The Megamaser Cosmology Project. VI. Observations of NGC 6323
C. Y. Kuo, J. A. Braatz, K. Y. Lo, M. J. Reid, S. H. Suyu, D. W. Pesce, J. J. Condon, C. Henkel, C. M. V. Impellizzeri
aa r X i v : . [ a s t r o - ph . GA ] J a n The Megamaser Cosmology Project. VI. Observations of NGC 6323
C. Y. Kuo , J. A. Braatz , K. Y. Lo , M. J. Reid , S. H. Suyu , D. W. Pesce , J. J. Condon , C.Henkel , , C. M. V. Impellizzeri Academia Sinica Institute of Astronomy and Astrophysics, P.O. Box 23-141, Taipei 10617, Taiwan National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA Department of Astronomy, University of Virginia, Charlottesville, VA 22904 Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany Astronomy Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, SaudiArabia
ABSTRACT
We present observations of the H O megamasers in the accretion disk of NGC 6323. By com-bining interferometric and spectral monitoring data, we estimate H = 73 +26 − km/s/Mpc, wherethe low strength of the systemic masers ( <
15 mJy) limits the accuracy of this estimate. Themethods developed here for dealing with weak maser emission provide guidance for observationsof similar sources, until significant increases in radio telescope sensitivity, such as anticipatedfrom the next generation Very Large Array, are realized.
Subject headings: accretion, accretion disks – galaxies: nuclei – galaxies: masers – galaxies: active– galaxies: ISM – galaxies: Seyfert
1. INTRODUCTION H O megamasers provide a direct determination of H independent of standard candles (e.g. Reid etal. 2009, Braatz et al. 2010, Reid et al. 2013, Kuo et al. 2013). This method involves sub-milliarcsecondresolution imaging of H O maser emission from sub-parsec circumnuclear disks at the center of active galaxies,and the geometric distance to each of the galaxies is determined based on measurements of the orbital sizeand velocity as well as the centripetal acceleration of maser clouds orbiting around the supermassive blackhole. Since this technique involves very few assumptions and can be applied to maser galaxies in the Hubbleflow in a single step, systematic errors are expected to be small. In the Megamaser Cosmology Project(MCP), we have currently obtained a H of 68 ± − Mpc − from UGC 3789 (Reid et al. 2013)and 68 ±
11 km s − Mpc − from NGC 6264 (Kuo et al. 2013). To further constrain H , we are currentlymeasuring additional maser galaxies and searching for more high quality megamaser disk systems which aresuitable for H determination.In this paper, we present observations of NGC 6323, a Seyfert 2 galaxy at a distance of ∼
100 Mpc. Themasers in this galaxy shows a Keplerian rotation curve and have the necessary maser components (i.e. thesystemic and high-velocity masers; see Kuo et al. 2011 for their definitions) for a H determination with theH O megamaser technique. It is different from our previously published maser galaxies (i.e. UGC 3789 and 2 –NGC 6264) in that the systemic masers, are quite weak. The typical signal-to-noise ratio (SNR) of a systemicmaser line is only ∼
10 in spectra taken by the Green Bank Telescope (GBT) with an integration time of ≈ H estimate,NGC 6323 provides a test case to explore the accuracy and precision one can achieve in determining H from a galaxy with faint systemic masers.In section 2, we present our VLBI and single-dish observations. In section 3, we show the analysis ofthe centripetal accelerations of the masers in NGC 6323. The analyses of the Hubble constant determinationare presented in section 4. Finally, we summarize the results in section 5.
2. Observations and Data Reduction2.1. GBT monitoring
We observed the H O maser in NGC 6323 with the GBT at 21 epochs between 2006 October 30 and 2009May 19. Except during the summer months when the humidity makes observations at 22 GHz inefficient,we took a spectrum on a monthly timescale. For these observations, we followed the same observing settingsand data reduction procedures as in Braatz et al. (2010). Table 1 shows the observing date and sensitivityfor each observation. Figure 1 shows a representative H O maser spectrum for NGC 6323.Fig. 1.— A characteristic H O maser spectrum of NGC 6323 obtained on 2007 April 6. The vertical axisis flux density in mJy and the horizontal axis is Local Standard of Rest velocity (optical definition). Notethat the systemic maser emission between ≈ − is weak ( <
10 mJy).
