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THE ASTROPHYSICAL JOURNAL, 504:761È772, 1998 September 10 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. A NEW &-D RELATION AND ITS APPLICATION TO THE GALACTIC SUPERNOVA

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THE ASTROPHYSICAL JOURNAL, 504:761È772, 1998 September 10 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. A NEW &-D RELATION AND ITS APPLICATION TO THE GALACTIC SUPERNOVA REMNANT DISTRIBUTION GARY L. CASE AND DIPEN BHATTACHARYA Institute of Geophysics and Planetary Physics, University of California, Riverside, CA 92521; case=tigre.ucr.edu, dipen=tigre.ucr.edu Received 1996 July 29; accepted 1998 April 14 ABSTRACT Technological advances in radio telescopes and X-ray instruments over the last 20 years have greatly increased the number of known supernova remnants (SNRs) and have led to a better determination of their properties. In particular, more SNRs now have reasonably determined distances. However, many of these distances were determined kinematically using old rotation curves (based on R \ 10 kpc and V \250 km s~1). A more modern rotation curve (based on R \ 8.5 kpc and V \ _ 220 km s~1) is used _ to verify or recalculate the distances to these remnants. We _ use a sample of _ 36 shell SNRs (37 including Cassiopeia A) with known distances to derive a new radio surface brightnessètoèdiameter (&-D) relation. The slopes derived here (b \[2.64 including Cas A, b \[2.38 without Cas A) are signiðcantly Ñatter than those derived in previous studies. An independent test of the accuracy of the &-D relation was performed by using the extragalactic SNRs in the Large and Small Magellanic Clouds. The limitations of the &-D relation and the assumptions necessary for its use are discussed. A revised Galactic distribution of SNRs is presented based on the revised distances as well as those calculated from this &-D relation. A scaling method is employed to compensate for observational selection e ects by computing scale factors based on individual telescope survey sensitivities, angular resolutions, and sky coverage. The radial distribution of the surface density of shell SNRs, corrected for selection e ects, is presented and compared with previous works. Subject headings: galaxies: ISM È Galaxy: kinematics and dynamics È Galaxy: structure È supernova remnants 1. INTRODUCTION Determining the distances to the Galactic supernova remnants (SNRs) is a difficult but important task. The indepth study of the remnants has depended largely on observations in the radio regime. However, radio telescope surveys searching for SNRs are biased by three selection e ects: (1) they overlook SNRs because of their low surface brightness, especially in a region of higher background, (2) they fail to detect SNRs because of their small angular size, and (3) they have an absence of uniform coverage of the sky (see also Green 1991). Recent observations of SNRs have been performed with radio telescopes with better sensitivities, higher angular resolutions, and more complete sky coverage than the previous generations, as well as with space-based X-ray telescopes. The use of these new instruments has led to the discovery of new SNRs with lower surface brightnesses and smaller angular sizes, resulting in a signiðcant increase in the number of known SNRs. It has also led to a better determination of the physical and observational properties of known remnants. However, most SNRs still do not have well-determined distances. Conventionally, SNRs are classiðed into three basic types: shell remnants, characterized by di use, shell-like emission with steep radio spectra; plerionic or Ðlled-center remnants, containing a central source with a Ñat radio spectrum but no shell structure; and composite remnants, which show signs of both a central source and a di use shell structure. Distances to the SNRs can be inferred from positional coincidences with H I, H II and molecular clouds, OB associations, or pulsars or from measuring optical velocities