Distances of Galactic Supernova Remnants Using Red Clump Stars

Supernova remnants (SNRs) play key roles in the final evolution of stars, reshaping and heating the interstellar medium, and the birth of high-energy cosmic rays. Reliable distances to SNRs are essential to constrain physical parameters such as age, physical size, expansion velocity, and the explosion energy of the progenitor supernovae, which reveal the evolutionary process of SNRs. However, obtaining reliable distances of SNRs is a challenging job. About 20% of Galactic SNRs have distance measurements (Green 2014a).

There are several popular methods to measure the distances to Galactic SNRs. First, the kinematic method is based on the flat rotation curve of the Milky Way. By combining 21 cm H i absorption with CO emission, Tian et al. (2007) developed an improved way to measure the distances of extended radio sources by minimizing the possibility of a false absorption spectrum. Their methods have been applied to several SNRs, e.g., SNRs Kes 69 and 75, and Tycho's SNR (Tian & Leahy 2008, 2011). Second, distance determinations to the shell-type SNRs can be inferred by the relation between the mean surface brightness (Σ) at a specific radio frequency and physical diameter (D) of an SNR, Σ = aD^β. Distance is the ratio of physical diameter and the angular diameter (e.g., Clark & Caswell 1976; Milne 1979; Case & Bhattacharya 1998). The Σ–D relation is frequently used since Σ is easy to observe in radio bands for most radio SNRs. Third, the distances can be accessible when SNRs are associated with objects with known distances like OB associations (e.g., Cha et al. 1999, Vela remnant) or pulsars (e.g., Cordes & Lazio 2002). Additionally, the proper motion and the shock velocity can be used to calculate the distance (e.g., Katsuda et al. 2008; Vink 2008, Kepler's SNR). For shell-type SNRs in the adiabatic phase, distances can be calculated by the X-ray flux and thermal temperature of X-ray-emitting gas (Kassim et al. 1994). Finally, the extinction measurements can also indicate distances (e.g., Chen et al. 2017; Zhao et al. 2018), which this paper focuses on.

Red clump (RC) stars are characterized by an obvious concentration region in the color–magnitude diagram (CMD). They are usually low-mass stars in the early stage of core He-burning. Their helium cores almost have the same mass. Meanwhile their absolute magnitude weakly depends on metal abundance and ages in the K band (Alves 2000). Hence, RC stars are good enough to be standard candles in the infrared band. Assuming that the intrinsic color of RC stars is homogeneous, then their CMD spread along the color is just caused by interstellar extinction. Therefore, RC stars can also be used as extinction probes (Gao et al. 2009; Girardi 2016).

RC stars are so abundant in our Galaxy that they are extensively used as an independent and reliable approach to trace distance. López-Corredoira et al. (2002) used RC stars to directly measure the density distribution of stars in the line of sight. Durant & van Kerkwijk (2006) measured the running of reddening with distance in the direction of Galactic anomalous X-ray pulsars and obtained the distances of 5 pulsars. Güver et al. (2010) gave a distance estimate to the low-mass X-ray binaries 4U 1608-52 through the interstellar extinction traced by RC stars. Zhu et al. (2015) applied a similar measurement to determine the distance of SNR G332.5-5.6.

We closely follow the RC method and systematically measure the distances to 47 SNRs with known extinction in the first Galactic quadrant, with the aim of enlarging the reliable distance sample of SNRs. In Section 2, the method is described in detail. We summarize methods of measuring the optical extinction, the hydrogen column density, and the distances of SNRs compiled from the literature in Section 3. The uncertainties of this method are analyzed in Section 4. In Section 5, we discuss our results and make a comparison with distances measured by other methods. Finally, a brief summary is given in the final section.

To better illustrate this method, we start with G29.7–0.3 as an example. We extract the stars from the 2MASS All-sky Point Source Catalog in the J and K_S (hereafter K) bands (Skrutskie et al. 2006) centered on the SNR in 1° × 05 ($\bigtriangleup l$ × $\bigtriangleup b$) area. The reason why we choose the size of 0.5 deg² will be discussed later in this section. Their magnitudes in the J and K bands are used to construct the CMD (K versus J – K), since the RC stars are easy to identify on CMDs (e.g., Gao et al. 2009). In Figure 1, RC stars are concentrated in the middle of the CMD. The bulk of the stars in the left region of the CMD are main-sequence stars; those in the right are mainly dwarfs and red-giant-branch stars.

