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Magnetic stars, 2004, 259-267

Mass distribution of massive magnetic white dwarf stars
Nalezyty M.1 , Madej J.
1 2

2

Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warsaw, Poland N. Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland

Abstract. We present the catalog of 112 massive isolated white dwarfs, b oth magnetic and nonmagnetic, with masses M 0.8M . Mass determinations and other parameters of the white dwarfs were taken from the literature available. For each star we present averaged values of mass, effective temp erature, logarithm of surface gravity log g , radius, distance, and the surface magnetic field for magnetic white dwarfs. Mass distribution of massive magnetic white dwarfs is flat, whereas nonmagnetic WDs exhibit steep er mass distribution towards the highest masses. We note that all four most massive stars with masses M 1.3M are magnetic white dwarfs. We also conclude that the secondary maximum at 1.04M , clearly seen at the mass distribution of all white dwarfs from our sample, is caused exclusively by nonmagnetic white dwarfs. Key words: catalogs ­ stars: white dwarfs

1

Intro duction

Masses of white dwarf stars are always smaller than the Chandrasekhar mass, which is equal to 1.44 solar masses in the case of hydrogen, non-rotating ob jects. It is well known that the mass distribution of isolated white dwarfs exhibits a distinct peak at about 0.6M (Weidemann 1990), with a substantial number of known ob jects with higher masses. Exact values of the peak mass are slightly different in particular papers, which presented various homogeneous samples of isolated white dwarfs. Bergeron et al. (1992) have analyzed a sample of 129 DA white dwarfs, and determined their masses by means of fitting hydrogen Balmer line profiles. They obtained a value of 0.562M for the peak mass. Liebert & Bergeron (1995) analyzed 200 white dwarfs from the Palomar Green survey (Green et al. 1986), with a peak mass of 0.56M . Most recently Marsh et al. (1997a,b) have performed determination of masses (and also other stellar parameters) for an extensive set of white dwarfs selected from the ROSAT all-sky survey in the extreme ultraviolet (EUV). They obtained a peak mass value 0.55M . Other values of the peak mass were determined as 0.603M (Weidemann & Koester 1984), 0.571M (McMahan 1989), and 0.570M (Finley et al. 1997). The shape of the mass distribution exhibits also a distinct tail towards higher masses. This tail is not satisfactorily reproduced in most of the papers. Nor did the above surveys reach much higher masses, and were only sparsely populated by white dwarfs > 1M . Marsh et al. (1997a,b) have distinguished between populations of normal ( 0.6M ) and massive ( 1.0M ) white dwarf stars. The latter consists of 13 white dwarfs only. Such a small sample of massive white dwarfs in their paper did not allow investigation of any details of the mass distribution in that region. In spite of that, Marsh et al. (1997a,b) suggested that the massive (M 0.8M ) white dwarf stars form the second population, clearly differing from the main population with a mass peak at about 0.6M , which probably were formed by coalescence of normal white dwarfs in a close binary system. Extensive determinations of WD mass distribution were also presented in recent papers by Vennes et al. (1997a,b, 1998), and Vennes (1999), which were based on the Extreme Ultraviolet Explorer (EUVE) observations.
c Sp ecial Astrophysical Observatory of the Russian AS, 2004