and proper motions. Where there is no direct distance determination, estimates can be made for shell remnants by utilizing the radio surface brightnessètoèdiameter relationship (&-D) (i.e., Clark & Caswell 1976; Milne 1979; Sakhibov & Smirnov 1982). The mean surface brightness at a speciðc radio frequency, &, is a distance-independent l parameter and, to a Ðrst approximation, is an intrinsic property of the SNR (Shklovsky 1960). If this relationship is given by & l \ ADb, (1) the distance d will be proportional to & or, in terms l of observable quantities, d P where S is the l l Ñux density at the observing frequency l and h is the angular diameter of the remnant. Composite SNRs may be characterized by a similar relation, but only a few have known distances, and hence a reasonable &-D relation is difficult to calculate for them. There exists considerable skepticism about using the &-D relation to obtain distance estimates (e.g., Green 1984, 1991). Green (1984) pointed out two signiðcant problems with the &-D relation. First, many of the independently determined distances have a degree of uncertainty. H I absorption measurements can be difficult to interpret and often give reliably only lower distance limits. Associations of SNRs with other objects such as molecular clouds, H I emission regions, and OB associations cannot always be made with great conðdence. Second, studies of SNRs in the Large Magellanic Cloud, which are all at approximately the same known distance, have shown a spread in intrinsic properties (see discussion in Green 1984). This suggests that for a given surface brightness, there may be a spread in linear diameters, making a unique distance estimate to individual remnants difficult and uncertain. This spread in intrinsic properties likely results from the variety of di erent environments into which the remnants are evolving. The density and structure of the ambient medium and the lingering e ects of the SNR progenitor star could all potentially 761 762 CASE & BHATTACHARYA Vol. 504 a ect the remnantïs evolution (Allakhverdiyev et al. 1983a, 1983b). However, in SNR samples that are thought to be observationally complete, there is a clear trend for the surface brightness of SNRs to decrease with increasing linear diameter. By using a large number of distance calibrators ÏÏ with distance measurements that are as reliable as possible, a &-D relation can be constructed and distance estimates can be made to shell remnants for which there is no other distance information available. However, investigators who use distances to individual SNRs based on the &-D relation must be aware of the inherent uncertainties and assumptions of this method. The impetus for this work arose from a need to determine the radial Galactic SNR distribution. The &-D relation was the only means by which distances could be obtained for most of the known shell SNRs. However, it became apparent that the &-D relations most often quoted for distance estimates (e.g., Clark & Caswell 1976; Milne 1979) needed to be updated in light of the new information available for SNRs. We show that even with the uncertainties involved in estimating distances to individual SNRs, it is possible to use the &-D relation for examining ensemble properties of the SNRs, such as the total number and their radial distribution. In this paper, revised distances are given for all SNRs in GreenÏs SNR catalog (Green 1996a) for which previous information is outdated or new information is available.1 These kinematic distances were recalculated when necessary using a more modern rotation curve (with R \ 8.5 _ kpc and V \ 220 km s~1). Other distances were taken _ from new pulsar-snr or molecular cloudèsnr associations. A new &-D relation for shell-type SNRs is presented using a sample of 36 calibrators ÏÏ (37 including Cassiopeia A), and the assumptions and limitations for the use of the &-D relation are discussed. The surface brightness distribution of the nearby remnants and a Monte Carlo simulation are used to calculate scale factors in an attempt to compensate for observational selection e ects. These results are used to derive the radial SNR surface density distribution in the Galaxy. 