Toward a New Geometric Distance to the Active Galaxy NGC4258: I. VLBI Monitoring of Water Maser Emission

3.4 MB·English

by  A. L. Argon

Toward a New Geometric Distance to the Active Galaxy
NGC4258:
I. VLBI Monitoring of Water Maser Emission
A. L. Argon, L. J. Greenhill, M. J. Reid, J. M. Moran, & E. M. L. Humphreys
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138
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n ABSTRACT
a
J We report a three year, 18 epoch, VLBI monitoring study of H O masers in the sub-parsec,
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2 warped,accretiondiskwithintheNGC4258AGN.Ourimmediategoalsaretotracethegeometry
1 oftheunderlyingdisk,trackrotationviameasurementofpropermotion,andascertaintheradiiof

masers for which centripetal acceleration may be measured separately. The monitoring includes
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∼ 4× as many epochs, ∼ 3× denser sampling, and tighter control over sources of systematic
v
6 errorthanearlierVLBIinvestigations. Coverageofa∼2400kms−1 bandwidthhasalsoenabled
9 mapping of molecular material ∼ 30% closer to the black hole than accomplished previously,
3 which will strengthen geometric and dynamical disk models. Through repeated observation we
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have also measured for the first time a 5µas (1σ) thickness of the maser medium. Assuming
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this corresponds to the thickness of the accretion disk, hydrostatic equilibrium requires a disk
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0 plane temperature of ≈ 600 K. Our long-term goal is a geometric distance to NGC4258 that is
/ accurate to ∼3%, a ∼2× improvement over the current best estimate. A geometric estimate of
h
distance can be compared to distances obtained from analysis of Cepheid light curves, with the
p
- intent to recalibrate the extragalacticdistance scale with reduced systematic uncertainties. This
o
is the first paper in a series. We present here VLBI observations, data reduction, and temporal
r
t and spatial characteristics of the maser emission. Later papers will report estimation of orbital
s
a accelerationandpropermotion,modelingofdisk3-Dgeometryanddynamics,andestimationof
: a “ maser distance.” Estimation of a “Cepheid distance” is presented in a parallel paper series.
v
i
X Subject headings: galaxies: individual (NGC,4258) — galaxies: kinematics and dynamics — galaxies:
nuclei— galaxies: active — masers — techniques: interferometric
r
a
1. Introduction
surrounding the central engine (Herrnstein et al.
The extragalactic distance scale (EDS) is un- 1999)—couldeitherreplaceorbeusedinconjunc-
derpinnedbymeasurementsof“standardcandles” tion with the LMC as anchor.
in the Large Magellanic Cloud (LMC) and other
In NGC4258, accretion disk material emits
nearbygalaxies(Freedman et al.2001). Thelong-
H O maser emission in the 6 −5 transition at
2 16 23
term importance of a high-accuracy EDS calibra-
22.235 GHz, which was first reported close to the
tionliesinpotentialprecisionestimationofcosmo-
systemic velocity(V )by Claussen et al.(1984).
sys
logical parameters, such as the equation of state
Akeydiscoverywashigh-velocityDopplercompo-
for dark energy (e.g., Hu 2005). One means by nentsat∼V ±1000kms−1(Nakai, Inoue, & Miyoshi
sys
which the EDS calibration might be improved is
1993) in NGC4258, where V = 472 ± 4
sys
byanchoring“standardcandle”calibrationtodis- km s−1, adopting the Local Standard of Rest
tances estimated by geometric techniques. To-
(LSR) and radio definition of Doppler shift
wardsthis end, NGC4258—forwhichageometric
(Cecil, Wilson, & Tully 1992). An early Very
distancehasbeenestimatedfrommodellingofthe
LongBaselineInterferometry(VLBI)study(Greenhill et al.
3-D geometry and dynamics of the accretion disk
1The VLBA is a facility of the National Radio Astronomy
Observatory, which isoperated byAssociated Universities
1 Inc., under cooperative agreement with the National Sci-
enceFoundation.