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2

The catalog

We prepared the catalog and the mass distribution of massive white dwarfs with masses M 0.8M . Our research is based on mass determinations available in the literature. We follow the opinion that investigation of mass distribution of white dwarfs on the massive branch can put significant constraints on both early and late stages of stellar evolution, including star forming stages in the Galaxy disk. The limiting mass 0.8M has been chosen arbitrarily. Masses presented in our catalog represent a rather inhomogeneous sample. We disregard differences between particular methods of mass determination1 , since we intended to collect as many massive white dwarf stars as possible. In this way we attempt to minimize uncertainties and random fluctuations caused by a very small number of massive stars available in previous investigations. The Massive White Dwarf Catalog (Nalezyty & Madej 2004) consists of 112 white dwarf stars, both magnetic and nonmagnetic WDs. A shortened version of the catalog is presented in Table 1. The full catalog of individual published measurements is available on the Internet at the address: http://www.astrouw.edu.pl/nalezyty/mwd/ . In Table 1 data on each star were compressed to a single row. Columns list the following data: WD designation by its equatorial coordinates (in most cases corresponding to the designations in the McCook & Sion (1999) white dwarfs catalog), name of the star, pairs of the Teff , log g , mass M /M , and their errors. The nineth and following columns give: radius R in kilometers, mean surface magnetic field Bs , polar field Bp , distance d in kiloparsecs, remarks, and reference list. In most cases stellar parameters were independently determined by several authors. Values of T eff , log g , M /M , and the remaining parameters presented in Table 1 are arithmetic averages of individual data. Errors are just formal errors of the above averages. In this way we could neglect error determinations given in individual papers. Parameters of white dwarfs determined in a single paper have no error estimates in Table 1. It should be stressed here that white dwarfs in interacting binaries (as, for example, cataclysmic variables) were not included in our catalog.

3
3.1

Massive magnetic vs. nonmagnetic stars
Distribution of masses

An essential result of our catalog is the mass distribution of massive white dwarfs, both for ob jects with a magnetic field and for nonmagnetic ones, i.e. without any magnetic field or with an existing magnetic field, but not yet discovered. Our catalog consists of 25 magnetic white dwarfs, and 87 nonmagnetic white dwarf stars. It is interesting to investigate the differences between mass distributions of both magnetic and nonmagnetic white dwarfs in our sample. We display our mass distributions in Figs. 1­2. Figure 1 presents the mass distribution of 25 isolated magnetic white dwarfs, with masses taken from our catalog. When constructing this histogram and the histograms in Figs. 2­4, we arbitrarily assumed that stars with masses located exactly at the edges between bins are attributed to the bin with stars of higher masses. I.e. if a star has its mass equal to 1.0M , then it falls into the 1.0 - 1.05M bin. The histogram consists of bins with a 0.05M width, and the Y-axis indicates the absolute number of white dwarfs. The mass distribution of massive magnetic white dwarfs seems to be flat and does not exhibit any particular features, except for the absence of stars with masses in the range 1.15 - 1.20M (Fig. 1). However, due to the very small number of stars in each bin, typically 1 ­ 4 stars, this gap is most likely statistically insignificant. Probability that this gap is accidental equals to 0.09. On the contrary, the mass distribution of nonmagnetic white dwarfs is qualitatively different from the distribution of magnetic WDs in that it shows a steeper decrease towards the highest masses. In particular, we did not find any nonmagnetic white dwarf with mass higher than 1.30M . The only stars (4 stars) with such extreme masses are known as magnetic white dwarfs and are shown in Fig. 1. Moreover, the mass
1 Masses of isolated white dwarfs are usually determined with help of sp ectral analysis. Observed visual sp ectra can b e fitted with theoretical sp ectra to determine effective temp eratures T eff and surface gravities log g for some assumed chemical comp osition, mostly pure hydrogen. Classical pap er by Shipman (1979) explained the metho d of radius R and mass M determination from known values of Teff , log g , distance d, and visual magnitude mV , based on some reasonable grid of synthetic sp ectra. Nowadays there exists three principal metho ds of mass and radius determination of isolated white dwarfs, which are used dep ending on the exact set of available observational parameters. They yield also estimates of the gravitational redshift (cf. discussion in Schmidt 1997). Other techniques of mass determination result from orbital solutions in isolated binaries containing a white dwarf (Sirius B, Pro cyon B, for instance). The review of various metho ds of mass determination has b een given by Bergeron et al. (1992), cf. also Ko ester (2002).


