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 Knowledge Base
List of Advisories and Known Errors This list is maintained on a regular basis and sent to registered users whenever an update occurs. Advisories are posted in chronological order from top to bottom.
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Date:         July 12, 2013
Topic:        Operating System
Reported by:  Jane Rigby (GSFC)
Impact:       Script for implementation of the source code

Description:
David Friedlander at GSFC wrote a patch file to make it simple for
others to install Starburst99 on Linux or Mac OS X. Running the patch file
makes the necessary changes to the source code and the makefile. The
file is available for download.

Here is how to use it:
gunzip galaxy.tar.gz
tar -xvf galaxy.tar
patch -p0 < starburst.patch
make

Thanks to David Friedlander and Jane Rigby for creating the file and making
it available.
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Date:         July 11, 2013
Topic:        Operating System
Reported by:  Christina Williams (UMass)
Impact:       Running Starburst99 locally on Mac OSX

Description:
The Starburst99 source code comes in two flavors: one for running in a Unix
(Solaris) environment, and the other for Windows PC's. The Unix version can
run on a Mac if an appropriate compiler is available and if some changes to
the environment variables are made. Christina Williams successfully installed
Starburst99 on a Macbook with Mountain Lion. She downloaded a compiler from
http://hpc.sourceforge.net/ and used the following compiler command:
g77 galaxy.f  -Wl,-no_pie -o galaxy -O
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Date:         July 18, 2012
Topic:        Variable Initialization
Reported by:  Erica Rosenblum (AMNH)
Impact:       Variable in the subroutine "density" not initialized

Description:
A variable in the subroutine "density was not properly initialized. The error
was reported by Erica Rosenblum, who also provided a fix.
The update was made in all Starburst99 distributions (web server, downloadable
unix package, PC version). The updated version is v6.0.4. Users are encouraged
to download the new version. The user impact is very minor.
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Date:         December 12, 2011
Topic:        Mass-loss rates in Padova tracks
Reported by:  Paul Torrey (CfA)
Impact:       Incorrect entries at the earliest ages

Description:
The input tables containing the evolution models are based on the published
tracks by the Geneva and Padova groups. When we generated the tables, we
extended the available age ranges to younger ages for numerical reasons.
The Starburst99 tables for the Padova models with Z=0.008, 0.004 and 0.0004
have incorrect entries with unreasonably high mass-loss rates for initial
masses around 12 solar masses. In almost all practical cases this is not
noticeable. However, when calculating the mass return for a very narrow
mass range around 12 solar masses, the returned values are too high during
the first 10,000 yr and cause the total accumulated mass to be too high as
well.
The errors were fixed in all Starburst99 distributions (web server,
downloadable unix package, PC version). The updated version is v6.0.3. Users are
encouraged to download the new version.
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Date:         January 25, 2011
Topic:        Mass loss of the most massive AGB stars
Reported by:  Mike Fall (STScI)
Impact:       Mass loss contribution of 5 - 7 M stars too low

Description:
Starburst99 uses the Vassiliadis & Wood (1993) prescriptions for AGB mass
loss and photometric properties. These models cover only masses of 5 Msol
and below. This leaves the range between 5 and 7 solar masses (or ages
between 40 and 100 Myr) essentially undefined. Above 7 solar masses SNe kick
in, and below 5 solar masses Vassiliadis & Wood apply. These massive AGB stars
do not contribute significantly to the overall light except at exactly these
ages. However, their omission becomes noticeable when the mass loss of the
full stellar population is integrated over time. As an approximate fix,
we manually added mass loss-rates chosen to bring down the stellar masses
to 1 solar mass at the end of the AGB phase for these stars.
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Date:         March 10, 2008
Topic:        Format of the input parameters
Reported by:  F. Shi (Beijing Astron. Obs.)
Impact:       Parameters may be truncated

Description:
The input of the model parameters on the Starburst99 website is not
format free. The format was intentionally chosen to limit the allowed
input to physically reasonable parameters. While this may be obvious
in most cases, the smallest allowed values for the star-formation rate
and the stellar mass need an explanation. The value is 0.001 in both
cases. Any additional digits after the decimal point will be truncated.
For instance, specifying 0.0001 will be interpreted as 0.000, with an
obviously undesired outcome.

One would not want to specify stellar masses lower than 0.001, which
corresponds to 1.e3 solar masses. Stochastic effect dominate for such
small systems, and the results are astrophysically meaningless.
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Date:         February 7, 2007
Topic:        Eruptive AGB mass loss incomplete
Reported by:  Mike Fall (STScI)
Impact:       Final AGB masses too low

Description:
The stellar mass loss during the AGB phase was taken from the models
of Vassiliadis & Woods (1993) and then merged with the Padova tracks.
The Vassiliadis & Woods models have very short phases of high mass
loss when the AGB stars eject material in rapid eruptions. These
phases are not significant for the photometric evolution of a stellar
population and were therefore not included in the original release
of Starburst99. However, the mass loss during this phase is important
for the overall mass budget of AGB stars. In particular, neglecting
this episode would lead to too high masses at the end of the AGB phase.
In order to predict final AGB masses in better agreement with
observations, we added the eruptive mass loss episodes to our models.
(Note that the Vassiliadis & Woods models do not account for the full
nucleosynthesis in the AGB phase.)

This change became effective on February 7, 2007.
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Date:         February 6, 2007
Topic:        Peculiar abundance patterns in the 9 M track
Reported by:  Nicolas Champavert (Observatoire de Lyon)
Impact:       Initial surface abundances are too high

Description:
The surface abundances of all elements in the 9 M Padova tracks are
too high. These tracks were interpolated and stitched together using
different input sources. The result obviously was not fully
satisfactory. A better version of the 9 M tracks was generated and
added to Starburst99 on February 6, 2007.
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Date:         October 30, 2006
Topic:        Nebular emission longward of 4.5 microns
Reported by:  Leslie Hunt (INAF, Florence)
Impact:       Incorrect results

Description:
Starburst99 uses the emission coefficients of Ferland (1980) for the
calculation of the nebular continuum. The longest wavelength covered
by these tables is 4.5 microns. The code uses the value at
4.5 microns and extrapolates to 160 microns, where the emission
coefficient is forced to zero. Obviously, this makes the predicted
values of the nebular continuum unreliable at these wavelengths, and
the Starburst99 output should not be used for the nebular continuum.
The stellar output, however, is correct to the extent that the model
atmospheres can be trusted.

