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Determination of a temporally and spatially resolved Supernova rate from OB-stars within 5kpc

We spatially and temporally resolve the future Supernova (SN) rate in the Solar vicinity and the whole Galaxy by comparing observational parameters of massive stars with theoretical models for estimating age and mass and, hence, the remaining life-time until the SN explosion. Our SN rate derived in time and space for the future (few Myr) should be the same as in the last few Myr by assuming a constant rate. From BVRIJHK photometry, parallax, spectral type, and luminosity class we compile a Hertzsprung-Russell diagram (H-R D) for 25027 massive stars and derive extinction, and luminosity, then mass, age, and remaining life-time from evolutionary models. Within 600pc our sample of SN progenitors and, hence, SN prediction, is complete, and all future SN events of our sample stars take place in 8% of the area of the sky, whereas 90% of the events take place in 7% of the area of the sky. The current SN rate within 600pc is increased by a factor of 5-6 compared with the Galactic rate. For a distance of 5kpc our sample is incomplete, nevertheless 90% of those SN events take place in only 12% of the area of the projected sky. If the SN rate in the near future is the same as the recent past, there should be unknown young neutron stars concentrated in those areas. Our distribution can be used as input for constraints of gravitational waves detection and for neutron star searches.


Introduction
The search for gravitational wave (GW) events and pulsars using Einstein@home 1 can work more efficient with spatial limits. The spatially and temporally resolved future Supernova (SN) rate is assumed to be roughly constant over some Myrs, and hence can indicate promising regions for the detection of probable GW sources such as precessing neutron stars (NSs) or binary NSs. The probability to find young NSs, which might be precessing and radiating GWs due to ellipticity, is larger in areas with a local increased SN rate. These sources can be detected with GW detectors (such as adLIGO). All sky surveys like Aasi et al. (2013) could be reduced to smaller areas in the sky by using our results. Thus the sensitivity of GW searches could be increased significantly. 100 to 140 NSs younger than 4 Myr should be expected within 600 pc from population synthesis (Popov et al. 2005), but only 15 of them are known yet in the ATNF pulsar catalogue (Manchester et al. 2005). The Galactic core collapse SN (ccSN) rate is estimated to 2.5 +0.8 −0.4 events per century by counting SNe from Milky Way like galaxies (Tammann et al. 1994). The amount of 26 Al (Diehl et al. 2006) implies a rate of (1.9±1.1) ccSNe per century in our Galaxy. Grenier (2004) found 20 to 27 SNe per Myr for the Gould Belt (Gould 1879), a local star form-ing region within 600 pc (for an historical overview see Stothers & Frogel 1974), by studying observed star counts. This local current rate is 5 to 6 times higher than the Galactic average. A spatially and temporally resolved SN rate of 21±5 SNe per Myr within 600 pc was published by Hohle, Neuhäuser & Schutz (2010). They analysed the SN rate on the base of massive stars observed with both HIPPARCOS and 2MASS. Hohle et al. (2010) derive mass and age for SN progenitors by using different evolutionary models, and determine the remaining life-time. Their sample is complete for stars brighter than the limiting magnitude of V =8.0 mag (van Leeuwen 2007) for HIPPARCOS. Thus all B4V and earlier stars within a distance of 600 pc are included, assuming a mean interstellar extinction of a V =1 mag/kpc for the solar vicinity (Lynga 1982). In this work we enhance the analysis of the SN rate for more distant stars. We use additional and more recent databases to find more ccSN progenitors in the solar vicinity up to 5 kpc. Furthermore, while all spectral types in Hohle et al. (2010) are taken from the HIPPARCOS catalogue (Perryman et al. 1997) or SIMBAD, we also use more recent spectral classifications. Each step of the analysis is reconsidered and improved. Wolf-Rayet stars (WR) were not included in Hohle et al. (2010) but will be included in this work. For a better evaluation of the numbers we calculate the completeness of our sample to specify the areas in the sky which should be explored in more detail in the future.  Skiff (2012) Fig. 1 Calculating the optimal aperture from the distribution of the separation of catalogue stars towards a sample star. The catalogues are 2MASS, the new reduction of HIPPARCOS, ASCC-2.5, Tycho, the massive star survey by Sota et al. (2011) and the catalogue from Skiff (2013). The optimal aperture is the first local minimum and is found to be 3. ′′ 0 for HIPPARCOS and 2MASS, indicated by the dashed vertical line.

