A COMPARISON OF THE VELOCITY PARAMETERS

The Astronomical Journal, 149:100 (8pp), 2015 March doi:10.1088/0004-6256/149/3/100 © 2015 The American Astronomical Society All rights reserved A COMPARISON OF THE VELOCITY PARAMETERS OF SIO V = 1, J = − 0, AND J = − MASER EMISSION IN SEMIREGULAR VARIABLES Gordon McIntosh1 and Balthasar Indermuehle2 Division of Science and Mathematics, University of Minnesota, Morris, 600 East 4th Street, Morris, MN 56267, USA; mcintogc@morris.umn.edu Australia Telescope National Facility, Locked Bag 194, Narrabri, NSW 2390, Australia; balt.indermuehle@csiro.au Received 2014 March 26; accepted 2015 January 9; published 2015 February 12 ABSTRACT We have determined and compared the SiO maser velocity parameters of semiregular variables in the v = 1, J = − (J101) and the v = 1, J = − (J21) transitions Fourteen sources in the Mopra SiO Maser Catalogue are classified as semiregular variables of types SR, SRa, SRb, or SRc (L2 Puppis, an SRa star with an unusual SiO maser spectrum, has been analyzed individually.) We have previously presented the overall and phase dependent velocity parameters of SiO masers associated with long period variables (LPVs) of well-established periods and maxima A comparison of the velocity centroid (VC) difference, VC21–VC10, shows mixed results for the variable types Some differences are negative and some positive The SRc difference is negative, large, and relatively stable The SRb difference has the widest distribution The velocity ranges (VRs) of the maser emission have been compared using arithmetic averages, Gaussian fits to the distributions, and Weibull fits to the distributions For LPVs, SRs, SRas, and SRcs the VR10 is one to a few km s−1 greater than the VR21 SRcs have the largest VRs by a factor of two or three indicating the greater range over which the conditions necessary for masers to originate exist in these supergiant stars SRbs are the only classification of semiregular variable in which the VR21 exceeds the VR10 The larger VR21 compared to VR10 for SRbs appears in all comparisons The difference in the SRb SiO maser velocity parameters may be due to a difference in the oscillation mechanism of the star The suggested overtone oscillations of SRbs may affect the circumstellar cloud dynamics Little theoretical work has specifically addressed the masers in semiregular variables Qualitative comparisons of the data with the existing models of the SiO masers in LPVs are made Key words: masers – radio lines: stars – stars: variables: general SRa semiregular late-type (M, C, S or Me, Ce, Se) giants displaying persistent periodicity and usually small (2000 days, while the shapes of the light curves are rather different and variable, and the amplitudes may be from several hundredths to several magnitudes (usually 1–2 mag in V) Throughout the paper the suffix 10 refers to the SiO v = 1, J = − transition, and the suffix 21 refers to the SiO v = 1, J = − transition The Astronomical Journal, 149:100 (8pp), 2015 March McIntosh & Indermuehle produced mixed results Alard et al (2001) used infrared photometry to conclude mass loss rates of SRs in Baadeʼs windows depended on stellar period Kerschbaum et al (1996) measured circumstellar CO rotational transition parameters and found “no correlation between mass-loss rate and period.” Table lists the sources, classifications, oscillation periods (if known), and spectral type of the sources These data have been taken from the GCVS (Samus et al 2012) Table Source Information Source U Men R Crt RT Vir W Hya RX Boo V446 Oph AH Sco V2108 Oph OH2.6-0.4 VX Sgr GY Aql S Pav X Pav T Mic Variable Type Period (days) Spectral Type SRa SRb SRb SRa SRb SR SRc SR SR SRc SR SRa SRb SRb 407 160 155 361 162 341 717.6 L L 732 204 380 199 347 Me M7 M8III M7.5e-M9ep M6.5e-M8IIIe M8 M4e-M5Ia-Iab M7-M9.8 M8 M4eIa-M10eIa M6IIIe-M8 M7IIe-M8III Mc M6e 1.2 Velocity Centroids (VCs) and Velocity Ranges (VRs) The VC is the emission weighted velocity or “center of mass” of the maser emission Mathematically, the VC is the sum of the antenna temperature (Ta) in each velocity channel times the velocity with respect to the local standard of rest (vlsr) of the velocity channel divided by the sum of the Ta in each velocity channel VC = They found that the photospheric shock had a smaller velocity amplitude in the SRa star Willson (2000) used this