1995a) suggested that maser emission might orig- distance indicators that are identifiable in the
inate from a rotating disk, as did a parallel in- Hubble Flow (e.g., Tully Fisher relation, type Ia
vestigation of secular velocity drifts for the peaks SNe), are calibrated using distances to Cepheid
of spectral features, i.e., centripetal accelerations host galaxies and are used in turn to estimate
(Haschick, Baan, & Peng 1994; Greenhill et al. H . High-precision estimates of H are also avail-
◦ ◦
1995b;Nakaietal. 1995;seealsoWatson&Wallin able from analysis of Cosmic Microwave Back-
1994). Low-velocity Doppler components (those ground (CMB) fluctuations (e.g., Spergel et al.
nearV )driftedby≈+10kms−1yr−1andhigh- 2006). However, degeneracies in analysis of CMB
sys
velocity components drifted by <±1kms−1yr−1, data do not allow independent determination of
thus localizing the former to the near side of bothH andtheequationofstatefordarkenergy,
◦
the disk and the latter near the mid-line (i.e., w. Note that Spergel et al. (2006) assumed a flat
the diameter perpendicular to the line of sight). universe with w=−1 and obtained a value of H
◦
The sub-parsec disk model was confirmed by in good agreement with Freedman et al. (2001).
Very Long Baseline Array (VLBA)1 observations, The mostsubstantialproblemwith the current
which traced, most importantly, the disk warp Cepheid-based calibration of the EDS is depen-
and the rotationcurve,the latter being Keplerian dence onthe LMC aszeropointanchorforPLre-
to better than 1% (Miyoshi et al. 1995; see also lations. Contributing factors include uncertainty
Herrnstein et al. 2005). in distance to the LMC, poorly understood inter-
For a Keplerian system, accurate first-order nal galactic structure, and controversy over the
estimates of geometric distance may be ob- impact of the difference in stellar metallicity be-
tained relatively simply from the geometry of the tween the LMC and HST Cepheid-sample galax-
warped disk and measurements of acceleration or ies.
proper motion for low-velocity emission. To date, The adopted uncertainty in the LMC distance
NGC4258 is the only galaxy for which this has by Freedman et al. (2001) is ∼ 5%. However,
been done. Herrnstein et al. (1999) obtained a LMC distance estimates obtained from different
distance to NGC4258 of 7.2 ± 0.3 (random) ± calibrations and analyses over the last decade
0.4 (systematic) Mpc, where the systematic term cover a ±23% range (±0.50 mag when expressed
is due mostly to a thus far weak constraint on in terms of distance moduli). This is well beyond
orbital eccentricity (< 0.1). Our major aim is uncertaintiesforindividualmeasurements(Figure
to reduce both random and systematic error. 8 of Benedict et al. 2002a) and likely indicative of
Herrnstein et al.(1999)usedfourepochsofVLBA unresolvedsystematicerrors. Althoughuncertain-
data spanning 3 years to estimate distance. In ties ≪10%havebeen obtainedfromthe distribu-
contrast,we have18epochs overa subsequent3.4 tions of distance estimates for different subsam-
year interval. This facilitates more detailed mod- ples of measurements (e.g., Freedman et al. 2001;
eling ofdisk substructure,formalincorporationof Benedict et al. 2002b), in the face of apparently
orbital eccentricity and periapsis angle as param- unresolvedsystematics,theaveragesandmoments
eters, more definitive tracking of disk rotation, may be statistically problematic.
and reduction of random and systematic error by
The uncertain structure of the LMC (e.g.,
a factor of at least two. Humphreys et al. (2005)
disk eccentricity, out-of-plane stellar component),
discuss early progress.
complicates interpretation of distance indicators
The current distance scale, as characterizedby (van der Marel2001;Nikolaev et al.2004,andref-
the Hubble constant (H◦), may be uncertain by erences therein). For instance, robust estimates
perhaps as little as 10% (Freedman et al. 2001). of distance have been obtained for eclipsing bina-
The most robust estimate depends on measured ries, with individual uncertainties of 2 - 3% (e.g.,
mean magnitudes of ∼800 Cepheid variable stars Fitzpatrick et al. 2002, and references therein).
in31galaxieswithin30Mpc,andcomparisonwith However, for the four systems well studied thus
the period luminosity (PL) relation for Cepheids far, the range of implied distances for the LMC
in the Large Magellanic Cloud (LMC). The LMC center covers 14% (Fitzpatrick et al. 2003).
