not yet worked on the isotopic or hyperfine splitting.
The isotopes are   0.9890 $^{12}$C and 0.0110 $^{13}$C.
 
I am now doing Si I in the same way.
 
{\bf S I}.  There were 61 even configuarations with 2161 levels and 61 odd configuartions
with 2270 levels.  They produced 225605 E1 lines of which 24722 had good
wavelengths.  I have added measured autoionization parameters to the ultraviolet
lines by hand.  There are 4 stable isotopes,
\vskip 5pt
\ni Isotopes  \ \ \ \ \ \ \ \ \ \ \ $^{32}$S \ \ \ \ \ $^{33}$S \ \ \ \ $^{34}$S \ \ \ \ $^{36}$S
 
\ni Fraction \ \ \ \ \ \ \ \ \ .9502 \ \ .0075 \ \  .0421 \ \  .0002
\vskip 5pt
\ni I have not yet worked on the isotopic or hyperfine splitting.
 
 
{\bf TiO}.     Schwenke (1998) calculated energy levels for TiO including in the Hamiltonian
the 20 lowest vibration states of the 13 lowest electronic states of TiO
(singlets a, b, c, d, f, g, h and triplets X, A, B, C, D, E) and their
interactions.  He determined parameters by fitting the observed
energies or by computing theoretical values. Using Langhoff's (1998) transition
moments Schwenke generated a linelist for J = 0 to 300 for the
\vskip 5pt
\ni Isotopomers $^{46}$TiO \ \ \ $^{47}$TiO \ \ \ $^{48}$TiO \ \ \ $^{49}$TiO \ \ \ $^{50}$TiO
 
\ni Fraction \ \ \ \ \ \  .080 \ \ \ \ \ \ \ .073 \ \ \ \ \ .738 \ \ \ \ \ \ \ .055 \ \ \ \ \ .054
\vskip 5pt
\ni My version has 37744499 lines.
 
{\bf Oxides}.  Good laboratory analyses and a semiempirical treatment similar to that for
TiO are needed for  CaOH, ScO, VO, YO, ZrO, LaO, etc.  Better laboratory
data could be used to further improve TiO.
 
 
 
\section{ Rapid Computation of Line Opacity in SYNTHE and DFSYNTHE}
 
Once we have the line data we need to compute opacities.
There is a paper on my website, ``Rapid Calculation of Line Opacity",
{\small KURUCZ.HARVARD.EDU/PAPERS/ OPACITYCALC}, that was never published,
like many of my papers.  It starts with a naive calculation and shows how
to speed it up by a factor of 1000.  Consult that for details.  Here I will
just mention some of the points.
 
There is no limit to the number of lines.  I expect to reach more than
one billion lines in the near future.
 
Do not compute to higher precision than the physics warrants.  Wavelengths
are the only physically accurate numbers in the whole problem.  For everything
else, 0.1 percent (1/2$^{10}$) is more than adequate.  Very few gf values are
accurate to 1 percent or even 10 percent.  The lower energy that
goes into the Boltzman factor needs only 0.1 percent accuracy.  Damping
constants are accurate from 1 to 100 percent.  Abundances are accurate from
1 to 100 percent.  Use a low precision Voigt function.  Use two-byte integers.
Never compute anything twice.  Factor out T dependences and do all pressures
together for a given T.
 
Once you have a program like {\small SYNTHE}, take a model (a T-P table), a
linelist, and the program and compute the opacity spectrum from the
far ultraviolet to the far infrared for 0 Vturb. You then
have an array of say 4 million points at 20 pressures at 50 temperatures.
To include microturbulent velocity for, say, five values, either broaden
the spectrum with a gaussian filter or Fourier transform the spectrum,
broaden the transform, and transform back.  Write out the log of the
spectrum packed as two byte integers. Repeat for all the Vturb values.  Do it
over and over again for a range of temperatures and pressures.
 
Transpose the array to 20 pressures at 50 temperatures at 5 Vturbs at 4
million points.  You can then generate a spectrum for a given model by
interpolating in the table and integrating to get the flux.  The table is
40 GB.  This method may actually be practical with a large amount of disk
space and a fast computer.  You could add in the continuous opacity and store
the total absorption and the total scattering in 80GB.  The model atmosphere
program would not have to compute any opacities; it would just interpolate in
the tables.
 
You can tabulate only a limited temperature, pressure, and wavelength
range, say with no molecules and no far infrared, or with no multiple ions
and no Lyman continuum, to save space and time.  You can compute the opacities
over only limited wavelength regions, a photometric system, a single echelle
order, a velocity template, and then recover the opacities by interpolation
from a small table.
 
You can leave out the big lines so that you can treat them separately.  You can
leave out hydrogen lines so you can treat H$_{\alpha}$ or H$_{\beta}$ separately.
You can leave out all the lines of one element.  You can include only the
lines of one element.  If you have very large storage you can tabulate the
opacity spectrum of each element separately and add them together weighted by
their abundances.  (But without molecules, and there may be problems with
broadening.)
 