In observed starburst galaxies, interstellar dust will most likely
dominate the mid-IR emission, and the nebular continuum predicted by
Starburst99 is irrelevant. This is the reason for the minimal effort
made at mid-IR wavelengths when the code was developed.

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Date:         April 10, 2006
Topic:        Errors in density and supernova subroutines
Reported by:  Ralph Sutherland (Australian National University)
Impact:       Code produces wrong results

Description:
1) The normalization constants for the multi-power law IMF are
incorrect. Depending on the chosen IMF, this may produce a grossly
wrong mass normalization. There is no error for a single power-law
IMF. The error becomes largest for IMFs with more than one power-law
index and whose mass break-point deviates from 1 M. This does not
apply to normalized quantities (like colors) with no low-mass
contribution; in this case, the mass normalization does not matter.
Ralph Sutherland fixed the error and provided an updated subroutine
"density". This subroutine was implemented in the source code on
April 10, 2006.

2) The calculation of the supernova energy as implemented can
introduce large errors. Ralph Sutherland revised the supernova
subroutine such that the energy is now directly calculated from the
power. The new subroutine was implemented on April 10, 2006 as well.

Version 5.1 of the source code includes the updates.

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Date:         February 8, 2006
Topic:        Data files for Figures 21 and 23
Reported by:  Mark Hancock (East Tenn. St. Univ.)
Impact:       Data are for a=3.3 instead of M=30

Description:
The data files linked to Figures 21 and 23 on the Starburst99 website
are actually copies of the files linked to Figures 17 and 19, i.e.,
they refer to an IMF with a=3.3 instead of the M=30 IMF. Therefore, the
links were disabled in February 8, 2006.

Users should be aware that the UV line spectra for IMFs deficient of
massive stars are inaccurate when calculated with the original v1.0
of Starburst99. This is because less massive B stars were only
implemented into the code in 2000 (see de Mello et al. 2000). All
models calculated with the current version of the code on our server
are of course correct in this respect and should be used instead of
the old figures.

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Date:         November 21, 2005
Topic:        Logarithmic time steps
Reported by:  Chris Matzner (CITA)
Impact:       Supernova rates incorrect

Description:
When logarithmic time steps are selected, the computed supernova rates
are incorrect, depending on the chosen number of steps. This is the
result of a parameter not being properly handed over to the supernova
subroutine. Only the supernova rates and the associated mass-loss
properties are affected. All other output parameters are correct. This
error does not occur when linear time steps are selected. We are
grateful to Chris Matzner (CITA) for reporting this error.

This error was fixed and the software on the Starburst99 server was
updated on 11/21/05. We also corrected several other minor programing
errors reported to us by Nicolas Champavert (Obs. de Lyon) and David
Valls-Gabaud (CFHT).

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Date:         March 10, 2005
Topic:        Starburst99 v5.0 output
Reported by:  Daniel Dale (Univ. of Wyoming)
Impact:       Figures posted on the website differ from v5.0

Description:
Starburst99 v5.0 was released in December 2005. A discussion of the
input physics as well as figures showing the major predictions were
published in ApJ, 621, 695 (2005). We did not reproduce this set of
figures for display on our website, nor did we expand the figure set
to provide all possible model predictions from Starburst99. Our website
allows interested users to easily generate the predictions themselves
using a dedicated server.

We decided to keep the older set of figures from the 1999 release
(ApJS, 123, 3, 1999) on our website. Many (but not all!) of these
figures are still up-to-date and useful for the community. They can
also be used as benchmarks to identify changes introduced by
Starburst99 v5.0. On the other hand, retaining the older set of
figures may give rise to confusion. Therefore we labeled the link to
these figures as "1999 Dataset". Users should be aware that they must
refer to the 2005 publication or run their own Starburst99 models
locally or on our server if they would like to obtain results from v5.0.

____________________________________________________________________


Date:         October 31, 2003
Topic:        Error in the subroutine temp_adjust
Reported by:  Marcello Castellanos (Toulouse) & Miguel Cervino (Granada)
Impact:       Output with Schmutz et al. models differs from web figures

Description:
Starburst99 v.4.0 (released in July 2002) was intended to offer older
generation models using the previous set of unblanketed WR atmospheres of
Schmutz et al. This option allows users to perform regression tests with
the new UCL atmospheres, which are the default. The released version
of the code assigns the stellar surface temperatures to the Schmutz et
al. atmospheres, and not the core temperatures. Therefore all WR related
properties differ from those plotted in the old set of figures posted on
the web site. For a fair comparison, the core temperature should be
used, as is the case for models calculated with the new UCL atmospheres.
User impact: If the new (default) UCL atmospheres are used: none. If the
old Schmutz et al. atmospheres are selected, the far-UV radiation field
(in particular shortward of 228 A) is softer than for a model using the
core temperatures.

As of October 31, 2003, the source code has been revised to link the
core temperatures to the Schmutz models. The web server has been updated,
and the user can download the revised code. Users who downloaded the
old source code and who would rather make a correction in their local
version should simply do the following: In the subroutine temp_adjust,
change
         c      temp(l)=tt_star(l)
to
                temp(l)=tt_star(l)

In other words, the statement needs to be uncommented. No other changes
are required.

I am grateful to M. Castellanos (Toulouse) for pointing out the
inconsistency between the Schmutz models calculated on the web server and
those shown in the figures and to M. Cervino (Granada) for tracking
down its cause.

____________________________________________________________________


Date:         March 21, 2003
Topic:        Modification of convergence boundary
Reported by:  Lisa Kewley (CfA)
Impact:       Faster convergence of Mappings

Description:
Mappings takes too long to converge to HII < 1.0% for large ionization
parameters. Mappings has an adaptive grid, and for very large ionization
parameters, it reaches HII ~ 4%, and then takes a step that is too large and
falls off the grid. Sometimes Mappings will crash, and other times it will
just freeze - i.e. the process will keep on running, but no more outputs will be
produced. Mappings is stuck in some loop trying to calculate the next grid
step.  This holds up any other models in the queue. Therefore we decided to
change the Mappings model ending from 1% HII to 5% HII.  This won't make
any difference to the output fluxes, but it avoids the overstepping
problem.  This is normally only a problem for power-law models, but may
also affect models using high ionization parameters and high densities
for SB99-mappings.

In summary, the convergence boundary has been set from 1% to 5% on
March 21, 2003. This should resolve any convergence problems some users
have experienced in the past.