2. SNR DISTANCES AND THE &-D RELATION The positional coincidences of Galactic SNRs with H I, H II and molecular clouds, OB associations, or pulsars may provide distance estimates to the remnants. However, of the 215 SNRs in GreenÏs present catalog (1996 August version), only 64 have independently determined distances (38 of 160 shell type, Ðve of nine Ðlled center, 18 of 31 composite, and three of 15 unknown type). In this analysis, any shell remnant that has an associated pulsar, regardless of whether or not any kind of radio plerion is observed, is considered a composite. Therefore, the numbers of shelland composite-type SNRs given here di er from the numbers in GreenÏs catalog. Using a number of known diameters (from the shell remnants with established distances), one can derive a &-D relationship for a given radio frequency. For those shell-type remnants that have no direct distance information, we can then estimate their distances using this relation. Unless stated otherwise, the Ñux densities and surface brightnesses used in this analysis are referenced to 1 GHz. 1 A Catalog of Galactic Supernova Remnants (1996 August version) (Mullard Radio Astronomy Observatory, Cambridge) is available on the World Wide Web at Previous &-D relations have indicated that the power-law index b in equation (1) lies in the range [2.8 to [4. Clark & Caswell (1976) used 20 SNRs (14 shell, two Ðlled center, two composite, one of unknown type, and one no longer regarded as an SNR) as distance calibrators and found b \[3 in the surface brightness range 2 ] 10~20 \ & \ 5 ] 10~19 Wm~2 Hz~1 (they suggested bb[10 for 408 & \ 2 ] 10~20). This surface brightness limitation excluded 408 the three brightest remnants including Cas A. They also excluded RCW 103, for which they had what they considered a reliable distance but which was far away from their Ðt in the &-D plane. In addition, nine of the 20 calibrators had only lower limits on the distance, and the lower limit was taken to be the actual distance. Milne (1979) used the 11 SNRs from Clark & Caswell with known distances, added back the four remnants that had been excluded, and added seven more with known distances for a total of 22 SNRs (18 shell, three composite, and one Ðlled center) and obtained b \[3.8. Lozinskaya (1981) used 21 of the 22 SNRs (excluding the Crab SNR) in MilneÏs list, with revised distances to three of them, and added Ðve others whose distances she had determined from optical observations for a total of 26 (22 shell and four composite), and found b \[3.45, roughly halfway between the values given by Clark & Caswell and Milne. Sakhibov & Smirnov (1982) used 38 SNRs (including those from Lozinskaya) that they classify as shell-type (but actually including at least four remnants that we classify as composite) out of a larger sample of 57 calibrators of all types to derive b \[3.4 ^ 0.5, agreeing closely with Lozinskaya and, within their error, with Clark & Caswell and Milne as well. For their larger sample, they obtain b \[2.8 ^ 0.4. Li & Wheeler (1984) have derived the Ñattest relation for shell SNRs with b \[2.77. Huang & Thaddeus (1985) attempted to use a more homogeneous subsample consisting of 12 shell SNRs located near large molecular clouds and found b \[3.21. However, all of these studies used old rotation curves. We have searched the literature to Ðnd recent and accurate distances to as many shell remnants as possible. Many of the remnants have more than one distance available. For these remnants, we have either chosen the most recent measurement or used an average of the available estimates (if the distance range is narrow). Our sample of 37 shell remnants with published distances, which is used to derive the &-D relation, is listed in Table 1. Only the references for the distances actually used are given in the table. The surface brightnesses and angular