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Table 1: Catalog of massive white dwarfs
WD 0000­345 0003+436J 0008+330 0009+501 0022+274 0033+016 0041+092 0046+051 0115+159 0136+251 0146+072 0235­125 0239+500J 0317­853 0346­011 0347+171 0349+247 0352+049 0406+169 HD27483 0443­037J 0518­105 0531­022 0548­001 0557­165J 0630­050 0633+200J 0642­166 0644+025 0653­564 0654+027 0659­063 0701­587 0729­384 0730+487 0743­391J 0816+376 0823­253 0827+328 0836+197 0836+199 0853+163 0856+331 0912+536 0913+442 0916­197J 0930+294 0943+472 0945+245.1 0945+245.2 0946+485 0946+534 0949+494 0957+854J 1015+014 1017+366 1024­303J 1031+234 1036­204 1038+633 1052+273 1055­072 1102+748 1127­311.1 1134+300 name GR406 RE0003+433 HS0008+3302 GR381 LP349­013 EG004 BD+08o 102 EG005 EG009 PG0136+251 HS0146+0723 PHL 1400 EUVE J0239+500 EUVE J0317­855 GD 50 V471 Tau EG025 KUV03520+0500 EG029 T
eff Teff

log g 9.01 8.35 8.66 8.50 8.40 8.38 9.01 8.27 8.49 8.517 9.19 9.12 8.40 8.69 8.71 8.30 8.5 8.946 8.67 8.587 8.32 8.88 8.32 8.398 8.61 8.66 8.88 8.51 8.71 8.562 8.5 8.49 8.66 9.02 8.39 8.45 8.34 8.84 8.28 8.24 9.12 8.38 8.75 8.5 8.5 8.69 8.45 8.39 8.32 8.95

log

g M /M 0.92 1.21 0.83 0.89 0.862 1.02 0.90 0.83 0.82 1.21 0.80 0.95 0.96 1.34 1.25 0.90 1.046 1.05 0.806 0.95 1.25 1.04 1.00 0.81 1.15 0.81 0.947 1.02 1.01 1.15 0.91 1.04 0.944 0.87 0.90 1.04 0.86 1.21 0.85 0.916 0.864 0.83 1.11 0.87 0.826 1.29 0.84 1.07 0.91 0.99 1.04 0.87 0.86 0.83 1.03 0.89 1.13 1.11 1.34 0.85 0.814 0.85 0.83 1.13 0.87

M

/M

R 3907 6960

B

s

B

p

d 101 85

Rem. References 5 1a, 1b, 2, 3, 4 14 m 17 b 8 6 b 27, 28 6 6 m 1a, 1b, 2, 3, 4, 18 14 1a, 1b, 2, 3, 12 2, 3 mb c 4, 5, 17, 22, 23, 24, 25 1a, 1b, 2, 4, 7, 12, 13 bc 1a, 1b, 29, 30, 31 7, 9, 11, 19, 32 4, 14 8, 9, 11, 16 bt 27 2, 3, 4 b 1a, 1b, 2, 3, 12 2, 3 m 5, 6 4 1a, 1b, 2, 3 3 b 1a, 1b, 15, 26 6 2, 4 6 6 13 bt 27, 33 7 2 m 5 m 4, 34 6 8, 9, 16 9 m 5 b 6 m 5, 6 bp 6, 11 b 2, 4 6 14 b 35 mb 5, 17, 35 14 6 14 2, 12 m 5 m 5, 37 b 1a, 1b, 3, 4 m 5 m 5 7 7, 13 6 7 mb 5 3, 7, 15 m

7000 45107 10300 6400 25000 10700 28960 6770 9800 39465 25000 32018 34211 43210 41743 34060 32180 36900 15190 22000 EUVE J0443­037 68740 RE0521­102 32727 EUVE J0534­022 29867 EG248 6400 1RXSJ0557.0­1635 56820 RE0632­050 43029 0630+200 75792 Sirius B 24700 GR484 7410 EUVE J0653­564 35200 EG181 9450 LHS1892 6520 BPM18398 15701 y Pup 43200 GD 86 15510 EUVE J0743­391 40200 GD 90 11000 1RXSJ0823.6­2525 43200 EG249 7270 LB 5893 21620 EG060 14060 GR904 2000 EG182 10390 EG250 7580 EG064 8620 EUVE J0916­197 56400 GR324 8330 HS0943+4724 16000 LB11146A 14500 LB11146B 16000 HS0946+4848 11700 EG251 8760 HS0949+4935 15000 EUVE J0957+854 51636 PG1015+015 14000 GD 116 16000 RE1024­302 35710 TON 527 25000 GR535 7500 PG1038+634 24800 GD 125 23064 EG074 7420 GD 466 19800 ESO439­162 5400 GD 140 21470

