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CONSTRAINING THE PROPERTIES OF THE ETA
CARINAE SYSTEM VIA THREE-DIMENSIONAL
SMOOTHED PARTICLE HYDRODYNAMICS MODELS
OF GROUND- AND SPACE-BASED OBSERVATIONS
by
Thomas Ignatius Madura
A dissertation submitted to the Faculty of the University of Delaware in
partial fulfillment of the requirements for the degree of Doctor of Philosophy in
Physics
Summer 2010
c
2010 Thomas Ignatius Madura
All Rights Reserved
CONSTRAINING THE PROPERTIES OF THE ETA
CARINAE SYSTEM VIA THREE-DIMENSIONAL
SMOOTHED PARTICLE HYDRODYNAMICS MODELS
OF GROUND- AND SPACE-BASED OBSERVATIONS
by
Thomas Ignatius Madura
Approved:
George Hadjipanayis, Ph.D.
Chair of the Department of Physics and Astronomy
Approved:
George H. Watson, Ph.D.
Dean of the College of Arts and Sciences
Approved:
Debra Hess Norris, M.S.
Vice Provost for Graduate and Professional Education
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
Stanley P. Owocki, Ph.D.
Professor in charge of dissertation
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
Theodore R. Gull, Ph.D.
Member of dissertation committee
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
James MacDonald, Ph.D.
Member of dissertation committee
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
John E. Gizis, Ph.D.
Member of dissertation committee
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
Michael Shay, Ph.D.
Member of dissertation committee
ACKNOWLEDGEMENTS
iv
TABLE OF CONTENTS
LIST OF FIGURES ............................... vi
LIST OF TABLES ................................vii
ABSTRACT ...................................viii
Chapter
1 SUMMARY AND CONCLUSIONS ................... 1
1.0.1 Overview of Current Work .................... 1
1.0.2 Future Research Goals ...................... 8
v
LIST OF FIGURES
1.1 Zoom of the X-ray minimum observed by RXTE over the last three
orbital cycles of Eta Carinae ...................... 11
vi
LIST OF TABLES
vii
ABSTRACT
viii
Chapter 1
SUMMARY AND CONCLUSIONS
1.0.1 Overview of Current Work
The main goal of this dissertation was to use complex three-dimensional
Smoothed Particle Hydrodynamics simulations of Eta Carinae to synthesize observ-
ables across a wide range of different wavelengths in the hopes of further constraining
the stellar, wind, and orbital parameters of the system. This section briefly sum-
marizes the most important results of this thesis.
Chapter 1 introduced us to Eta Carinae and highlighted the reasons why it
is so interesting and worth studying. We learned it provides us with a unique astro-
physical laboratory for the study of star formation, stellar evolution, LBVs, stellar
mass-loss, rapid stellar rotation, colliding wind binaries, stellar atmospheres, radia-
tive transfer theory, dust formation, and the chemical enrichment of the surrounding
interstellar medium.
In Chapter 2, the detailed physics of radiation-driven winds from hot, massive
stars was presented. These effects are important since Eta Carinae is a very massive
(>90M⊙) star exhibiting extreme mass loss. The effects of rapid stellar rotation
on radiation-driven outflows and the consequences of a massive star exceeding the
Eddington limit were also discussed, with a particular focus on the implications for
Eta Carinae. Chapter 2 also outlined the key observational diagnostics and physics
of colliding wind binary systems, which is relevant since Eta Carinae is now generally
believed to be such a CWB.
1
Passive
The discussion in Chapter 3 focused on the key observational diagnostics im-
plying binarity in Eta Carinae. The latest estimate for the present-day period of the
system derived from the many lines in the optical spectrum, combined with observa-
tions from broad-band X-ray, optical, and near-infrared studies is P= 2022.7±1.3
days (Damineli et al. 2008a). Past hydrodynamical modeling efforts of Eta Carinae
were also summarized in Chapter 3, and we learned that with the exception of X-
rays, very little work has been done on the numerical modeling and interpretation
of observations in other wavebands.