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In principle, there is a maximal density of RC stars in each range of K apparent magnitude. We divide the stars into a number of horizontal strips in K through the CMD. The locations of the RC stars in different strips indicate different distances and reddening. The width of each strip is usually 0.3 mag and it will be extended to 0.5 mag or 0.7 mag when the counts of the RC's peak density are less than 10. The length of each strip in J − K is fixed by the RC's distribution in order to include most of the RC stars and minimize the contamination of stars of other types. For each strip, we apply an empirical function to fit the histogram of star counts (Durant & van Kerkwijk 2006):

$$\begin{eqnarray}&&y={A}_{\mathrm{RCs}}\exp \left\{\displaystyle \frac{-{[(J-K)-{(J-K)}_{\mathrm{peak}}]}^{2}}{2{\sigma }^{2}}\right\}+{A}_{{\rm{C}}}{(J-K)}^{\alpha }.\end{eqnarray} \tag{ 1 }$$

Here, (J − K) represents the stellar color, and A_RCs and A_C stand for the normalizations of the RC stars and the contaminant stars, respectively. The first term is a Gaussian of (J − K)_peak and the width σ to fit the RC stars distribution; the second term is a power law to fit the contaminant stars. For instance, Figure 2 shows the best fit for the 11.1 < K < 11.4 strip: the stellar color (J − K) at the peak density of the RC stars (J − K)_peak is 1.56 mag and the σ is 0.19 mag. The (J − K)_peak value is applied to calculate the average extinction of this field as Equation (2). We assume that the intrinsic color (J − K)₀ is 0.63 mag and the mean absolute magnitude of RC stars in K band is −1.61 mag. We discuss this further in Section 4. Then, the extinction and the corresponding distance are derived from the following functions (Indebetouw et al. 2005):

$$\begin{eqnarray}&&{A}_{K}=0.67\times [{(J-K)}_{\mathrm{peak}}-{(J-K)}_{0}],\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{A}_{K}}{{A}_{V}}=0.1615-\displaystyle \frac{0.1483}{{R}_{V}},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&D(\mathrm{kpc})={10}^{[0.2({m}_{K}-{M}_{K}+5-(0.1137\pm 0.003)\times {A}_{V})]}/1000,\end{eqnarray} \tag{ 4 }$$

where A_V and A_K are extinction in the V and K bands, R_V = 3.1 ± 0.18 (we discuss the value of R_V in Section 3.1). In Equation (3), the conversion from A_K to A_V follows the empirical relation of Cardelli et al. (1989), which contributes an uncertainty of ∼3% to the optical extinction.

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This process is repeated for all strips until the 2MASS observational limit is reached. Since the extinction grows with increasing distance in a given line of sight, there is a one-to-one correspondence between the extinction and distance. Hence, the distance of G29.7–0.3 is obtained by overlapping its extinction value on the A_V–D relation in its direction.

We tempt to find an optimal bin size for each SNR. On the one hand, a larger bin size can help increase the accuracy of determining the extinction. This would enlarge the amount of RC stars, then decrease the uncertainty of RC's color (J − K)_peak. Meanwhile it would allow a narrow horizontal strip in m_K that is used to perform the fits of Equation (1), then yield a better sampling of the pairs of extinction and distance. On the other hand, a smaller bin size can decrease the dispersion of extinction in the line of sight.

