Analyzing SN2003Z with PHOENIX
aa r X i v : . [ a s t r o - ph . S R ] F e b Astronomy&Astrophysicsmanuscript no. paper c (cid:13)
ESO 2018November 2, 2018
Analyzing SN 2003Z ⋆ with PHOENIX
Sebastian Knop , Peter H. Hauschildt , E. Baron , , , and Stefan Dreizler Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germanyemail: [email protected];[email protected] University of Oklahoma, 440 West Brooks St, Rm 100, Norman, OK 73019, USAemail: [email protected] Computational Research Division, Lawrence Berkeley National Laboratory, MS 50F-1650, 1 Cyclotron Rd, Berkeley, CA 94720-8139 USA Institut f¨ur Astrophysik, University of G¨ottingen, Friedrich-Hund-Platz 1, 37077 G¨ottingen, Germanyemail: [email protected]
Received Accepted
ABSTRACT
Aims.
We present synthetic spectra around maximum for the type II supernova SN 2003Z, which was first detected on January 29.72003. Comparison with observed spectra aim at the determination of physical parameters for SN 2003Z.
Methods.
Synthetic spectra are calculated with our stellar atmosphere code
PHOENIX . It solves the special relativistic equation of ra-diative transfer, including large NLTE-calculations and line blanketing by design, in 1-dimensional spherical symmetry. The observedspectra were obtained at the 3.5 meter telescope at Calar Alto. The TWIN instrument was used so that a spectral range from about3600 to 7500 Å was covered. The spectra were taken on Feb. 4, 5, 9, and 11, 2003.
Results.
The physical parameters of the models give the luminosities, a range of possible velocity profiles for the SN, an estimate ofthe colour excess, and the observed metalicity.
Key words. supernovae: SN 2003Z – Radiative transfer
1. Introduction
Type II supernovae (SNe II) are thought to originate from thecore collapse of massive stars. By definition SNe II show strongBalmer lines in their spectra, and thus are thought to be fromstars with much of their hydrogen envelopes intact at the timeof the explosion. Largely through the use of
HST , progenitorshave been identified for several SNe II, and they seem to comefrom rather low mass stars 9 ∼ > M ∼ <
12 M ⊙ (Maund et al. 2005;Maund & Smartt 2005; Smartt et al. 2003; Smartt et al. 2004;Van Dyk et al. 2003a,b,c).Since the spectra of SNe II form in hydrogen dominated at-mospheres with relatively simple density structures, they shouldbe among the most accurate spectra to model with detailedmodel atmosphere codes.Indeed, SNe II can be modeled in detail and reddening,primordial metalicity, and even distances can be determined(Baron et al. 2000, 2003, 2004). Thus, through detailed spectralmodeling we can determine important physical parameters thatcan be compared with stellar evolution and explosion modeling.Here, we use the PHOENIX relativistic model atmospherecode package (Hauschildt & Baron 1999; Hauschildt et al.1997; Baron & Hauschildt 1998; Hauschildt et al. 2001) to sim-ulate the SN II atmosphere for SN 2003Z during its opticallythick (photospheric) phase.In the following we first describe the observations of SN2003Z, and then describe our modeling process including the as- ⋆ Based on observations collected at the Centro Astronmico HispanoAlemn (CAHA) at Calar Alto, operated jointly by the Max-PlanckInstitut fr Astronomie and the Instituto de Astrofsica de Andaluca(CSIC) sumptions made to construct a model. After that we present ourresults about luminosities, extinction, velocity profiles. Finallythe results are summarized in the conclusion.
2. The supernova SN 2003Z
SN 2003Z was discovered on January 29, 2003 (Boles et al.2003) and is a type II supernova (Matheson et al. 2003).The SN was observed on the 4th, 5th, 9th, and 11th ofFebruary 2003 with the 3.5 meter telescope at Calar Alto. TheTWIN spectrograph was used, covering the spectral range fromabout 3600 to 7400 Å. The SN is located near the galaxy NGC2742 and is believed to lie in the outer part of a spiral arm ofthe galaxy, typical for a Type II supernova. The redshift of NGC2742 is z = . the foreground colour excess of the galaxy is E ( B − V ) = .