establishes a zero point for calibration of Cepheid
The impact of metallicity could be as large at
lightcurvesinothergalaxies. Commonsecondary
±10%indistance. Limitedtheoreticalandempiri-
2
calunderstandinghasledtolongtermcontroversy maser, i.e., three 200kms−1-wide line complexes
overthe magnitude and signofthe effect ofmetal distributed over ∼ 2000kms−1 (e.g., Bragg et al.
content on Cepheid brightness (Sasselov et al. 2000); (3) tight control over sources of systematic
1997; Kochanek 1997; Kennicutt et al. 1998; error; and (4) relatively uniform sensitivity from
Groenewegen et al.2004;Sakai et al.2004;Romaniello et aelp.och to epoch.
2006). Attempts to make definitive measure- We observed NGC4258 18 times between 1997
ments have been complicated by the magnitude March6and2000August12,usingtheVLBA,the
of observable metallicity gradients in well studied Very Large Array (VLA), and the Effelsberg 100-
galaxies,the sizes of Cepheid samples, and the ef- m telescope (EFLS) of the Max-Planck-Institut
fects ofreddening andcrowdinginlow-metallicity fu¨r Radioastronomie(Table 1). Twelve “medium-
fields at smaller galactocentric radii. Consensus sensitivity” epochs involved the VLBA alone; the
theoretical models have not emerged because of remainingsix“high-sensitivity”VLBIepochswere
computational difficulty, with some doubt as to interleavedandinvolvedtheVLBA,augmentedby
whether or not metal content alone needs to be the phased VLA and EFLS.
considered (Fiorentino et al. 2002).
In medium-sensitivity epochs, we recorded
Precision estimation of cosmological parame- eight 16 MHz (≈ 216kms−1) basebands with
ters is best achieved by multiple approaches. Hu 1-bit sampling. We overlapped seven bands by
(2005) argues that percent level accuracy in H◦, 15%, resulting in observing bandpasses of ∼ 362
combined with measurements of CMB fluctua- to 1676kms−1 (covering low-velocity and red-
tions, would enable robust constraint on w in- shifted high-velocity emission) and ∼ −706 to
dependent of those provided by measurements 608kms−1 (coveringlow-velocityandblue-shifted
of, e.g., weak lensing and large scale structure. high-velocityemission),dependingupontheepoch
Spergel et al. (2006) also demonstrate the im- (Table2). We tuned the eighth band to enable
pact on estimates of curvature by independent dual polarization observations of the emission
constraint on H◦. A new “maser distance” for peak (spanning the velocity range 362-578 km
NGC4258 is a first step, with the immediate goal s−1 for red-shiftedepochs and 392-608km s−1 for
of ∼ 3%. This paper is the first in a series. Here blue-shiftedepochs),thusincreasingthesignal-to-
wepresentthe VLBI dataandbrieflydiscuss gen- noise ratio available for tracking atmospheric and
eral trends such as time evolution of position- instrumentalresponsefluctuations during calibra-
velocitytraces. Laterworkwillpresenttime-series tion. Because the ∼ 2000kms−1 bandwidth of
maserspectroscopyandmodelingofthecombined the source was difficult to accommodate instan-
datasetstoobtainanimprovedgeometricdistance taneously with VLBI data acquisition systems,
(cf.Herrnstein et al.1999). Parallelanalysisofre- we alternated month-to-month between observ-
cent Cepheid photometry obtained with the Hub- ing two offset ∼ 1500kms−1 bands. One covered
ble Space Telescope, beginning with Macri et al. low-velocity and red-shifted high-velocity maser
(2007), will provide an improved “Cepheid dis- emission, and the other covered low-velocity and
tance” (cf. Newman et al. 2001). Ultimately, blue-shifted high-velocity emission. Combining
the two programs will culminate in comparison data from adjacent months, we effectively ob-
ofmaserandCepheiddistancesandre-assessment served ∼ 2400kms−1, centered approximately on
of the EDS and implications for cosmology. the systemic velocity.