We present two typical examples (one with high stellar density, the other one with low stellar density) to illustrate how to select the bin size. For an SNR with high stellar density in the sightlines, the A_V–D relations are constructed within bin sizes of 0.5 deg² (10 × 05), 0.125 deg² (05 × 025), 0.0625 deg² (025 × 025, the smallest possible area around the target), respectively (See Figure 3(a)). It is found that the three A_V–D relations are fully consistent with each other. In this case, the effect of bin size can be neglected when deriving the distance of SNRs. For an SNR with low stellar density , the A_V–D relations are constructed within bin sizes of 1.5 deg² ($\bigtriangleup l\,1\buildrel{\circ}\over{.} 5$ × $\bigtriangleup b\,1^\circ$), 0.5 deg² (10 × 05), 0.125 deg² (05 × 025, the smallest possible area around the target), respectively (See Figure 3(b)). The numbers of sampling points are 9, 7, 6, respectively. The A_V–D relations of 0.5 deg² and 0.125 deg² are almost the same, while the data points of 1.5 deg² are systematically lower. As Equation (2) shows, A_V is determined by the stellar colors of RC stars located in the peak density (J − K)_peak. The lower A_V for 1.5 deg² is a result of the sample of 1.5 deg² concentrating in stellar colors (J − K)_peak lower than those of 0.5 deg² and 0.125 deg². The A_V–D relations indicate that extending the area to 1.5 deg² might enlarge the extinction dispersion. In principle, we choose a larger bin size when the dispersion of extinctions is at the same level. The bin size of 0.5 deg² is a good balance between the two examples. Then, we test the bin sizes of 0.5 deg² and 0.125 deg² for the objects almost at an interval of 15° in longitude. In addition to Figure 3, Figure 4 presents results in four typical directions. In each of the panels, the two curves are consistent with each other, except the number of sampling points within 0.125 deg² is less than that of 0.5 deg² for some objects. Hence, we usually build the A_V–D curve within 0.5 deg² when deriving the distance of an SNR.

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In recent years, both theory and observations have shown the fine structure of RC, which includes two subclass stars, main RC stars and secondary RC stars (SRCs) . The main RC stars with low mass that we usually take as standard candles have almost the same luminosity and electronic-degenerate core; while the SRCs whose luminosity are greatly changed contain non-degenerate He-cores (Girardi 1999). The largest sample of RC stars identified based on LAMOST survey DR3 (Wan et al. 2015, 2017) shows that the ratio of the main and secondary RC stars is about 3:1. To investigate the effects of SRCs for this method, we use a double Gaussian function to fit the distribution of RC stars of each strip. No apparent secondary Gaussian component can be found. Hence, the effects of the SRCs can be neglected in this method.

Drawing from the catalogs of Green (2014b) and Ferrand & Safi-Harb (2012), we investigate 161 SNRs in the first Galactic quadrant. Among them, 47 SNRs have optical extinction or hydrogen column density data in the literature. We collect their parameters on optical extinction A_V, hydrogen column density N_H, and distance D, then discuss the methods for determining the three parameters. The three parameters and the corresponding methods are listed in Tables 1 and 2.

Table 1.  Optical Extinction A_V and Distances D

Source	AV	Method	Dknown	Method	Dthispaper	References
Name	(mag)		(kpc)		(kpc)
G54.1+0.3	7.3 ± 0.4	associated stars	6.2	kinematic measurement	6.3−0.7+0.8	1, 2, 3
G65.8−0.5	2.4 ± 0.4	Hα/Hβ	⋯	⋯	${2.4}_{-0.5}^{+0.3}$	4
G66.0−0.0	2.0 ± 0.2	Hα/Hβ	⋯	⋯	2.3 ± 0.3	4
G67.6+0.9	1.9 ± 0.2	Hα/Hβ	⋯	⋯	2.0 ± 0.2	4
G67.7+1.8	1.7 ± 0.7	Hα/Hβ	7–17	Σ–D+Extinction	${2.0}_{-0.5}^{+3.7}$	5, 6
G69.0+2.7	2.5 ± 0.3	Hα/Hβ	1.5, 3±2	kinematic measurement	4.6 ± 0.8	7, 8, 9
G82.2+5.3	2.8 ± 0.2	Hα/Hβ	1.6, 2.0	Σ–D, H ii distance	3.2 ± 0.4	10–12
G89.0+4.7	1.6 ± 0.3	Hα/Hβ	0.8–1.7	kinematic measurement	${1.9}_{-0.2}^{+0.3}$	7, 13, 14

References. (1) Kim et al. (2013), (2) Leahy et al. (2008), (3) Lu et al. (2002), (4) Sabin et al. (2013), (5) Gök et al. (2008), (6) Hui & Becker (2009), (7) Zhu et al. (2017), (8) Leahy & Green (2012), (9) Verbiest et al. (2012), (10) Mavromatakis et al. (2004), (11) Uyaniker et al. (2003), (12) Rosado & Gonzalez (1981), (13) Byun et al. (2006), (14) Tatematsu et al. (1990).

