arXiv:astro-ph/9510070v1 13 Oct 1995 o.Nt .Ato.Soc. Astron. R. Not. Mon. ih uv a ugse eylwms o h ejecta, the for the mass of low modeling very Further a 1994I. suggested M SN has curve of paths light evolutionary progenitor possible the several ruled for described are (1994) have al. models on Wolf-Rayet and et star Based out Nomoto single 1994). 1994I, that SN al., proposed of have et curve light early Nomoto Woosley, very the 1992; 1993; & Weaver, Hsu, Porter, & & Langer, Filippenko, Joss, inter- Podsiadlowski, 1990; binary 1990; via Harkness, Sargent, or & been phase, have (Wheeler Wolf-Rayet envelopes stars, a action massive helium either of and in cores hydrogen C+O stripped of the collapse progenitors Branch, both to the & due where are Young, that behavior Ic (Baron, suggested time SNe have 1984L of long interaction. groups SN the binary Several of fit a curve 1993). to through light fails the or model of wind, a a envelope such in hydrogen However, whose lost of star, collapse been massive the su- a has to Ib of due Type core are helium in SNe the lines these I that He Type suggests of and pernovae Ib prominence Type The models of supernovae. several progenitors result Ic dwarf, the the white for are proposed a Ia been of have SNe al. disruption that et complete doubt the Clocchiatti little of 1994; is (Phillips, there has Ic While M51 SN 1994). in a features 1994I as these by Supernova classified supernovae supernovae altogether. been Ic absent Ib Type or Type weak in and are lines, lines I II He char- Si prominent are strong supernovae Ia by Type Balmer acterized Whereas strong spectra. of their understood. lack in the well by lines least classified progeni the are supernovae the are I supernovae subclasses, Type Ib/c the Type all of Of supernovae tors observed subclass. well every produced nearly have of years few last The INTRODUCTION 1 agr evr 95 on,Brn rnh 1995). Branch, & Baron, Young, 1995; Weaver, & Langer, .Baron E. 1994I SN of Analysis Spectral Preliminary