observations and other information to conclude that LPVs have larger amplitude and fundamental mode photospheric shocks while semiregular variables experience smaller, overtone shocks Several authors (Christensen-Dalsgaard et al 2001; Bedding 2003; Mosser et al 2013) have suggested that semiregular variables pulsate with solar-like (stochastically excited) oscillations rather than Mira-like (self-excitation) oscillations The effects of different stellar oscillation modes or mechanisms on the circumstellar environment and SiO maser velocity parameters have not been investigated Alcolea et al (1990) reported on single observations of the SiO maser emission from 31 semiregular variables, 20 supergiants, and 19 LPVs They observed that the supergiants and semiregular variables emissions had a larger “equivalent width defined as (profile-area/peak-intensity)” than LPVs in the J21 transition (pp.432–433) They suggested that some semiregular variables and supergiants lacked the necessary conditions in the “inner envelope” of the circumstellar region to support maser emission They concluded that the conditions of the inner envelope are “expected to be related to the pulsation of the star” (p.437) Chen et al (2007) and Su et al (2012) carried out very long baseline interferometry (VLBI) observations of VX Sgr, an SRc star These authors assumed the LPV shock models applied to this star and found some qualitative agreement with the predictions of the circumstellar shock model of Humphreys et al (2002) Su et al (2012) concluded that the masers of VX Sgr are likely to be pumped by a combination of radiational and collisional pumping Su et al (2012) observed fewer overlapping J10 and v = 2, J = − maser spots in the outer areas of maser emission compared to the inner areas Based on this observation they concluded that the decline with distance from the star of the shock wave (responsible for the collisional pumping) decreased the influence of the shock in the outer regions of the circumstellar envelope Wood (1989) found a linear relationship between the expansion velocity of the circumstellar material determined from CO rotational transition measurements and the periods of LPVs He then related the period to the stellar mass loss rates Observations of the mass loss and periods of SRs have S ( Ta * v lsr ) STa (1) The summations extend over the range of emission The VR is calculated to be the region where the Ta exceeds three times the standard deviation of the antenna temperature of the background noise The standard deviation is determined from velocity channels far away from the emission range of the source, which, given the IF bandwidth of 137 MHz and resolution of 4096 channels is easily obtainable by masking the central emission 1.3 Observations of Maser Locations and VRs As reviewed in McIntosh & Indermuehle (2013; hereafter MI13) for LPVs VLBI observations indicate that the distance of the J21 emission is comparable to or greater than the distance of the J10 emission from the central star but not indicate a clear relationship concerning the VRs A recent paper by Richter et al (2013) examined the locations of J10, J21 and v = 2, J = − SiO maser transitions in the supergiant VY CMa They found “significantly higher spatial overlap between the v = 1, J = − and J = − features than previously reported.” VLBI measurements usually recover 20%–70% of a sourceʼs SiO maser emission Yi et al (2005) concluded that a superposition of weak maser spots accounted for the SiO maser emission not detected by VLBI observations The VLBI information may not accurately correlate with the location of non-detected emission Conclusions concerning maser locations based on VLBI maps may not accurately apply to the single dish measurements presented in this analysis 1.4 Theoretical Models of Maser Velocity Parameters and Locations in LPVs Gray et al (2009; hereafter G09) investigated the dynamics of the circumstellar region in which the SiO masers originate in LPVs They modeled a shock traveling out from the star generating maser features at different distances from the star at different phases G09 predicted a VR10 of ∼10 km s−1 From the graphs in G09 the VR21s are generally less than 10 km s−1 G09 indicate that the J21 emission should originate at similar or greater distances from the star than the J10 emission depending on the phase In this