Chapter 4 explained the 3D SPH method used in this thesis and why it was
chosen over a more standard grid-based approach. We showed that the SPH method
is ideal for modeling Eta Carinae because it is so naturally adaptive, less compu-
tationally expensive, and designed for 3D nonaxisymmetric astrophysical problems.
Details of the SPLASH code (Price 2007), which was extensively modified for the
purposes of this thesis, was also discussed in Chapter 4.
A detailed three-dimensional dynamical model for the high-ionization forbid-
den line emission observed by HST /STIS in Eta Carinae was presented in Chapter
5. Large scale (∼1500 AU ) 3D SPH simulations of the wind-wind collision and
radiative transfer calculations performed with a modified version of SPLASH were
used to generate synthetic position versus velocity spectrograms at various orbital
phases and STIS slit position angles. When compared to the available observations,
these model spectro-images provide important details about the physical mecha-
nism responsible for the emission, as well as the location and orientation of the
observed emitting structures. By comparing model spectro-images from two differ-
ent 3D SPH simulations to the observations, and taking into account the ionization
volume created by the secondary near periastron, the primary mass-loss rate could
be constrained. The results show that at the time of the HST observations, the
primary star had a mass-loss rate that was >2.5×10−4M⊙yr−1and .10−3M⊙
2
yr−1. A primary mass-loss rate that is .2.5×10−4M⊙yr−1requires a companion
star with a significantly reduced ionizing flux, which appears to be in conflict with
results from CLOUDY photoionization modeling of the Weigelt blobs by Verner et al.
(2005) and Mehner et al. (2010).
The model spectro-images show that most of the high-ionization forbidden
line emission originates in the central ±0.1 arcsec region of the system and comes
from the current wind-wind interaction region which is illuminated by far-UV ra-
diation from Eta Car B. The blue-shifted, ring-like emission features that extend
up to ∼0.35 arcsec from the central stars, seen when the STIS slit is oriented
at positive PAs, are formed in the dense shells of primary wind material ejected
during the previous periastron passage. In the basic interpretation for the for-
mation of the high-ionization forbidden lines, far-UV radiation from Eta Car B
leads to highly ionized regions extending outward from its low-density wind. In the
current and post-periastron wind-wind interaction regions, gas from the colliding
winds gets compressed, leading to collisional excitation and increasing emission of
the high-ionization forbidden lines until the critical density of the line is reached.
The spectro-images of different lines obtained with HST /STIS reveal different but
related regions of formation which depend on the ionization potential, temperature,
and critical density of the respective line. Spectral variations as a function of phase
are due to the orbital motion of Eta Car B in its highly eccentric orbit, which causes
different portions of the extended wind structures to be ionized. The disappearance
of the high-ionization forbidden emission during periastron passage is attributed to
the wrapping of the dense primary star wind around the binary system, trapping
the far-UV radiation from Eta Car B, and preventing it from ionizing the outer,
extended wind structures responsible for the emission. Observed variations in the
emitting structures with STIS position angle are due to the narrow STIS aperture
sampling different specific regions of the projected wind structures.
3
The most important result of Chapter 5 is that the 3D dynamical model
of the high-ionization forbidden line emission constrains the absolute orientation
of the binary orbit on the sky. In order to simultaneously reproduce the observed
blue-shifted ring-like emission features at phase 0.976 and PA = +38◦, the partially
red-shifted, spatially extended emission features at PA = −28◦, and the temporal
variations in emission seen at other phases and slit PAs, the binary system must
have an inclination of i≃40◦, an argument of periapsis ω≈255◦±15◦, and a
projected orbital axis with a PA = 312◦±15◦. Such an orientation places apastron
on the observer’s side of the system, with Eta Car B on the far side of Eta Car A
during periastron. This orientation also implies that the orbital axis is aligned in
three-dimensional space with the symmetry axis of the Homunculus. Furthermore,
the resulting projected orbit on the sky has Eta Car B moving clockwise relative to
Eta Car A, with Eta Car B approaching Eta Car A from the SW prior to periastron,
and receding to the NE after. This orientation is supported by the spatial map of
the flux of the blue shifted component of the [Fe III]λ4659 emission by Mehner et
al. (2010), and the images of Smith et al. (2004), which show excess UV emission
to the SW side of Eta Carinae just before periastron and to the NE just after. It
is important to note that the results of Chapter 5 are the first time detailed 3D
hydrodynamical models have been used together with high quality observations to
constrain the absolute orientation of Eta Carinae’s binary orbit in three-dimensional
space.