diameters (used to calculate the linear diameters) are taken from GreenÏs catalog. Most of the kinematic distances given in GreenÏs catalog, as well as the distances used by the authors above, were calculated using 10 kpc as the solar distance from the Galactic center and a solar velocity of 250 km s~1. Some of these remnants now have more recently determined distances, where modern rotation curves with R \ 8.5 kpc and V \ 220 km s~1 were employed. For those _ SNRs that still do _ not have kinematic distances based on a modern rotation curve, the original references for the distance information were checked in order to obtain the kinematic velocities determined from H I absorption, mean optical velocities, or associated CO or H I emission. The distances were then recalculated using the rotation curve given by Burton & Gordon (1978), with corrections by Fich, Blitz, & Stark (1989), for the inner Galaxy and a Ñat rotation curve No. 2, 1998 NEW &-D RELATION 763 TABLE 1 SHELL SNRs WITH KNOWN DISTANCES Surface Brightness Distance Diameter Catalog Name Other Name (W m~2 Hz~1 sr~1) (kpc) (pc) Referencea G4.5] KeplerÏs SNR 3.2 ] 10~ G13.3[1.3b G18.8] Kes ]10~ * G31.9] C ]10~ , 4 G33.6] Kes ]10~ * G43.3[ W49B 4.8 ] 10~ * G46.8[ HC ]10~ * G49.2[ W51 2.7]10~ G53.6[ C ] 10~ * G54.4[ HC ]10~ * G74.0[ Cygnus Loop 8.6 ] 10~ G78.2] c Cygni 1.4 ] 10~ , 8 G84.2[ ]10~ G89.0] HB ]10~ G111.7[ Cas A 1.6]10~ G116.5] ]10~ * G116.9] CTB 1 1.2]10~ G119.5] CTA 1 6.7]10~ G120.1] TychoÏs SNR 1.3 ] 10~ G132.7] HB 3 1.1]10~ , 16 G156.2] ]10~ , 18 G160.9] HB 9 9.9]10~ * G166.0] VRO ] 10~ G166.2] OA ]10~ G189.1] IC ]10~ G205.5] Monoceros 5.0 ] 10~ G260.4[ Pup A 6.5]10~ G296.5] PKS ] 10~ , * G304.6] Kes ]10~ * G309.8] ]10~ G315.4[ RCW ]10~ G327.6] SN ] 10~ , 26 G330.0] Lupus Loop 1.6 ] 10~ G332.4[ RCW ]10~ * G348.5] CTB 37A 4.8]10~ * G348.7] CTB 37B 1.4]10~ * G349.7] ]10~ * G359.1[ ]10~ a Distances to remnants marked with an asterisk are recalculated from the references in Table 2. b G13.3[1.3 is an SNR recently identiðed in X-rays (by ROSAT) and has not yet had a radio surface brightness published. REFERENCES.È(1) Bandiera 1987; (2) Seward et al. 1995; (3) Reynolds & Mo ett 1993; (4) Wilner, Reynolds, & Mo ett 1998; (5) Koo, Kim, & Seward 1995; (6) Minkowski 1958; (7) Huang & Thaddeus 1985; (8) Green 1989b ; (9) Feldt & Green 1993; (10) Tatematsu et al. 1990; (11) Reed et al. 1995; (12) Hailey & Craig 1994; (13) Pineault et al. 1993; (14) Schwarz et al. 1995; (15) Routledge et al. 1991; (16) Normandeau, Taylor, & Dewdney 1997; (17) Reich, Fu rst, & Arnal 1992; (18) Pfe ermann, Aschenbach, & Predehl 1991; (19) Landecker et al. 1989; (20) Fesen 1984; (21) Odegard 1986; (22) Reynoso et al. 1995; (23) Roger et al. 1988; (24) Rosado et al. 1996; (25) Long, Blair, & van den Bergh 1988; (26) Winkler & Long 1997; (27) Leahy, Nousek, & Hamilton 1991; (28) Uchida, Morris, & Yusef-Zadeh outside the solar circle. Saken, Fesen, & Shull (1992) used the modern rotation curve of Clemens (1985), with the modiðcation that a Ñat curve was used outside 5 kpc, to derive distances to several remnants. However, this is a nonstandard rotation curve implementation, as Ðducial rotation curves employ a Ñat curve only outside the solar circle. For this reason, the distances derived by Saken et al. are not used in Table 1. In total, kinematic distances for 17 remnants (14 shell, one composite, and two Ðlled center) were recalculated and are listed in Table 2. Distances to 11 other composite remnants were assigned the distance to their associated pulsars. Those shell remnants in Table 1 that had kinematic distances recalculated have an asterisk in the reference column. For distances to the other shell remnants in Table 1, two were obtained from an association of the SNR with an H II region and an OB association (G189.1]3.0, G205.5]0.5), three from associations with a molecular cloud and an OB association (78.2]2.1, G89.0]4.7, G309.8]0.0), one from optical kinematics and historical observations (G4.5]6.8), three from optical proper motions (G74.0[8.5, G111.7[2.1, G327.6]14.6), one from the modeling of its X-ray emission (G330.0]15.0), one from the modeling of its X-ray emission and from associated H I emission (G119.5]10.2), two from X-ray absorption and associated H I emission (G296.5]10.0, G156.2]5.7), and 11 from the literature in which a modern rotation curve had already been used (G31.9]0.0, G49.2[0.7, G84.2[0.8, G116.9]0.2, G120.1]1.4, G132.7]1.3, G166.0]4.3, G166.2]2.5, G260.4[3.4, G315.4[2.3, G359.1[0.5). Note that the distances listed in Table 1 are the revised distances (where relevant). 