We observed NGC 6323 with thirteen 12-hour tracks of VLBI observations between 2007 and 2009using the Very Long Baseline Array (VLBA) , augmented by the 100-m Green Bank Telescope and the The Green Bank Telescope is a facility of the National Radio Astronomy Observatory. The VLBA is a facility of the National Radio Astronomy Observatory, which is operated by the Associated Universities,Inc. under a cooperative agreement with the National Science Foundation (NSF). . These observations have been presented in Kuo et al. (2011), who usedthe inteferometric maps to estimate the supermassive black hole mass, using a distance given by assuming H = 73 km s − Mpc − and a recessional velocity of 7848 km s − .We have improved on the previous analysis by dividing the calibrated interferometer (u,v)-data intoyearly groups, periods A, B, and C (see Table 1), merging data within a group, and then imaging. We couldnot combine all the data when imaging, since most maser spots changed amplitude significantly over thethree year span of the observations. By comparing maser positions from different periods, we can estimatethe magnitude of systematic position offsets in the maser astrometry, owing to independent phase and delaycalibration. When comparing maser positions, we use the data from period C as the reference because wehave the most complete data in this period and this data dominate the sensitivity of the entire dataset. Wefound that there is no systematic offset between maser positions measured in period A and C, and the averagemaser positions from these two periods agree within 2 µ as. However, when comparing positions measuredfrom periods B and C, we found systematic position offsets for the systemic and blueshifted masers. Thereis no position offset for the redshifted masers in period B and C as expected because all maser positions arereferenced to the average position of the redshifted masers as a result of the self-calibration process.The average position of the systemic masers in period B has an offset of 1 ± µ as in the easterly ( x )direction and 10 ± µ as in the northerly ( y ) direction from that of the systemic masers in period C. Forthe blueshifted masers, the average offsets in x and y between period B and C are 7 ± µ as and 22 ± µ as, respectively. Since the systemic and blueshifed masers have average frequency offsets of 31 MHz and64 MHz, respectively, from the average frequency of the spectral channels of the redshifted masers used forself-calibration, the systematic position offsets in the y direction appear to be frequency dependent in nature,implying a residual error of ∼ The Effelsberg 100-m telescope is a facility of the Max-Planck-Institut f¨ur Radioastronomie.
Epoch Date Day Number T sys (K) rms Noise (mJy) Period0 2006 October 30 0 42.4 2.2 A1 2006 December 2 33 36.0 1.4 A2 2007 February 22 115 44.0 2.2 A3 2007 April 6 158 35.9 1.8 A4 2007 October 29 364 34.3 1.4 B5 2007 November 28 394 35.7 1.6 B6 2007 December 26 422 55.0 2.9 B7 2008 February 2 460 39.3 1.5 B8 2008 February 29 487 44.0 1.7 B9 2008 March 25 512 34.2 1.3 B10 2008 April 24 542 56.5 1.8 B11 2008 May 6 554 41.1 2.4 B12 2008 May 29 577 49.4 2.0 B13 2008 September 29 700 47.7 2.2 C14 2008 October 31 732 43.5 1.7 C15 2008 November 28 760 35.9 1.1 C16 2008 December 29 791 35.2 1.3 C17 2009 January 30 823 33.8 1.1 C18 2009 March 4 856 31.5 1.2 C19 2009 March 31 883 38.2 1.3 C20 2009 May 19 932 35.3 1.5 CNote. — The sensitivities are calculated without performing Hanning smoothing to thespectra and are based on 0.33 km s − channels. We label Period A, B, and C to those timeswhen we have continuous observations on a monthly timescale. These periods are separatedby summer months during which the humidity makes observations inefficient. V opa Θ x b σ Θ x b Θ y b σ Θ y b A c σ A c (km s − ) (mas) (mas) (mas) (mas) (km s − yr − ) (km s − yr − )8372.94 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − V opa Θ x b σ Θ x b Θ y b σ Θ y b A c σ A c (km s − ) (mas) (mas) (mas) (mas) (km s − yr − ) (km s − yr − )7882.35 − − − − − − − − − − a Velocity referenced to the LSR and using the optical definition (no relativistic cor-rections). 7 – b East-west and north-south position offsets and uncertainties. Position uncertaintiesreflect fitted random errors only. c Measured or estimated acceleration and its uncertainty for each maser component. 8 –