1Mrh2018 March 21 4 3 2 1 c et fAtooy nvriyo aiona ekly CA Berkeley, California, of University 02138. Astronomy, MA T of Cambridge, University, Dept. Street, State Garden Arizona 440 60 Astronomy, Oklahoma, CfA, and of Physics University of Astronomy, Dept. and Physics of Dept. ejecta 00RAS 0000 ≈ 0 . 9 1 − .H Hauschildt H. P. , 1 . M 4 ⊙ 000 Iaooe l,19;Woosley, 1994; al., et (Iwamoto 0–0 00)Pitd2 ac 08(NL (MN 2018 March 21 Printed (0000) 000–000 , 1994I). e words: Key unlikely. seems helium pcr,ormdl antrl u ml mut fhlu.Mr t More helium. of amounts small helium for out evidence rule direct cannot no M51 find models we in our While 1994I w stars. spectra, inconsistent supernova massive not of Ic are cores models Type Our C+O spectra. the the of of analysis non-LTE spectra optical present We ABSTRACT 2 .Branch D. , tr:eouin—sproa:gnrl—sproa:individual supernovae: — general supernovae: — evolution stars: 94720-3411. me Z85287-1504. AZ empe, - , .Bok,R 3,Nra,O 73019-0225. OK Norman, 131, Rm Brooks, W. 1 .P Kirshner P. R. , utb oee ndti.W s h eeaie tla at- stellar generalized the spectra use code We observed mosphere detail. the in constraints modeled model be must provide to order In MODELS SPECTRAL 2 efcnitnl,ln lneigo h otiprat( important most the 10 of blanketing line self-consistently, Best, (Hauschildt, SNe 1991). expan- typical Wehrse, high in the observed at velocities important sion effect are order aberration, first and the advection particular in scheme. effects, relativistic correction The Uns¨old-Lucy temperature been modified have lineariza a I partial or a Ne Lagrang either and using the I, 1992b) in rela- (Hauschildt, Na equilibrium frame special II, radiative the of Ca condition for II, tivistic Mg solve II, we He Simultaneously I, implemented. He I, atoms H Models method 1993). for Hauschildt, ALI 1991; an Hummer, & using rate (Rybicki self-consistently non-LTE solved multi-level, are The ab equations and 1992a). advection, (Hauschildt, shift, Doppler ration relativistic of effects the aea ad h ie r yaial eetdaccording the selected for dynamically important are are lines them to the of close hand; all contains at not list but case entire lines, The million (1993). Kurucz 42 of list line infrlnsadcniu,t l resin orders all to continua, and lines for spher- independent, tion time the symmetric, solve ically to method splitting) tor ashlt rnh(94,adi ao ta.(1995). al. methods et calculational the outline Baron briefly Baron in only in we and (1995), here al. Thus, (1994), et Branch Hauschildt & of in there, (1994), Hauschildt, spectra described al. early 1994), et the al., Allard et of in analysis ver- (Hauschildt the 1992 updated for Cygni an used Nova is code This the 1994I. of SN sion for spectra synthetic and 5 ea ie eetdfo h aetaoi n ionic and atomic latest the from selected lines metal ) nadto otennLElns h oesinclude, models the lines, non-LTE the to addition In PHOENIX ssa ceeae -trto AIo opera- or (ALI Λ-iteration accelerated an uses A HEI 4.8 PHOENIX T E tl l v1.4) file style X fully 3 n .V Filippenko V. A. and , eaiitcrdaietase equa- transfer radiative relativistic ocmuemdlatmospheres model compute to t h xlsosof explosions the ith n preliminary and a . M 0.1 han nteoptical the in v/c including ⊙ (SN tion of s ian er- of ≈ & 4 , . 2 E. Baron et al. to whether the ratio Γ ≡ κl/κc is larger than a pre-specified Table 1. Abundances of Presented Models −3 value (usually 10 ), where κl, κc are the absorption coef- ficients in the line center, and in the corresponding (LTE Model XHe XC XO + non-LTE) continuum, respectively. In the subsequent ra- April 3, low helium 0.05 0.25 0.68 diative transfer calculations all lines selected in this way April 3, high helium 0.35 0.17 0.46 −4 are taken into account as individual lines by opacity sam- April 11 1.8 × 10 0.27 0.71 . −4 . . pling, and all others from the large line list are neglected. April 18 1 8 × 10 0 27 0 71 We treat line scattering in the metal lines by parameteriz- The mass fractions of helium, carbon, and oxygen used in the ing the albedo for single scattering, α. The calculation of α models. would require a full non-LTE treatment of all lines and con- tinua, which is outside of the scope of this paper. Tests have to the supernova of E(B − V ) = 0.45 mag, which we discuss shown that as a direct result of the velocity gradient in nova further in §4. In order to avoid calculational difficulties, we and supernova photospheres, the shape of the lines does not have treated He II in LTE. depend sensitively on α and our approach is a reasonable Since our models do not include NLTE treatments of all first approximation. Therefore, we adopt a constant value of the relevant ions (in particular O I, O II, C I, C II, Si II, and α = 0.95 for all metal lines. The continuous absorption and Fe II are treated in LTE), we cannot, as yet, provide quan- scattering coefficients are calculated using the cross-sections titative abundance estimates. We