David J. Jeffery Department of Physics New Mexico Tech 801 Leroy Place Socorro, New Mexico 87801-4796 U.S.A. Office Tel: 505-835-5610 Email: jeffery@kestrel.nmt.edu Office: Rm 349, Bldg. Workman Center Homepage: http://www.physics.nmt.edu/jeffery/jefferyfrontpage Departmental Tel: 505-835-5328 Departmental FAX: 505-835-5707 Departmental Email: physics@kestrel.nmt.edu Departmental Homepage: http://www.physics.nmt.edu/ 2002 July 6 Hi Koji: I have improved (I hope) suggested replies to the concerns of the referee. The replies are rather lengthy, but there's no page limit on replies and I think the referee was asking for arguments. I hope I've been diplomatic and stuck to the issues. The referee has made some valid points. Regards David Replies Major concern 1 We should first say our proposal of a jet is very speculative and we do say this in our abstract. The purpose of the jet is to explain a component of the polarization of the supernova data for Feburary that we identify from the data. This component measured as polarized flux appears to be a polarized, redshifted reflection of the flux spectrum: the redshift being that caused by a velocity of order 0.23c. The identification cannot be certain because there is not exact agreement between the flux spectrum redshifted and scaled to the observed polarized flux. And in fact we would not expect exact agreement. If a jet or jets are thrown out of a supernova during the explosion phase, the supernova is likely to exhibit other asymmetries that contribute to polarization. We note that Leonard et al. (2002, astro-ph/0206368) agrees with us that the flux spectrum redshifted and appropriately scaled does provide a partial match to the observed polarized flux spectrum. In Section 4.3, we suggested some jet parameters (i.e., 0.05 M_sun at of order 0.23c, etc.) that can yield the right order of polarization component we have identified and account for its disappearance by our later observations. The parameters we suggest are not a unique choice, and we do emphasize this in the paper. The particular choice we made was partially made because one of us (Jeffery) had the results in hand from a calculation that preceded the discovery of SN 2002ap. According to the referee and the paper by Berger et al. (2002, astro-ph/0206183), that reports the radio observations and modeling of SN 2002ap, our suggested jet parameters and the radio observations and modeling are inconsistent. The referee asks us to address this inconsistency. We note that we are not experts in radio observations and modeling ourselves, and so here we will not challenge the conclusions of Berger et al. Consistency can perhaps be achieved by reducing the speed of the jet model. The redshift of 0.23c is what our data suggests, but this can be obtained without having the characteristic scattering location of the jet moving a 0.23c. If the jet is not at 90 degrees to the line of sight but at a smaller angle $\theta$ and behind the supernova, then there are in effect two redshifts: one from going into the jet frame and one from coming out of it in the somewhat opposite direction: the redshift of the scattered polarized flux would then be given by \lambda'=\lambda[ 1 + (1+\cos\theta)(v/c) ] If theta is smallish, then our requirement on (v/c) can be made smaller. Of course, the polarization by Thomson scattering decreases as \theta is made smaller. It is left to later work if we can get the required polarization with v significantly smaller than 0.23c. In this regard it would be useful to find out how large a (v/c) the Berger et al. observations and modeling can tolerate. We have decided to drop from the paper all mention of parameters for the jet, except the essential velocity 0.23c causing the redshift that we use to explain the polarization component we have speculatively identified. Our original set of parameters are inconsistent with the Berger et al. observations and modeling as noted above. Proposing another, more consistent set would take more modeling which is not appropriate for letter of which our jet speculation is only part. Also it seems that any set we propose may be taken as a claim to have established a reliable set no matter what we say to the contrary. For example, Berger et al. imply that we made a claim for reliability for our original set when we explicitly did not. (Koji, well I havn't made the answer more concise. But I have addressed the referee's concern fairly I think. It would be interesting to know just how reliable the Berger et al. results are. The results are model-dependent too and the model insofar as I can tell is a spherically symmetric one. However, I'm not one to challenge the radio people on their own ground. If the jet model is at right, then nature has found a way to achieve consistency. I think you've agreed we should drop the parameters from my model. It was a mistake of mine to introduce them since it leads people mistaking their intent. I merely wanted to show how the polarization could arise from a jet, not how it actually did.) Major Concern 2 If there is a jet is thrown out of the core of the exploding supernova, then it is plausible that it carries some radioactive Ni-56. The gamma-rays from decay would keep the jet ionized to some degree just as they later keep the nebular phase bulk ejecta ionized. We now mention this possibility briefly. We could also say here that the jet is illuminated from below by the supernovae and this may provide some ionization. X-rays from the circumstellar interaction