maser model pumping is accomplished through radiative and collisional mechanisms The Astronomical Journal, 149:100 (8pp), 2015 March McIntosh & Indermuehle Yun & Park (2012; hereafter YP12) developed an SiO maser emission model for LPVs using a coupled escape probability The graphs in this work indicate the VR21 exceeds the VR10 at all epochs presented No clear difference between the VCs is indicated at any epoch The J21 emission is generated at similar or slightly greater distances from the star than the J10 emission in this model The shock traveling out from the star is modeled to change the velocity field of the maser emission with distance and phase The observations of the velocity parameters of the emission provide information on the relative locations as well as the motion of the masing material Pijpers and co-authors (Pijpers & Habing 1989; Pijpers et al 1994) have theoretically and observationally investigated the possibility acoustic waves propagating out from the star and through the circumstellar environment These acoustic waves would be of shorter period and smaller amplitude than the shock waves of the previously mentioned models These waves could contribute to the variations in the VCs and VRs measured in the present observations In order to support or challenge this model, extensive observations separated by a few days would be necessary to measure the short term variations in the maser velocity parameters and compare them with the longer term variations presented here For purposes of comparison it is assumed that the same sort of shock physics theorized to occur in the circumstellar environment of LPVs is occurring in the region around semiregular variables If some types of semiregular variable stars are oscillating in overtone modes the models developed for LPVs may not accurately represent these stars 3.1 VC Comparison We determined the VC21–VC10 differences, for the SR, SRa, SRb, and SRc observations The VC pairs are from the same source and were obtained within 24 hr of each other The differences were histogrammed into windows 0.25 km s−1 wide and fit assuming a Gaussian distribution Figures 1–4 display the histograms and Gaussian fits of VC21–VC10 for SRs, SRa, SRb, and SRcs, respectively The arithmetic average and σ, the square root of the variance, and the center and standard deviation of the Gaussian fits are included in Table along with the LPV data for comparison The SR distribution shows a number of occurrences above +1 km s−1 compared to the Gaussian fit, but the center for the Gaussian is −0.6 km s−1 so the overall distribution is dominated by negative values of VC21–VC10 The SRa histogram is the only distribution that has a positive average and Gaussian fit center It shows a few excess occurrences at negative velocity differences The SRb distribution is not particularly well described by the Gaussian fit to the histogram of the data The poor fit is indicated by the number of occurrences below −3 km s−1 The SRc average and Gaussian center are both approximately −1 km s−1 The SRc VC differences appear to be stable for longer periods of time than those for LPVs and SRs (The data shown represent observations over yr.) The magnitude of the negative value of VC21–VC10 may be a result of the particular observation epoch and not indicate a different physical situation for these stars (VY CMa, a supergiant with SiO maser emission included in the Mopra SiO Maser Catalog, has consistently shown a positive value for VC21–VC10.) The LPV distribution of the difference in VCs showed an excess of occurrences at relatively large negative velocity differences (MI13) though the average and Gaussian center are both close to km s−1 Further observations and observations of more sources are necessary to draw definite conclusions of the relative velocities of the J10 and J21 transitions, but these observations indicate a general dominance of negative VC21–VC10 differences It is difficult to compare the VC difference results, even qualitatively, with the G09 and YP12 models The G09 modeled spectra indicate a blueshifted J10 emission compared to the J21 emission for some combinations of phase and dust regime Other combinations produce a relative redshift of J10 compared to J21 The graphs in YP12 indicate that the VCs are approximately equal for all epochs presented OBSERVATIONS The details of the