can, however, draw quali- as described in Hauschildt et al. (1992). tative conclusions based on our modeling. In future work we The effects of non-thermal collisional ionization by pri- will present calculations including a ≈ 617 level Fe II model mary electrons produced by collisions with gamma rays due atom (Hauschildt & Baron, 1995). to the decay of 56Ni and 56Co are modeled using the contin- While we only present results of our “best fits” (as de- uous slowing down approximation (Garvey & Green, 1976; termined by eye, comparing to the complete observed spec- Swartz, 1991). We have also included ionizations due to sec- trum) we have in fact calculated more than 100 models, ondary electrons (Swartz, 1991), but most of their energy is where we have varied the He abundance by factors of 10,000, thermalized and therefore has only a small effect on the level we have examined models from 1/2 solar to 6 times solar populations (Meyerott, 1980). The collisional cross sections metallicity, and we have varied the C/O production ratio by are taken from the work of Lotz (1967a,b, 1968a,b,c). a factor of 3. All of the models discussed in this paper are The model atmospheres are characterized by the follow- available upon request. ing parameters (see Hauschildt et al., 1992; Baron et al., 1995, for details): (i) the reference radius R0, which is the radius where the continuum optical depth in extinction at 3 SPECTRA AND RESULTS 5000 A˚ (τstd) is unity, (ii) the effective temperature Teff , which is defined by means of the luminosity, L, and the ref- Figure 1 displays the data obtained on April 3.5, 1994 UT at 2 1/4 erence radius, R0, (Teff = (L/4πR0 σ) where σ is Ste- the MMT as well as our calculated model with Teff = 8300 K, −1 fan’s constant), (iii) the density structure parameter, ve, v0 = 12000 km s , N =6,XNi = 0.01, [He/H]= 12, He/O= −N (ρ(r) ∝ exp(−v/ve)), or N (ρ(r) ∝ (v/v0) ), (iv) the ex- 0.3, C/O= 0.5, and z = 3. Our boundary conditions were 15 pansion velocity, v0, at the reference radius, (v) the density, for the outer radius and density were Rout = 1.96 × 10 cm −17 −3 ρout, at the outer edge of the envelope, (vi) the albedo for and ρout = 3.93×10 g cm . The line identifications cor- line scattering (metal lines only, here set to 0.95), (vii) the respond to the results of our theoretical models and we try statistical velocity ξ, treated as depth-independent isotropic to indicate where model limitations may be inaccurate. The − turbulence and set to 50 km s 1 for the models presented synthetic spectrum is dominated by Ca II and C II lines, here, and (viii) the element abundances. although Fe II and O II lines are also present. The synthetic In order to minimize the parameters in setting the ele- spectrum fits the Ca II H+K emission profile very well, but ment abundances we begin with a solar abundance (Anders the emission near 4500 A˚ is too weak. It fits the broad ab- & Grevesse, 1989), and then “burn” hydrogen to helium sorption feature near 5000 A˚ reasonably well, but there is with a final number ratio given by [He/H] = log10(nHe/nH ). too little absorption and the emission is too strong. In our Next we “burn” helium to carbon and oxygen with a final model spectrum the emission is due to Fe II and Mg I lines. number ratio He/O, and a production ratio (by number) It is likely that NLTE treatments of S II, Si II and C II of carbon to oxygen C/O. Finally we allow metals heavier would better reproduce the observed spectrum. Also plot- than oxygen to be scaled by the factor z. Thus, our abun- ted in Figure 1 is the synthetic spectrum for a model with dance parameters consist of [He/H], He/O, C/O, and z. In N = 8, giving a steeper atmosphere. The other parameters order to further reduce the size of parameter space we have were the same but in order to better reproduce the observed −1 used the results from the models of Iwamoto et al. (1994) spectrum v0 = 15000 km s . The lines are too narrow in and Woosley, Langer, & Weaver (1995) as guidance to fix the steeper model in spite of the fact that the velocity is the parameter C/O= 0.5. The mass fractions for the models larger. As to be expected, the steeper model only enhances presented are listed in Table 1. the mismatch with the observed spectrum in the red since For convenience, we have assumed an explosion date of the Fe II and C II lines become more pronounced. There March 30, 1994 to scale the radii of our models. We have is no clear evidence of He I lines in our synthetic spectrum confirmed that changes of a few days in the explosion date and reducing the helium abundance by a factor of 10 does have very small effects on the shape of the output spectrum not significantly affect the spectrum. Increasing the helium although the absolute flux obviously scales with the square abundance by a factor of 10 still fails to show clear evidence of the radius, which we account for. We adopt an extinction for He I lines, but the quality of the overall fit is signif-