The sample
The base of the whole analysis is a set of potential SN progenitors (M > 8 M ⊙ ) that is queried for observational parameters. We select all ccSN progenitors regarding the spectral type classification (SpT): we cover all SpT for luminosity classes (LCs) I and II, all stars earlier than or equal to SpT B9 for LC III, and all known stars earlier than or equal to spectral type B4 with LC IV, V, or an unknown LC will be also included ( Table 1). The basic set of stars comes from a select by criteria query in SIMBAD (see Appendix A), consisting of 18 146 objects (as of 2013-03-04). We expand the sample from SIMBAD with the catalogues in Table 2 using the VizieR Online Database . There are 13 741 additional stars fulfilling our selection criteria from Table 1 plus 226 WR stars from van der Hucht (2001). Thus our sample expands to 32 113 stars. Some catalogues are including bright stars not belonging to our Galaxy. We avoid an extragalactic overpopulation in our sample by excluding 7 165 stars in the sky area of the Large and the Small Magellanic Cloud.
We use a cross correlation to re-identify stars in different catalogues. To avoid a misidentification of stars, we determine an optimal aperture from counting the spatial separation of the catalogue stars towards a sample star within a maximum aperture radius of 20 ′′ (Figure 1). Given the location of the minimum in the separation distribution we consider an optimal aperture of 3. ′′ 0 for 2MASS and HIPPAR-COS coordinates and use this result for all other catalogues. The star with the minimal spatial separation between sam- Table 2 Number of identified stars in different catalogues within a search aperture of 3. ′′ 0, the references are [1] Skrutskie et al. (2006), [2] Kharchenko & Roeser (2009) ple and catalogue coordinates within the optimal aperture is identified to be the correct counterpart. If identifiers like DM, HD or HIP number are available, we check those as well. The numbers of identified sample stars in different catalogues are listed in Table 2. The spatial distribution in galactic coordinates, of our whole sample stars is plotted in Figure 2.

Fig. 2
The spatial distribution of our sample stars in galactic coordinates created with SIMBAD and various VizieR catalogues (see section 2), the grey dots indicate stars in the sky area of the Large and Small Magellanic Cloud which we exclude from our sample. data from Lang (1992) 2 and for main sequence stars from Kenyon & Hartmann (1995). The temperature error is calculated from the given uncertainty in the SpT. If there is no given uncertainty we assume an error of the SpT by ±1 subclass. We interpolate the temperature between neighbouring grid points for a decimal SpT linearly. For spectral types without a LC (3 886 stars) we conservatively assume dwarf stars. If there is an uncertain LC (3 800 stars), we consider the class with the lower luminosity (e.g. II/III is set to III). In total we collect full spectral classification for 24 120 stars.