observations have been reported in MI13 and are only briefly reviewed here For J21 observations the rms noise was about 1.8 Jy For J10 observations the rms noise was about 0.6 Jy The velocity resolution was 0.234 km s−1 (J10) and 0.117 km s−1 (J21) In order to make a more accurate comparison between J21 and J10 the velocity resolution of the J21 transition was degraded to 0.234 km s−1 to match the J10 velocity resolution Degrading the J21 velocity resolution decreased the J21 rms noise to about 1.3 Jy It is not possible to match the rms noise values of the observations of the two transitions without reducing the time spent observing the J10 transition or ignoring some of the data We chose to include all the J10 data The LPV J21 spectra from MI13 were also reanalyzed with the 0.234 km s−1 velocity resolution for more accurate comparisons The Mopra monitoring program observed 121 sources between 2008 and early 2012 and is continuing with a reduced rate of observations LPVs, semiregular variables, irregular variables, OH-IR stars, and the Orion SiO maser source were observed approximately monthly in J10 and J21 The present analysis examined semiregular variables’ spectra and reanalyzed LPV spectra taken between 2008 and 2012 April 3.2 VR Comparisons Along with arithmetic calculations and fits to Gaussian distributions we have used fits to the Weibull distribution (Weibull 1951) to model the VR data and histograms Table gives the results of averaging the VRs, calculating σ (the square root of the variance), and the number of data points used in the analysis The LPV VR10 and reanalyzed VR21 data are included in this table and in the following tables comparing the variable types For all variable types except SRbs the average VR10 exceeds the VR21 by 1.4–4.2 km s−1 For SRbs the average VR21 exceeds the VR10 by 2.9 km s−1 SRcs have the largest average ranges approximately three times as broad as the other types of variables SRas have the largest σs of 4.2 and 4.0 km s−1 for the VRs in the two transitions Figures 5–8 show the histograms of the VR10s for SRs, SRa, SRb, and SRcs with the Weibull and Gaussian fits to the VELOCITY PARAMETERS AND RESULTS Table presents the number of J10 and J21 observations of each source, the first VC10 and VC21 observed and the mean VR10 and VR21 The Astronomical Journal, 149:100 (8pp), 2015 March McIntosh & Indermuehle Figure Histogram of VC21–VC10 for observations within day of each other from the Mopra data base for 59 J21 and J10 spectra pairs from SRs The solid line is the Gaussian fit to the histogram of the data Figure As Figure for 54 J21 and J10 spectra pairs from SRbs Figure As Figure for 41 J21 and J10 spectra pairs from SRcs Figure As Figure for 56 J21 and J10 spectra pairs from SRas Table Sources, VCs, and VRs Source U Men R Crt RT Vir W Hya RX Boo V446Oph AH Sco V2108 Oph OH2.6-0.4 VX Sgr GY Aql S Pav X Pav T Mic Number of Observations J10 (J21) First Observed VC10 (km s−1) Mean VR10 (km s−1) First Observed VC21 (km s−1) Mean VR21 (km s−1) 19 (19) 17 (19) 14 (18) 23 (25) (7) 21 (14) 21 (23) 22 (18) 21 (17) 21 (22) 18 (17) 21 (16) 16 (18) 14 (15) 20.5 14.1 18.5 39.4 2.3 9.8 −2.8 15.7 −4.6 5.0 34.2 −18.9 −19.2 29.2 9.26 3.94 2.38 14.36 2.52 7.06 17.84 10.07 8.23 22.88 8.65 5.65 6.91 4.06 18.8 9.5 16.2 41.4 −0.1 9.7 −4.8 13.7 −5.4 3.7 34.6 −21.0 −17.7 23.8 5.66 8.12 6.30 12.34 5.52 4.78 15.60 4.53 3.76 18.61 4.27 4.79 8.52 5.59 distributions Figures 9–12 show the histograms and fits of the VR21s Table gives the center, standard deviation, and amplitude of Gaussian fits to the histogrammed data The fit widths of the distributions are indicated by the standard deviation For all types except SRbs the distribution center for VR10 exceeds VR21 by 1.63–5.42 km s−1 For SRbs the VR21 distribution center exceeds the VR10 by 3.57 km s−1 The SRb VR10 and SRa VR21 are poorly fit by a Gaussian distribution as indicated graphically by relatively large values for a VR at km s−1 The The Astronomical Journal, 149:100 (8pp), 2015 March McIntosh & Indermuehle Table VC Results Variable Types, VC21–VC10 Results Variable Type LPV SR SRa SRb SRc Average VC21– VC10 (km s−1) −0.1 −0.2 0.2 −0.6 −1.2 σVC21−VC10 (km s−1) Gaussian Distribution Center (km s−1) Gaussian Distribution σ (km s−1) 1.0 1.4 0.8 2.0 0.6 0.1 −0.6 0.2 −0.1 −1.05 0.8 0.5 0.6 1.4 0.3 Table Arithmetic Analysis and Number of