In high-sensitivity epochs, we recorded eight 8
2. Observations and Data Reduction
MHz (≈ 108kms−1) basebands with 2-bit sam-
pling,alternatingbasebandtuningoverthecourse
2.1. The Observations
of each track to cover the three emission com-
The design of the observing program was in- plexes. The narrower instantaneous bandwidth
tended to enable (1) unambiguous tracking of accommodated the limited IF bandwidth of the
evolution in the source spectrum and disk struc- VLA(2×50MHz). Inthefirstfivehigh-sensitivity
ture,throughclosespacingofepochs;(2)monitor- epochs, we recorded both upper and lower side-
ing to detect possible transient emission outside bands to limit the number of baseband mixers re-
the historically recognized velocity range of the quired and thereby accommodate a reduced com-
3
plement at Effelsberg. To avoid band gaps at median for medium-sensitivity epochs (Table 1).
mixer frequencies,we overlappedthe sidebands of Earlier studies of low- and high-velocity emission
adjacent mixers and obtained ≈ 300kms−1 cov- togetherachievedsensitivitiesof3.0-6.5mJywith
erage of low-velocity,red-shifted, and blue-shifted a 5.6 mJy median (Herrnstein et al. 2005).
emission complexes. In the last high-sensitivity
epoch, we took advantage of a new complement 2.3. Calibration and Imaging
ofmixersatEffelsberg,recordingonlyupperside-
Calibration and synthesis imaging were per-
bands with 20% overlap and 365kms−1 coverage
formed using the Astronomical Image Processing
of each emission line complex.
System(AIPS)softwarepackagewithlargelystan-
dard techniques for spectral-line VLBI2. We dis-
2.2. Strengths of the Current Study
cuss notable elements of the processing below.
TimeSampling—Spacingbetweenhigh-sensitivity
epochs, ∼ 8 months, was comparable to spac- 2.3.1. Array and Sky Geometry
ing between epochs in an earlier VLBI study
We sought to ensure consistency in the an-
(Herrnstein et al. 2005, their Table 1), but the
tenna coordinates used for each correlation over
1-2 month time interval between most medium-
the 3 years of monitoring. This was achieved by
sensitivity epochs was comparable to the typi-
implementing (post-processing) the station posi-
cal known timescale for spectral variability (e.g.,
tions and (tectonic) velocities estimated by the
Bragg et al. 2000). A minimum 8 day separation
United States Naval Observatory (USNO) in so-
betweenepochsalsoenabledtestingforshort-term
lution N9810 (Table 3). Because the VLA does
source structure variability.
not have dual-frequency geodetic VLBI receivers
Bandwidth — The high-sensitivity epochs (as in
and is absent from solution N9810, we adopted
allpreviousVLBI studies)focusedonthe velocity
a position estimated by the NRAO using single-
ranges in which Nakai, Inoue, & Miyoshi (1993)
frequency data for epoch 2000.9 and the average
identified emission. In contrast, medium sensi-
velocity for the nearby Pietown and Los Alamos
tivity observations monitored all velocities from
stations (C. Walker, private communication). Af-
vLSR ∼−706to 1676kms−1, achievinga detection ter correction, station positions were accurate to
threshold ≈ 2× below that of earlier broadband
≈ 1 mm for the VLBA and EFLS and ≈ 3cm for
(−1200 to 2650kms−1) single-dish studies by
the VLA.
Nakai, Inoue, & Miyoshi (1993) and Nakai et al.
To ensure consistency in the maser posi-
(1995), scaledto the samechannelspacing. Emis-
tion and error budget from epoch to epoch, we
sion at “new” velocities was sought because it
adopted a maser position obtained from analysis
would presumably arise in previously unmapped
ofearlyVLBIdata: α(J2000)=12h18m57s.5046±
portions ofthe accretiondisk. For eachepoch,we
0s.0003; δ(J2000)=47◦18′14′.′303±0′.′003(Herrnstein et al.
recorded eight basebands (which were correlated
2005). This was used in correlation of all but
in two passes). Each baseband was divided into
the first three epochs, for which we applied a
512 spectral channels.
frequency-dependent shift to the measured maser
Quality and Consistency — The same observ-
spot positions, after Herrnstein et al. (2005). The
ing setup and data reduction path were used for shift corresponded to an error of −0s.0054 and
each medium-sensitivity epoch. A separate com- 0′.′033 in right ascension and declination, respec-
mon setup and reduction path was used for high-
tively, in thea priori position. A priori calibrator
sensitivityepochs. Deliberaterepetition(e.g.,u,v- positions were accurate to . 1mas, and no cor-
coverage, choice and timing of calibrators, base-
rections were made. A priori earth orientation
band tuning) limited systematic errors in differ-
parameters were compared to “final” values pub-
ential measurements of dynamical quantities (i.e.,
lished by the USNO and found to be accuarateto
proper motion, acceleration).