Photometry and Extinction
We use BVRIJHK photometry with Johnson BV from the HIPPARCOS and Tycho catalogues given in Kharchenko & Roeser (2009), BV from UCAC4 Zacharias et al. (2013), the Cousins JHK photometry from 2MASS, and BVRIJHK from SIMBAD. Having two different fluxes X and V the interstellar reddening A V due 2 taken from Schmidt-Kaler (1982) to interstellar extinction is calculated with the measured colour (X − V ) m and the modelled colour (X − V ) 0 according to: We  Bessell et al. (1998). The model depends on log g and temperature, and hence on spectral classification. As an example Figure 3 shows the A V calculated from (J-K) and (B-V) as well as the number density of the values to emphasize the most frequent data points. The results of the error weighted linear fits are listed in Table 4. The final A V is calculated as an error weighted mean using all the values from the different colours mentioned above. Since the constants AX AV published by Cardelli et al. (1989), Rieke & Lebofsky (1985) and Savage & Mathis (1979) are slightly different, the mean of these values is used.
WR stars have typically very broad emission lines, so we use available Smith narrowband photometry and extinction A v given by van der Hucht (2001) and calculate A V = 0.9149 · A v as recommended in their paper.
We distinguish between an excess due to circumstellar dust and interstellar reddening by using infrared colourcolour diagrams (e.g. Figure 4). There are 679 stars with an infrared excess due to circumstellar dust of more than 3σ (colour error) in the JHK colour-colour diagram, which we take into account and correct for. Thus we avoid nonphysical values of A V .

Multiplicity
Unresolved multiple stars would appear more luminous than resolved stars, hence the measured flux of unresolved multiple systems needs to be distributed among the components. Spectroscopic binaries are identified with catalogues from

Fig. 3
Comparison of the derived A V using the colours B-V and J-K with 1σ error bars. The one to one relation is indicated with a dashed line, the black line indicates the error weighted linear fit, and the coloured region shows the number density of stars from low (blue) to high (red). See Table 4 for the results of the other colour combinations.
(1999), Dommanget & Nys (2002), Mason et al. (2010), Docobo & Andrade (2006), Surkova & Svechnikov (2004) and the SIMBAD object type (Table 5). We assume an identical interstellar extinction for unresolved members of a particular multiple and correct the apparent measured magnitudes for the components with: X sys,m indicates the measured magnitude of the system in the band X and V n,0 is the magnitude in the V-band of the nth component. Thus we take into account the spectral classification and the measured magnitudes of the resolved components.
In our whole sample there are 4 332 stars (17% of our whole set) known to be members of 2 131 multiple systems. This number is too small given the fact that 60-80% of the massive stars are expected to be components of a multiple system (Zinnecker & Yorke 2007). For the visually resolved multiple systems we list all resolved components with spectral classifications fulfilling our criteria from Table 1 as additional entries in Table 3.
In total we count 24 948 stars in Table 3 plus 79 additional visual resolved massive companions. There are 925 unresolved multiples with additional known components not fulfilling our selection criteria, and 1 197 unresolved multiples where nothing else (except their existence) is known about the companions, which we assume to be binaries with the same spectral type. Table 4 The results of the error weighted fits A V 1 = m · A V 2 + n, where A V 1 and A V 2 are interstellar extinction values derived from the named colours,σ AV 1,2 is the median of the respective error in mag, # is the number of stars with an error smaller than 3σ AV 1,2 that are used for the fit. All results are consistent with a one-to-one relation and an offset of n = 0.

Distance
The distance is calculated from the trigonometric parallax π using the HIPPARCOS data of the recent reduction by van Leeuwen (2007). If there is no HIPPARCOS value available for a star, the Tycho data or the catalogue from Kharchenko & Roeser (2009) is used. The trigonometric parallax is available for 18 300 sample stars. Among them, we count 11 862 stars with π ≥ 0.2 mas, 10 102 stars with  Table 6 Number of stars with measured parallax π and transformed parallax π t higher than its error σ. Transformed parallax π t compared to the measured parallax π using the transformation from Smith & Eichhorn (1996) for 6 407 stars with |π t − π| ≤ 1 mas. The solid line indicates the one-to-one relation. The interval up to 10 mas is shown in the lower right.
a value higher than its error | σπ π | ≤ 1, and 6 191 with a negative parallax. All parallaxes π are transformed to the expectation value π t using Eq. 21 from Smith & Eichhorn (1996). The influence of this transformation on parallaxes with large errors is seen in Table 6. There would be an overpopulation of 7 945 stars with significantly underestimated distances resulting in inconsistent luminosities compared to their SpT and LC.
Since negative parallaxes are converted to small positive values within their errorbars, we flag those values as uncertain to exclude them from further calculations. We use the transformation to utilize those parallaxes which are comparable to their expectation value and select 6 407 stars with |π t − π| ≤ 1 mas ( Figure 5). Thus we avoid uncertain par- single stars unresolved multiple stars resolved multiple stars ZAMS