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Date:         January 31, 2003
Topic:        Colors and magnitudes for arbitrary filters
Reported by:  Claus Leitherer (STScI)
Impact:       Filter changes require recalculation of zero points

Description:
Starburst99 uses a standard filter set to compute magnitudes and colors.
While the filters are hardcoded, it is easy to replace them by different
transmission functions (e.g., the F555W filter of HST's WFPC2) in the
Block Data section of the code. This must be done in the downloaded
version of the code, not via the web interface. When replacing/adding
filters, care is required in order not to corrupt the arrays and common
blocks. Furthermore, it is essential to suppress any red/blue leaks by
adding filter points at zero transmission.

Once the filters are in place, the zero points need to be redetermined.
This requires modifications in two subroutines: specsyn and colors. In
specsyn, one has to manually force the code to use a Vega-like star.
Search for the following lines:

c CALCULATE THE EFFECTIVE TEMPERATURE AND LOG G FOR EACH MASS. THEN GET THE
c NUMBER OF PHOTONS PER UNIT SURFACE FOR EACH STAR. AFTERWARDS MULTIPLICATION
c BY THE STELLAR SURFACE AND THE STELLAR NUMBER DENSITY.
c
        do 10 l=lmin,lmax
        teff=10.**temp(l)
        grav(l)=alog10(zmass(l))+4.*temp(l)-bol(l)-10.6
        blogg=grav(l)
        radius = 10.**(10.8426 + 0.5*bol(l) - 2.*temp(l) + 7.52)
        if(bol(l). lt. -19.) goto 4000
        if(iatmos-2) 1000,2000,3000
c

Modify this to become the following: ($$$ indicates changes)

do 10 l=lmin,lmax
 $$$ teff=9400.
        grav(l)=alog10(zmass(l))+4.*temp(l)-bol(l)-10.6
 $$$ blogg=3.95
        radius = 10.**(10.8426 + 0.5*bol(l) - 2.*temp(l) + 7.52)
        if(bol(l). lt. -19.) goto 4000
        if(iatmos-2) 1000,2000,3000

Next one would go to the colors subroutine and search for the following:

c CALCULATE THE COLORS. THE NORMALIZATIONS ARE CHOSEN TO GIVE ZERO COLORS FOR
c 9400/3.95 AND Z = Z_SOLAR.
c
 cuv1v= xmag(1) - xmag(6)  - 5.844
 cuv2v= xmag(2) - xmag(6)  - 2.949
 cub  = xmag(3) - xmag(4)  - 1.093
 cbv  = xmag(5) - xmag(6)  + 0.728
 cvr  = xmag(6) - xmag(7)  - 0.219
 cvi  = xmag(6) - xmag(8)  + 0.440
 cvj  = xmag(6) - xmag(9)  + 1.304
 cvh  = xmag(6) - xmag(10) + 1.898
 cvk  = xmag(6) - xmag(11) + 2.771
 cvl  = xmag(6) - xmag(12) + 4.410
c

This calculates the zero points. The nomenclature should be obvious. E.g.,
"cbv" stands for color (B-V), or whatever filter is in index 5 and 6. When
the filter profiles are changed, the values for the scalars on the left are
no longer zero for a Vega-like star but need to be recalculated. One does
this by removing the constant on the right. E.g., one would remove
(=set to zero) the 0.728 for the cbv equation. Therefore the new equations
are like this:

 cuv1v= xmag(1) - xmag(6)
 cuv2v= xmag(2) - xmag(6)
 cub  = xmag(3) - xmag(4)
 cbv  = xmag(5) - xmag(6)
 cvr  = xmag(6) - xmag(7)
 cvi  = xmag(6) - xmag(8)
 cvj  = xmag(6) - xmag(9)
 cvh  = xmag(6) - xmag(10)
 cvk  = xmag(6) - xmag(11)
 cvl  = xmag(6) - xmag(12)

Now one runs SB99, entering the default input values, except: (i) a short
time interval is used, like 1 Myr. This will give 10 output points if the
default of 0.1 for the step is used. One chooses spectrum and colors for
the output, but not quanta, because we do not want the nebular spectrum
added to the star. The output file for colors should give identical colors
for all time steps (all being for Vega). The colors are just the offset we
are looking for. Ideally, they should be zero, but of course they are not.
Now one reads off the colors and subtracts them in the equations for the
cbv (etc.) equations. Then we run SB99 again. If all went well, the colors
should be zero now. If so, we are happy, and one can replace the statements
in specsyn which enforce the 9400/3.95 star. Do not forget to do this!

At this stage, Starburst99 will compute correct colors for the new
filters. However, the absolute magnitudes are still incorrect (except for
MBol, which is calculated by direct integration of the SED). MV is
calculated from MBol and B.C: MBol = MV + B.C. The zero point is defined
via a solar model of Teff=5770 K and log g =4.44, which has B.C= -0.190.
Note: this is what SB99 assumes but those who prefer different values
are free to change this.

In principle, one could run SB99 with exactly one track corresponding
to 1 M, calculate the MV of the sun, and add an offset until it agrees
with the observations. For numerical reasons (interpolation at low M),
this does not work well because SB99 was not designed to deal with single
stars (it does populations). Therefore the preferred method is to find
the offset by comparing MBol and MV of a star with Teff=5770 K,
log g =4.44 and imposing a B.C. of -0.190. Locate this section in the colors
subroutine:

c CALCULATE M_V, M_B, AND M_BOL OF THE SYNTHETIC SPECTRUM. M_BOL IS OBTAINED
c VIA INTEGRATION OF THE SPECTRUM OVER THE ENTIRE WAVELENGTH RANGE.
c 38.70 IS DERIVED AS FOLLOWS: M_BOL=-2.5*LOG L + 4.75, CONVERSION INTO SOLAR
c LUMINOSITIES, AND A FACTOR OF 10.**20. ===> -2.5*(20.-33.58)+4.75.
c M_V IS OBTAINED FROM M_BOL AND THE BOLOMETRIC CORRECTION. BC = -0.190 FOR
c T_EFF = 5770 K AND LOG G = 4.44 AT SOLAR METALLICITY.
c
        call fliwgt(wave,stflux,weight,absbol,1221)
        absbol=-2.5*alog10(-1.e0*absbol+1.e-30) + 38.70
	absv=xmag(6)+36.551
	absb=absv + cbv
c

As a reminder, "absb=absv + cbv" means "M_B = M_V - (B-V)". Now add the line
"absb=absbol+0.190" below the current absb=absv + cbv. This new line is
nothing else than M_V of the sun. (We are abusing the absb scalar for M_V but
we just want to get the number into the output file and therefore overwrite the
existing M_B. Later this will be removed again.) Next we go back to the section
in specsyn and enforce a star with 5770 K and 4.44. This is exactly the same
game we played for the Vega-like star before. Modify specsyn, use the scheme as
for the Vega star, and run the code. The output for color contains ten identical
lines. The interesting columns are "MB" (which now has the absolute V magnitude
of the sun) and "MV", which does not yet have it. Obviously we have to change
the constant in "absv=xmag(6)+36.551" such that the two columns show the same
numbers. An additional test run is always a good idea. Once everything is
consistent, one would remove the "absb=absbol+0.190" in colors and the
5770/4.44 in specsyn.