If you have only a workstation and less disk space, you need to start making
approximations.  Instead of writing out a spectrum for a given P,T,Vturb
you can statistically analyze it in wavelength intervals and represent
thousands of points in an interval with only a small number of coefficients.
A distribution function tells you the fraction of the interval occupied by
high, medium, and low opacity (actually in 12 steps in {\small DFSYNTHE}).
The distribution function approximation is valid if the shape of the spectrum
is similar at different temperatures and pressures, i.e., the maxima and minima
line up, and if the source function does not vary strongly across the
wavelength interval.
 
Fiorella Castelli in Trieste is the expert on using DFSYNTHE.  She has
recomputed most of my old ODFs using updated opacities including the
new H$_{2}$O and TiO linelists.  She is also the expert on using the ODFs
to compute new grids of ATLAS9 models (Castelli and Kurucz 2003).
 
 
Each spectrum can be processed more than once, say with different size
wavelength intervals.  You can purposefully select wavelength intervals that
have various sizes and follow features, or make distribution functions for
whole continua to try to minimize the number of points.
 
 
There are other procedures for processing the opacity spectra.  You can
make opacity sampling tables by saving only every one hundredth point,
leaving 40000 points in only 400MB, which would fit on a CD and even in memory
on some computers.  Then {\small ATLAS12} could run without line data or
opacity routines, just interpolations.  Once you have pretabulated the opacity,
you can pretabulate the Rosseland mean.  With pretabulated Rosseland opacity
{\small ATLAS12} would converge much faster.   Of course, {\small ATLAS12}
would lose the ability to change abundances.
 
You can purposefully select the wavelengths that are saved, or the wavelength
intervals, or make selective means, or intermix different strategies.
Instead of doing opacity sampling that maintains the dynamic range in the
opacity, you can throw away the dynamic range and use mean opacities.  Instead
of sampling at every hundredth point, average every hundred points (inversely
or in the log).  This would work in {\small ATLAS12} and would result in a
mean fluxes at resolving power 5000.  The fluxes would not be physically
correct, but they can be checked by computing the spectrum point by point and
averaging.  It may be no worse than other shoddy physics, such as mixing-length
convection, in the model atmosphere programs.
 
 
\section {ATLAS12, SYNTHE, ATLAS9, WIDTH9, et cetera}
 
Once programs had been developed to compute a realistic opacity spectrum
for large numbers of lines ({\small SYNTHE}, Kurucz and Avrett 1981)  it
became possible consider including all the lines in a model atmosphere
calculation.  I can do this directly but it would take about a month per
model with the fastest Alpha workstation, and perhaps a day using the full
power of a parallel supercomputer.  More practical methods involve
statistical treatments of the line opacity.  I have programmed two different
treatments.  First, opacity distribution functions, ODFs, using {\small
DFSYNTHE} to pretabulate the opacity, then {\small ATLAS9} to compute
the models and low resolution emergent flux, and finally {\small SYNTHE} and
{\small SPECTR} to generate the high-resolution spectrum.  Second, opacity
sampling using {\small ATLAS12} to compute both the opacity at a small
number of points (30000) and a model that conserves energy but does not
produce accurate fluxes.  Then {\small SYNTHE} and {\small SPECTR} are
used to generate the emergent high-resolution spectrum.
 
{\small SYNTHE} and {\small SPECTR} can also generate specific intensity spectra
across the disk that {\small ROTATE} uses to produce rotationally broadened
flux spectra.  The intensity spectra themselves are the limbdarkening.  Spectra
can be transmitted through the terrestrial atmosphere using the {\small
TRANSYNTHE} suite of programs.  The spectra can be convolved with filters to
generate any color system using {\small INTEGRATEFILTER}.  The spectra can be
convolved with instrumental bandpasees to generate energy distributions, SEDs,
or spectra at any resolution using {\small BROADEN}.
The final computed spectra can be plotted together with the observed
spectra with the lines labelled using {\small PLOTSYN}.
 
 
With a fast, large-memory workstation it is now possible to compute, for
a fixed set of abundances, tables of ODF opacities in one day,
and then to compute a whole grid of models in another day.  A small
section of spectrum, enough to calibrate a photometric system, or echelle
orders, can be computed in another day for the whole grid of hundreds of models.
 
Alternatively, to work on individual stars with arbitrary abundances,
including isotopic abundances, one can use {\small ATLAS12} to generate in one day
a small grid for one star that varies temperature, gravity, and
abundances.  In another day a small region of the spectram can be
computed for each model and compared to observation.  The whole spectrum
can be computed for the best fitting model.
 