Fig. 6
Our derived H-R D: the red dashed line marks the zero age main sequence (ZAMS), grey dots indicate resolved stars in a multiple system, black circles denote unresolved multiples, and black dots stand for single stars, the mean errorbar is indicated by the black cross on the left side.
allaxes with large errors but include measurements accurate down to sub-mas. The results of the remaining part of the paper are calculated with and without an applied transformation to study systematic uncertainties that may arise from Eq. 21 by Smith & Eichhorn (1996). All values are consistent within their errorbars (see Appendix B).

Luminosity
The bolometric luminosity in solar units is with the distance d in pc, the bolometric correction in the Vband BC V , the apparent magnitude in the V-band m V , and the interstellar extinction in the V-band A V . The BC V from Bessell et al. (1998) is calibrated to M bol⊙ = 4.74 mag and is consistent with the apparent magnitude of V ⊙ = −26.76 mag as mentioned in their paper. This test is suggested by Torres (2010), because the zero point of the BC V is arbitrary, but the bolometric magnitude of the sun is not.

Derived stellar parameters: mass, age, and life-time
We estimate mass and age by comparing our calculated bolometric luminosities and temperatures with the theoretical H-R D from Bertelli et al. (1994), Schaller et al. (1992), and Claret (2004) (2004) and Schaller et al. (1992). The theoretical H-R D from Bertelli et al. (1994), Schaller et al. (1992), and Claret (2004) are applied for stars with M < 35 M ⊙ . For WR stars we only use the model from Meynet & Maeder (2003). There are 8 143 stars below the zero-age-main-sequence (ZAMS) due to large uncertainties of the distance, which are conservatively assumed to have at least a luminosity consistent with the ZAMS (as seen in Figure 6). So far we cannot distinguish between stars with underestimated distances and misidentified subdwarfs that also lie below the ZAMS, thus we flag those stars. From our 6 407 stars from the subsample with sufficiently measured distances (subsection 3.4), we correct 2 663 stars to be on the ZAMS. Those stars probably have erroneous distances which are not consistent to be within 1 kpc, however they should have distances smaller than 5 kpc due to the completeness of the catalogues for the parallax and the apparent magnitudes.
Since the spectroscopic binary catalogues from Table 5 list dynamical masses, we use these instead of model dependent masses if available. For main sequence stars those dynamical masses are consistent with our masses estimated from the H-R D within their 1 σ errorbars (Docobo & Andrade 2013).
Massive multiple systems where at least two components have masses above 8 M ⊙ are important for the study of the evolution of compact binary systems. The spatial distribution of those massive binaries is shown in Figure 7 (listed in Table C1). In the near future, we will also study the binary evolution and interaction in those systems.
The empirical mass luminosity relation L ∼ M β yields β = 3.93 ± 0.78 for main sequence stars from our sample and is plotted in Figure 8. That error weighted result is consistent with the values from Hilditch (2001)  for stars with a mass less than 10 M ⊙ and β = 3.6 for stars with a higher mass, from Andersen (1991) with β = 3.84, and with β = 3.66 ± 0.12 from Hohle et al. (2010).
As another consistency check we calculate the mass function N ∼ M Γ for massive stars by using an error weighted fit yielding Γ = −3.1 ± 0.5 (see Figure 9), that is in good agreement with Γ = −2.7 ± 0.7 from the initial mass function by Kroupa et al. (1993).
The H-and He-burning phases specify the life-time of a star due to the long duration (Myr) while other burning processes like C-burning lasts a few kyr only. The life-time Table 7 List of L bol , mass, age, remaining life-time τ r , and number N of known additional components of the first ten SN progenitors in Table 3 of a star can be calculated from its mass by using models of Kodama (1997) and Maeder & Meynet (1989). The remaining life-time τ r of a star is the difference between the mean of the expected modelled life-time τ m and the age τ age .
Since τ m is not well calibrated for the theoretical H-R D, there are 9 563 stars in our sample with a negative remaining life-time. All stars with a negative remaining life-time are randomly set to plausible life-times according to the distribution of positive life-times of their respective mass bin. Hence, the remaining life-time distribution of every mass bin itself is not changed by this correction. The corrected life-times are marked with a leading colon in Table 7. If there is no positive life-time distribution for a mass bin, we flag those life-times with a question mark. We count 2 643 stars with a corrected remaining life-time from the subsample of 6 407 stars with sufficient distances (subsection 3.4).
The calculated L bol , the mass, the age, the remaining life-time τ r , and the number N of known additional components are listed in Table 7.