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Table 2.  Hydrogen Column Density N_H and Distances D

Source	NH	AV	Modela	Dknown	Method	Dthispaper	References
Name	(1021 H cm−2)	(mag)		(kpc)		(kpc)
G5.7−0.1	13.0 ± 1.0	6.4 ± 0.5	TP	3.1 or 13.7	kinematic measurement	2.9 ± 0.3	1, 2
G11.0−0.0	8.0 ± 3.0	3.9 ± 1.5	PL	2.6	absorption column	2.4 ± 0.7	3
G18.0−0.7	10.0 ± 2.0	4.9 ± 1.0	PL	3.9 ± 0.4	pulsar distance	3.1 ± 0.2	4, 5
G18.9−1.1	8.3±0.5	4.1 ± 0.2	TP	2.0	kinematic measurement	1.8 ± 0.2	6, 7
G34.7−0.4	13.0 ± 2.0	6.4 ± 1.0	TP+PL	2.6–3.2, 2.5	kinematic measurement	2.1 ± 0.2	8–10
G49.2−0.7	17.0	8.3 ± 1.7	TP	4.3, 5.6	kinematic measurement	${5.7}_{-0.8}^{+0.7}$	11–13
G85.4+0.7	8.3	4.1 ± 0.8	TP	2.5–4.5	kinematic measurement	4.4 ± 0.8	14, 15

Notes.

^aModel abbreviations: TP: thermal plasma; PL: power law; BB: blackbody; TT:a two-component thermal model.

References. (1) Joubert et al. (2016), (2) Hewitt & Yusef-Zadeh (2009), (3) Bamba et al. (2003), (4) Gaensler et al. (2003), (5) Cordes & Lazio (2002), (6) Harrus et al. (2004), (7) Aschenbach et al. (1991), (8) Uchida et al. (2012), (9) Park et al. (2013), (10) Frail (2011), (11) Hanabata et al. (2013), (12) Tian & Leahy (2013), (13) Koo et al. (1995), (14) Jackson et al. (2008), (15) Kothes et al. (2001).

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3.1. Optical Extinction A_V

3.2. N_H

3.3. Distance

The uncertainties of the derived distances to SNRs are mainly attributed to the errors of the SNRs' A_V and the RC's distances. The errors of the SNRs' A_V are calculated by a standard deviation formula. Here, we focus on the errors caused by RC stars. The errors of the RC's distances mainly include the dispersion of absolute magnitude and extinction traced by RC stars.

The absolute magnitude M_K of RC stars is extensively studied from the perspective of observations, especially in the K band (e.g., Alves 2000; van Helshoecht & Groenewegen 2007; Groenewegen 2008; Laney et al. 2012; Yaz Gökçe et al. 2013). In this work, we assume that the mean value of M_K is −1.61 mag, which is consistent with M_K = −1.61 ± 0.03 from Alves (2000) from a sample of 238 Hipparcos RC stars in the solar neighborhood, with M_K = −1.61 ± 0.04 mag derived by Grocholski & Sarajedini (2002) based on 14 open clusters, and also with the latest value M_K = −1.61 ± 0.01 mag determined by Hawkins et al. (2017) based on the 2MASS, Gaia, and WISE data. However, van Helshoecht & Groenewegen (2007) estimated a larger value of RC stars, M_K = −1.57 ± 0.05 mag, from 2MASS data on 24 open clusters, which is in agreement with the value M_K = −1.54 ± 0.04 mag measured by Groenewegen (2008) based on the revised Hipparcos parallaxes. Taking all of these studies into consideration, the variance of the absolute magnitude M_K leads to a systematic uncertainty of 0.1 mag that contributes about 5% error in the mean distance calculated by Equation (3).