 
\subsection{ATLAS12}
{\small ATLAS12} still does not work as originally advertised (Kurucz 1995).
It is supposed
to be able to treat abitrary abundances, including depth-dependent isotopic
abundances.  At that time I had become interested in isotopes;  I had
isotopomeric molecular line lists that could show variation from dredge-ups,
and also I was interested in isotopic splittings of atomic lines and diffusion.
There were two problems, treating Rosseland opacities and treating the equation
of state, that had to be solved to get {\small ATLAS12} to work.  All of my
model atmosphere programs except the first few use a Rosseland opacity scale.
This is the ``natural" scale for coupling the structure of the atmosphere to
the radiation field. Convective flux also depends on the Rosseland opacity.
But for arbitrary, and espcially for depth-dependent
abundances, the Rosseland opacity cannot be pretabulated.  It has to be
computed as the model is computed.   It took me years to figure out how to
generate a starting guess for the Rosseland opacity and to extrapolate from
iteration to iteration as the temperature was changing.  The guessing procedure
worked and allowed {\small ATLAS12} models to converge.  At that point I started
to let others use the program.  Later it was pointed out to me by Tsymbal
(Tsymbal and Shulyak 2003) that
I could have chosen a continuum monochromatic optical depth scale that behaves
similarly to the Rosseland depth scale, and that I could have computed the
models on that depth scale.  At each iteration I could compute the Rosseland
opacity and use it to compute the convection.  Once the model converged I
could interpolate it to the Rosseland scale.  This should work except in
cases where there are big abundance changes that cause big opacity changes.
Some users may wish to make a $\tau$$_{500nm}$ or $\tau$$_{1000nm}$ or
$\tau$$_{whatever}$ version of {\small ATLAS12}.
 
Some of the equation of state routines date from the 1960s.  If there were
not good laboratory data for the energy levels, the partition functions
generated then were wrong and the ionization potentials were uncertain,
especially for the heavier elements, and they are still wrong.
The molecules need a separate partition function for each isotopomer.
I planned, and still plan, to write a new equation of state routine that uses
partition function tables for each species including each isotopomer.  Whenever
I compute a new line list I automatically generate the energy levels and the
partition function.  When I computed an iron group line list
(Kurucz 1988a), I generated a partition function table for each species.
Those are stored in the file {\small PFIRON}.  I am computing or recomputing
all the atoms to fill out the line data so I will generate all the partitiion
functions and the problem will be solved.  However those calculations are
going slowly, especially since I do not have funding.  I have decided to try
to do a quick Hartree-Fock calculation of the energy levels and the partition
functions so that I can finish {\small ATLAS12}.  Now that memory is not a problem,
putting in the new partition functions and depth-dependent abundances should
be simple.
 
The 30000 fluxes that {\small ATLAS12} computes are accurate enough to compute the
total flux but not good enough for intermediate band photometry such as uvby.
It is necessary to make a separate flux calculation using {\small SYNTHE}
after a model is converged.  I use the following procedure:
 
I first run {\small ATLAS12} only through the point where it selects the line data
from the line list files.  I write out and save the file.  That file is
in a packed format where all information not essential to the opacity
calculation has been removed.  The lines for any similar stars will be the
same, so models for those stars can be computed from the same line list.
Models with lower abundances will also work.  Higher abundance models would
need a new line selection.
 
To compute the spectrum for an {\small ATLAS12} model with {\small SYNTHE},
use program {\small RPACKEDLINE} to read the line file.  Since there are
no identifications in the packed file, {\small SYNTHE} does not save any
information about the lines.  {\small ATLAS9}, or any other models, can be
used with these line lists.  A complete spectrum may have to be computed
in pieces and patched together with {\small MERGESYN}.  The packed line
list can also be edited for computing shorter intervals for photomtery, etc.
 
 
 
These spectra do not reproduce real high resolution observed spectra.
Stronger lines tend to have good data but the weaker lines are incomplete
and they include the predicted lines with uncertain wavelengths that fill
in the opacity between big lines.  At lower resolution most of the wavelength
errors should average out.  Also models are generally computed with an
overestimate of the Fe abundance and an overestimate of the microturbulent
velocity to make up for some of the missing line opacity.
 
 
To make a detailed comparison to a high resolution spectrum, only the line
lists with laboratory wavelengths should be used, and the gf values and
damping constants need to be hand adjusted to match.  The normal procedure
is to work differentially by adjusting the line data to match a high
resolution, high-signal-to-noise atlas for a star for which a good model
atmosphere is available.
 
\subsection{Depth-dependent microturbulent velocity}
Microturbulent velocity is a parameter that is generally not considered
physically except in the sun.  Usually it is treated as the parameter that
minimizes scatter among lines of the same ion in abundance analyses.  Figure 5
shows the temperature versus optical depth for the empirical solar Model C of
Fontenla, Avrett, and Loeser (1993). It also shows the empirical
microturbulent velocity versus optical depth determined from (central
intensity) line profiles.  I have schematically divided it
into microturbulent velocity that is produced by convective motions that must
go to zero at or below the temperature minimum, and into microturbulent velocity
that is produced by the waves that heat the chromosphere.  The minimum Vturb is
about 0.28 of the maximum Vturb.  The minimum temperature is about 0.76 Teff.
I suggest that all ``normally" convective cool stars have behavior like this.
%
\begin{figure}[]
\includegraphics[0,0][212,281]{nicelinesfig5.eps}
 
\ni {\bf Fig. 5.} The empirical solar model C by Fontenla, Avrett, and Loeser
(1993) that has a chromosphere, a temperature minimum, and also an
empirical microturbulent velocity distribution that I have divided into
Vturb from convection and Vturb from waves.
 
