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The light curve and distance of Kepler supernova: news from four centuries ago

We study the light curve of SN 1604 using the historical data collected at the time of observation of the outburst. Comparing the supernova with recent SNe Ia of various rates of decline after maximum light, we find that this event looks like a normal SNIa (stretch s close to 0.9: 0.9 \pm 0.13), a fact which is also favoured by the late light curve. The supernova is heavily obscured by 2.7 \pm 0.1 magnitudes in V. We obtain an estimate of the distance to the explosion with a value of d = 5 \pm 0.7 kpc. This can help to settle ongoing discussions on the distance to the supernova. It also shows that this supernova is of the same kind as those of the SNIa sets that we use for cosmology nowadays.


Introduction
The supernova of 1604 was observed by Johannes Kepler and other astronomers in Europe, Korea, and China. Not so many years before, the supernova SN1572, currently named Tycho's supernova, was the subject of extensive studies, both astronomical and philosophical, by Tycho Brahe (Brahe 1603).
The supernova in 1604 inspired as well observational measurements and philosophical considerations by Kepler. The philosophical disquisitions were on the nature of the heavens.
The idea of crystal spheres carrying each one a planet, and rolling over one another, had already been shattered by the discovery of SN 1572. The possibility of a heaven that gives birth to natural objects grew along the following years, and was reenhanced by the discovery of the supernova of 1604. Kepler  Because of the importance of Kepler as a physicist, and of the records collected by him from SN 1604, this supernova is often called Kepler's supernova.
For many years, it was not clear which type of supernova it was. There were discussions on whether it was a core-collapse supernova or a thermonuclear one. X-ray studies have shown that the O/Fe ratio in the remnant of SN 1604 corresponds to that of a Type Ia supernova (Reynolds et al. 2007). In this supernova remnant, there are signs that the system might have been relatively massive, one of its components creating a detached circumstellar shell (CSM) of 1 M ⊙ expanding into the interstellar medium (Vink -4 -2008). Recent studies of this CMS suggest that it had lost contact with the inner evolving stars years before the explosion (Katsuda et al. 2015).
In agreement with the abovementioned, some authors have suggested that the companion star could have been an Asymptotic Giant Branch (AGB) star that had lost its envelope (Chiotellis et al. 2012).
All the discussions concerning the progenitor of Kepler supernova are haunted by the lack of precision in the estimated distance. The supernova is located well above the Galactic plane, at l= 4.5 o , b=6.4 o (Vink 2008). It has an angular size of 2 arcmin. The suggested distances to the remnant lies between 3 and 7 kpc. One of the first distances were obtained by Reynoso and Goss (1999), using the H I absorption to the remnant to give a constraint of 4.8 < d Kepler < 6.2 kpc. The first distance given by Sankrit et al (2005), using the proper motion of the optical filaments, had a value of 3.9 +1.4 −0.9 kpc. Vink (2008) gave a distance ∼ 6 kpc, from arguments related to the velocity of the forward shock. Based on the non-detection of TeV gamma-rays by HESS, Aharonian et al. (2008) suggested a distance of > 6 kpc. Most recently, Sankrit et al. (2016) have revisited the method based on the proper motion of the filaments to derive as distance 5.1 +0.8 −0.7 kpc.
In the present work, we go back to the method, previously used for understanding Tycho supernova in nowadays cosmological terms (Ruiz-Lapuente 2004), and we make use of the historical records of SN 1604 to reconstruct its light curve. We determine the best stretch of the light curve and the distance to the remnant.
Knowing the distance to the supernova is crucial in the searches from a possible surviving companion in this supernova (Kerzendorf et al. 2014;Ruiz-Lapuente 2014). This knowledge allows to place luminosity limits to the searches and inform with accuracy of the kind of -5potential companions surveyed.