039 (Schlegel et al. 1998). Information about theradial velocity of the SN itself or the colour excess of the hostgalaxy are unavailable.The physical structure of the atmosphere changes over timedue to the expansion and the gradual cooling of the ejected mate-rial. Therefore, the spectrum also changes over time. From dayto day the changes are small; however, the spectra of the firstand the last day of the observations show large di ff erences asdisplayed in Fig. 1.The gradual change in the wavelength shift of the spectrallines originates from the changing optical depth of the cooling This research has made use of the NASA / IPAC ExtragalacticDatabase (NED) which is operated by the Jet Propulsion Laboratory,California Institute of Technology, under contract with the NationalAeronautics and Space Administration. Sebastian Knop et al.: Analyzing SN 2003Z with
PHOENIX
Fig. 1.
Comparison of the spectra of the first and last day of theobservations. A shift in wavelength towards the red and a de-crease of flux in the blue part are visible, indicating the coolingand slowing of the material producing the spectra.and expanding envelope. As time progresses we see into slowerand “deeper” layers of the atmosphere so that the lines showsmaller redshifts in the later spectra.
3. Modeling
PHOENIX is a general purpose NLTE stellar atmosphere codepackage. For the calculation of the radiative transfer with
PHOENIX the structure of the atmosphere is approximated by aspherically symmetric shell, thereby reducing the system to onespatial dimension. Furthermore, the envelope is assumed to behomologously expanding, giving a linearly increasing velocityfield (Sedov solution) v ( r ) = v rR (1)with v being the velocity and R the radius at τ = ρ ( r ) = rR ! − n (2)Due to the fact that the atmosphere of a SN is expandingat ≃
10 percent of the speed of light, the special relativisticequation (Mihalas & Weibel Mihalas 1984) of radiative transferin moving media must be solved. In co-moving form written interms of wavelengths we have η λ − χ λ I λ = ∂ I λ ∂ s + a λ ∂λ I λ ∂λ + a λ I λ (3)with : a λ = γ " β (1 − µ ′ ) r + γ µ ′ ( µ ′ + β ) ∂β∂ r where I λ is the specific intensity and the di ff erentiation of thepath-length s is the di ff erentiation along the monochromaticpath of a photon in the co-moving frame. Furthermore, η λ isthe emissivity and χ λ the extinction coe ffi cient. The emissiv-ity η depends via scattering on the mean intensity J λ itself,therefore, the problem is not a mere di ff erential equation butan integro-di ff erential equation. The radiative transfer problemis solved with an operator splitting technique in the co-moving frame (Hauschildt & Baron 2004; Hauschildt 1992). For theNLTE models, the coupled radiation transport and rate equa-tion problem is solved by a multi-level operator splitting method(Hauschildt 1993).Details of the code and the numerical methods used in PHOENIX can be found in Hauschildt & Baron (1999).All models were calculated on a radial grid with 100 layers,using a logarithmic optical depth grid ( τ -grid) in the continuumat 5000 Å with a range from τ = − − .Other model parameters vary from model to model. For in-stance the final model for the first day of the observation had apressure at τ = . · − bar and the corresponding radiuswas 9 . · cm.Unstable nuclei – most importantly Ni – are created in SNoutburst and, therefore, the input of radioactive energy plays animportant role in the formation of the spectrum. The treatment ofthe influence of radioactivity is simplified by the assumption that γ -ray deposition follows the density profile and the total mass ofradiative nuclei is a parameter in the modeling. In all modelswe iterated the temperature structure to fulfill the condition ofenergy conservation in the co-moving frame. Furthermore, themost important species were treated in complete NLTE. (seeTable 1). The decision which ionization stages were includedin NLTE was made by taking into account the partial pressuresof those stages. An ion was ignored for the NLTE calculationonly if the pressure of an ion was for all layers was at least 15dex smaller than the pressure of the dominant ion of the species.To model SN atmospheres, a few physical parameters mustbe specified. For example, the luminosity, the exponent n of thedensity power law (2), and the velocity field of the atmospheremust be specified. These parameters are not known in advance.Therefore, several models with di ff erent physical parameters hadto be calculated and the best set of parameters was determined bycomparison of the observed and synthetic spectra. The first ob-servation was modeled to determine the basic parameters of theSN and the following observations were reproduced by changingthe physical parameters appropriately.