\end{figure}
%
 
%
\begin{figure}[]
\includegraphics[0,0][210,294]{nicelinesfig6.eps}
 
\ni{\bf Fig. 6.} Maximum convective velocity at any depth in each model for a solar
abundance grid.
 
\end{figure}
%
%
\begin{figure}[]
\includegraphics[0,0][210,294]{nicelinesfig7.eps}
 
\ni {\bf Fig. 7.} Maximum fraction of convective flux at any depth in each
model for a solar abundance grid.
 
\end{figure}
%
%
\begin{figure}[]
\includegraphics[0,0][210,294]{nicelinesfig8.eps}
 
\ni {\bf Fig. 8.} The product of Fig. 2 times Fig. 3, the flux-weighted convective
velocity, which I use as the estimator of Vturb at the bottom of a model.
 
\end{figure}
%
 
This convective microturbulent
velocity is not the microturbulent velocity found in equivalent width
abundance analyses.  In the sun an equivalent width determination of
microturbulent velocity from the flux spectrum yields Vturb $<$ 1 km s$^{-1}$.
It is also not the Vturb of line opacity tables.  My solar model, ASUN,
(Kurucz 1992) has Vturb = 1.5 km s$^{-1}$ in order to make up for missing
lines that have not yet been included in the line list.  We know
for certain that the microturbulent velocity varies with depth, that the
opacity is strongly dependent on microturbulent velocity, and that the model
atmospheres do not include depth-dependent microturbulent velocity.
 
In Figure 6 I show the maximum convective velocity for a grid of solar abundance
convective models.  In Figure 7 I show the maximum fraction of convective flux
at any depth for each model in Figure 6.  In Figure 8 I have weighted the
maximum convective velocity by the maximum convective fraction.  I treat
this weighted velocity V$_{W}$ as the microturbulent velocity at the bottom of
the atmosphere.  It agrees with the empirical value in the sun.  Then I take the
depth dependence of the microturbulent velocity produced by convection in the
sun and I scale to V$_{W}$.  I ignore outwardly increasing Vturb from waves
and set the minimum Vturb to max(Vturb, 0.28 V$_{W}$) as in the sun.
Figure 8 then gives the variation of microturbulent
velocity with temperature and gravity as long as we stay on the cool side of the
maximum.  And, since we do not understand what is happening on the hot side,
let us blindly do the same there.  One thing we know for certain is that there
can be no microturbulent velocity produced by convective motions if there is no
convection.  Convection deeper in the star can generate waves that propagate
through the atmosphere and produce a ``wave" Vturb.  One can also guess that
the ``mean" microturbulent velocity must be on the order of V$_{W}$/2 which
should roughly correspond to the number found from curves of growth.
 
 
Microturbulent velocity varies with effective temperature and gravity and
abundance because convection varies with effective temperature, gravity, and
abundance.  When comparing the properties of two stars, the difference in
microturbulent velocity must be accounted for.  When comparing two stages
along an evolutionary track, the change in microturbulent velocity must be
accounted for.  By using grids with depth-dependent microturbulent velocity
as described here, this effect is automatically included.  Vturb is no longer
a free parameter. This may not be true for low-gravity stars hotter than the
sun that have only weak convection.
 
If two stars have the same effective temperature and gravity,
the one with the higher abundances will have higher microturbulent velocity
because it is more convective.  I have not yet computed the grids to work out
the numbers.  I expect that in {\small ATLAS12} the Vturb varies with the
convection, the convection varies with the Rosseland opacity at $\tau$=1, and
the Rosseland opacity at $\tau$=1 varies with the abundances.
 
\subsection {Rotation and differential rotation}
 
Rotational broadening is computed in program {\small ROTATE} by generating intensity
spectra for a range of angles (currently 17, $\mu$ =
1.0, .9, .8, .7, .6, .5, .4, .3, .25, .2, .15, .125, .1, .075, .05, .025, .01),
then defining a rectilinear grid over the disk of the star (currently 200x200,
or 100x100 quadrant), then interpolating the spectrum for
the angle and projected velocity at each point, and finally summing all the points.
There are two more approximations.  First the spectra are interpolated to 100
angles ($\mu$ = 0.005 to 0.995 by .010) and pretabulated.  The spectrum at each point
on the disk is found by choosing the nearest angle in the pretabulation.
Second, the spectrum is doppler shifted by the nearest integral number of points.
If the resolving power is 500000 the shift can have an error of one part in one
million.  Most of the errors are random and cancel but they should be checked
for critical work.  Increase the resolving power or the grid size or the number
of angles and see if the output spectrum is affected.
 
More physics can be put in.  I have added differential rotation using the
empirical fit for the sun from Libbrecht and Morrow 1991 for latitude $\phi$ and \rsun \ in km,
 
\ni V$_{rot}$($\phi$)=
 
(462 --75sin$^{2}$$\phi$ --50sin$^{4}$$\phi$)10$^{-9}$ 2$\pi$\rsun,
 
\ni V$_{rot}$(0) = 2.020 km/s at the equator,
 
\ni V$_{rot}$(1) = 1.474 km/s at the pole,
 
\ni V$_{rot}$($\phi$)/V$_{rot}$(0) =
 
(1 --75/462 sin$^{2}$$\phi$ --50/462 sin$^{4}$$\phi$).
 