The uncertainties of extinction are caused by the dispersion of intrinsic color and random errors of the Gaussian fitting. The absolute magnitudes of RC stars are more sensitive to [Fe/H] and age in the J band rather than K band, which leads to variation of the intrinsic color (J − K)₀ (Güver et al. 2010). The values of intrinsic color (J − K)₀ for RC stars concentrate in the range from 0.5 to 0.75 mag (e.g., Grocholski & Sarajedini 2002; Yaz Gökçe et al. 2013). We adopt (J − K)₀ as 0.63 mag, and assume that its dispersion is 0.1 mag, which leads to about 3% uncertainty in the distance, according to Equations (2) and (3). Meanwhile, we estimate the uncertainty of mean color on the peak density location of RC stars : ${\sigma }_{J-{\text{}}K}=\sigma {N}_{\mathrm{RC}}^{-1/2}$, where ${N}_{\mathrm{RC}}={A}_{\mathrm{RC}}\sigma \sqrt{2\pi }$ is the sum of RC stars in each magnitude strip (Durant & van Kerkwijk 2006). It is a good estimate if the Gaussian fit is valid and the contamination is not significant. The typical error of the mean color is about 0.05 mag, which brings ∼2% uncertainties in distance estimation.

In summary, the systematic uncertainties of the distances traced by the RC stars are about 10% in total.

We measure the run of reddening along distance using the RC method in each line of sight of 47 SNRs in the first Galactic quadrant. Among them, 32 SNRs' extinctions are beyond the range of A_V traced by the RC method, hence the upper/lower limits of distances are obtained. Fortunately, there are 15 SNR extinction bands overlapping with the extinction measured by the RC stars, which provides an opportunity to estimate the distance accurately and with precision. Figure 5 presents CMDs with the locations of the RC's peak density for each of the 15 SNRs. Figure 6 shows corresponding A_V–D relations and the probability distribution over distance to the SNRs.

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View figure set (15 panels)

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5.1. Derive the Distances of SNR

To determine the distances of SNRs, we calculate the probability distribution of distance using the product of two probability distributions and marginalizing over the extinction (Güver et al. 2010):

$$\begin{eqnarray}&&P(D)=\int {P}_{\mathrm{SNR}}({A}_{K}){P}_{\mathrm{RC}}(D| {A}_{V}){{dA}}_{V},\end{eqnarray} \tag{ 5 }$$

where P_SNR(A_V) presents the probability distribution of an SNR's extinction. We assume ${P}_{\mathrm{RC}}(D| {A}_{V})={P}_{\mathrm{RC}}({A}_{V}| D)$. ${P}_{\mathrm{RC}}({A}_{V}| D)$ presents the distribution of the extinction traced by the RC at each distance bin. Both distributions are denoted as Gaussian functions.

In Figure 6 (right column), the panels show the probability distributions over distance calculated by Equation (5). Then, we fit these distributions with a Gaussian function, yielding the distance with the highest probability. For the objects with good Gaussian fitting, the uncertainty of the distance is equal to the standard deviation of the Gaussian. However, for some objects there are apparent and sudden decreases in the distance probability. The red lines mark such decreases (see Figure 6). In this case, the uncertainty of the distance reflects the cutoff distance. The results are listed in Tables 1 and 2.

5.2. Summarize the Results

5.3. Discussion

We have estimated distances for 15 SNRs and upper or lower limits for 32 SNRs using the RC method. (The limit distances are listed in Tables 3 and 4. Figures 8 and 9 show the CMDs and A_V –D relations in the directions of 32 SNRs, respectively.)