might also contribute. However, the modeling of the ionization state of a jet is beyond the scope of our letter. (Koji, I think it safe to mention this possibility. If one accepts the premise of a jet from the core, that it carries Ni-56 with it seems entirely plausible. I should say that personally, I'm not a NLTE modeler. So can't undertake modeling of ionization state of a jet on any short notice.) Major Concern 3 We disagree that it is really critical to present more details of the jet model that we are thinking terms of. Since we are dropping the mention of possible parameters, the details of the model would become rather superfluous. Our paper is a letter of which the jet hypothesis is only a part. Also the basic picture is clear enough. A fraction of the supernova flux is redshifted, polarized, and reflected into the line of sight by a jet (or a clump) that breaks the symmetry of the supernova. The polarized flux is diluted by the flux from the bulk of the supernova (which is itself somewhat polarized). The net polarization level turns out to be smallish: of order 0.4 % or less in the continuum. However, even such small polarization requires significant asymmetry of some sort. As we remark in the paper, the ellipsoidal ejecta polarization model would require an axis ratio on the plane of the sky that differed from 1 by of order 10 %. For the referee's interest, the polarization jet model (Jeffery 2002, in preparation) is a very simple, semi-analytic, non-relativistic model. The purpose of the model is to allow a semi-quantitative understanding of the polarization a jet would cause including it's time dependence and to allow a 1st order analyis of the observed data. The model has a number of free parameters which unfortunately are hard to set independently. Because it is a very simple and semi-analytic model, it cannot span the set of all possible jet models. The model was in fact invented in 2001 and the paper on it has not been finished merely because of time constraints on the author. Relativistic effects were not included in the model because they are a complication and because Jeffery does not believe highly relativistic jets could contribute to the optical polarization. The referee is correct that moderate relativistic effects would make it harder (although not overwhelmingly so) to obtain simultaneously the redshift and polarization of the scattered flux that we require from the jet model for SN 2002ap. If we do decrease jet velocity below 0.23c, the relativistic problem is decreased. Major Concern 4 The referee has not understood the effect of redshift in the model. Say that the bulk of the supernova ejecta emits a flux F(lambda) toward the observer. A fraction f of this flux is redshifted, scattered and polarized by the jet emitted in the direction of the observer. Assuming f is rather small and the non-relativistic approximation can be made and the bulk supernova flux is unpolarized, then the polarization of the net flux at wavelength lambda is P(lambda) = f P(theta) F( lambda(1+(1+cos\theta)(v/c) ) / F(lambda) , where theta is the angle of the jet from the line of sight and P(theta) is the polarization of the scattered flux (100 % for 90 degree scattering). The polarizaed flux at lambda comes from a bluer part of the spectrum. If v/c=0, then the polarization would be constant: such a jet is not tenable: the jet must be well outside of the photosphere for the approximation to be made that jet and photosphere are point-like. For v/c of significant size, the polarization will vary with wavelength because of the variation of F(lambda) with wavelength. The variation would be particularly strong about line profiles. We have added a clarifying remark in the text. (Koji, can we add a clarifying remark without lengthening the letter? I thought the effect was clear without saying more than we did---clear diagrammatically---but maybe I'm too familiar with the effect.) Minor Concern 1 We do not reference the papers of Cropper et al (1988) and Barrett et al (1988) because the former does not correct the data for interstellar polarization (ISP) and the latter uses an outdated ISP value. Our references to the SN 1987A polarization data are to support effects that are only reliably seen after a good ISP correction. We use a reference that uses the best ISP correction we know of for SN 1987A data: i.e., Jeffery, 1991, ApJS, 77, 405. The Wang et al. (1996) reference is an important one and we will include it. (Koji, the Wang et al. reference is the first one to empircally strongly support the notion that SN II's are generally polarized. I didn't make it originally because it's somewhat outdated by later papers and doesn't have anything to say about the trends in SN polarization (for lack of data in those old days). If you can fit it in (I know you are trying to cut down the size), then I would advocate including. It's not so important, however, and we can argue that it's outdated.) Minor Concern 2 We agree with the referee that it would be interesting to see if the data from the February and March epochs can be analyzed on a day by day basis. However, for a 1st order analysis in a letter, using February and March averages seemed reasonable since the day to day changes in those epochs are not striking. We do, in fact, present all the day to day data in Figure 1. A day by day analysis would be particularly enhanced if our data were combined with that from other groups (Leonard et al. 2002, astro-ph/0206368; Wang et al 2002, astro-ph/0206386).