c 0000 RAS, MNRAS 000, 000–000 Preliminary Spectral Analysis of SN 1994I 3 icantly reduced, (see Figure 1); the Ca II H+K emission SN 1994I; The observed position of the supernova coincides becomes too broad, and the feature near 4500 A˚ becomes with a dust finger in the host galaxy M51. Based on an over- very flat in absorption with only weak emission. Thus, at all fit to the light curve Iwamoto et al. (1995) find an ex- present, we can not easily determine the amount of helium tinction of AV = 1.4 mag, while an analysis of the Na D ab- +3.1 in the ejecta. Higher amounts of helium do begin to show sorption finds AV = 3.1 −1.5 mag (Ho & Filippenko, 1995). the effects of He I. In the model with high helium abundance One can use the earliest spectrum on April 3 to estimate (He/O= 3.0), the helium mass fraction is Y = 0.35 and the the reddening. The observed spectrum displays strong ab- total mass above the τstd = 1 (30) is 0.08 (0.34) M⊙, re- sorption in Ca II H+K. However, as the reddening increases, spectively. For the model with He/O= 0.3, the helium mass the color temperature of the synthetic continuum spectrum fraction is Y = 0.05. Near-IR spectra including the He I must also increase in order to match the observed spectrum. λ10830 line would be extremely useful for determining the But this higher temperature depopulates the lower level of helium abundance. the Ca H+K lines and hence the strong absorption seen in We display in Figure 2 the observed spectrum for April the spectrum cannot be reproduced. Figure 4 displays our 11.5, 1994 UT obtained at the MMT along with our best calculated spectra for Teff = 8300, 8600, and 9100 K. We find fit synthetic spectrum. The model parameters are: Teff = that the temperature is fairly well determined Teff ≈ 8300 K, −1 6650 K, v0 = 8000 km s , N =8, XNi = 0.02, [He/H]= 12, although it may be possible to go to higher temperatures by 15 He/O= 0.001, C/O= 0.5, z = 4, Rout = 2.13 × 10 cm, and confining calcium to cooler regions. On the other hand, our −17 −3 ρout = 5.04×10 g cm . The observed spectrum now dis- models produce reasonably good agreement with the red plays lines of S II, Si II, Na I, and O I, in addition to Ca II edge of the calcium absorption which indicates that we do and Fe II lines. The O I λ7773 line is clearly evident (and not have calcium mixed too deeply. Using the reddening law not too badly fit). The calculated Ca II H+K red absorption of Cardelli, Clayton, & Mathis (1989) we find that extinc- edge does not quite extend far enough to the blue although tions 0.9 ∼