The new code will give consistent colors and magnitudes for the new filters.

____________________________________________________________________


Date:         April 13, 2002
Topic:        Error in the help file for the input page
Reported by:  Patrik Jonsson (Lick Observatory)
Impact:       Starburst99 ends with error if mass < 0

Description:
Starburst99 allows the user to specify either continuous or instantaneous
star formation. When Starburst99 is not run via the web interface, a
flag specifies the star formation history. A negative integer indicates
an instantaneous burst, and only the input in the "mass" field is
considered. Alternatively, an integer equal to or larger than zero
indicates that the input comes from the "star formation rate" field.
Neither the mass nor the star formation rates themselves should ever
be negative.

The web help was adopted from the help documentation in the downloadable
software package which makes use of the above flag. In the web version
of the interface, radio buttons are used instead of the flag. Therefore
the help file becomes misleading and appears to suggest that the mass or
the star formation rate themselves must be negative. This is incorrect.
Once a choice has been made with the radio button, positive numbers
for either the SFR or the mass must be entered. The parameter which
was not selected with the radio button will be ignored.

The web documentation was corrected on April 13, 2002.

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Date:         March 5, 2002
Topic:        Mass-loss rates in the Geneva tracks
Reported by:  Claus Leitherer (STScI)
Impact:       "Standard" rates are ***not*** the default

Description:
The stellar evolutionary tracks in Starburst99 are described in Meynet
et al. (1994; A&AS, 103, 97). We follow the nomenclature adopted in
that paper: mass-loss rates are called "high" because they are higher
than observed for pre-WR stars. Meynet et al. demonstrate that the
high rates lead to evolutionary models in better agreement with the
empirical properties of the upper HRD. Most likely, this is the result
of some missing ingredients in the evolution models, such as rotation.
Therefore the high rates make up for some other deficiency in the
input physics, but overall they lead to better agreement with the
observations. While "high" may imply a non-default parameter, and
"standard" may suggest the "default", the opposite is the case. This
is why the Starburst99 input page has the "high" rates as default.

There is some confusion among the Starburst99 users as to which stellar
phases are affected by high and standard mass-loss rates. Only pre-WR
phases are concerned. The WR mass-loss rates are identical in both
sets of tracks.

We point out that the mechanical energy release by winds is decoupled
from the evolution models in Starburst99. For the above reasons, the
default is ***not*** to use the evolutionary mass-loss rates, but
rather a combination of theoretical and empirical rates across the
HRD. While this is unsatisfactory from a consistency point of view,
it is unavoidable because of our incomplete understanding of massive
star evolution.

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Date:         October 18, 2001
Topic:        Predicted [Fe II] line luminosities
Reported by:  George Bendo (Univ. of Hawaii)
Impact:       Relation between [Fe II] and the SN rate is uncertain

Description:
The Starburst99 model, as it was published in Leitherer et al. (1999),
required the supernova rate to be converted to an Fe II line luminosity
with a conversion factor in Calzetti (1997, AJ, 113, 162). The conversion
factor that Calzetti used is the same as the one in van der Werf et al.
(1993, ApJ, 405, 522) but scaled for a different transition. van der
Werf et al. find the conversion from supernova rate to Fe II luminosity
at 1.64 microns as

    L(FeII) = 5.4x10^7 eta nu_sn (E_0 / 10^51 erg) L_sun

where eta is a scaling value assumed to be 0.9, nu_sn is the supernova
rate in number per yr, and E_0 is the total energy released in a single
supernova. From this equation, they derive a conversion factor of
4.9 x 10^7. However, Colina (1993, ApJ, 411, 565) derived a different
conversion factor for the same transition. He applies the formula

    L(FeII) = L_snr nu_sn t_snr

where L_snr is the Fe II luminosity of a single supernova remnant and
t_snr is the time during which the supernova remnant produces Fe II line
emission. His conversion factor is 4.4 x 10^6 L_sun, a factor of 10 lower
than the values determined by van der Werf et al. The difference may be
in how the two different rates are derived, although environmental effects
could play a major role in determining Fe II luminosities. van der Werf et
al. make several assumptioms about the total energy output in the Fe II
line, while Colina uses observational values. Colina's conversion factor,
however, relies on knowing the period of time during which a supernova
remnant produces Fe II line emission. These assumptions make both
conversion factors questionable for converting supernova rates into
Fe II line luminosities. Further work needs to be done on calibrating
the Fe II lines for use as quantitative supernovae indicators.

______________________________________________________________________


Date:         August 30, 2001
Topic:        Lower mass limit of the IMF
Reported by:  Michael Fellhauer and Pavel Kroupa (Univ. of Kiel)
Impact:       M_low = 1 affects photometric properties at old ages

Description:
The default truncation at the low-mass end of the IMF is at 1 M_sol. This
is driven by the Geneva evolutionary tracks, which are not optimized for
low-mass stars, and are therefore not included in Starburst99. Users can
choose their preferred value of M_low, even one that would be < 1 M_sol.
This has the benefit of calculating the correct mass normalization for
quantities which depend only on massive stars, and for which the mass
of low-mass stars enters as a normalization factor. Obviously this
approach will not work if low-mass stars themselves are relevant for the
luminosity of the population.