3. Acceleration Analysis
Following Kuo et al. (2013), we adopted two approaches to measure accelerations of maser spots: initialestimates from the eye-tracking method for high velocity masers followed by two methods of global least-squares fitting (Humphreys et al. 2008; Braatz et al. 2010; Reid et al. 2013; Kuo et al. 2013) for systemicmasers. In essence, the eye-tracking approach yields estimates of acceleration by fitting a straight line tospectral peak velocities, identified by eye from the spectra, as a function of time. The global least-squaresfitting method fits the amplitudes for a range of channels in all selected spectra simultaneously, with a modelconsisting of multiple Gaussian-shaped lines that drift linearly in time.
In Figure 2, we plot the radial velocities of the high-velocity maser peaks as a function of time. Note thatwhile the blueshifted and redshifted maser lines are distributed over a velocity range of ∼
200 km s − , not allmaser features are represented in Figure 2. This is because maser lines blend with their neighboring maserfeatures significantly. To measure the accelerations of the maser features seen in Figure 2, we first identifythe lines that are persistent in time and then fit a straight line to the data to measure the accelerationsdirectly. The uncertainty of the measurements is estimated by scaling the fitting error by the square root ofreduced χ .The variance weighted average accelerations of the redshifted and blueshifted masers are − .
14 and − .
01 km s − yr − respectively. The rms scatter of accelerations of the redshifted and blueshifted masersare 0.26 and 0.21 km s − yr − . The small accelerations and rms scatter indicate that the high velocitymasers are close to the mid-line of the accretion disk as expected. To account for possible uncertainty causedby line blending, we use the rms scatter of the acceleration measurement as an estimate of the systematicerror and include this error in the total uncertainty before performing disk modeling described in Section 4.Fitted accelerations and uncertainties that include the systematic errors are listed in Table 2. The systemic features of NGC 6323 have low signal-to-noise ratios (SNRs) and significant line-blendingthat make acceleration fitting difficult. To facilitate more reliable and stable acceleration fitting, we followKuo et al. (2013) and separate the maser lines into velocity sub-groups having similar apparent accelerations.Assignment to an acceleration sub-group was done by examining dynamic spectra to identify persistentpatterns. Dynamic spectra plot the flux density as color-coded intensity as a function of velocity versus time(see Figure 3). Flux densities were interpolated between monthly monitoring gaps, but not across longer(summer) gaps. Based on the dynamic spectra, we identify seven groups of masers that show coherentdrifting patterns. Then, we estimated accelerations for the maser features in each group separately withglobal least-sqaures fitting.When fitting the spectra for accelerations, we divide the data into periods based on seeing coherentdrifting patterns in the dynamic spectra. We show the epochs used in the acceleration fitting for all masergroups in the 3rd column in Table 3. Note that we were unsuccessful fitting for masers in Group 5 and6 between epochs 14 (Day 732) through 20 (Day 932), as a result of low SNR, severe line-blending, andespecially the short time baseline. 9 –Fig. 2.— We plot the radial velocities of NGC 6323 maser peaks as a function of time (the crosses) for theblue-shifted masers (the left panel), the systemic masers (the middle panel), and the red-shifted masers (theright panel). On top of these plots, we overplot the fitting results from the eye-tracking method for thehigh-velocity masers and from the least-squares fitting for the systemic masers. The data between Day 100and 400 come from spectra taken in Period A; the data between Day 500 to 800 from spectra in Period B;and the data between Day 800 to 1200 are from spectra in Period C.We followed
Method 1 and