Completeness
The substantial completeness of our sample is conservatively calculated in Figure 10 by dividing the cumulative number of stars at a certain distance by the value from a fitted power-law growth N ∼ d Φ . The scale height of the spiral arm population is ≈ 120 pc and the young disc population has ≈ 200 pc in Mihalas & Binney (1981). Our sample corresponds to a cubic growth (Φ =3) for distances from 1 to 170 pc as expected for increasing the observed spheric volume and counting the star numbers. Thus, the scale height of our stars is 170 pc. The scale height of the Galactic disc yields 260 pc (Harding et al. 2001 dense populated region up to the scale height. Corresponding to an increase of the observed area within the Galactic disc a quadratic growth (Φ =2) fits for distances from 260 pc to 500 pc. After 500 pc the incompleteness of our sample increases, hence we cannot longer fit a powerlaw growth to the cumulative number. Dividing the cumulative number by the value from the continued quadratic powerlaw for distances higher than 500 pc our set of stars is 85 % complete within 600 pc, 45 % within 1 kpc, 6 % within 3 kpc, and 2 % within 5 kpc. Thus, for distances larger than 1 kpc our sample is highly incomplete.

Discussion on Supernova progenitor distribution
If the current local SN rate is roughly constant for some 10 to 20 Myr, then all ccSN progenitors with a mass higher than 8 M ⊙ and a remaining life-time shorter than 10 Myr are indicators for regions with young neutron stars and potential GW sources. We can discuss our observed set of stars only within the next 10 Myr because afterwards new star formation must be taken into account e.g. by performing a population synthesis.  Fig. 12 The spatial distribution of regions with a local increased SN rate within 1 kpc for the next 10 Myr; all SN progenitors (black dots) are distributed among 12.2 % area of the whole sky and 90 % of the SN events are in 9.5 % of the whole sky. The bin size is 7 • ×7 • .
in Figure 11. The SN rate is increased for OB clusters like Carina, Orion, Vela, Scorpius, Centaurus, Cygnus, Cepheus, and Perseus, which all belong to the Gould Belt. All SN progenitors are distributed among 8.6 % area of the whole sky and 90 % of the progenitors are within 7.2 % area of the whole sky. Within 1 kpc (Figure 12) all SN events will occur in 12.2 % of the whole sky and 90 % of the SNe are in 9.5 % of the whole sky.
The regions with a locally increased SN rate within 5 kpc from the sun are plotted in Figure 13. All SN progenitors are distributed among 21.0 % area of the whole sky and 90 % of the SN events will occur in 12.2 % area of the whole sky.
While our sample is incomplete outside ≈1 kpc, the missing SN progenitors are possibly mostly in the same areas as the known ones. These results can be used e.g. for reducing the parameter space of Einstein@home, because GW sources or young neutron stars should be concentrated  Fig. 13 The spatial distribution of regions with local increased SN rate within 5 kpc for the next 10 Myr; all SN events (black dots) in 21.0% of the whole sky and 90 % SNe in 12.1 % of the whole sky. The bin size is 7 • ×7 • .
in our marked regions, even when taking into account high kick velocities (Palomba 2005). Thus a blind search for these sources could be reduced to our regions. The temporally resolved ccSN rate for the next 10 Myr within 600 pc yields 17.0 +4.5 −3.6 ccSNe/Myr and is shown in Figure 14. Our result can be compared to the range from 20 to 27 ccSNe per Myr for the Gould Belt from Grenier (2004) and also with 21 ± 5 ccSNe/Myr from Hohle et al. (2010). The value between 2 and 3 Myr, seen as a peak in Hohle et al. (2010), is now consistent with a constant rate. Within 2 Myr the SN rate seems to be slightly below the average.