\noindent The parameter read by {\small ROTATE} is the stellar equitorial velocity.
Differential rotation is assumed to have the same behavior for all stars.
It is computed only if it is explicitly turned on.
 
As long as physical variables can be defined on an array of points and there
is a procedure for interpolating in a grid of spectra that vary in those
physical variables, one can treat any shape star, or binaries, spots, rapid
rotators, etc. using similar methods.
 
 
 
\subsection{Atmospheric transmission}
 
%
\begin{figure}[]
\resizebox{\hsize}{!}{\rotatebox{90}{\includegraphics[0,0][188,373]{nicelinesfig9.eps}}}
 
\centerline{{\bf Fig. 9.} Telluric O$_{3}$ transmission from 300 to 1000 nm.}
 
\end{figure}
%
%
\begin{figure}[]
\vspace{-30pt}
 
\scalebox{.94}{\rotatebox{90}{\includegraphics[0,0][210,294]{nicelinesfig10.eps}}}
 
\centerline{{\bf Fig. 10.} Telluric [O$_{2}$]$_2$ transmission from 300 to 1500 nm.}
 
\end{figure}
%
%
\begin{figure}[]
 
\vspace{-20pt}
\scalebox{.94}{\rotatebox{90}{\includegraphics[0,0][210,294]{nicelinesfig11.eps}}}
 
\centerline{{\bf Fig. 11.} Telluric O$_{3}$ and [O$_{2}$]$_{2}$ transmission from 300 to 1500 nm.}
 
 
\vspace{10pt}
\ni [Fig. 12 is a large color ledger page on the Kurucz website
{\small KURUCZ.HARVARD. EDU/PAPERS/TRANSMISSION/FIG5}.  It will be
mailed by post on request.]
 
\vspace{5pt}
 
 
\ni{\bf Fig 12.} Telluric lines of O$_{2}$ and H$_{2}$O that were computed
for the flux scans in the Kitt Peak Solar Flux Atlas (Kurucz 2005) and
pieced together in the solar laboratory frame with gravitational red shift
removed.
\vspace{5pt}
\end{figure}
%
In 1988 I discovered (Kurucz 1988b) that there were broad features in
Kitt Peak FTS solar spectra (taken by James Brault) that were produced by
ozone and by [O$_2$]$_2$ (O$_2$ dimer) that I had not known about and had not
considered in the reduction of the Solar Flux Atlas (Kurucz, Furenlid, Brault,
and Testerman 1984).  The [O$_2$]$_2$ number density is quadratic in O$_2$ so
is concentrated near the ground.  It produces strong features at sunset and
sunrise.  Figure 9, 10, and 11 show the features produced by O$_3$, [O$_2$]$_2$,
and their product in the visible.  There are also many lines of O$_2$ and
H$_2$O that blend with, or that mask, solar lines in the FTS spectra shown
in Figure 12.
 
Much of the research on atmospheric transmission has been done by the United
States Air Force (Air Force Research Laboratory, formerly Air Force
Geophysics Laboratory, formerly Air Force Cambridge Research Laboratory).
They have produced empirical model atmospheres, line data ({\small HITRAN}),
and computer programs for calculating transfer through the atmosphere
({\small LOWTRAN}, {\small MODTRAN}).  These programs are not designed for
doing the whole spectrum at once in high resolution.
 
Astronomers should measure the atmosphere over their heads and determine
the run of temperature, pressure, O$_3$, and H$_2$O with altitude because
it affects their observations, but they do not care.  The Air Force had
a program of measuring these quantities and has produced averaged models
for the whole year, or quarterly, or monthly, for temperate latitudes,
tropical latitudes, etc. (Anderson et al. 1986).  From those models I have
made up four models {\small MODMIDWIN, MODSPRING, MODMIDSUM,} and
{\small MODAUTUMN} that I use to represent the atmosphere above Kitt Peak.
They can be used as starting guesses at any observatory except in Antarctica.
The temperatures, pressures, O$_3$, and H$_2$O, must be adjusted to get a
good fit for any observed spectrum.  {\small MODMIDSUM} is listed in Table 2.
%
\begin{figure}[]
 
\includegraphics[0,0][172,400]{nicelinestable2.eps}
 
\end{figure}
%
 
Laboratory ozone cross-sections for the ultraviolet Hartley and Huggins
(Bass and Paur 1981, Griggs 1968, Freeman et al. 1983) and the visible
Chappuis and Wulf (tabulated by Shettle and Anderson 1995) bands are
tabulated for several temperatures and
interpolated.  Widths and strengths of individual O$_2$ dimer features have
been measured in the laboratory (Greenblatt et al. 1990; Dianov-Klokov 1959)
and computed from those parameters.
 