Method 2 described in Reid et al. (2013) to fit the accelerations of thesystemic masers. These methods differ in the choice of initial parameter values and the number of Gaus-sian components used. Also, Method 1 allows each Gaussian component to have independently estimatedaccelerations, whereas Method 2 assumes maser accelerations are a linear function of velocity, defined as asingle acceleration ( A sys ) at the center of the velocity range and its velocity derivative (d A sys /dv). Thedifference between the measurements from these two methods allows an estimate of uncertainty in measuredacceleration, based on fitting methodology.In Figure 4, we show the results of the acceleration measurements using both methods. Overall, themeasurements from the two methods agree very well, as do the accelerations obtained from the same groupfitted over different periods of time. For the disk fitting presented in Section 4, we adopted the acceleratonmeasurements from Method 1 (see Table 3), because this method makes less restrictive assumptions. Typicalreduced χ ν values for these fits are 0.92-1.13 for all maser groups except for Group 4, which typically had χ ν ≈ .
36. Only for the weak masers with velocites between 7882 and 7885 km s − do we see a marginallysignificant difference between measurements made between epochs 4–13 (in group 7a) and 14–20 (in group 10 –Fig. 3.— Dynamic spectra of the systemic masers in NGC 6323.The left panel shows the maser flux density as a function oftime and velocity. The white ticks at the bottom of the figure show the epochs at which we took the maser spectra. Exceptfor epochs separated by a summer gap, the maser flux at the time between these epochs is obtained by linearly interpolatingthe flux densities measured in consecutive epochs. No interpolation is used for consecutive spectra that are separated by asummer gap (i.e. Day 160-360 and Day 580-700), and these regions are intentionally left blank. The vertical white lines in thefigure show the velocity windows in which we can see clear drifting pattern of maser lines and the accelerations of the masercomponents within the window can be assumed to be approximately the same. The numbers adjacent to the white lines are thegroup numbers we assign to the velocity windows. In the right panel, we overplot the straight lines that represent the best-fitaccelerations from the least-squares fitting on the plot shown in the left panel. H caused by the slightly discrepant acceleration measurementsfor masers in group 7a and 7b.
4. Modeling the Accretion Disk and Determining H The Hubble constant determination with the disk modeling method developed in Reid et al. (2013)relies on modeling the sub-parsec scale maser disk in three dimensions and adjusting model parameters tominimize the position, velocity, and acceleration residuals for each maser spot. Global model parametersinclude H , black hole mass ( M ), recession velocity of the galaxy ( V ), and other parameters that describe 11 –Fig. 4.— The left panel shows the centripetal acceleration of the systemic masers measured from the global least-squaresfitting method. The red data points show the measurement assuming that the maser acceleration is a linear function of maservelocity (Method 2, Sect. 3.2.1) whereas the blue ones show the measurement without such an assumption (Method 1, Sect.3.2.2). The measurements shown in the right panel are the same as the ones shown in the left panel except in the velocityrange between 7873 km s − and 7888 km s − . We have different accelerations in this velocity window because we measure theacceleration in two different sets of epochs. The left panel show the measurements using spectra measured between epoch 0and 13 (Day 0 − Day 700; Group 7a; see also Table 4); the right panel shows the measurement using data taken between epoch14 and 20 (Day 732 − Day 932; Group 7b). the orientation and warping of the disk. Key elements for estimating H are the Keplerian position-velocity(rotation) curve described by the high velocity masers, the centripetal accelerations of the systemic masers,and their angular offsets and velocities relative to the dynamical center. In essence, the Keplerian rotationof the disk measured from high-velocity masers determines M/D , where D is the distance to the galaxy and M is the black hole mass, whereas the position, velocity, and acceleration information of the systemic masersgive