764 CASE & BHATTACHARYA Vol. 504 TABLE 2 SNRs WITH REVISED DISTANCES Distance Name Typea (kpc) Method Reference G5.4[ C? 4.6 Pulsar coincidence 1 G6.4[ C 3.3 Mean optical velocity 2 G8.7[ C?b 3.9 Pulsar coincidence 1 G18.8] S 8.1 H I absorption 3 G21.5[ F 6.3 H I absorption 4 G33.6] S 7.1 H I absorption 5 G34.7[ C?b 3.3 Pulsar coincidence 1 G43.3[ S 7.5 H I absorption 6 G46.8[ S 6.4 H I absorption 7 G53.6[ S 5.0 optical kinematics 8 G54.4[ S 3.3 CO association 9 G69.0] C?b 2.5 Pulsar coincidence 10 G114.3] C?b 2.5 Pulsar coincidence 1 G116.5] S 5.0 H I absorption 11 G130.7] F 3.3 H I absorption 12 G160.9] S 2.2c Mean optical velocity 2 G180.0[ C?b 1.5 Pulsar coincidence 10 G296.5] S 1.6 Associated H I shell 13 G304.6] S 7.9 H I absorption 3 G308.8[ C? 8.7 Pulsar coincidence 1 G320.4[ C 4.4 Pulsar coincidence 1 G332.4[ S 3.4 H I absorption 3 G341.2] C? 6.9 Pulsar coincidence 1 G343.1[ C? 1.8 Pulsar coincidence 1 G348.5] S 9.0 H I absorption 3 G348.7] S 9.0 H I absorption 3 G349.7] S 13.8 H I absorption 3 G354.1] C? 4.2 Pulsar coincidence 1 a S \ shell remnant; F \ Ðlled-center remnant; C \ composite remnant. b These SNRs are classiðed in GreenÏs catalog as shell or unknown type. They have been classiðed here as possible composite type because of the association of the remnant with a pulsar. c Possible association with a pulsar at 1.8 kpc. REFERENCES.È(1) Frail, Goss, & Whiteoak 1994; (2) Lozinskaya 1981; (3) Caswell et al. 1975; (4) Davelaar, Smith, & Becker 1986; (5) Frail & Clifton 1989; (6) Radhakrishnan et al. 1972; (7) Sato 1979; (8) Rosado 1983; (9) Junkes, Fu rst, & Reich 1992; (10) Anderson et al. 1996; (11) Reich & Braunsfurth 1981; (12) Roberts et al. 1993; (13) Dubner, Colomb, & Giancani The diameters derived from the new distances are shown in Figure 1, from which the relation & \ 5.43 `8.16 ] 10~17 1GHz ~3.26 ] D(~2.64B0.26) Wm~2 Hz~1 sr~1 (2) is obtained. The typical errors in the kinematic distances are about 10%È25%, depending on the resolution and sensitivity of the measurements and the error in the rotation curve parameters. This error does not include the uncertainty due to the presence of noncircular motions associated with the object (i.e., CO cloud) or feature (i.e., H I emission), which is hard to quantify. The error in distances derived from the modeling of X-ray emission is typically 30% (Kassim et al. 1994). For distances estimated by associating the remnant with an object such as an OB association, CO cloud, or H II region, the distance to the object may be fairly well determined, but the association itself may be less certain, making an error estimate difficult. In these cases, we do not incorporate the SNR into Table 1 unless there is at least one other corroborating distance estimate. Since it is difficult to assign realistic errors to the diameters, equal weighting was used in these &-D Ðts. This &-D relation is Ñatter than those obtained in the studies mentioned above. Some used fewer remnants than our study, some used nonshell remnants, and they all used old rotation curves. Radio and X-ray observations made in recent years have had better sensitivities and angular resolutions, which has led to the addition of new shell remnants with lower & (with large D) and smaller h to the current catalog. Newly determined distances and revised FIG. 1.ÈThe surface brightness vs. diameter (&-D) relation for shell SNRs using the distance calibrators i
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