Spectra Variable Type LPV VR10 LPV VR21 SR VR10 SR VR21 SRa VR10 SRa VR21 SRb VR10 SRb VR21 SRc VR10 SRc VR21 Average (km s−1) σ (km s−1) Number of Spectra 6.4 5.0 8.5 4.3 9.9 8.2 4.2 7.1 20.4 17.1 3.4 2.9 2.9 2.2 4.2 4.0 2.4 3.2 3.0 3.6 638 490 82 66 63 60 69 77 42 45 Figure As Figure for 63 J10 observations of SRas Figure As Figure for 69 J10 observations of SRbs Figure Number of occurrences of VR10 vs the range of emission from the Mopra SR sources There are 82 J10 observations included The solid line is the Gaussian fit to the distribution The dotted line is the Weibull fit to the distribution SRc distribution is not well described by a single Gaussian fit because the two SRc sources have quite different VRs These poor fits indicate that Gaussians distributions are not accurately describing wind VRs The Weibull distribution is one of a family of extreme value distributions that has been used to describe wind distributions on earth (Conradsen et al 1984; Bett et al 2013) and Titan (Lorenz et al 1995) The Weibull distribution is characterized by a shape parameter and a scale parameter and is zero at VR values of km s−1 This distribution interpolates between an exponential distribution when the shape parameter is one and a Rayleigh distribution when the shape parameter is two The shape parameter is dimensionless A small shape parameter indicates quite variable wind speeds A large shape parameter Figure As Figure for 42 J10 observations of SRcs indicates fairly regular wind speeds For wind distributions on earth the shape parameter is usually between and For a fixed scale parameter the distribution narrows and the peak shifts away from zero as the shape parameter increases The scale parameter is related to the average value of the distribution and has the units of the quantities measured For a fixed shape parameter the distribution broadens and the peak decreases and shifts away from zero as the scale parameter The Astronomical Journal, 149:100 (8pp), 2015 March McIntosh & Indermuehle Figure 12 As Figure for 45 J21 observations of SRcs Figure Number of occurrences of VR21 vs the range of emission from the Mopra SR sources There are 66 J10 observations included The solid line is the Gaussian fit to the distribution The dotted line is the Weibull fit to the distribution Table Fit Gaussian Parameters Variable Type LPV VR10 LPV VR21 SR VR10 SR VR21 SRa VR10 SRa VR21 SRb VR10 SRb VR21 SRc VR10 SRc VR21 Center (km s−1) σ (km s−1) Amplitude 5.55 3.92 8.91 3.49 10.15 7.78 3.55 7.12 20.27 16.94 3.90 3.64 2.98 1.75 4.89 5.20 2.90 3.48 3.95 3.30 69.91 62.16 10.99 13.73 5.41 5.10 10.64 9.05 4.56 5.24 Table Fit Weibull Parameters Variable Type Figure 10 As Figure for 60 J21 observations of SRas LPV VR10 LPV VR21 SR VR10 SR VR21 SRa VR10 SRa VR21 SRb VR10 SRb VR21 SRc VR10 SRc VR21 Mean (km s−1) √Variance (km s−1) Shape Scale (km s−1) 6.41 5.03 8.52 4.33 9.88 8.21 4.18 7.04 20.40 18.90 3.43 7.85 2.76 2.12 4.21 4.00 2.39 3.17 3.14 3.43 1.95 1.83 3.41 2.15 2.51 2.16 1.81 2.36 7.69 6.44 7.23 5.66 9.48 4.89 11.13 9.27 4.70 7.95 21.71 20.29 but larger than the VR21s For the SRbs the parameters are larger for the VR21s The modeled spectra presented in G09 indicate a VR10 that exceeds the VR21 by approximately km s−1 at all phases and for all dust regimes The difference in the VRs is a few km s−1 This difference represents the results for all variable types except SRbs The YP12 modeled spectra show the VR21 as larger than the VR10 for all epochs and is not consistent with the observations Figure 13 shows the range of VR21 versus the VR10 for simultaneous observations for the variable type sources The number of times the VR21 is greater than the VR10 is variable type dependent For SR and SRa sources the VR10 is almost Figure 11 As Figure for 77 J21 observations of SRbs increases Table gives the Weibull shape and scale parameters The Weibull distribution means and square roots of the variances are also reported For all variable types, except SRbs, the VR10 parameters are larger than the VR21 parameters indicating the VR10s are generally more regular The Astronomical Journal, 149:100 (8pp), 2015 March McIntosh & Indermuehle Figure 14 The average VR for individual sources vs stellar oscillation period The J10 data are indicated by the solid symbols SRs (), SRas (▴ ), SRbs (♦), and SRcs (•) The J21 data are indicated by the open