< 1mas (pole position in X and Y) and < 0.1ms
Sensitivity—Noiselevels(1σ)insynthesisimages
were2.3-4.7mJywitha3.0mJymedianforhigh- 2AIPS cookbook, chapter 9:
sensitivityepochsand3.6-5.8mJywitha4.3mJy http://www.aoc.nrao.edu/aips/cook.html
4
(UT1-UTC) for each epoch. We discuss the im- ment of the slowly time variable electronic phase
pact of these uncertainties and limits in §2.5 (see offsets among basebands, using observations of
also Table 4). quasars made approximately every hour for that
purpose. Specifically, the wide spacing in fre-
2.3.2. Amplitude Calibration quency among bands increased susceptibility to
(nonphysical) phase wraps entering the interpo-
To calibrate VLBA fringe amplitudes, we ap-
lationofphaseoffsets betweenadjacentcalibrator
plied observatory-standard antenna gain curves
scans. Because the phase wraps were readily de-
and time-series system temperature measure-
tected, straight-forwardediting of single-bandde-
ments. An ≈ 40% depression in the system tem-
lay and rate data enabled removaland estimation
peratures of the red-shifted high-velocity base-
of offsets with accuracies on the order of 10◦ or
bands in high-sensitivity epochs rendered some of
∼3% of a fringe on the sky.
these calibrations suspect. Such large changes in
system temperature is not likely and is probably
2.3.4. Self-calibration
due to a measurement problem. To compensate,
we computed a system temperature time-series Weappliedself-calibrationsolutionstothedata
characteristic of the several low-velocity base- in each baseband to correct for fluctuations in
bands and applied it to all basebands. fringe amplitude and phase. These fluctuations
Accurate system temperature time-series were arose from instabilities in the atmosphere and in
typically not available for the VLA and EFLS. the frequency standards at the stations and from
For these two stations, we calibrated amplitudes antenna gain changes. For each epoch, we identi-
through a comparison of fringe amplitudes on fiedarelativelyunblendedDopplercomponent(>∼
4C39.25among VLBA stations (after calibration) 1Jy)toprovidethereferencesignal. Imagesofthe
and fringe amplitudes for baselines including the reference component achieved dynamic ranges of
VLAorEFLS.Timesamplingoftheresultingcal- 40-300, defined with respect to the 5σ noise level
ibration was relatively coarse, but we anticipated or strongest artifact.
later self-calibration would enable refinement. Weobservedunusuallylargeartifactsinimages
We note that in the three cases for which we ofhigh-velocityred-shiftedemissionforafewhigh-
made nonstandard amplitude corrections (i.e., sensitivity epochs. Dynamic ranges were reduced
VLA, EFLS, and the red-shifted high-velocity by a factor of ∼ 4. We were unable to identify a
VLBA basebands in high-sensitivity epochs) am- cause and adopted an empirical strategy to cor-
plitude errors for some basebands could survive rectthe problem. For these epochs, we performed
self-calibration, because gain corrections are cal- asecondself-calibrationonthestrongestobserved
culated for emission in just one (low-velocity) red-shiftedDoppler component. Thoughtypically
baseband. Though a matter of concern, ampli- only a few tenths of a Jy, this secondaryreference
tude errors on the order of a few tens of percent was detectable because the initial self-calibration
on a small fraction of baselines are anticipated to extended the phase coherence of the data. We
have a relatively small impact on astrometry for applied the additional, slowly varying amplitude
point-like sources, i.e., maser spots. andphasecorrectionstothedatainallred-shifted
basebands. To recover relative position informa-
We expect the overall flux scale for a given
tion (with respect to the primary reference emis-
epoch to be accurate to ≈ 30% for medium-
sion), we appliedthe angularoffset betweenrefer-
sensitivity epochs and ≈ 50% for high-sensitivity
ence features, measured prior to the second self-
epochs. However,whencomparingtheoverallflux
calibration.
scalebetweenoramongepochs,weexpectanaccu-
racy of ≈ 15% for medium-sensitivity epochs and Secondary self-calibration of the blue-shifted
≈25% for high-sensitivity epochs. high-velocity emission was not possible because
the peak flux density was too low (< 100mJy).