Next, Chapter 6 presented a 3D “bore hole” model for explaining the periodic
eclipse-like events seen in ground-based photometric observations of Eta Carinae.
Using a combination of 3D SPH simulations, CMFGEN radiative transfer models, and
radiative transfer performed with SPLASH, synthetic photometric light curves in
the optical BVRI and NIR JHKL wavebands were generated and compared to the
observations. The synthetic light curves reproduce the observed steep rise and drop
4
before periastron, and also give roughly the same peak-to-peak change in magnitude
and “eclipse” duration. Rises to maximum in the model start at almost exactly the
same phases as those in the observations, and the slopes of the rises, drops, and
recovery to egress maxima match as well. Several key trends with wavelength are
also reproduced, including the change in magnitude of the rise to maximum as a
function of wavelength and the lengths of the respective parts of the event, including
the total time taken to rise to light maximum, the time to drop to minimum during
eclipse, and the time needed to recover from eclipse to egress maximum.
The biggest deficiencies of the bore hole model are the failure to reproduce the
height of the egress maxima after eclipse, and the failure to reproduce the extreme
dip depths seen in the Kand Lbands. This indicates that the bore hole effect alone
is not responsible for the entire shape of the light curves. This is likely due to extra
emission sources that are not currently included in the model, such as the secondary
star, the Weigelt blobs, and dust.
The bore hole model also helps to constrain the orientation of the binary
orbit. An argument of periapsis of ω≃210◦−240◦is required, consistent with the
results of Chapter 5 and the X-ray analyses of Okazaki et al. (2008) and Parkin et al.
(2009). However, much larger inclinations of i≃80◦are required to reproduce the
observed magnitudes of the rise before and drop during periastron passage. Chapter
6 discussed the possibility that a change of the stellar wind and/or orbital parame-
ters, together with the inclusion of currently unaccounted for emission sources, could
rectify the current model discrepancies. Again though, this is the first time detailed
3D hydrodynamic simulations of the interacting winds and radiative transfer models
of the primary star have been used to explain the periodic photometric events.
Chapter 7 presented definitive evidence for the detection of high velocity
material, up to ∼1900 km s−1, in the Eta Carinae system during the 2009.0 pe-
riastron passage. VLT/CRIRES observations show broad, high velocity absorption
5
in He Iλ10833 in the spectrum obtained at phases 11.991 to 11.998, implying that
it is connected to the spectroscopic event. Near-infrared observations obtained at
OPD/LNA from 1992 to 2009 show that this high-velocity absorption in He Iis pe-
riodic. Based on the OPD/LNA dataset, timescale of detection of the high-velocity
gas is constrained from 95 d to 206 d (0.047 to 0.102 in phase) around phase zero.
Several reasons are given in Chapter 7 for why the high-velocity absorption
is unlikely to be due to a transitory high-velocity wind of Eta Car A, or due to
a wind eclipse of Eta Car B. Rather it is suggested that the observations provide
direct detection of high-velocity material flowing from the wind-wind collision zone
in the binary system. Detailed 3D SPH simulations of the wind-wind collision
show that dense high-velocity gas is in the line-of-sight to the primary star only if
the binary system is oriented such that the companion is behind the primary star
during periastron, corresponding to a longitude of periastron of 240◦.ω.270◦.