symbols SRs (), SRas (D), SRbs (♢), and SRcs (◦) The solid line represents the fit to the data Figure 13 VR21 vs VR10 for simultaneous observations The solid line represents equal velocity ranges in the two transitions Included in this plot are 59 simultaneous observations of the SRs (), 56 SRa observations (▴ ), 59 SRb observations (♦), and 41 SRc observations (•) pulsators LPVs are generally thought to oscillate in the fundamental mode always greater than the VR21, 58 out of 59 for SRs and 52 out of 56 for SRas For LPVs (reanalyzed MI13 data) the VR10 is greater than the VR21 in 403 out of 452 coincidental measurements SRcs have an approximately even split 23 VR10 out of 41 coincidental measurement are greater than the VR21 measurements SRbs are unusual in that out of 59 coincidental measurements, 49 times the VR21 exceeds the VR10 The difference in the VR10 and VR21 parameters may be associated with a difference in location or the range of possible locations of the masers in the two transitions For SR and SRa sources the J21 emission appears to occur in a region of the circumstellar envelop that generates features moving in a smaller VR than the J10 emission The VLBI observations of simultaneous J10 and J21 transitions indicate that the J21 emission arises further from the star than the J10 emission at least in some cases The J21 has not been observed closer to the star If the VLBI results accurately indicate the distances of the J10 and J21 emission observed in this project, the more distant J21 transition must originate in material that has decelerated as it has moved further from the star The SRc type indicates that the stars are supergiants VRs for SRcs are approximately three times as broad as the VRs for other types of stars This breadth reflects the much more extensive region in which the conditions necessary for maser emission exist The SRc VR21 is generally a few km s−1 smaller than VR10, but it is not uncommon at individual epochs for VR21 > VR10 This relatively equal relationship is consistent with Richter et al (2013) result of observing overlapping J21 and J10 emission regions from VY CMa, a supergiant star If shocks are propagating through the masing material they are not disrupting the velocity difference over approximately two periods of the SRc stars SRc VCs increase and decrease together maintaining a relatively stable difference The stability may indicate that the masers originate outside the radius at which the shock disrupts the environment The SRbs are the only semiregular variable type where VR21 normally exceeds VR10 It is possible that this change in the relationship of the VRs is caused by a different oscillation mechanism of the source As discussed above several authors suggest semiregular variables or SRbs may be overtone VR AND OSCILLATION PERIOD The VR is determined from the line of sight velocities of the masing material This material exists in the turbulent circumstellar environment within a few stellar radii of the stellar surface Figure 14 shows that there is a direct relationship between the average VR for a source and the stellar period This conclusion is based limited number of semiregular variables available for this analysis Fitting a line to these data results in the equation: VR = 0.023 * Period + 0.52 (2) Whether or not the mass loss of SR variables is dependent on the oscillation period of the star is still being debated The VR of the SiO maser emission, which based on our data is related to the stellar pulsation period, may indicate the energy of the material elevated above the stellar surface This energy may affect the amount of material that reaches a distance at which the condensation of grains occurs and radiation pressure on the grains generates the mass loss from the star CONCLUSIONS The Mopra database provides the first large data set of SiO maser spectra (essentially simultaneous observations in J21 and J10 over yr) to allow the comparison of the VCs and VRs for the J10 and J21 transitions among LPVs and semiregular variable types The velocity parameter comparisons extracted from these observations will inform and constrain the development of future models of the circumstellar environment and maser dynamics There is a tendency for more positive (redder) VC10s than VC21s in LPVs, SRs, SRbs, and SRcs This difference between the two transitions may