Users should be aware that even keeping M_low at and above 1 M_sol can
produce some unexpected effects at old ages, which are nevertheless
consistent with the tracks and the IMF. At approximately 10 Gyr, the
turn-off mass of the least massive stars having evolutionary tracks in
Starburst99 is reached. For a single stellar population, this means
that the photometric properties will briefly exhibit an excursion to the
red, followed by a rapid drop of the luminosity and an increase of M/L.
This effect was discussed by Charlot et al. (ApJ, 419, L57, 1993). The
behavior of the colors can be understood as due to the last generations
of red giants which are seen without additional main-sequence stars of
lower mass.

______________________________________________________________________


Date:         May 29, 2001
Topic:        Upper mass limit of the IMF
Reported by:  Sangeeta Malhotra (JHU)
Impact:       Starburst99 gives wrong results if M_up > 120

Description:
Starburst99 assigns stellar parameters by interpolation in the set of
evolutionary tracks. The Geneva tracks terminate at 120 M. Therefore
no quantities of stars with larger masses can be calculated by
Starburst99. The IMF parameters in the input file are independent of
the stellar evolutionary tracks. It is possibly to specify a value
for the upper cut-off mass (and for the lower cut-off as well) which
is outside the mass range of the tracks. This may be desirable at the
low end where stars do not contribute in a young starburst. In this
case, specifying an M_low below the evolutionary track cut-off will
at least make sure that the mass normalization is correct.
The same approach leads to incorrect results at the high mass end. If,
e.g., M_up = 200 is specified, the mass normalization is again performed
such as to distribute all stars between M_up = 200 and M_low. However,
since there are no tracks between 120 and 200 M, the output from these
stars (like luminosity) is zero. Suppose there are two models with the
same total mass and model a) having M_up =100 and model b) having
M_up = 200. The ionizing flux of model b) would actually be lower than
for model a) since there are fewer stars below 120 M, and more stars
above 120, but stars with M > 120 do not produce any flux.

In practice, the effect is hardly noticable for standard IMFs because
there are so few stars with masses above 100. Nevertheless this is a
bug, and Starburst99 should at least produce a warning. This will be
fixed in the next release of Starburst99.

______________________________________________________________________


Date:         May 15, 2001
Topic:        Nebular contribution to the total flux
Reported by:  Claus Leitherer (STScI)
Impact:       Nebular emission lines are not accounted for

Description:
There appears to be confusion as to how nebular emission is accounted
for in Starburst99. To spell it out clearly: Starburst99 is not a
photoionization code. If nebular line emission is significant, the
Starburst99 SEDs should be fed into a photoionization code, such as
Cloudy, Mappings, or Photo.

This is what Starburst99 does: The stellar continua are computed, and
nebular CONTINUOUS emission is added by default. The continuous
emission includes free-free, free-bound, and 2-photon emission. The
user can manually override this default by specifying not to compute
the number of ionizing photons. However, since the SEDs are written
into the output file both with and without the nebular contribution,
the default set-up will most likely suit most users' needs.

Line-emission is never added to the SEDs. For a rough estimate of the
effects of nebular recombination lines, the following can be done. The
line fluxes and equivalent widths of the most important hydrogen
recombination lines are given in the file "width". One could, for
instance, compare the equivalent width of Halpha to the FWHM of a broad
R filter, and correct the V-R color accordingly. This would obviously
only work well for recombination lines. In general, a photo-ionization
code is required for lines like OIII or NII. To get a rough idea of
how the strongest non-recombination lines can affect the broadband
colors computed by Starburst99, see the Appendix of the paper by
Johnson et al. 1999 (AJ, 117, 1708).

______________________________________________________________________


Date:         April 30, 2001
Topic:        Definition of cluster mass
Reported by:  Linda Smith (UCL)
Impact:       The starburst mass can be variable with time

Description:
The Starburst99 code assumes that the total mass of an instantaneous
burst of star formation is constant throughout the evolution. This is
not really true for a massive cluster where the mass lost through
stellar winds and supernovae explosions is expelled, and thus the mass
of the cluster is decreasing with time. It is possible to correct for
this effect by switching on the 'yields' output. This file contains
the output of the subroutine 'nucleo' which calculates for each time
step the mass loss due to winds (yield1), the mass loss due to
supernovae (yield2), the total mass loss due to winds and SNe (yield),
and the accumulated total mass lost (tmass=yield*tstep). All values
printed in the yields output are log_10 values. To correct for the
mass loss from the cluster, simply subtract the value of tmass at each
time step from the initial cluster mass. It should be noted that this
approach is probably only valid for clusters with ages greater than
~30 Myr since young clusters (~10 Myr) are observed to contain
residual gas.

______________________________________________________________________


Date:         April 13, 2001
Topic:        Computing magnitudes in narrow-band filters
Reported by:  Nate Bastian (Univ. of Utrecht)
Impact:       Atmosphere wavelength resolution limits the accuracy

Description:
The model atmospheres used for the computation of the stellar continuum
have a wavelength resolution of typically 20 A. This limits the
accuracy of the magnitude and color calculations. The computed colors
in broad- and medium-band filters (>100 A FWHM) are correct, but the
results for narrow-band filters should be taken with care if the
central wavelength of the filter is close to a stellar absorption
line (e.g., Ha).

______________________________________________________________________


Date:         February 16, 2001
Topic:        How to interpret the sp.dat file
Reported by:  Anne-Laure Melchior (Marseille Observatory)
Impact:       Receipe to extract individual spectra from sp.dat

Description:
The sp.dat file contains the normalized UV line spectra used
in the linesyn subroutine. Each number is the normalized
flux at a fixed wavelength. The wavelength grid itself is
not given in the file. Instead it is generated in the code:

do 85 k=1,np
wavel(k)=rlam0+(float(k-1)*dell)
85 continue

with np=860, rlam0=1205.5, dell=0.75. In other words, the
spectra start at 1205.5, end at 1849.75, and have a spacing
of 0.75 A. Each line has 5 entries, therefore one complete
spectrum extends over 860/5=172 lines. sp.dat contains spectra
for 450 diferent spectral types. Therefore it has 172x450=
77400 lines.