M/D (see Kuo et al. 2013). Therefore, one can measure D by solving the above two equations, and H can be directly inferred from D and the galaxy’s Hubble flow speed, V , also obtained from the high-velocityrotation curve. We refer the readers to Reid et al. (2012) and Kuo et al. (2013) for detailed information ofthe disk modeling.In the disk modeling, we associated maser positions and velocities with accelerations measured fromthe GBT monitoring of maser spectra by choosing the VLBI channel with the velocity closest to thatof an acceleration fit. For the high velocity masers, since there are fewer acceleration fits than VLBImeasurements of maser position and velocity as results of the line-blending effect and of using the eye-trackingmethod to measure the acceleration of high-velocity masers, not all VLBI measurements have correspondingaccelerations. For maser features without acceleration measurements, we use only the position and velocitydata in the disk modeling. We show the input data (including the velocity, position, and acceleration foreach maser feature) for the disk modeling in Table 2.Rather than using formal fitting uncertainties for maser position and velocity, which tend to be opti-mistic, we added estimates of systematic uncertainty (“error floors”) in quadrature with the formal uncer-tainties. For the x − and y − data, we followed Reid et al. (2013) to adopt an error floor of 0.01 mas. Formaser velocity, the precise value for the error floor is not important, because it only affects the convergencerate of the disk fitting and does not affect the best-fit result. Therefore, as a rough estimate of the systematicerror for maser velocity, we adopt 1.8 km s − ( ≈ − ±
163 km s − for NGC 6323(Masters; private communication). This comes from galaxy flow models of the local supercluster (Masters2005). Note that this peculiar velocity is relatively small, because toward the Perseus-Pisces superclusterdeviations from Hubble’s flow are modest. Given the recession velocity of NGC 6323 is ∼ − , theprecise value of the peculiar velocity is unimportant as it contributes only ≈
2% to the total H uncertainty.We modeled the maser disk in 3 dimensions with the same 10 global parameters used in modeling themaser disk in UGC 3789 (Reid et al. 2013) and perform the model fitting with a Markov Chain MonteCarlo (MCMC) approach (e.g. Geyer 1992; Gilks, Richardson & Spiegelhalter 1996) to obtain the posterioriprobability density distributions of the model parameters. Optimum values of the model parameters wereestimated from the posteriori probability density functions (PDFs), marginalized over all other parameters.To verify convergence of the MCMC fitting, we adopted the power-spectrum method by Dunkley et al.(2005). In this method, one measures the variance of the mean of the probability distribution and thecorrelation length of the MCMC chain from its power spectrum, followed by evaluation of the degree ofconvergence based on these two parameters. A MCMC chain is considered to have converged if r < .
01 and j ∗ ≥
20. Here, r is the convergence ratio, defined as the ratio between the variance of the sample mean andvariance of the underlying probability distribution ( σ x / σ ), and j ∗ = k ∗ ( N/ π ) indicates the region in thepower spectrum (i.e. the wavenumber k ∗ ) of the MCMC chain where the chain starts to deviate from thewhite noise regime (see Dunkley et al. 2005 for details). N in the above expression for j ∗ is the total numberof samples in the MCMC chain. Finally, our estimates of the best global parameter values come from themarginalized PDFs; we adopted the median of the marginalized PDF, with the uncertainties showing the16th and 84th percentiles (spanning the 68% confidence interval). H Estimation
To fully explore the parameter space, we ran 10 independent MCMC chains with different starting condi-tions. In particular, we choose the starting value for H uniformly in the range 60 < H <