The main source of line data is the {\small HITRAN} (HIgh-resolution TRANsmission)
database (Rothman et al. 2005).  Smithsonian Astrophysical Observatory has
taken over management of the database from the Air Force.  Historically the Air
Force concentrated on infrared data beyond 1$\mu$m aiming for very accurate
line positions, strengths, pressure-shifts, and damping constants.  Researchers
all over the world work on and with {\small HITRAN}, not just the Air Force.  The
visible data were poor quality.  Much of it was missing or wrong.  Now about half
of the O$_2$ and H$_2$O are good.  I have tried to fill in missing lines for
O$_2$ by calculating them and by fitting them in solar spectra.  There are
calculations available for H$_2$O but they do not work very well.  I have tried
to adjust many of the lines by hand.  One of the main problems with these lines,
one that astronomers have not yet had to face, except in Stark broadening, is pressure
shifts.  The measured positions of telluric lines in the solar spectra are not the
real line positions.  If they are used to generate molecular constants, they introduce
systematic errors.  Laboratory work is required to measure the line positions
as a function of pressure and to extrapolate to zero pressure.  Only the
strongest bands of O$_2$ have been well measured.
 
I have written subroutines {\small OZONE} and {\small O2DIMER} for computing
the transmission spectra of the broad features and the {\small TRANSYNTHE} suite of
programs  for treating telluric lines.  The cause of the delay, as for solar
lines, is that the telluric data are still not good enough to treat the problem
without hand adjustment, even for O$_2$, and there are many missing lines.
 
Files {\small AIR1, AIR2, AIR3, ..., AIR10, AIR20, AIR100,  AIREND}  have
telluric line data for 0 to 1 $\mu$m, 1 to 2 $\mu$m, etc.  Most of the data
except in {\small AIR1} are from {\small HITRAN} reformatted like other data in
the Kurucz linelists.  Some of the data have hand corrections. The overall quality at
short wavelengths is not good.  Every line should be checked for critical
work.
 
{\small TRANSYNBEG} reads the input parameters.  The wavelength range and resolution
must be the same as in any subsequent stellar spectrum calculation.  The
lines are shifted by the radial velocity of the star which must be specified.
In wavelength regions where sharp telluric lines are present, the resolving
power of the calculation must be at least 2 million to treat the sub-300K doppler
width.  Any computed stellar spectra must have the same resolution.
 
{\small RMOLAIR} reads the line data from the {\small AIR*} files.
 
{\small TRANSYNTHE} computes the opacity spectrum.
 
{\small TRANSPECTR} computes the mean transmission spectrum from the given starting
and stopping airmass, starting and stopping hour angle, mean declination,
latitude, and altitude.  It also computes the residual depth of each line.
The line data and depth are passed along with the spectrum for labelling plots.
 
{\small TRANSMIT} multiplies a stellar spectrum by the transmission spectrum.
 
 
\subsection{Spectrophotometry}
 
Once the computed spectrum has been computationally transmitted from the star
to the instrument it is instrumentally broadened for comparison to observation.
Program {\small BROADEN} convolves a Gaussian, sin(x)/x, or rectangular profile
specified by FWHM in velocity, wavelength, wavenumber, or resolving power.
It also can use instrumental profiles specified at the computed point spacing.
When the profile is rapidly changing, program {\small BROADENX} linearly
interpolates between profiles specified at the ends of a wavelength
interval.
 
Now, when I compute a model that I think might be of general interest,
I compute the spectrum as far to the ultraviolet and infrared as I can.
Then I broaden it to resolving powers of 500000, 100000, 50000, 30000, 20000,
10000, 5000, 3000, 2000, 1000, 500, 300, 200, and 100 and put those spectra
on my website in the {\small STARS} directory so people can find predictions``off the
shelf" to compare to their observations.  It takes about one day per model.
 
\subsection{Photometry}
 
Photometry is computed by convolving the spectra output from the {\small SYNTHE} suite
of programs with a theoretical model of the observation.  That model would
include detector response, filter transmission, transmission of the obtical
system, and, for an observation from the ground, transmission of the atmosphere.
I have written a simple program {\small INTEGRATEFILTER} that convolves {\small SYNTHE} output
spectrum with a response function in this way. {\small INTEGRATEFILTER} will read any
number of response functions.  The Asiago Database (Moro and Munari 2000) has the most
photometric systems so I suggest that some user make up a general input file from it
and a program to generate all the colors.
 
The atmospheric transmission is computed with the
{\small TRANSYNTHE} suite of programs and is applied to the spectra before
{\small INTEGRATEFILTER} is used.  Most filter systems in the visible and near
infrared are insensitive to the atmospheric transmission, while ultraviolet and
infrared systems are sensitive.
 
\subsection {Limbdarkening}
 
Limbdarkening is automatically produced when I generate a spectrum for
a rotating star but the files are so big that I have been throwing
them away.  The rotation program computes the intensity spectrum at a
number of angles across the disk (currently 17 angles) and interpolates
the spectrum at each point on a rectangular mesh overlaid on the disk.
Those spectra are tabulated at all the angles for each wavelength.  If the
file is transposed
to all the wavelengths at each angle, limbdarkening is computed by convolving
those spectra with a theoretical model of the observation.  That model would
include detector response, filter transmission, transmission of the obtical
system, and, for an observation from the ground, transmission of the atmosphere.
I have written simple programs {\small SPLIT17SYN} and {\small INTEGRATEFILTER} that convolve
a {\small SYNTHE} output spectrum with a response function in this way. {\small
INTEGRATEFILTER} will read any number of reponse functions. The atmospheric
transmission is computed with the {\small TRANSYNTHE} suite of programs and is applied
to the intensity spectra before {\small INTEGRATEFILTER} is used.  Most filter systems
in the visible and near infrared are insensitive to the atmospheric transmission.
 