Observations
We have compared the historical records gathered by European and Korean astronomers at the time of the explosion in 1604 with the family of SNe Ia as known today. The supernova occurred in a region of the sky which was often observed, because the supernova appeared 3 degrees to the northwest of Mars and Jupiter, which were in conjunction, and about 4 degrees to the east of Saturn. So, there were plenty of observations that allowed to place the time of the appearence of the supernova at October 10, being unseen before. The early light curve is very complete, with daily reports on the brightness of the supernova.
The discovery preceded by 20 days the visual maximum. This means that we have data for three weeks, a lapse which compares well with the best follow-ups currently done on early discovered supernovae. But, unlike Tycho's SN which was circumpolar, SN 1604 was observed from Europe and Korea at relative low latitude, and during the months of November and December, the supernova was not observable during the night.
The most recent reconstruction of the historical records has been made by Clark and Stephenson (1977), who compare the records obtained by Korean astronomers with those obtained by the European astronomers, previously examined by Baade (1943). The comparison between the Korean and European records gives a good agreement in the early part of the light curve, before and around maximum, with some disagreement in the phase after maximum.
The high surveillance of the supernova in epochs before its maximum (the visual maximum was on Nov 1, according to the fit to the light curve) was done in Europe by a group of anonymous observers. Only on Oct 17 Kepler had a chance to see the supernova. We assign -6 -0.5 mag to the individual magnitude errors in these premaximum observation as they were mostly done by untrained observers.
Concerning the records after maximum, they are often single records and sometimes by untrained observers. Tycho Brahe's observations of the supernova of 1572 showed that the Danish astronomer achieved the maximum accuracy of the human eye and was able to distinguish changes in brightness at a few tenths of a magnitude. Therefore, we could assign 0.25 mag and even 0.2 mag to some of his observations. Johannes Kepler, the magnificient Imperial Mathematician who followed Tycho Brahe in ths court of Prague, would bring physics to a modern era, when the laws of motion of the planets discovered by him were explained by Isaac Newton. He took interest in the supernova SN 1604, but his contribution can not be compared with his explanation of the orbit of Mars. Kepler used glasses as he was shortsighted . He had difficulties in differentiating the brightnesses differing by 0.25 magnitudes or more. CS77 found the comment by Kepler in De Stella Nova that "the star it was seen with almost the same magnitude during the whole month of October". Kepler started to see the "nova" on Oct 17, but until Nov 1st it had an increase in magnitude by more than 0.3 mag. Kepler also wrote on Feb 6 "I left the observatory, not sure whether I had seen any trace of the star.
Therefore, it seems to have become too small to be seen even in this clear morning, if it has survived" (see CS77,p.199). The other records are from untrained astronomers. It would have benefitted the reconstruction of the light curve of SN 1604 that the observations by Fabricius had been preserved, as he was known to be an accurate astronomer. Baade (1943) was only able to recover some mention to these observations in Kepler's collected works.
Thus, in general, we judge that the error in the European observations after maximum can be of 0.5 mag.
-7 - The descriptions of the brightness of SN 1604 written by the Korean astronomers are simple and the colors that they gave at premaximum are at odds with those of the European astronomers. Thus, we assign 0.5 mag uncertainty to the values derived for the brightness, the same error bar as for the premaximum values by European observers.
From both the early and the total light curve, it can be excluded that Kepler SNIa were a subluminous SN 1991bg-like event. The European records have a late slope declining more slowly than a SN 1991bg-like SNIa. However, it does not look either as an overluminous SN 1991T-like one. The best agreement would be with something of the type of a "normal" SNIa (see Figures 1 and 2 ).
2.1. Early light curve up to 60 days past maximum SN Ia are not standard candles but calibrated ones. There is a well-known correlation between the brightness at peak of the light curve and its rate of decline. Phillips (1993) gave a first correlation in terms of a parameter ∆m 15 , which is the number of magnitudes of decline of the B light curve in 15 days after maximum brightness.  used it to calibrate the Calan Tololo SN Ia. This way to obtain the absolute magnitude of a SNIa in relation to the Hubble constant did also include a correction for the extinction suffered by the supernova due to dust, mostly in the host galaxy.
The early way to calibrate SNe Ia treated separately the correction from stretch (this one including the intrinsic color of a given SNIa of a particular stretch) and the extinction by dust. Later on, Tripp (1998) advocated for the use of two simultaneous determinations of the parameter of stretch and the one of color, the latter taking into account the intrinsic color of the SNIa and the extrinsic one due to dust.
-8 -In our present case, the extinction by dust in the Galaxy is very large and it is very well known. This is why we prefer to use the early version of stretch that did not require to fit a global color term, but to estimate the extinction. The excess E(B-V) is then estimated separately, for SN 1604.
Therefore, the data on SN 1604 are compared using the stretch factor s for the characterization of the rate of decline (Perlmutter et al. 1999;Goldhaber et al. 2001;Nobili et al. 2003). The stretch factor s method, used by the Supernova Cosmology Project, quantifies the decline rate of the supernova from data extending up to 60 days after maximum. In the absence of a mesurement of the brightness at maximum, the method allows to locate the event within the family of light curves of SNe Ia.
The best agreement of the light curve of SN 1604 is with a supernova of s ∼ 0.9 (s = 0.9 ± 0.13). In this sense, as in the case of SN 1572, we show a comparison in Figure   1 with the normal supernova SN 1996X, which has an s of 0.889. Also for comparison, we Comparing the historical records with a stretch s = 0.9 supernova template, we obtain a  SNIa.