The challenge is to figure out what spectrum corresponds to
what spectral type. Here we go:

The matrix defining the spectral types is as follows:


Luminosity Class V

O3 O3.5 O4 O4.5 O5 O5.5 O6 O6.5 O7 O7.5 O8 O8.5 O9 O9.5                14   14
B0 B0.5 B1 B1.5 B2 B2.5 B3 B4 B5 B5.5 B6 B6.5 B7 B7.5 B8 B8.5 B9 B9.5  18   32
A0 A0.5 A1 A1.5 A2 A2.5 A3 A4 A5 A6 A7 A7.5 A8 A9                      14   46
F0 F1 F2 F3.5 F5 F6.5 F8 F9                                             8   54
G0 G1 G2 G3.5 G5 G6.5 G8 G9                                             8   62
K0 K0.5 K1 K1.5 K2 K2.5 K3 K3.5 K4 K4.5 K5 K6 K7 K8.5                  14   76
M0 M0.5 M1 M1.5 M2 M2.5 M3 M3.5 M4 M4.5 M5 M5.5 M6                     13   89

Luminosity Class IV

O3 O3.5 O4 O4.5 O5 O5.5 O6 O6.5 O7 O7.5 O8 O8.5 O9 O9.5                14  103
B0 B0.5 B1 B1.5 B2 B2.5 B3 B4 B5 B5.5 B6 B6.5 B7 B7.5 B8 B8.5 B9 B9.5  18  121
A0 A0.5 A1 A1.5 A2 A2.5 A3 A4 A5 A6 A7 A7.5 A8 A9                      14  135
F0 F1 F2 F3.5 F5 F6.5 F8 F9                                             8  143
G0 G1 G2 G3.5 G5 G6.5 G8 G9                                             8  151
K0 K0.5 K1 K1.5 K2 K2.5 K3 K3.5 K4 K4.5 K5 K6 K7 K8.5                  14  165
M0 M0.5 M1 M1.5 M2 M2.5 M3 M3.5 M4 M4.5 M5 M5.5 M6                     13  178

Luminosity Class III

O3 O3.5 O4 O4.5 O5 O5.5 O6 O6.5 O7 O7.5 O8 O8.5 O9 O9.5                14  192
B0 B0.5 B1 B1.5 B2 B2.5 B3 B4 B5 B5.5 B6 B6.5 B7 B7.5 B8 B8.5 B9 B9.5  18  210
A0 A0.5 A1 A1.5 A2 A2.5 A3 A4 A5 A6 A7 A7.5 A8 A9                      14  224
F0 F1 F2 F3.5 F5 F6.5 F8 F9                                             8  232
G0 G1 G2 G3.5 G5 G6.5 G8 G9                                             8  240
K0 K0.5 K1 K1.5 K2 K2.5 K3 K3.5 K4 K4.5 K5 K6 K7 K8.5                  14  254
M0 M0.5 M1 M1.5 M2 M2.5 M3 M3.5 M4 M4.5 M5 M5.5 M6                     13  267

Luminosity Class II

O3 O3.5 O4 O4.5 O5 O5.5 O6 O6.5 O7 O7.5 O8 O8.5 O9 O9.5                14  281
B0 B0.5 B1 B1.5 B2 B2.5 B3 B4 B5 B5.5 B6 B6.5 B7 B7.5 B8 B8.5 B9 B9.5  18  299
A0 A0.5 A1 A1.5 A2 A2.5 A3 A4 A5 A6 A7 A7.5 A8 A9                      14  313
F0 F1 F2 F3.5 F5 F6.5 F8 F9                                             8  321
G0 G1 G2 G3.5 G5 G6.5 G8 G9                                             8  329
K0 K0.5 K1 K1.5 K2 K2.5 K3 K3.5 K4 K4.5 K5 K6 K7 K8.5                  14  343
M0 M0.5 M1 M1.5 M2 M2.5 M3 M3.5 M4 M4.5 M5 M5.5 M6                     13  356

Luminosity Class I

O3 O3.5 O4 O4.5 O5 O5.5 O6 O6.5 O7 O7.5 O8 O8.5 O9 O9.5                14  370
B0 B0.5 B1 B1.5 B2 B2.5 B3 B4 B5 B5.5 B6 B6.5 B7 B7.5 B8 B8.5 B9 B9.5  18  388
A0 A0.5 A1 A1.5 A2 A2.5 A3 A4 A5 A6 A7 A7.5 A8 A9                      14  402
F0 F1 F2 F3.5 F5 F6.5 F8 F9                                             8  410
G0 G1 G2 G3.5 G5 G6.5 G8 G9                                             8  418
K0 K0.5 K1 K1.5 K2 K2.5 K3 K3.5 K4 K4.5 K5 K6 K7 K8.5                  14  432
M0 M0.5 M1 M1.5 M2 M2.5 M3 M3.5 M4 M4.5 M5 M5.5 M6                     13  445

Wolf-Rayet Stars

WNL WNE WCL WCE WO                                                      5  450


In this table we list all spectral types are included. The types
listed in the same order as they are in the sp.dat file, going
from left to right, top to bottom. The are ordered by luminosity
class from class V to I, and within luminosity class from earlier
to later temperature class. In other words, we begin with O3V, O3.5V,
O9.5V, B0V, .... until we are at M6V. Then we continue we O3IV,
O3.5IV,.... until we reach M6IV. This eventually goes down to M6I.
Finally, we include WNL, WNE, WCL, WCE, WO. WO is star number 450.

The two columns on the right side of the table are helpful for
navigation. The first column gives the total number of stars in
each line. The second column gives the cumulative running index
at the end of each line. Example: Number 254 tells us that entry
254 corresponds to a K8.5III star.

Combining the cumulative running index with the length of each
spectrum (860 points) allows us to select the spectra in the
sp.dat file. Example: Suppose we want to find the spectrum of the O4I
star. This star has the index 359. Therefore we need to skip 358
stars in the sp.dat file. Since each stellar spectrum extends over
172 lines, the O4I spectrum appears after 172x348=59856 lines. It
begins with line 59857 and ends with (including) line 60028.

______________________________________________________________________


Date:         November 27, 2000
Topic:        Strength of near-IR absorption lines
Reported by:  George Bendo (Univ. of Hawaii)
Impact:       Default values inconsistent with publication

Description:
There is a difference between the H-band absorptions of Si and CO
currently returned by Starburst99 and those published in Leitherer et
al. (1999). The published figures and tables were computed with a
microturbulent velocity of 3 km/s (although this is not stated in the
paper) whereas the webpage defaults to a value of 1 km/s -- contrary to
what the help file says. If the Starburst99 is run with a velocity of
3 km/s, both the computed values and those in the paper agree. As of
December 22, 2000, 3 km/s is the default in Starburst99, and both sets
agree.