c 0000 RAS, MNRAS 000, 000–000 4 E. Baron et al.

8.0

Ca II

6.0 FeII OII FeII MgI 4.0 (arbitrary units) λ F

CII 2.0 CII

0.0 3000.0 4000.0 5000.0 6000.0 7000.0 8000.0 λ (angstroms)

Figure 1.

Observed and synthetic spectra for April 3, 1994. The observed spectrum has been dereddened with E(B-V) = 0.45 mag. The absorption features near 6860 A˚ and 7600 A˚ are telluric. For the calculated models the parameters are Teff = 8300 K, −1 v0 = 12000 km s , N =6, XNi = 0.01, [He/H]= 12, He/O= 0.3, C/O= 0.5, and z = 3 (thick solid line), the same parameters but −1 He/O= 3.0 (dot-dashed line) and the same parameters but N = 8, v0 = 15000 km s , and He/O= 0.3 (dashed line). The thin solid line corresponds to a model with the same parameters as the thick solid line, but C II lines have been removed from the line-list in the theoretical spectrum. epochs with one before maximum light, makes such a deter- modeling of each calculation it is difficult for us to favor one mination ambiguous. The rise-time should which should be stellar evolution scenario or the other. compared to the results of Iwamoto et al. (1994), who find Our calculations lend credence to the identification of a 12 day rise-time for models of the light-curve of SN 1994I. SNe Ic progenitors as C+O cores formed in an interacting Comparing our results to published hydrodynamical binary (Wheeler & Harkness, 1990). In order to make defini- models of the light curve of SN 1994I, we find that our tive statements about abundances, more intermediate mass models have substantial mass above the reference radius. elements need to be included in NLTE. Additionally, non- On April 18, the mass above the reference radius ranges uniform compositions need to be treated. However, once the from 0.5 M⊙ for our shallowest models to 1.6 M⊙ for our atmospheres become inhomogeneous, parameter space be- steepest models. The steeper, more massive model produces comes larger than can be adequately covered. A better way a significantly better fit to the observed spectrum than the to proceed is to perform spectroscopic diagnostics on hy- shallower, less massive model, but since the Ca II profile is drodynamical models. In order to do this in an objective sensitive to the density profile and given our simplifying as- manner, hydrodynamical calculations must fully resolve the sumptions of uniform compositions and a power law density density profile in the atmosphere. profile it would be premature to draw conclusions about the density structure from our models. Although the two published hydrodynamical models of ACKNOWLEDGMENTS the light curve of SN 1994I are from very different stel- lar evolution scenarios (Woosley, Langer, & Weaver, 1995; We are most grateful to Brian Schmidt for providing the Iwamoto et al., 1994), the actual models are very simi- MMT spectra quickly and for helpful comments on the lar in total ejected mass, total nickel mass, and energy of manuscript. We thank Adam Fisher and Sumner Starrfield explosion. Without performing detailed synthetic spectral for helpful discussions, and Ken Nomoto for providing us

c 0000 RAS, MNRAS 000, 000–000 Preliminary Spectral Analysis of SN 1994I 5

6.0 CaII FeII CII

SII

4.0 FeIII TiII FeII CII CII

(arbitrary units) CII λ OI F 2.0 CII NaI

0.0 3000.0 4000.0 5000.0 6000.0 7000.0 8000.0 λ (angstroms)

Figure 2.

Observed and synthetic spectra for April 11.5, 1994. The observed spectrum has been dereddened with E(B-V) = 0.45 mag. The absorption features near 6860 A˚ and 7600 A˚ are telluric. with the results of his hydro models. Assistance with the Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, observations and reductions at Lick Observatory was pro- 345, 245 vided by Luis C. Ho and Aaron J. Barth. This work was Clocchiatti, A., Brotherton, M., Harkness, R. P., & supported in part by NASA grant NAGW-2999, a NASA Wheeler, J. C. 1994, IAU Circ., No. 5972 LTSA grant to ASU, NASA grant GO-2563.01-87A from Diaz, A. I., Terlevich, E., Vilchez, J., Pagel, B., & Ed- the Space Telescope Science Institute, which is operated by munds, M. G. 1991, MNRAS, 253, 245 the Association of Universities for Research in Astronomy, Filippenko, A. V., Porter, A. C., & Sargent, W. L. W. 1990, Inc., and by NSF grants AST-9115061 and AST-9115174. AJ, 100, 1575 Some of the calculations in this paper were performed at Garvey, R. H., & Green, A. E. S. 1976, Phys. Rev. A, 14, the NERSC, supported by the U.S. DoE, and at the San 946 Diego Supercomputer Center, supported by the NSF; we Hauschildt, P. H. 1992a, JQSRT, 47, 433 thank them for a generous allocation of computer time. Hauschildt, P. H. 1992b, ApJ, 398, 224 Hauschildt, P. H. 1993, JQSRT, 50, 301 Hauschildt, P. H., & Baron, E. 1995, JQSRT, in press REFERENCES Hauschildt, P. H., Best, M., & Wehrse, R. 1991, A&A, 247, Allard, F., Hauschildt, P. H., Miller, S., & Tennyson, J. L21 1994, ApJ (Letters), 426, L39 Hauschildt, P. H., Wehrse, R., Starrfield, S., & Shaviv, G. Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim. 1992, ApJ, 393, 307 Acta, 53, 197 Hauschildt, P. H., Starrfield, S., Austin, S., Wagner, R. M., Baron, E., Young, T., & Branch, D. 1993, ApJ, 409, 471 Shore, S. N., & Sonneborn, G. 1994, ApJ, 422, 831 Baron, E., Hauschildt, P. H., & Branch, D. 1994, ApJ, 426, Hauschildt, P. H., Starrfield, S., Shore, S. N., Allard, F., & 334 Baron, E. 1995, ApJ, 447, 829 Baron, E., Hauschildt, P. H., Branch, D., Austin, S., Gar- Ho, L. C., & Filippenko, A. V. 1995, ApJ, 444, 165 navich, P., Ann, H. B., Wagner, R. M., Filippenko, A. V., Iwamoto, K., Nomoto, K., H¨oflich, P., Yamaoka, H., Kuma- Matheson, T., & Liebert, J. 1995, ApJ, 441, 170 gai, S., & Shigeyama, T. 1994, ApJ (Letters), 437, L115

