A COMPARISON OF THE VELOCITY PARAMETERS

SRbs are the only classification of semiregular variable in which the VR21 exceeds the VR10.. The difference in the SRb SiO maser velocity parameters may be due to a difference in the osc

A COMPARISON OF THE VELOCITY PARAMETERS OF SIO V = 1, J = 1 − 0, AND J = 2 − 1 MASER EMISSION IN SEMIREGULAR VARIABLES

Gordon McIntosh1and Balthasar Indermuehle2

1

Division of Science and Mathematics, University of Minnesota, Morris, 600 East 4th Street, Morris, MN 56267, USA; mcintogc@morris.umn.edu

2 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= 1 − 0 (J101) and the v = 1, J = 2 − 1 (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−1greater 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

1 BACKGROUND SiO masers originate in the circumstellar region between the

stellar photosphere and the cooler regions where the SiO

condenses out onto grains In this region the masers provide a

probe of the dynamics between the photospheric shocks

traveling out from the variable star and the usually spherical

outflow The exact mechanisms that connect the stellar shock

with the mass loss have not been determined, but studies of SiO

maser parameters provide information to inform and constrain

mass loss models It has been suggested that different variable

types oscillate in different modes—fundamental, first overtone

Different oscillation modes may produce variations in the SiO

maser velocity parameters

1.1 Semiregular Variables The General Catalogue of Variable Star (GCVS) (Samus

et al 2012) defines the semiregular variable types which are

included in the Mopra observing program

SR semiregular variables, which are giants or supergiants of

intermediate and late spectral types showing noticeable

periodicity in their light changes, accompanied or sometimes

interrupted by various irregularities Periods lie in the range

from 20 to >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)

SRa semiregular late-type (M, C, S or Me, Ce, Se) giants displaying persistent periodicity and usually small(<2.5 mag in

V) light amplitudes Amplitudes and light-curve shapes generally vary and periods are in the range of 35–1200 days Many of these stars differ from Miras only by showing smaller light amplitudes

SRb semiregular late-type (M, C, S or Me, Ce, Se) giants with poorly defined periodicity (mean cycles in the range of

20–2300 days) or with alternating intervals of periodic and slow irregular changes, and even with light constancy intervals Every star of this type may usually be assigned a certain mean period (cycle), which is the value given in the catalog In a number of cases, the simultaneous presence of two or more periods of light variation is observed

SRc semiregular late-type (M, C, S or Me, Ce, Se) supergiants with amplitudes of about 1 mag and periods of light variation from 30 days to several 1000 days

Differences in the pulsation modes of long period variables (LPVs) and semiregular variables have been suggested Kerschbaum & Hron (1992) concluded that, “SRas are a mixture of“intrinsic” Miras and SRbs” and that the “red” SRbs having mass loss, luminosities, and main sequence masses comparable to Miras have periods consistent withfirst overtone pulsations This conclusion assumes Miras pulsate in the fundamental mode(Wood 1990) Kerschbaum & Hron (1992) suggest an evolutionary path from SRbs to “classical” Mira stars with a change from overtone pulsations to fundamental mode pulsations Other evidence also indicates LPVs oscillate

in the fundamental mode while semiregular variables oscillate

in thefirst or second overtone Hinkle et al (1984) observed the CO vibrational emission from eight LPVs and one SRa

© 2015 The American Astronomical Society All rights reserved.

1 Throughout the paper the suf fix 10 refers to the SiO v = 1, J = 1 − 0

transition, and the suf fix 21 refers to the SiO v = 1, J = 2 − 1 transition.

They found that the photospheric shock had a smaller velocity

amplitude in the SRa star Willson (2000) used this

observa-tions 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

over-lapping J10 and v= 2, J = 1 − 0 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

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 1 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)

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 Tain each velocity channel

S

a a

lsr

The summations extend over the range of emission

The VR is calculated to be the region where the Taexceeds 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 do 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 = 1 − 0 SiO maser transitions in the supergiant VY CMa They found

“significantly higher spatial overlap between the v = 1, J = 1 − 0 and J= 2 − 1 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 loca-tions 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

Table 1 Source Information Source Variable Type Period Spectral Type

(days)

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

2 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−1to 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 VELOCITY PARAMETERS AND RESULTS

Table 2 presents the number of J10 and J21 observations of

each source, thefirst VC10 and VC21 observed and the mean

VR10 and VR21

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−1wide andfit assuming a Gaussian distribution Figures 1–4 display the histograms and Gaussianfits of VC21–VC10 for SRs, SRa, SRb, and SRcs, respectively The arithmetic average andσ, the square root of the variance, and the center and standard deviation of the Gaussian fits are included in Table 3 along with the LPV data for comparison

The SR distribution shows a number of occurrences above +1 km s−1compared to the Gaussianfit, but the center for the Gaussian is−0.6 km s−1so 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 Gaussianfit 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 4 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 0 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

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 4 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 largestσs of 4.2 and 4.0 km s−1for 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

distributions Figures 9–12 show the histograms and fits of the

VR21s

Table 5 gives the center, standard deviation, and amplitude

of Gaussianfits 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 poorlyfit by a Gaussian distribution as indicated graphically by relatively large values for a VR at 0 km s−1 The

Figure 1 Histogram of VC21–VC10 for observations within 1 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 2 As Figure 1 for 56 J21 and J10 spectra pairs from SRas.

Table 2 Sources, VCs, and VRs Source Number of Observations First Observed VC10 Mean VR10 First Observed VC21 Mean VR21

Figure 3 As Figure 1 for 54 J21 and J10 spectra pairs from SRbs.

Figure 4 As Figure 1 for 41 J21 and J10 spectra pairs from SRcs.

SRc distribution is not well described by a single Gaussian fit

because the two SRc sources have quite different VRs These

poorfits 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 0 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

indicates fairly regular wind speeds For wind distributions on earth the shape parameter is usually between 2 and 3 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

afixed shape parameter the distribution broadens and the peak decreases and shifts away from zero as the scale parameter

Table 3

VC Results Variable Types, VC21 –VC10 Results

Variable

Type

Average

VC21 –

VC10 σ VC21−VC10

Gaussian Dis-tribution Center

Gaussian Dis-tribution σ (km s −1 ) (km s −1 ) (km s −1 ) (km s −1 )

Table 4 Arithmetic Analysis and Number of Spectra

(km s −1 ) (km s −1 )

Figure 5 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.

Figure 6 As Figure 5 for 63 J10 observations of SRas.

Figure 7 As Figure 5 for 69 J10 observations of SRbs.

Figure 8 As Figure 5 for 42 J10 observations of SRcs.

increases Table 6 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

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 1 km s−1at 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 9 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.

Figure 10 As Figure 9 for 60 J21 observations of SRas.

Figure 11 As Figure 9 for 77 J21 observations of SRbs.

Figure 12 As Figure 9 for 45 J21 observations of SRcs.

Table 5 Fit Gaussian Parameters

Table 6 Fit Weibull Parameters

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

pulsators LPVs are generally thought to oscillate in the fundamental mode

4 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

5 CONCLUSIONS The Mopra database provides thefirst large data set of SiO maser spectra(essentially simultaneous observations in J21 and J10 over 4 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

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 (•).

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.

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,

over-tone 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

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

develop-ment of this research

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