80 km s − Mpc − .The length of each independent run was set to be 10 MCMC trials. The combined MCMC chains from the10 indepedent runs fully satisfied the convergence criteria set by Dunkley et al. (2005), with convergenceratio r = 0 . j ∗ = 33.Figure 5 shows the results of the Bayesian fitting by comparing the most-probable MCMC trial modelwith the observed maser map, the position-velocity diagram, and the acceleration measurements. In Figure6, we show the model maser distribution from a view along the disk spin axis (left panel) and the warpingstructure with a nearly edge on view (right panel). In general, the model matches the observations well,and the differences between the data and model are consistent within realistic uncertainties except for a fewhigh-velocity maser spots with relatively large acceleration (i.e. ∼− − yr − ; see the bottom panelof Figure 5). The total reduced χ ( χ ν ) of the fit is 1.352 for 107 degrees of freedom (291 data points). Wesummarize the most-probable values for all model parameters in Table 4. Note that since χ ν >
1, we followour conservative practice of inflating parameter uncertainties by p χ ν .We show the posteriori PDF for H from the Bayesian fitting in Figure 7. The PDF is slightly asymmetricabout the peak of the distribution at H = 67 km s − Mpc − . The median of this PDF is 73 km s − Mpc − and the 16th and 84th percentiles span 51 to 99 km s − Mpc − . From the fitted recessional velocity of7853 . ± . − , the corresponding distance to NGC 6323 is D = V /H =107 +42 − Mpc.Note that in Section 3.2 we show that there is a marginally signifcant discrepancy in the acceleration 13 –measurements for group 7a and group 7b, especially at the high end of the velocity window (see Figure 4).To explore the magnitude of the systematic error in H caused by the systematic uncertainty in acceleration,we perform the disk modeling again without including the systemic maser feature with velocity at 7885.9km s − in Table 2. The resultant H is 68 +26 − km s − Mpc − . One can see that the H decreases by 5km s − Mpc − and this represents the maximum systematic error in H that the discrepant accelerationmeasurements for the maser features in group 7 at the high velocity end can introduce. Since this number issignificantly smaller than the current measurement error in H , one can infer that the systematic error in theaccelerations for group 7 has little impact on our current H estimate which is dominated by measurementerror. H In the context of a thin maser disk with well-measured Keplerian rotation curve, as those cases shownin Kuo et al. (2011), the precision of the H measurement with the megamaser technique relies primarilyupon the precision of position and acceleration measurement of the systemic masers. In addition, the spatialand velocity range over which systemic masers can be detected also plays an important role.For the maser disk in NGC 6323, the large H uncertainty (compared to other MCP galaxies) primarilyresults from the lower precision of the maser position measurements, owing to weaker maser emission and thefact that the maser disk orients in the north-south direction where we have the poorest angular resolution.The accuracy of acceleration measurements is sufficient so that it is not a dominant contributor to the H uncertainty.Besides position accuracy, the narrower velocity range of detectable systemic masers in NGC 6323 isalso a limiting factor for an accurate H measurement. The velocity range covered by the maser spots withposition measurements to better than ± µ as is less than 50 km s − , whereas in NGC 4258 (Humphreys etal. 2008) and UGC 3789 (Reid et al. 2013) the corresponding velocity ranges are ≈
100 km s − . Therefore,for NGC 6323 our constraints on H are quite limited. 14 –Fig. 5.— Data (colored dots) and best-fit model (lines and black dots). Top panel: Positions on the sky. Middle panel:LSR velocity versus position along the disk. Bottom panel: Accelerations versus impact parameter. In all three panels, thered, green, and blue dots show the redshifted masers, the systemic masers, and the blueshifted masers, respectively. Notethat in the bottom panel, there are three redshifted maser spots with acceleration below − − yr − , which are largerthan the typical acceleration (i.e. ∼ − yr − ) for high-velocity masers and these values are very likely a result of severeline-blending. Excluding these maser features does not change the H from the disk modeling because the H determination isdominated by the systemic masers. The accelerations of the high-velocity masers play a negligible role in the H measurement.