The model, when compared to the observations, rules out all orbital orientations in
the range 0◦.ω.180◦, regardless of the assumed inclination i, as they do not
produce a significant column density of high-velocity gas in our line-of-sight. The
observational data modeled is also broadly consistent with an orbital inclination in
the range 40◦.i.60◦. Unfortunately, the data and models are not adequate to
constrain the PA of the projected orbital axis on the sky, but the allowed ranges of i
and ωvalues are very similar to those found in earlier chapters, and still consistent
with an orbital axis that is aligned in three-dimensional space with the symmetry
axis of the Homunculus. The analysis of the results from the 3D SPH simulation
further shows that the high-velocity absorbing material is likely located at distances
of 15 to 45 AU from Eta Car A (in line-of-sight).
Finally, in Chapter 8, the published K-band continuum interferometric data
of Eta Carinae obtained at orbital phases φ= 0.92 −0.93 and φ= 0.27 −0.30 were
analyzed with the goal of constraining the rotational velocity and spatial orientation
6
of the rotation axis of Eta Car A based on the effects of rotation on the wind
density structure, which determines the geometry of the K-band emitting region.
The influence of Eta Car B on the inner wind of Eta Car A through the presence of
a low-density wind cavity and density-enhanced wind-wind collision zone was also
investigated with the goal of determining how these may affect the interpretation of
the VINCI data set obtained near periastron passage. To accomplish these goals,
two-dimensional radiative transfer models of latitude-dependent winds generated
by rapid stellar rotation, and of a modified primary wind which includes a wind
cavity and colliding wind interaction region, were applied to Eta Carinae for the
first time. Synthetic interferometric observables were computed from the radiative
transfer models and compared to the observations.
If one ignores the presence of Eta Car B, the two-dimensional modeling
shows that both single-star prolate- and oblate-wind models are able to explain
the observed elongation of the K-band emitting region of Eta Car A and the avail-
able closure phase (CP) measurements. Moderately fast rotation and high inclina-
tion angles are required to simultaneously fit the VINCI and AMBER data sets,
with W= 0.77 −0.92 and i= 60◦−90◦for the best prolate-wind models and
W= 0.73 −0.90 and i= 80◦−90◦for the best oblate-wind models (recall that
Wis defined as the ratio of the rotational velocity of Eta Car A to its critical
velocity). Interestingly, both require nearly the same range of Wvalues, but the
possible tilting between the current rotation axis of Eta Car A and the Homunculus
symmetry axis is a bit puzzling. This is because one of the most favored models
for explaining the shape of the Homunculus involves latitudinal mass-loss from a
rapidly-rotating primary star during the Giant Eruption, which naturally requires
that the Homunculus and rotation axes be aligned.
The results of Chapter 8 further show that, assuming the standard orbital
and wind parameters of Eta Carinae, even if Eta Car A has a spherical wind, its
7
inner density structure can be sufficiently disturbed by Eta Car B at certain or-
bital phases, mimicking the effects of a prolate/oblate latitude-dependent wind in
the available interferometric observables in the K-band continuum. Thus, rapid
stellar rotation may not be the only explanation for the interferometric observa-
tions. Unfortunately, if Eta Car A’s mass loss is latitudinally dependent, based on
the available interferometric data alone, one cannot differentiate between a prolate
wind or an oblate wind scenario to explain the observations. Furthermore, one can-
not determine whether the rotation axis is aligned in three-dimensional space with
the Homunculus symmetry axis. The fact that the wind-wind collision zone can
mimic the effects of a latitude-dependent wind further complicates matters. Thus,
more interferometric observations and improved multi-dimensional radiative transfer
models are needed to resolve these issues.
1.0.2 Future Research Goals
This thesis has attempted to improve our understanding of the Eta Carinae
system via the merging of complex 3D simulations and the synthesis of high quality
observational diagnostics. Still, there is much work and science to be done. Firstly,
improvements can be made to the models discussed above, specifically regarding
the radiative transfer approaches. In the case of the high-ionization forbidden line
emission modeling, a more detailed ray-tracing method for performing the radiative
transfer on the pre-computed SPH density fields would lead to a better understand
of the ionization state of different regions of the winds of the two stars and the wind-
wind interaction region. Such a method would not only allow for better modeling of
the forbidden line emission, but it would be of great help in modeling other, more
complicated and unusual lines, such as the He I P Cygni lines (Nielsen et al. 2007b;
Damineli et al. 2008a) that are a part of Eta Carinae’s spectrum. Improved radiative
transfer models would also allow tighter constraints to be placed on the ionizing flux
of UV photons from the unseen secondary star, providing important information
8
about its spectral type. Thus, one future goal is to develop radiative transfer codes
capable of producing line profiles of various optically thin and thick lines which
can then be compared to the various lines of interest found in the spectrum of Eta
Carinae.