70 0.06 70 5440 6180 6620 6740 3830 7520 6170 6130 2408 3520 6240 5081 5280 7300 6300 3970 5380 5760 7040 4490 7790 7090 5670 5420 4490 6110 5190 5861 6100 6220 5500 3910 6780 6550 7240 4610 7230 7760 3600 6820 5000 6200 6100 5300 6400 6800 7470 4520 500 150 0.047 6780 7031 6550 6850 67 0.03 6310 15.3 12.2 29 32.9 55 4.3 15.4 80 210 66 96 505 395 29 47 106 53.2 46 144 99 101 11.1 309 2.64 18.5 107 38.5 12.3 172 147 8 3 105 22.3 174 20.5 10.3 28.9 164 32.1 120 40 40 80 23.0 190 139 64

1362

0.15

50 294 252 389 3290 736 580 320 500 3600 323 133 100 686 100

0.04 0.05 0.043 0.30 0.04 0.14 0.05 0.15 0.174 0.02 0.054 0.13 0.04

0.03 0.03 0.02 0.01 0.03 0.07 0.012 0.08 0.013 0.04 0.01 0.02 0.03 0.07 0.01 0.01

8

200

0.04 0.01 0.01 0.007 0.021 0.12 0.093 0.02

310

3 70

420 130

0.05 0.2

0.09

375 670

325 520

0.06 0.15

0.02 0.06

85 56

314

8.39 8.340 0.071 8.42 8.37 8.46 0.02

220


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Table 1: Catalog of massive white dwarfs ­ continued
WD 1136­285 1215+323 1236­495 1241+482 1309+853 1334­160 1350­090 1440+750J 1444­174 1446+286 1501+664 1531­022 1535­774J 1543­366 1609+135 1609+631 1625+093 1642+413 1658+440 1705+030 1711+667J 1725+586 1727­360 1740­706 1743­521 1745+607J 1748+708 1814+248 1829+547 1900+705 2010+310 2020­425 2039­682 2043­635 2055+164 2107­216 2126+191 2157+815 2220+133 2246+223 2251­070 2257­073 2303+465 2312­024 2348­444J 2359­434 Hya name ESO439­026 EG089 LTT 4816 HS1241+4821 GR436 EG101 LP 907­037 HS1440+7518 LHS 378 TON 214 H 1504+65 GD 185 EUVE J1535­774 RE1546­364 EG117 PG1609+631 GR327 RE J1643+411 EUVE J1659+440 GR494 RE1711+664 RE J1726+583 EUVE J1727­360 RE1746­703 BPM25114 HS1745+6043 GR372 G183­035 GR374 Grw+70o 8247 GD 229 REJ2024­42 EG140 BPM13537 EUVE J2055+1627 GR581 IK Peg HS2157+8153 PG2220+134 EG155 GR453 BD­07o 5906B PSR B2303+46 GR554 ESO292­43 EG165 HR3665 T
eff Teff

log g 9.02 8.68 8.70 8.54 8.32 8.71 8.37 8.327 8.0 8.39 9.12 8.875 8.75 8.408 8.44 8.376 9.36 8.35 8.957 8.32 9.04 8.95 8.68 8.36 8.50 8.58

log

g M /M 1.19 1.02 1.03 0.95 0.83 0.811 0.98 1.04 0.81 0.815 0.86 0.84 1.29 1.168 1.07 0.893 0.88 0.858 1.32 0.80 1.191 0.869 1.21 1.16 1.34 1.05 0.98 0.83 1.02 1.09 1.28 0.911 0.872 0.855 0.85 0.85 1.13 1.05 1.10 0.97 0.82 0.92 1.1 0.84 1.04 0.956 0.83

M

/M

R 3880 5320 5250 6100

B

s

Bp d 40.8 31.1 16.4 90

Rem. References 6 6 6, 10, 13 14 5 7, 11 5 2, 4, 12, 17 6 3, 7 38 7 2, 4 3 6 3 6 3, 12 2, 4, 5, 12, 17, 18 6 3, 12 1a, 1b, 3, 12 4 1a, 1b, 3, 4, 39 5 14 5, 6 5 5, 6 5, 6, 36 5 1a, 1b, 3 13 3 4, 40 6 27, 28, 41 14 14 6 6 28 42 6 6 13 27