 
 
\subsection{PLOTSYN}
 
I make large plots that compare computed and observed spectra and that actually
show errors and provide information to the reader.  The features are labelled
and the wavelengths and energy levels can actually be read off the plots, and
there is a file giving complete information for each labelled line.  In addition
there is a hand-editable file that gives the input data for evey line that
contributed to the spectrum.  That file can be read back in to iterate on
the fit.
 
My plotting software was written before Postscript was invented.  At present
{\small PLOTSYN} writes a binary vector file that must be translated
to Postscript.  I am going to rewrite the plotting utilities, {\small PLOTPACK},
to write Postscript directly.  (It is simple.)  This will make the files smaller,
scalable, and editable.  I am considering ways to put plots on CDs or DVDs.
Perhaps solar spectra at 1\AA \ per page with line identifications to be used as
a reference, or big continuous plots that can be windowed.
 
\section{New Atlases for Solar Flux, Irradiance, Central Intensity, and Limb Intensity}
 
     The low resolution, low-signal-to-noise spectra that astronomers normally
work with do not contain enough information, in themselves, for interpretation.
Without a priori knowledge of the atomic and molecular line data for each
significant line in the blended features any inferences about abundances have
large uncertainties.  Reliable atomic and molecular data are not available
from the laboratory or from theory except for a small fraction of the lines.
Atlases of high-resolution, high signal-to-noise spectra of stars with low
projected rotation velocity provide information about details and blending
in the spectra.  People who work with stellar spectra should always check
their wavelength region in high quality atlases.  If the atlas was taken
from the ground, it will also show the telluric lines and their contribution
to blends.
 
I have been trying to make atlases with line identifications for the sun
for 25 yeers so that I could check my calculated spectra
against reality.  When I can find patterns in the errors, I try to correct
the physics.  However, the calculated spectra have been so poor that almost
every line needs to be adjusted to match the observed spectra.
Many of the lines in the observed spectra are missing altogether from the
line list.  The calculations are also needed for the reduction of the
observed spectra themselves because the continuum placement depends on many
weak blends and on the damping treatment of the wings of many lines.
 
Matching observed spectra seems to be hopeless, at least in the near future.
I have finally decided that the continuum placement is good enough, and
that I should publish the spectra with only ``suggestive" calculations and
identifications to give the user an idea of where to begin and what the
problems are.
 
\subsection {New atlases}
 
I have fifty solar FTS scans taken by James Brault and Larry Testerman at
Kitt Peak.  The scans cover the central intensity, limb ($\mu$=0.2), and flux
spectrum from 0.3 to 5.5 $\mu$m.  The central intensity for 1.0 to 5.5 $\mu$m
was published by Delbuille, Roland, Brault, and Testerman (1981).  The flux
spectrum from 0.3 to 1.3 $\mu$m was published as Solar Flux Atlas (Kurucz,
Furenlid, Brault, and Testerman 1984).  However, since then I have learned
that broad O$_{3}$ and O$_{2}$ dimer ( or [O$_{2}$]$_{2}$) features are present
in the spectrum, and I have improved the line data and the continuum treatment.
I have produced an improved version of the flux atlas (Kurucz 2005a)
that is available on my web site {\small KURUCZ.HARVARD.EDU}.  I have merged
the scans into a single spectrum, but I also present each scan separately because
each FTS scan has its own atmospheric model, air mass, telluric spectrum, and
radial velocity.  The resolving power and signal-to-noise vary from scan to
scan and are on the order of 300000 and 3000 respectively.
I am now working on similar atlases for central intensity and limb spectra.
If I get funding, I will continue the atlases into the infrared to 5.5$\mu$m.
I will produce atlases plotted at one \AA/page that include the computed
spectrum and line identifications.  If I can get funding, I will distribute
paper and DVD copies.
 
 
 
The telluric line spectrum was computed using HITRAN (Rothman et al. 2005)
and other line data for H$_{2}$O, O$_{2}$, and CO$_{2}$.  The line parameters
were adjusted for an approximate match to the observed spectra.
I was able, through many hand adjustments, to remove the telluric absorption
spectrum for the flux atlas and to recover the residual irradiance spectrum
above the atmosphere for the region from 0.3 to 1.0 $\mu$m.  Figure
captions 1 to 13 outline the reduction procedure.  In wavelength regions with
heavy absorption the quality has been compromised by more than an order of
magnitude.  I have produced a continuous atlas of this irradiance spectrum
(Kurucz 2005b).  Most of the irradiance atlas has the same resolution and
signal-to-noise as the flux atlas.
 