______________________________________________________________________


Date:         October 20, 2000
Topic:        Fe II 1.26 mu
Reported by:  George Bendo (Univ. of Hawaii)
Impact:       Starburst99 does not compute Fe II 1.26 mu

Description:
The Fe II 1.26 mu line is actually not calculated directly in the code.
The results reported in the paper by Leitherer et al. were obtained by
taking the supernova rate and multiplying  by Daniela Calzetti's (1997)
conversion factor. It was decided not to include it in the output because
we thought this would be trivial and would only take space in  the output
file. Therefore users should reproduce the Fe II figures via the SN rates
and the conversion factor.

______________________________________________________________________


Date:         July 26, 2000
Topic:        Predicting dust production rates
Reported by:  Claus Leitherer (STScI)
Impact:       Figure 108 can be used to estimate the dust production

Description:
Predicting dust production rates is much more difficult and
by far more uncertain than the gas rates. Here is an attempt
to get the user started. A good source is Eli Dewk's paper in ApJ,
501, 643 (1998).

I used his discussion to scale the SB99 predictions. The two
dust species are silicates and carbon-rich dust. The former
comes mostly from massive stars (SNII, WR stars), and the latter
from low- and intermediate stars. Also, silicates are the major
contributor to the total dust mass, in particular during the
early (< 1 Gyr) phase of a starburst. This means, silicates
are most likely to be considered to construct a figure that
reflects Fig. 108 for dust.

In order to modify Fig. 108 for dust, we need to know the relative
contribution of WR stars and SNII. While the absolute dust
masses ejected by the two species are uncertain, their relative
importance appears clear: except during the brief phase when
SNII are not present at all, the WR dust output is small in
comparison with SNe (most WR dust is in the form of carbon from
late WC stars, and those are relatively rare in comparison
with the WN population).

Therefore the conclusion is that the dust mass returned to the
ISM is mostly from SNII. If we knew the mass release in a tpyical
SNII, we could simply scale Fig108. The only case with relatively
good observations is SN 1987A. Even in this case the uncertainties
are larger. A dust/gas mass ratio of a few percent may be reasonable.
If so, and if all SNII supernovae behave like SN1987A, one could
take Fig108 and scale the results by a factor of 0.01-0.1. This
may be an underestimate at older ages (close to 1 Gyr) when SNI
kick in.

______________________________________________________________________


Date:         May 6, 2000
Topic:        Mass units in input file
Reported by:  Joseph Carson (Cornell Univ.)
Impact:       Burst mass is off by a factor of 10^6 M_sol

Description:
There is a small error in the downloadable Starburst code. In the
parameter input file, it states

"TOTAL STELLAR MASS [SOLAR MASSES] IF 'FIXED MASS' IS CHOSEN: [TOMA]"

while at the Starburst99 site, the parameter input file correctly
states

"TOTAL STELLAR MASS [10e6 SOLAR MASSES] IF 'FIXED MASS' IS CHOSEN: [TOMA]"

So both files expect units of 10e6 solar masses while one erroneously
says that units should be in solar masses.

This error was fixed on May 7, 2000. Masses are in units of 10^6 M_sol.

______________________________________________________________________


Date:         March 8, 2000
Topic:        Synthetic color magnitude diagrams
Reported by:  Peter Linda (Lund Observatory)
Impact:       Starburst99 CMDs have no random number generator

Description:
Starburst99 is optimized for application to the integrated properties
of stellar populations, like average colors, etc. It can, to some extent,
be used to construct HRD's and CMD's as well. This can be done within
the HRD subroutine. However, comparison with observations would still
require addition of a random-noise generator, which is not presently
included. Therefore it is recommended to use a package which is optimized
for the interpretation of resolved stars. Authors who come to mind are
Carme Galart, Laura Greggio, Eva Grebel, or Eline Tolstoy. They may
be willing to share their software.

______________________________________________________________________


Date:         February 14, 2000
Topic:        Printing out star number vs. mass
Reported by:  Daniel Devost (Cornell Univ.)
Impact:       The mass intervals in isochrone synthesis are variable

Description:
An IMF graph produced by printing out the cmass(i) and dens(i) vectors
from the density subroutine at the first step of integration (icount=1)
shows ugly discontinuities. cmass and lmin,lmax have a definition which
differs between isochrone synthesis and the fixed grid. See

c SET UP THE MASS GRID:
c      JMG=0 - SMALL GRID
c      JMG=1 - LARGE GRID
c      JMG=2 - ISOCHRONE SYNTHESIS WITH LARGE GRID
c      JMG=3 - ISOCHRONE SYNTHESIS WITH VARIABLE GRID; IN THIS CASE THE
c              INPUT VALUES FOR LMIN, LMAX HAVE NO INFLUENCE. THEY WILL
BE SET
c              LATER AUTOMATICALLY. SAME FOR CMASS. (IN STARPARA_ISO).
c

The cmass is continuously adjusted in the isochrone approach. For
instance it could be 10.14, 10.15, 10.16, then switch to 11.1, 11.2, etc.,
whereas for the fixed grid it is 10,11,12,13, etc.:

c
c COPY VALUES FROM ISOCHRONE WITH VARIABLE MASS GRID INTO VARIABLES USED
IN
c OTHER SUBROUTINES.
c
         do i=lmin,lmax
            cmass(i) = xminit(i)
            temp(i)  = xt(i)
            bol(i)   = xl(i)
            zmass(i) = xmact(i)
            bmdot(i) = x_mdot(i)
            xsurf(i) = x_h(i)
            ysurf(i) = x_he(i)
            xc12s(i) = x_c(i)
            xn14s(i) = x_n(i)
            xo16s(i) = x_o(i)
         enddo
      endif

Plotting the number vs. mass is straightforward as long as the mass
interval remains the same. However, when the isochrone synthesis switches
to a mass interval with different size, the number of stars in this
interval becomes different. The other subroutines "know" about this
(see the section of the code above) and take this into account.
Numerically what happens is that there are smaller mass intervals
(as expressed by the difference between cmass(i+1) and cmass(i)) but
the lmin,lmax are adjusted, so the density comes out right. Therefore
an IMF plot should not be generated with the isochrone synthesis option,
but rather with the fixed mass grid.

______________________________________________________________________


Date:         February 9, 2000
Topic:        Different model atmospheres in Starburst99
Reported by:  claus Leitherer (STScI)
Impact:       Clarification of different modes

Description:
This is a clarification is reponse to user confusion. Starburst99
has three options for the choice of model atmospheres:

Option 1): Pure black bodies for all stars. Obviously this is
not the most sophisticated approach.