4490 7100 12210 14800 5600 18790 9500 38260 4960 22839 170000 18870 54800 45208 9080 31033 6870 27677 30410 7050 47556 55100 32600 47690 20000 35600 6550 7000 6640 13540 23000 29028 16065 25971 38400 5830 34320 10700 22600 10330 4580 37517 45000 6840 5400 8715 28000

340 210 1680 102 3200

0.04

0.02 0.010 0.03 0.006 0.03

15 7180 5470 6770 7143 10700 6740 3580 4546 5030 6806 6510 6944 2780 6870 4185 7410 3830 4270 5400 6850 6150 5760 6878 6450 7054 6940 6700 5890 5200 4700 5890 6740 8290 3000 6590 5130 5770 5900 0.1 7.7 98 14.5 630 107 107 18.3 23.4 2.3 27 17.5

0.10 0.034 0.02

m bp m m

1139 100 1434 1083 1120 960 360 1470 431

0.156 0.067 0.08 0.04

0.105 0.02 0.050 0.052 0.03 0.17 0.12 0.07 0.059

m b

25 150 10 120 230 500 120 6.1 15.0 13.0

m m m m m m

750

8.412 0.128 8.444 8.358 8.37 8.40 8.5 0.3 8.71 8.81 8.57 8.38 8.25 8.41 8.72 8.581 8.5

0.05

104 23.7 50 35 50 19.0 8.1 111 2500 26.7 26.2 40

bc

b b

b

REMARKS: (m) magnetic white dwarfs; (b) white dwarfs with companion(s); (c) close binary or multiple systems; (t) triple systems; (p) common prop er-motion binaries. REFERENCES: (1a) Marsh et al. 1997a; (1b) Marsh et al. 1997b; (2) Vennes et al. 1997; (3) Finley, Ko ester, Basri 1997; (4) Vennes 1999; (5) Fabrika, Valyavin 1998; (6) Bergeron, Leggett, Ruiz 2001; (7) Bergeron, Saffer, Lieb ert 1992; (8) Reid 1996; (9) Claver et al. 2001; (10) Bergeron et al. 1995; (11) Bergeron, Lieb ert, Fulbright 1995; (12) Napiwotzki, Green, Saffer 1999; (13) Bragaglia, Renzini, Bergeron 1995; (14) Homeier et al. 1998; (15) Provencal et al. 1998; (16) Heb er, Napiwotzki, Reid 1997; (17) Wickramasinghe, Ferrario 2000; (18) Schmidt et al. 1992; (19) Wegner, Reid, McMahan 1989; (20) Putney 1997; (21) Bergeron et al. 1994; (22) Barstow et al 1995; (23) Burleigh, Jordan, Schweizer 1999; (24) Ferrario et al. 1997; (25) Jordan, Burleigh 1999; (26) Holb erg et al. 1998; (27) Burleigh 1999; (28) Vennes, Christian, Thorstensen 1998; (29) Barstow et al. 1997; (30) Werner, Rauch 1997; (31) O'Brien, Bond, Sion 2001; (32) Wegner, Reid, McMahan 1991; (33) Burleigh, Barstow 1998; (34) Ferrario, Vennes, Wickramasinghe 1998; (35) Lieb ert, Bergeron, Schmidt, Saffer 1993; (36) Suh, Mathews 2000; (37) Saffer et al. 1989; (38) Werner 1991; (39) Dupuis, Vennes 1997; (40) Vennes, Korp ela, Bowyer 1997; (41) Wonnacott, Kellett, Stickland 1993; (42) van Kerkwijk, Kulkarni 1999; (43) Moran, Marsh, Dhillon 1998.


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Figure 1: Mass distribution of magnetic massive white dwarf stars. Mass distribution is flat, and no local maximum can be seen in the figure.

Figure 2: Mass distribution of nonmagnetic massive white dwarf stars. Local maximum at 1.04M , as shown in Figure 1, should be attributed solely to the above nonmagnetic white dwarfs.