5. Summary
This work presents the third H estimate from the Megamaser Cosmology Project (MCP). Unfortu-nately, the low flux densities of the systemic masers in NGC 6323 preclude an accurate estimate of H . Wediscussed several approaches for handling low signal to noise data, but conclude that with current telescope 15 –Table 3. Acceleration Measurements for the Systemic Masers Group Velocity Epochs Ref. Epoch Linewidth Acceleration A σ (km s − ) Components (km s − yr − ) (km s − yr − )1 7805.2 10 −
20 15 2.6 1.47 0.272 7812.8 10 −
20 15 1.8 1.27 0.363 7845.3 0 −
20 8 1.8 1.07 0.114 7850.2 4 −
20 8 1.7 0.80 0.245 7853.2 3 −
13 8 2.9 1.27 0.545 7855.1 3 −
13 8 2.2 1.05 0.296 7865.5 3 −
14 8 2.7 1.12 0.156 7868.6 3 −
14 8 2.7 0.79 0.147a 7874.8 4 −
13 8 2.9 0.92 0.237a 7878.9 4 −
13 8 2.9 0.69 0.277a 7881.3 4 −
13 8 1.8 0.35 0.357a 7882.8 4 −
13 8 1.8 0.36 1.037b 7873.9 4 −
13 16 2.7 0.75 0.717b 7876.4 14 −
20 16 2.5 0.83 0.537b 7879.3 14 −
20 16 2.4 0.25 0.707b 7881.0 14 −
20 16 2.3 1.64 0.837b 7883.0 14 −
20 16 2.2 1.48 0.477b 7885.6 14 −
20 16 2.1 1.49 0.41Note. — Col(1): maser group number; Col(2): the best-fit velocity of the model maser component,with a typical uncertainty of 0.25 km s − ; Col(3): the epochs of the spectra used for fitting (for the datessee Table 1); Col(4): the reference epoch for velocity shown in Column(2); Col(5): the average linewidth;Col(6): the best-fit acceleration; and Col(7): the uncertainty of the acceleration. All fitted value comefrom accelertion fitting Method 1. Table 4. NGC 6323 H O Maser Model
Parameter Priors Posterioris Units H ... 73 +26 − km s − Mpc − V ... 7853.4 +2 . − . km s − V p − +163 − − +190 − km s − M ... 0.94 +0 . − . M ⊙ x ... 0.015 +0 . − . masy ... 0.011 +0 . − . mas i ... 88.5 +0 . − . deg di/dr ... 6.0 +9 . − . deg mas − p ... 189.5 +0 . − . deg dp/dr ... 13.2 +2 . − . deg mas − Note. — Parameters are as follows: Hubble constant ( H ),recession velocity of the galaxy in optical convention relativeto the Local Standard of Rest ( V sys ), peculiar velocity withrespect to Hubble flow in cosmic microwave background frame( V p ), black hole mass ( M ), eastward (x ) and northward (y )position of black hole relative to a conveniently chosen pointclose to the average position of all maser features, disk in-clination ( i ) and inclination warping (change of inclinationwith radius: di/dr ), disk position angle ( p ) and position an-gle warping (change of position position angle with radius: dp/dr ). Flat priors were used, except where listed. Parametervalues given in Table 4 were produced from binned histogramsfor each parameter. The quoted values here are the mediansof the marginalized probability density functions, with the un-certainties showing the 16th and 84th percentiles (i.e., the 68%credible interval).
16 –Fig. 6.—
The left panel shows the maser distribution of our best-fit model for NGC 6323 from the overhead perspective. Theright panel shows the best-fit model from the observer’s perspective with model maser spots plotted on top of the warp model.The red, green, and blue dots in both panels show the redshifted masers, the systemic masers, and the blueshifted masers,respectively. In the right panel, for the illustration purpose, we changed the observer’s viewing angle from 89 ◦ to 83 ◦ to showthe degree of disk warping more clearly. sensitivities the MCP should concentrate on sources with maser spots stronger than ≈
20 mJy. However, iffuture radio telescopes can achieve significantly higher collecting areas and/or lower system temperatures,then we can make substntially better measurements for galaxies such as NGC 6323. We hope that the nextgeneration Very Large Array will ultimately provide such an improvement.
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