be the result of relatively small numbers of observations or may indicate a physical difference More spectra will be examined in the future to see if this trend continues and has physical significance For SRas VC21 is slightly more positive than VC10 The VC difference in SRcs is large and stable over several stellar periods If the material generating the maser emission The Astronomical Journal, 149:100 (8pp), 2015 March McIntosh & Indermuehle undergoes a shock passage, the passage does not destroy or randomize the velocity structure of the masing material Except for SRbs, VR10 is larger than the VR21 This result indicates that the two transitions originate in different parts of the circumstellar envelope and experience the proposed shock propagation differently The larger VR10 is qualitatively consistent with the predictions of G09 However a quantitative comparison of the predicted and observed J10 and J21 VCs and VRs is not possible at this point If different oscillation mechanisms are occurring in LPVs (self-excited, larger amplitude, fundamental mode) and semiregulars (stochastically excited, smaller amplitude, overtone mode), the different mechanisms have generally the same effect on SiO maser velocity parameters The SRb difference may be a result of a different oscillation mechanism occurring in these stars as suggested by Kerschbaum & Hron (1992) and Willson (2000) The semiregular VRs are linearly related to the stellar period This relationship may affect the mechanism though which stellar mass loss takes place Further observational and theoretical studies are needed to investigate stellar oscillations, SiO maser velocity parameters, and stellar mass-loss Further observational and theoretical work is necessary to investigate the possibility of different oscillation mechanisms affecting the velocity parameters of the SiO maser emission REFERENCES Alard, C., Blommaert, J., Cesarsky, C., et al 2001, ApJ, 552, 289 Alcolea, J., Bujarrabal, V., & Gomez-Gonzalez, J 1990, A&A, 231, 431 Bedding, T 2003, Ap&SS, 284, 61 Bett, P E., Thornton, H E., & Clark, R T 2013, AdSR, 10, 51 Chen, X., Shen, Z., & Jiang, D 2007, in IAU Symp 242, Astrophysical Masers and Their Environments, ed J M Chapman & W A Baan (Cambridge: Cambridge Univ Press), 312 Christensen-Dalsgaard, J., Kjeldsen, H., & Mattei, J 2001, ApJL, 562, L141 Conradsen, K., Nielsen, L B., & Prahm, L P 1984, JCAM, 23, 1173 Gray, M D., Wittkowski, M., Scholz, M., et al 2009, MNRAS, 394, 51 Hinkle, K., Scharlach, W W G., & Hall, D B 1984, ApJS, 56, Humphreys, E., Gray, M., Yates, J., et al 2002, A&A, 386, 256 Indermuehle, B., Edwards, P., Brooks, K., & Urquhart, J 2013, The Mopra SiO Maser Catalogue v1, CSIRO, Data Collection Indermuehle, B., & McIntosh, G 2014, MNRAS, 441, 3226 Kerschbaum, F., & Hron, J 1992, A&A, 263, 97 Kerschbaum, F., Olofsson, H., & Hron, J 1996, A&A, 311, 273 Lorenz, R D., Lunine, J I., Grier, J A., & Fisher, M A 1995, JGR, 100, 26377 McIntosh, G., & Indermuehle, B 2013, AJ, 145, 131 Mosser, B., Dziembowski, W A., Belkacem, K., et al 2013, A&A, 559, 137 Pijpers, F P., & Habing, H J 1989, A&A, 215, 334 Pijpers, F P., Pardo, J R., & Bujarrabal, V 1994, A&A, 286, 501 Richter, L., Kimball, A., & Jonas, J 2013, MNRAS, 436, 1708 Samus, N N., Durlevich, O V., Kazarovets, E V., et al 2012, General Catalogue of Variable Stars (Samus+2007-2012), VizieR On-line Data Catalog: B/gcrs Su, J., Shen, Z., Chen, X., et al 2012, ApJ, 754, 47 Weibull, W 1951, ATJAM, 18, 293 Willson, L A 2000, ARA&A, 38, 573 Wood, P 1989, in From Miras to Planetary Nebulae, ed M O Mennessier (Gif-sur-Yvette: Editions Frontieres), 67 Wood, P 1990, in ASP Conf Ser II, Confrontation between Stellar Pulsation and Evolution, ed C Cacciari & G Clementini (San Francisco, CA: ASP), 355 Yi, J., Booth, R S., Conway, J E., & Diamond, P J 2005, A&A, 432, 531 Yun, Y., & Park, Y.-S 2012, A&A, 545, 136 The Mopra radio telescope is part of the Australia Telescope National Facility which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO The University of New South Wales Digital Filter Bank used for the observations with the Mopra Telescope was provided with support from the Australia research Council GMc would like to thank the University of Minnesota, Morris, MIT Haystack Observatory, Wesley Brand, Clare Miller, and other UMM students for supporting the development of this research