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Figure 3: Mass distribution of al l 112 massive white dwarf stars of our catalog (gray scale). The histogram shows the local maximum of mass distribution in the range 1.0 - 1.05M . The inserted dark tone histogram with a finer resolution of 0.01M clearly suggests that the local maximum of WD mass distribution is located at 1.04M . distribution of these stars clearly shows the secondary maximum of mass distribution in the single bin of 1.0 - 1.05M , which contains a significantly larger number of stars (12 ob jects, see Fig. 2). Of course, the mass distribution of all massive white dwarfs in our catalog, both magnetic and nonmagnetic, shows the same single bin consisting of 15 stars (Fig. 3), which seems to demonstrate the existence of the secondary maximum in the mass distribution of massive, isolated white dwarfs. Of course, our mass distributions determined in such an inhomogeneous sample is unintentionally blurred by the fact that mass determinations have been made by different methods. One cannot rule out the possibility that in future some nonmagnetic white dwarfs in Fig. 2 will move to the histogram in Fig. 1 if a nonzero magnetic field is detected there. We point out here that our mass distribution of magnetic massive white dwarfs (Fig. 1) differs significantly from the distribution obtained by Valyavin and Fabrika (1998, 1999). Both authors claim that the mass distribution of magnetic white dwarf stars exhibits the main maximum at 0.8M , and the secondary maximum at 1.15M (see Figure 2 in their paper). Both maxima in their paper are separated by a deep minimum of mass distribution at 1.05M . Our Fig. 1 does not exhibit any such features.

3.2

Incidence of magnetism in massive stars

Based on Table 1, we can immediately estimate a relative fraction of magnetic white dwarfs in the whole group of massive white dwarfs with masses higher than 0.8M . Among 112 massive stars listed in Table 1 we collected 25 stars, which are presently known as magnetic ob jects. Therefore the average relative fraction of isolated magnetic massive white dwarfs equals to 22 % in our sample. This result is very similar to the conclusion made by Vennes (1999) who found that the fraction of magnetic white dwarfs equals approximately 25 % for hot stars with masses exceeding 1M . However, we stress the essential difference between both analyses: the sample of hot massive white dwarfs searched by Vennes (1999) was derived from the EUVE catalog of hot stars, whereas our sample is not restricted only to hot ob jects.


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Figure 4: Relative fractions of magnetic white dwarfs as a function of stel lar mass, N mag /Ntot . One can note that the incidence of magnetism increases with white dwarf mass. The dashed line shows the average fraction of magnetic white dwarfs among isolated massive WDs.

Data collected in Table 1 allow us to study the distribution of magnetic white dwarfs in more detail. Figure 4 presents relative fractions of magnetic white dwarfs as a function of mass. Fig. 4 clearly suggests that the incidence of magnetism increases with mass of isolated white dwarfs, and reaches 100 % in the highest mass bin, 1.30 - 1.35M . We are aware, however, that the number of considered magnetic stars is low and cannot exclude strictly the impact of random fluctuations.

4

Conclusions

We have performed an extensive search of the available literature and selected all known white dwarfs of masses 0.80M . The list contains stars which are believed to be isolated, or are members of detached (noninteracting) binary systems. We excluded white dwarfs which are members of close (interacting) binary systems. A total of 112 massive white dwarfs were selected, and some of them are known as strongly magnetic stars with a surface field Bs approaching 500 megagauss. The mass distribution of massive magnetic white dwarfs seems to be flat, whereas the distribution of nonmagnetic stars looks steeper, decreasing towards the Chandrasekhar maximum mass. The mass distribution of all massive isolated white dwarfs apparently exhibits a local maximum at 1.04M , which is caused exclusively by nonmagnetic white dwarfs. We report here that a small group of the most massive stars in our sample, M > 1.30M , includes 4 magnetic white dwarfs. Nonmagnetic white dwarfs in the sample are likely to have masses less than 1.30M .

Acknowledgements. This research has been supported by grant No. 2 P03D 021 22 from the Polish Committee for Scientific Research.


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NALEZYTY, MADEJ

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