The true SN rate can be larger due to SNe of type Ia, (≈15-25 % of all SNe) plus more unknown multiple massive companions. For these stars we take into account the probability of putative 8 M ⊙ companions with the same age as the host star by using the binary fraction from Oudmaijer & Parr (2010). This slight increase is illustrated by the grey dots in Figure 14.
Many neutron stars are expected to be nearby the Galactic Center, but there is no major contribution to the spatial distribution in that direction due to high uncertainties in the parallax and high extinction values. The accurate photometric and astrometric results of the Gaia mission (de Bruijne 2012) could improve the completeness and the precision of our work significantly.
We consider stars with a mass higher than 8 M ⊙ as SN progenitors and with a mass higher than 30 M ⊙ as probable black hole (BH) progenitors (Woosley et al. 2002). In Table 8 we give the derived ccSN rate, the numbers of SN progenitors, and BH progenitors within a certain distance. We calculate the Galactic ccSN rate by extrapolating the local ccSN rate of our observed volume to the whole Galaxy as described in Reed (2005) using his Equations (5) and (16). We use as distance to the Galactic Center 8.5 kpc, a thick disc scale height of 0.9 kpc, and a scale length of 3.6 kpc (Jurić et al. 2008). The observed volume is then cal-  Grenier (2004). The increase of the SN rate due to putative massive companions of possible multiple stars is shown by grey dots. culated within the disc using the distances given in Table 8. Comparing the ccSN rate in the Solar vicinity with the Galactic ccSN rate of 2.5 SNe per century (Tammann et al. 1994) suggests that the current ccSN rate within 600 pc and 1 kpc is increased due to the Gould Belt as found by Grenier (2004) and Popov et al. (2005) by about a factor of 5-6.

Conclusions
The sample contains one order of magnitude more stars than Hohle et al. (2010), is more complete, and includes more recent input parameters. Our consistency checks for the mass luminosity relation, the mass function, and the completeness confirmed known relations and published values from different authors. We found regions with a locally increased ccSN rate implying a higher probability of the presence of young neutron stars. The blind search for young nearby neutron stars and GW sources can work more efficient, if the parameter space of an all sky survey can be reduced to our predicted areas. Given the results of this work a blind search for GW sources and young neutron stars within 600 pc could be decreased to only 9 % area of the whole sky. Regarding our highly incomplete sample within 5 kpc, the all sky survey could be restricted to 21 % area of the whole sky. The discovery of new radio quiet neutron stars, like in Pires et al. (2009) in Carina, which shows an enhanced probability in our maps, is more probable in these special regions than in a blind search. Table 8 The number of SN progenitors with M > 8 M ⊙ and BH progenitors with M > 30 M ⊙ within a specific distance. The lower number is obtained by subtracting the 1σ error from the masses and the upper value is obtained by adding the 1σ error to the masses. The ccSN rate is given for those progenitors which should explode within the next 10 Myr, the errors are 3σ. In this table we give the calculated ccSN rate for our Galaxy by extrapolating from the local SN rate (given in that row) to the whole Galaxy, with a distance to the Galactic Center of 8.5 kpc, a thick disc scale height of 0.9 kpc, and a scale length of 3.6 kpc (Jurić et al. 2008). In the last column we give the completeness from Figure 10. in Equation A1 filters out 410 stars without listed coordinates. We expand the sample from SIMBAD by querying catalogues containing spectral classifications in the order of descending priority: Sota et al. (2011), CSSC by Skiff (2013), ASCC-2.5 by Kharchenko & Roeser (2009), HIP-PARCOS by Perryman et al. (1997). The VizieR Online Database (Ochsenbein et al. 2000) was used to download these catalogues.