Similar improvements can also be made to the bore hole model. The simple
pin-hole approximation used in Chapter 6 could be improved upon by using a Monte
Carlo radiative transfer code to determine the emerging radiation field. Such mod-
eling, coupled with continued observations, could lead to a better understanding of
the different emitting regions in the Eta Carinae system.
There are other aspects of Eta Carinae worth investigating further as well.
One of these is the influence of the companion star and wind-wind interaction region
on the primary star and its observed spectrum. There are currently a significant
number of discrepancies between the available CMFGEN models and the observations.
For instance, the current model is unable to simultaneously fit both the observed
optical and UV spectra. Also, the current model produces too much absorption in
the optical lines, particularly in H and Fe. Finally, the UV spectrum is observed to
change during the spectroscopic event, which the current model does not adequately
explain. Thus, another future research goal is to develop an improved CMFGEN model
for the observed spectrum. This would be done in a similar way to the 2D radiative
transfer models of Chapter 7 that include a wind cavity and wind-wind interaction
region. Ionization and density changes in the wind cavity carved by the secondary
could lead to less absorption in the key optical lines and thus provide a better
fit to the spectrum. The distortion of the wind cavity during the spectroscopic
events could also potentially explain the observed changes to the UV spectrum
during periastron passage. Such modeling should be relatively straight forward and
achievable in the near future.
There are also natural improvements that could be made to the 3D SPH
9
simulations. These include the implementation of radiative cooling, a velocity law
for the stellar winds, inclusion of the effects of radiative braking and radiative inhi-
bition, a latitudinal-dependent mass loss for the primary star, among many others.
There is also the possibility of moving beyond SPH and performing simulations
with a 3D Adaptive Mesh Refinement (AMR) hydrodynamics code. We are cur-
rently testing the 3D AMR hydrodynamics code PLUTO (http://plutocode.to.
astro.it/index.html) for this purpose. The PLUTO code was chosen because
it has two qualities essential for any future grid-based modeling of Eta Carinae,
namely, adaptive mesh refinement to cover the large dynamic range involved, and
radiative cooling for the shocks. A 3D colliding wind binary subroutine has already
been written and tested for the simple cases of binary systems with circular orbits
and low eccentricities, with adiabatic and radiative cooling. The goal is to even-
tually perform a full 3D simulation of Eta Carinae that includes proper radiative
cooling.
Finally, there is the bigger mystery of explaining the recently observed changes
occurring in Eta Carinae. RXTE X-ray monitoring of the 2009.0 periastron passage
revealed that the duration of the most recent X-ray minimum was approximately
one month shorter than that of the last two cycles (Figure 1.1). The observed X-ray
flux is also ∼20% lower since the recovery from the 2009.0 minimum compared to
the level from the previous two cycles. Preliminary modeling suggests that a 2 −4
factor drop in the mass-loss rate of Eta Car A could result in a shortened minimum
that closely resembles the observations. However, when, how, and why such a sig-
nificant change in mass loss occurred in unknown. There is also a current lack of
observational data to support the conclusion that a drop in the mass-loss rate of the
primary has actually taken place. It appears that Eta Carinae is almost as much a
mystery today as it was nearly 200 years ago.
10
Figure 1.1: Zoom of the X-ray minimum observed by RXTE over the last
three orbital cycles of Eta Carinae. Note the shorter dura-
tion of the minimum of the 2009.0 event, and the lower X-
ray flux after recovery compared to the level from the previ-
ous two cycles. Credit: Courtesy of Michael Corcoran’s web-
site at http://asd.gsfc.nasa.gov/Michael.Corcoran/eta_car/
etacar_rxte_lightcurve/index.html
11
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