To further understand the precision of the distances indicated using the RC method, we compare these results with the previous studies by two steps. First, we compare 8 new SNRs' RC distances with their kinematic distances. The kinematic distances are denoted as D_Kinematic. When the corresponding uncertainties are not given by the literature, we will empirically assume 20% of their distances as uncertainties. The distances measured by the RC method are denoted as D_RC. Assuming that each measurement has no errors for the same source, the regression function will be D_RC = D_Kinematic. The MPFITXY routine based on the MPFIT package is used to fit a straight line via data with errors in both coordinates (Markwardt 2009; Williams et al. 2010). In Figure 7(a) the fitted regression equation, D_RC = (1.0 ± 0.1) × D_Kinematic, indicates that the RC distances of SNRs are highly consistent with their kinematic method within the range of uncertainty. Second, we compare 44 distances constrained by the RC method with the corresponding distances measured by other methods. As Figure 7(b) shows, all distances estimated by the RC method are in the range of 1.5–8 kpc, which is consistent with our expectations. All 20 SNR distance lower limits coincide with the trend of the fitting lines, while 6 of the 12 upper limits are in agreement with other distance measurements. We conclude that most RC distances are in agreement with the previous measurements, and the lower limit distances are more reliable. Therefore, SNR distances can be independently constrained by the RC method.

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We analyze the reasons why the RC method only can trace either upper or lower limits. For 20 relatively distant SNRs, we only draw their lower limits for two reasons. One restricted condition is the 2MASS Survey completeness limit as J = 15.8, K_S = 14.3 mag. The other is that the RC stars are likely mixed with the highly reddening main-sequence stars in CMDs when the apparent magnitudes begin to be fainter than 13 mag (see Figure 5). For 12 relatively closer SNRs, we only obtain their upper limits because the sample of RC stars is not enough for statistics when their apparent magnitudes are brighter than 9 mag in most cases. Hence, the RC method based on 2MASS data can be effective in the range from 1.5 kpc to 8 kpc and the specific range of distance it can trace depends on the RC star sample in a given direction.

We next check the seven discrepant measurements. First, the differences between old and new distances for G32.8–0.1, G39.7–2.0, and G73.9+0.9 are less than 30%, which may be caused by the uncertainties of the two different methods. Then, a key investigation is conducted for the other four SNRs. The optical extinction values toward SNRs G13.3–1.3, G85.9–0.6 are smaller than 1 mag. We expected that the extinction values would not be sensitive to the distance when extinction is extremely slight in the line of sight. For G32.1–0.9, the difference between the RC and kinematic distance is greater than 50%, likely due to the large error of N_H that is up to 40%. Note that the distance of G67.7+1.8 listed in Table 1 is not reliable, since its probability distribution over distance is not well fitted by a Gaussian function. This might be a product of the broad range of the SNR's A_V and the slight extinction, which is much lower than the average magnitudes of extinction per kiloparsec (c_V ∼ 0.7 mag kpc⁻¹) along the line of sight (Indebetouw et al. 2005). These discrepant results suggest that the slight extinction or large uncertainties of extinction might significantly affect the accuracy of the RC method.

We have taken advantage of the RC stars from 2MASS data to construct the A_V–D relations along the directions of 47 SNRs in the first Galactic quadrant. In total, 15 distances and 32 upper or lower limit distances of SNRs have been obtained by overlapping their extinction values with A_V–D relations. Among them, the distances of SNRs G65.8–0.5, G66.0–0.0, and G67.6+0.9 are estimated as 2.4 kpc, 2.3 kpc, and 2.0 kpc for the first time. The distances of SNRs G5.7–0.1, G15.1–1.6, G28.8+1.5, and G78.2+2.1 have been better constrained as about 3 kpc, 2.2 kpc, 3.4 kpc, and 1.9 kpc, respectively.

By comparison, distances estimated by the RC method are consistent with kinematic measurements within the range of the allowed errors. In addition, the RC method tends to give a reliable lower limit distance. In addition, we analyze the possible reasons why six upper limits are incompatible with the previous results. Finally, we note that the RC method can independently constrain the distances of SNRs in the range of 1.5–8 kpc and the distances can be determined by this method when the samples of RC stars are relatively abundant along the line of sight.

We all acknowledge support from NSFC programs (11473038, 11603039, U1831128). We thank the referee for providing constructive comments and useful suggestions. We also thank Dr. Liu Chao, Dr. Xiang Mao-Sheng, Dr. Chen Bing-Qiu, and Dr. Wan Jun-Chen for helpful discussions. This publication makes use of data products from the Two Micron All Sky Survey.