B Calculations and Results without transformed Parallax
In this section we give all results derived without applying Eq. (21) from Smith & Eichhorn (1996). The values are consistent within their errorbars compared to the values in the main part of the paper. The calculated H-R D using spectral classification and Equation 3 is seen in Figure B1. There are in total 4 504 stars below the zero-age-main-sequence (ZAMS) due to large uncertainties of the distance. Those stars are flagged and assumed to have at least a luminosity consistent with the ZAMS. From our 6 407 stars with sufficiently measured distances (subsection 3.4), 518 stars are below the ZAMS.
The error-weighted fit for the mass luminosity relation of main sequence stars ( Figure B2) yields β = 4.14 ± 0.92 and is consistent with β =4.0 for stars with M ≤ 10 M ⊙ and β =3.6 for stars with a higher mass from Hilditch (2001)  The spatial distribution of 130 binaries, where both components have M > 8 M ⊙ is plotted in Figure B4. The regions with a locally increased SN rate within a range of up to 600 pc are seen in Figure B5. All SN events will occur in 8.3 % area of the whole sky and 90 % SN events in 7.1 % area of the whole sky. The distribution within 1 kpc yields that all SN progenitors are in 12.0 % of the whole sky and 90 % SN progenitors are in 9.5 % of the whole sky ( Figure B6). Within 5 kpc ( Figure B7) all SN progenitors are distributed among 20.3% area of the whole sky and 90 % SNe are in 12.1 % area of the whole sky. The temporally resolved SN rate of 19.1 +4.2 −5.4 ( Figure B8) can be compared to the apparent lower limit of 20..27 ccSNe/Myr for the Gould Belt from Grenier (2004) Fig. B7 The spatial distribution of areas with local increased SN rate within 5 kpc; all SN events in 20.3% area of the whole sky and 90 % SNe in 12.1 % area of the whole sky. The bin size is 7 • ×7 • .

Table B2
The number of ccSN progenitors with M > 8 M ⊙ and BH progenitors with M > 30 M ⊙ within a specific distance. The lower number is obtained by subtracting the 1σ error from the masses and the upper value is obtained by adding the 1σ error to the masses. The ccSN rate is given for those progenitors which should explode within the next 10 Myr, the errors are 3σ. In this table we give the calculated ccSN rate for our Galaxy by extrapolating from the local ccSN rate (given in that row) to the whole Galaxy, with a distance to the Galactic center of 8.5 kpc, a thick disc scale height of 0.9 kpc, and a scale length of 3.6 kpc (Jurić et al. 2008). In the last column we give the completeness from Figure 10.   Grenier (2004). The increase of the ccSN rate due to putative massive companions of possible multiple stars is shown by grey dots. Table C2 List of those 6 SN progenitors within 3 kpc which might be also BH progenitors (see Table 8): SIM-BAD identifier, distance, and spectral type from Table 3 Table C1 List of those 35 Binaries a with at least two massive components, which were also studied in Hohle et al. (2010), with updated parameters: SIMBAD identifier and distance from B2.5IV-VN-B2.5IV-V