 
 
Given a calculated or semiempirical solar model, the continuum level
can be computed and multiplied by the residual irradiance spectrum
to produce the absolute irradiance spectrum at high resolution.
Alternatively, the high resolution residual irradiance spectrum can
be broadened and smoothed to match the resolution of any low resolution
irradiance spectrum and normalized to the low resolution spectrum.
That normalization can be applied to the high resolution spectrum
to obtain a high resolution absolute irradiance spectrum.  An example
for each method is presented below.  This is the spectrum that illuminates the
Earth and all other bodies in the solar system.  This is a typical
G star spectrum like those that illuminate extra-solar planets.
 
 
\subsection {Figure captions for irradiance atlas}
 
The figures are in color, are ledger size, and are too large for this
volume.  The figures and a table of the observations are on my web site
{\small KURUCZ.HARVARD.EDU/ PAPERS/TRANSMISSION}.  They are large files.  I will
send paper copies of a poster on the irradiance atlas (Kurucz 2005c) by
post on request.  The figure captions, in themselves, provide an explanation
of the reduction procedure.
 
 
\ni {\bf Table 1.}  Record of the observations.
 
\ni {\bf Fig. 1.} The old Kitt Peak Solar Flux Atlas.
There are eight overlapping FTS scans that were normalized and pieced
together to form a continuous residual spectrum.  The observational data
for the scans is listed in Table 1.  (There are only seven scans in this
figure because the eigth is beyond 1000 nm.)   The next figures show the
re-reduction of these scans.
 
\ni {\bf Fig. 2.} Broad atmospheric features of O$_{3}$ and [O$_{2}$]$_{2}$
that were present in the scans but not considered.  Each scan was assigned to an
atmospheric model listed in Table 2.  The O$_{3}$ and [O$_{2}$]$_{2}$ transmission was
computed using programs available on my website, kurucz.harvard.edu,
and divided out.  (The transmissions for the seven scans were pieced together
for the plot.)
 
\ni {\bf Fig. 3.} The blue end of one of the FTS scans is shown in green.  A
continuum, smooth green line, is subjectively fitted to the scans by
comparing to predictions from calculations of the solar spectrum and
the telluric spectrum.  When a reasonable looking fit has been obtained
through iteration, the spectrum is divided by the continuum value to
produce a residual spectrum shown in red.  The top 1 percent of the
residual spectrum is replotted in red as well.  The blue curve is the
the transmission curve for O$_{3}$ and [O$_{2}$]$_{2}$ that has already
been divided out.
 
\ni In {\bf Fig. 4.} the scans were blueshifted to remove the gravitational
red shift and pieced together in the solar laboratory frame in air.
This is the revised spectrum of the Kitt Peak Solar Flux Atlas.
 
\ni {\bf Fig. 5.} Telluric lines of O$_{2}$ and H$_{2}$O that were computed
from the atmospheric model for each scan in the solar laboratory frame
with gravitational red shift removed.  (The seven scans are pieced together.)
 
\ni {\bf Fig. 6.} A sample calculation of the spectrum for a relatively empty
angstrom at 599.1 nm in the Solar Flux Atlas shown in Figure 4.  The telluric,
solar, and observed spectra are labelled at normal scale and 10 times scale.
 
\ni {\bf Fig. 7.} shows the irradiance spectrum obtained from the spectra in
Figure 6 by dividing out the telluric spectrum.  For stronger telluric lines
and lines with incorrect wavelengths, there are artifacts that appear in the
irradiance spectrum that were removed by hand and replaced with a linear
interpolation.
 
\ni {\bf Fig. 8.} The residual irradiance spectrum after all the scans have
been processed and pieced together in the solar laboratory frame in vacuum
with gravitational red shift included.
 
\ni {\bf Fig. 9.} The predicted level of the continuum for theoretical solar
model ASUN (Kurucz 1992).
 
\ni {\bf Fig.10.} The absolute irradiance spectrum obtained by normalizing
the residual irradiance spectrum shown in Figure 8 to the continuum level
shown in Fig. 9.
 
\ni {\bf Fig.11.} The reference irradiance spectrum proposed by Thuillier et al.
(2004).
 
 
\ni {\bf Fig.12.} The Kitt Peak absolute irradiance spectrum smoothed using
a 0.5 nm triangular bandpass that approximates the resolution of Thuillier et al.
and then compares the two spectra.  Note the
probable overestimation of the ozone below 320 nm and around 600 nm in the
Kitt Peak atlas.  (Remember that ozone has been divided out.)  I will probably
have to re-reduce those scans.  Note the flux discrepency in the G band.  It
appears that model ASUN does not produce enough flux, perhaps becase of
insufficient opacity below 300 nm that results in too low a temperature gradient.
I am adding more line opacity.  I will try to produce a better model.  Of course,
there may also be errors in Thuillier et al. as well.
 
\ni {\bf Fig.13.} The Kitt Peak irradiance spectrum subjectively normalized
to the Thuillier et al. irradiance spectrum.  I recommend this spectrum as the
high resolution irradiance spectrum.  The procedure for removing telluric lines
introduces noise into the irradiance spectrum where there were telluric lines.
The flux atlas itself should be used for abundance analysis or other critical work.
 
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\eject
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