4. Results
To compare the model spectra with the observation a couple ofe ff ects have to be taken into account, such as the redshift of theSN, and extinction.Nothing is known about the intra-galactic extinction in NGC2742, hence we only correct for the known foreground extinctionof NGC 2742 E ( B − V ) = . z = . .First we ran a couple of models varying the luminosity(model temperature) and the velocity field to get a first guess forthose basic parameters. After including the first four ionizationstages of iron as well as hydrogen and helium in complete NLTE,a spectrum was obtained that fits some of the key features of theobserved spectrum, see Fig. 2. The displayed model spectrumhas T model = n =
11 and v = − (see Eq. 1). The model spectrum is blue shifted with re-spect to the observation. This is due to di ffi culties with the con-vergence of the models that had lower photospheric velocities.This initial result is clearly due to a velocity that was too largein the models. This simple preliminary model had few species in This correction is very small and we apply it only for completeness.ebastian Knop et al.: Analyzing SN 2003Z with
PHOENIX NLTE and it was di ffi cult to converge models with lower veloc-ities. As we improved the input physics in our calculations, thisproblem did not persist.The most obvious flaw besides the wrong velocity, is thesteepness of the continuum in the wavelength range from 5200to 6200 Å. After calculating a grid of models it became clear thatthere is no combination of the model parameters that reproducesthis slope of the continuum.However, it is plausible and to be expected that there is ad-ditional extinction present in the host galaxy. Therefore, we cor-rect the observation for additional reddening. With an assumedextinction of E ( B − V ) = .
3, the continuum of the model fromFig. 2 was matched very well (See Fig. 3). Since the assumedvalue of extinction is an arbitrary choice and is only a lowerboundary for possible values of the extinction we ran a numberof tests to place limits on the extinction coe ffi cient. Large valuesof E ( B − V ) demand high model temperatures, but higher temper-atures yield synthetic spectra that are dominated by the Balmerseries of hydrogen and other spectral features were diminished.Hence we decided to choose the extinction as small asneeded to match the model. During the progress of the analy-sis, due to extensive NLTE calculations, non-solar abundancesand taking the other observed epochs into account. In the finalmodel the extinction was chosen to E ( B − V ) = .
4. Since thecontinuum wasn’t a reliable temperature indicator anymore wehad to rely on reproduced spectral details to determine the modeltemperatures.Because the model spectrum in Fig. 2 was very promising,we have based our further modeling on the parameters of thismodel. It already includes hydrogen, helium and the first fourionization stages of iron in NLTE. During the course of the mod-eling we included all the species in Table 1 in NLTE. Furtherextensive model grids were calculated, varying the model tem-perature, the density exponent, time since explosion (importantfor the radioactive decays), and the velocity field.
Table 1.
This table lists all ionization stages that were treated inNLTE.
Z Ions Z Ions1 H i
14 Si i - iii i
15 P i - ii i - ii
16 S i - ii i - ii
19 K i - ii i - ii
20 Ca i - iii
10 Ne i
25 Mn i - ii
11 Na i - ii
26 Fe i - iv
12 Mg i - iii
27 Co i - iii
13 Al i - ii
28 Ni i - iv We found that the spectrum of Feb. 4th was best fitted withan e ff ective temperature of 5800 K and a density exponent n = / H] = − ff ectson the spectra. The most noticeable e ff ect resulted from an over-all under abundance of all the metals. The spectra fit significantlybetter if the metalicity was [M / H] = log ≈ − .
5. However,
Fig. 2.
The plot shows the first model that reproduced some ofthe observed spectral features. No model was found that matchedthe observed rise of the continuum, hence the extinction insidethe parent galaxy appears to be important. The spectra were nor-malized in such a way that they match the continuum above 6900Å.
Fig. 3.
The same model as in Fig. 2 is shown. The observationwas dereddened using a higher extinction of E ( B − V ) = .
3. Thespectra were normalized to match the continuum above 6900 Å.since the fit is not good enough to use quantitative methods thisis only determined by eye. Lower metalicities seem to fit theobservation for a broader range of values. Hence the progenitorseems to have been a metal-poor star.The variation of the velocity field was required in order forthe models to match the observations. Gradually changing thevelocity field resulted in a di ff erent wavelength shift and onlyslightly changing spectral features. No particular velocity couldbe favoured other another in a range of a few hundred km s − .The variation of the velocity was problematic in the firstmodels due to the fact that slower models didn’t converge prop-erly or didn’t reproduce the spectra as well as before. However,due to the refining of the atmosphere structure via inclusionof more NLTE species the models became more robust to thechange of the velocity parameter.In Figs. 5–8 we show the final model spectra for all fourobserved epochs. In all Figs. the observations were corrected foran extinction of E ( B − V ) = .