Option 2): Lejeune's model atmospheres for all stars. This helps
identifying differences with respect to other evolutionary synthesis
codes, like those of Bruzual/Charlot and Fioc/Rocca-Volmerange who use
the same model atmospheres (but different evolution models).

Option 3): Schmutz's models for stars with strong winds and Lejeune
for everything else. This affects phases in particular when
Wolf Rayet stars are present.

Lejeune's model atmospheres are nothing else than the latest set
Kurucz atmospheres at the warm and hot end (Teff above about 4000 K)
and special cool star atmospheres, like those of Allard, linked to
together. Applied to hot-star populations, the Lejeune data set is
identical to the Kurucz set, as cool stars are negligible.

______________________________________________________________________


Date:         December 7, 1999
Topic:        IMF parameterization in Starburst99
Reported by:  Peter Berczik (MAO, Kiev)
Impact:       Starburst99 can be modified to accommodate different IMFs

Description:
A log-normal IMF can be approximated by 3 power laws, two of which are
connected at M=1. This makes it very simple to apply an analytical
scaling relation to the Starburst99 results without even fiddling with
the code.  Since the mass range below 1 M is used purely for normalization
purposes in the code, there is no point adding a particular IMF below 1 M
in the code. At some time later in the future we will add evolutionary
tracks below 1 M, and then we can include more complex IMF parameterizations
in this mass range as well. In the meantime, here is the simple solution:

If a user would like to know what Starburst99 predicts with a Kroupa IMF
for ***non-normalized*** properties which are dependent only on massive
stars, one would do the following: Run Starburst99 with alpha=2.7 and
cutoffs of 1 and 100 M. This gives exactly the properties of stars as
described by the high-mass part of the Kroupa IMF. Then one only needs
to apply the scaling factor to account for the fact that too many massive
stars were produced since we "forgot" those stars between 0.1 and 1 M.
This scaling factor is 0.41. In other words, if we found, e.g., a V
luminosity of 10^38 erg/s/A for the 2.7/1--100 IMF, we would find a
luminosity of 0.41 x 10^38 if we had done the model with the Kroupa IMF.
This factor is always the same as long as we look at a property that is
not affected by M < 1 M stars. Of course, if we look at a normalized
quantity, like an equivalent width (again with M<1M stars negligible),
one would not apply any factor at all.

The factor was derived by analytical integration of the different IMFs,
weighted by mass. Basically it means comparing the "A" constant (0.31
for Kroupa) to other IMFs. "A" simply differs by a factor of 0.41 between
Kroupa and 2.7,1--100. For completeness, these are the factors for a few
other IMFs:

Kroupa, 0.1 --> 100:  1.00  (normalization)
a=2.7,  0.1     100:  2.13
a=2.7,  1.0     100:  0.41
a=2.35, 0.1     100:  1.85
a=2.35, 1.0     100:  0.72

Note that Salpeter between 1 and 100 is close to unity, supporting the
claim that a Salpeter IMF between these limits can be used to fake a
log-normal IMF.

______________________________________________________________________


Date:         November 21, 2000
Topic:        Asymptotic value of colors
Reported by:  Nick Devereux (Embry-Riddle Univ.)
Impact:       Published colors not old enough for comp. with ellipticals

Description:
The observed B-V colors for old stellar populations (bulges of spirals,
ellipticals etc) are ~ 1.0. One would expect this to be the end point
B-V color for instantaneous burst model. However, the figures indicate
that the B-V color does not get much redder than 0.5. If we had plotted
the (B-V) colors to ages older than 1 Gyr, one would actually see them
approach 1.0. Keep in mind that 1 Gyr is not really old. One would call
this an intermediate-age population. From looking at A&AS, 96, 269 one
would agree that B-V=0.55 makes sense for a 1 Gyr old population. Let's
assume the color is dominated by the MS turn-off mass. The mentioned
paper then gives the corresponding spectral type: about mid to late F.
Then one would look at some color/spec Type relation, and one finds that
these stars have about (B-V)=0.55.

______________________________________________________________________


Date:         November 6, 1999
Topic:        Figures 21 and 23 in Starburst99
Reported by:  Aaron Barth (CfA)
Impact:       The published figures are partially incorrect

Description:
Figures 21 and 23 of Starburst99 are incorrect, both on the web site
and in the publication. Fig 21 and the associated data file is just a
copy of Fig 17. Fig 17 is correct. It is the a=3.3 case, whereas Fig.
21 should be a truncated Salpeter IMF with M_up=30. The same problem
exists for Fig. 23 as well. To summarize: Figs 21 and 23 are just
copies of 17 and 19. Users who are interested in these cases should
rerun a Starburst99 model interactively.

______________________________________________________________________


Date:         September 20, 1999
Topic:        Flux contribution of massive stars at 1500 A
Reported by:  Claus Leitherer (STScI)
Impact:       The most massive stars have litte contribution at 1500A

Description:
This posting is a clarification in response to a user inquiry.
Stars in the 80 to 100 M range are completely negligible for the
1500 A luminosity.

1) The mass-luminosity relation on the main sequence is no
   simple power-law. If one approximates the relation by a
   power law, one finds that the exponent is close to 3 around
   5 M, and close to 1 around 150 M.

2) Stars not only become more luminous with higher mass, they
   become hotter as well along the main sequence. The M-L
   relation refers to the bolometric luminosity whereas L_1500
   is a monochromatic luminosity. It is true that L_Bol increases
   with higher mass, but most of this increase goes into the
   far-UV, not into L_1500.

3) On top of this, there is a significant contribution from
   post-main-sequence stars, something which is difficult to take
   into account with scaling relations. The bottom line is, almost
   all the flux at 1500 A comes from stars with ZAMS masses of
   50 M and less.

______________________________________________________________________


Date:         August 9, 1999
Topic:        Model atmospheres at T > 50,000 K
Reported by:  Sally Heap (NASA Goddard)
Impact:       Kurucz atmospheres above 50,000 K are an extrapolation

Description:
The Kurucz/Lejeune atmospheres do not extend beyond 50,000 K. The
hottest main-sequence stars in the Geneva tracks, in particular at
low metallicity have higher temperatures, and therefore hotter
atmospheres are needed. Rather than taking an unblanketed black body,
we decided to take the 50,000 K Kurucz model and then scaled it by the
flux ratios of, e.g., a 60,000 over 50,000 K blackbody, while preserving
the total luminosity.



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