Late light curve
If one compares the magnitudes attributed by Baade and those attributed by Clark and Stephenson (1977) along the post-maximum decline, one often finds that Baade (1943) substracts 0.2 magnitudes to what would have been the right magnitude assignment. So, the European magnitudes in CS77 are a bit different from those of Baade (1943), and brighter.
Examples of this are the records of April and August. When the recorded comparison says that the star is as bright as η Oph, which has a visual magnitude of 2.43, Baade assigns to the record 2.6. CS77 assign 2.40 in one ocassion (April 21), but in another one they judge the magnitude to be 2.25 (April 12). When the last written records say that the star is as bright as ξ Oph, which is 4.39 magnitudes in V, Baade (1943) rounds the number to 4.5, and Clark and Stephenson (1977) give 4.45. The two last records are similar in Baade (1943) and in CS77, with only a 0.1 magnitude difference in the assigned brightness of the supernova. Baade (1943) assigns to the record "fainter than ξ Oph", 5 and 4.8 in visual magnitude, whereas CS77 assign 4.95 and 4.7. Therefore, the disagreement is not significant. However it shows a lack of complete agreement and it suggests that we should assign an error of 0.5 magnitudes to the records.
CS77 located a few postmaximum data in the light curves reported by the Korean astronomers. They plot huge error bars for those records, which come from the mean of several observations in every case. These are the only points for which CS77 have reported error bars. We assign errors of 0.7 magnitudes to these data.
In Figure 2,  After 100 days, the rate of decline is 1.37 ± 0.12 V magnitudes in 100 days, according to Baade (1943). This also places the light curve decline amongs those of normal SNe Ia, which have decline rates of 1.35-1.5 magnitudes in 100 days (see declines for 1990N, SN 1999bu; for references, Ruiz-Lapuente 2004).

Kepler was neither a SNIa-CMS nor any other type of peculiar SNIa
SNe Ia that interact heavily with the circumstellar medium have been named SNe Ia-CMS.
They are charactherized by a narrow Hα line on top of an overluminous spectrum. They have much more luminous and flat declines than 91T-like SNe Ia (Silverman et al. 2013).
SNe Ia-CMS (only 0.1-1 % of all SNe Ia) were discovered by Hamuy et al (2003), in SN 2002ic, which suggested that this supernova could have arised from a binary system containing a C+O white dwarf plus a massive (3-7 M ⊙ ) AGB star, where the total mass loss in H can reach a few solar masses. Another well discussed SNIa-CMS is PTF11kx, observed by Dilday et al. (2012), who suggested that it came from a symbiotic nova progenitor. Soker et al. (2013) noted, however, that the mass around PTF11kx is too high to have been produced by a recurrent nova, and suggested a violent prompt merger of a white dwarf with the core of a massive AGB star. Katsuda et al. (2015) find that Kepler SN, unlike SNIa-CMS, should have a dense/knotty CMS located far away from the progenitor star. They discuss that the CMS knots were already ∼ 2 pc away from the progenitor star at the time of the SN explosion. They also -12 - Fig. 2.-Visual light curve of SN 1604 from the records collected by Baade (1943) and Clark and Stephenson (1977). The supernova is compared with the normal supernova SN 1996X, as well as with the overluminous SN 1991T and the subluminous SN 1991bg -13add as evidence that the interactions between the CMS and the blast wave started ≥ 200 yrs after the explosion, And the third piece of evidence is the difference between the historical light curve of Kepler and the light curves of SNIa-CMS.
In the paper of Katsuda et al.(2015), it is argued, from the amount of Fe found in the X-ray spectrum of the supernova, that it should have syhthesized around 1 M ⊙ of Ni. We

The distance to Kepler supernova
We aim now to estimate the distance to Kepler. We think that we have the elements to provide a fairly good estimate.

Summary and conclusions
The nature of SN 1604, the most recently observed Galactic SN, was an object of debate since its discovery, Johannes Kepler being its most famous observer and the most prominent figure in the ensuing disquisitions. Even when its SN nature was acknowledged, there were still discussions about its classification, either as Type I or a Type II SN. This point of debate was settled some 10 years ago, by X-ray observations of the remnant. In spite of being acknowledged as a Type Ia, thermonuclear SN, its further classification within the SN Ia family has remained unclear.
We have used the historical records on SN 1604, coming from European and Korean astronomers, to reconstruct the light curve of this SN Ia. That has been based on the combination of the attribution of magnitudes by Baade (1945) and by Clark & Stevenson (1977) to the ancient records. We assign a precision according to the information about the records.
The data have then been fitted with template light curves, parameterized by the stretch factor s, The best fit corresponds to a "normal" SN Ia, (s = 0.9 ± 0.13). The fit excludes both overluminous events like SN 1991T and subluminous ones like SN 1991bg.
The absolute magnitude of SN 1604 at maximum should have been M V max = −19.2 and the error is calculated according to the error in magnitude coming from the error in stretch and in the calibration linked with H 0 . It is of 0.2 magnitudes in V.
SN 1604 was heavily obscured. Therefore, the amount of extinction suffered plays an important role in the determination of its distance. Based on several coincident measurements, we have A V = 2.7 ± 0.1 mag.
-16 - We obtain a distance to SN 1604 of d = 5 ± 0.7 kpc, in agreement with recent estimates based on the proper motions of the optical filaments of the remnant of the SN, but discarding suggested distances of ∼ 6 kpc or more. That is very important for the direct search of a possible surviving companion to the SN.