4. This change of the extinc-
Sebastian Knop et al.: Analyzing SN 2003Z with
PHOENIX
Fig. 4.
A model is compared to the observation on Feb. 4. Solarabundances are assumed. The other key-parameters are T model = v = − . The observation was correctedfor E ( B − V ) = .
4. The spectra were normalized by area.
Fig. 5.
The best fitting synthetic spectrum is compared to theobservation on Feb. 4. All model parameters are the same asin Fig. 4 with the exception of the metalicity which is [M / H] ≈− .
5. The observation was corrected for E ( B − V ) = .
4. In com-parison with the model from Fig. 4 the fit is now much better.The spectra were normalized by area.tion from the initial guess is mainly due to the use of non-solarabundances. The under-abundance of the metals increased theflux in the blue part of the spectrum and therefore the observa-tions demanded more de-reddening. In order to support the largereddening that we find, we have searched for Na ID interstellarabsorption lines in the host galaxy. Since there is a strong broadSN feature just as the wavelength of the Na ID lines they don’tclearly stand out, but there is a hint of an extra narrow absorptionline at the right wavelength. Thus, our somewhat high extinctionvalue is reasonable.The important model parameters of the di ff erent observa-tions are summarized in Table 2.
5. Conclusion
We have modeled the early spectra of the Type II supernova SN2003Z. The results show that there is substantial extragalactic
Fig. 6.
The best fitting synthetic spectrum for Feb. 5 is com-pared to the observation. The model has T model = v = − . The spectra were normalized by area. Fig. 7.
The best fitting synthetic spectrum for Feb. 9 is com-pared to the observation. The model has T model = v = − . The spectra were normalized by area. Fig. 8.
The best fitting synthetic spectrum for Feb. 11 is com-pared to the observation. The model has T model = v = − . The spectra were normalized by area. ebastian Knop et al.: Analyzing SN 2003Z with PHOENIX Table 2.
Summary of the basic parameters T model and velocityfor the di ff erent days. There is no error estimation for the ve-locity as a range of velocities fit the spectra and the given valuewas just picked to match the observed redshift. The models fitbest with metalicities [M / H] ≈ − .
5, however, there is quite arange of possible values that cannot be ruled completely out, so[M / H] = − . + / − . / .
5. The luminosities are relatively welldetermined – ∆ T model = ± p is deter-mined at τ = τ -grid. February T model [M / H] v n p [K] [km s − ] [10 − bar]4th 5800 -0.5 4900 9 4.435th 5700 -0.5 4850 9 5.419th 5600 -0.5 4500 9 6.8311th 5400 -0.5 4300 9 9.76 reddening towards the SN, probably due to dust in the plane ofits parent galaxy. For each observed epoch we have determinedthe best-fit parameters of the NLTE models as summarized inTable 2.The best fits require sub-solar metalicities of about [M / H] ≈− .
5, indicating that the progenitor of SN 2003Z was a quitemetal-poor star (see also Baron et al. (2003)). Unfortunatelythere are only very few observations available for this object andin particular, no accurate light curve is known, therefore we haveassumed that the relative fluxes are accurate. Without photome-try we can not calibrate the relative fluxes and thus our resultsare sensitive to the accuracy of the relative flux calibration.
Acknowledgements.
This work was supported in part by NASA grants NAG5-3505 and NAG5-12127, and NSF grants AST-0204771 and AST-0307323, PHHwas supported in part by the Pˆole Scientifique de Mod´elisation Num´eriqueat ENS-Lyon. Some of the calculations presented here were performed at theH¨ochstleistungs Rechenzentrum Nord (HLRN), and at the National EnergyResearch Supercomputer Center (NERSC) which is supported by the O ffi ce ofScience of the U.S. Department of Energy under contract DE-AC03-76SF00098.We thank all these institutions for a generous allocation of computer time. References
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