c 0000 RAS, MNRAS 000, 000–000 6 E. Baron et al.

3.0 FeII CaII BaII TiII FeII TiII ScII TiII BaII BaII 2.0 TiII FeII ScII CaI CaI OI CII

(arbitrary units) CI

λ CaII

F TiII 1.0 CI NaI

0.0 2000.0 4000.0 6000.0 8000.0 10000.0 λ (angstroms)

Figure 3.

Observed and synthetic spectra for April 18, 1994.The observed spectrum has been dereddened with E(B-V) = 0.45 mag. All telluric features have been removed.

Kurucz, R. 1993, CDROM No. 1 Atomic Data for Opacity Woosley, S. E., Langer, N., & Weaver, T. A. 1995, ApJ, Calculations, SAO Cambridge, MA 448, 315 Lotz, W. 1967a, ApJ Suppl., 14, 207 Young, T. R., Baron, E., & Branch, D. 1995, ApJ (Letters), Lotz, W. 1967b, Journal Opt. Soc. America, 57, 873 449, L51 Lotz, W. 1968a, Journal Opt. Soc. America, 58, 236 Lotz, W. 1968b, Journal Opt. Soc. America, 58, 915 Lotz, W. 1968c, Z. Physik, 216, 241 Meyerott, R. E. 1980, ApJ, 239, 257 Nomoto, K., Yamaoka, H., Pols, O. R., van den Heuvel, E. P. J., Iwamoto, K., & Shigeyama, T. 1994, Nature, 371, 227 Nugent, P., Baron, E., Hauschildt, P., & Branch, D. 1995, ApJ (Letters), 441, L33 Phillips, M. M. 1994, IAU Circ., No. 5966 Podsiadlowski, P., Joss, P. C., & Hsu, J. J. L. 1992, ApJ, 391, 245 Rybicki, G. B., & Hummer, D. G. 1991, A&A, 245, 171 Swartz, D. 1991, ApJ, 373, 604 Wheeler, J. C., & Harkness, R. 1990, Repts. Prog. Phys., 53, 1467 Wheeler, J. C., Harkness, R. P., Clocchiatti, A., Benetti, S., Brotherton, M. S., DePoy, D. L., & Elias, J. 1995, ApJ (Letters), 436, L135 Woosley, S. E., Langer, N., & Weaver, T. A. 1993, ApJ, 411, 823

c 0000 RAS, MNRAS 000, 000–000 Preliminary Spectral Analysis of SN 1994I 7

40.0

30.0

20.0 (arbitrary units) λ F

10.0

0.0 2000.0 3000.0 4000.0 5000.0 λ (Angstroms)

Figure 4.

Synthetic spectra with Teff = 8300 (solid line), 8600 (dot-dashed line), and 9100 K (dashed line).

c 0000 RAS, MNRAS 000, 000–000