2.3.3. Global Fringe fitting Wetestedtwosecondarycalibrationsforthe“blue
data”. The first was achieved by applying the
The most demanding element of the global
“reddata”self-calibrationcorrectionstothe“blue
fringe fitting process was the accurate measure-
data” and the second by applying the complex
5
conjugate of the “red data” corrections to the breadth appeared consistent with blending
“blue data”. In the first case we implicitly mod- of individual maser spots, we attempted to
eledtheunexplainederrorsasphase-only,whilein fit multi-component Gaussian models.
the second case as delay-only. Neither approach
improved the signal-to-noise in images of blue- In each epoch, there are on the order of
shifted emission, and was therefore not adopted. 107 independent pixels among the image cubes.
Some losses in imaging blue-shifted emission re- The probability that one or more will exceed
main possible. 6σ, in the absence of a signal, is ≈ 10% (e.g.,
Thompson, Moran, & Swenson 2001, Fig. 9.5).
2.3.5. Imaging and Deconvolution By requiring three adjacent channels to satisfy
this criterion, with a constraint on position, the
We imaged and CLEANed a 25.6 × 25.6mas
chancesoffalsedetectionareonthe orderof10−7
field (in medium-sensitivity epochs) or a 30.72×
(where we have accounted for correlation among
30.72mas field (in high-sensitivity epochs) over
channels consistent with the FX architecture and
theinner96%ofeachbandpass. Theknownangu-
time-windowing of data in the VLBA correlator).
larextentofthemasersourceis∼1×16mas. Syn-
Where we had a priori information as to the
thesizedbeamsizes andtypicalnoiselevels forin-
locationinvelocityandpositionofamaser,were-
dividualspectralchannelsaregiveninTable1. We
laxed the 6σ selection criterion. There were three
used a hybrid weighting scheme midway between
instances.
uniform and natural weighting (ROBUST=0 in
the AIPS task IMAGR), in order to balance the
• High-velocity features (> 3.5σ) were ac-
desireforasmallbeammeasuredatthehalf-power
cepted if emission at corresponding po-
points and low rms noise. In five of the six high-
sitions and velocities had been detected
sensitivity epochs, we extended imaging outside
above the formal detection threshold in
the inner 96% of the bandpasses, because a blue-
other epochs. The probability of false de-
shifted Doppler component hadbeen found in the
tection of a 3.5σ emission peak over one
medium-sensitivity epochs. The anticipatedemis-
independent point (one beam) is < 10−3.
sion was detected in one epoch (BM081A).
Blue-shiftedDopplercomponentsfallinginto
2.4. Identification of Maser Spots and this category were found at −285 km s−1
Continuum Emission (BM081A), −367 km s−1 (BM112G), −373
km s−1 (BM081B and BM112C), and −515
Wefita2-DGaussianbrightnessdistributionto km s−1 (BM112C,BM112E,and BM112H).
all peaks in channel maps and required that they Red-shiftedDopplercomponentsfallinginto
satisfy the following requirements, in order to be this category were found at 1566 km s−1
judged bona fide maser “spots.” (BM112F and BM112M).
• Emissioncentroidsliewithinonebeamwidth • High-velocity blue-shifted emission (> 2σ)
over at least three adjacent channels at or was accepted in spectral channels adja-
above the 6σ level. cent to already identified blue-shifted fea-
tures, if in the same epoch and at the
• Fitted peak intensities exceed the intensity same angular position to within a beam
ofimagingartifacts,i.e.,intensitiesmustex- width. Blue-shifted emission was identi-
ceed the local peak intensity divided by the fied in this way at −285 km s−1 (BM112C,
dynamic range. We note that this dynamic BM112E, BM112G, BM112L, BM112N,
range cut was only relevant to channels in and BM112P), −367 km s−1 (BM112C),
high-sensitivity epochs with strong emission −373kms−1 (BM056C,BM112E,BM112G,
features and candidate secondary features. BM112H, and BM112L), −435 km s−1
(BM056C and BM081A), −441 km s−1
• Half-power major and minor axes are both
(BM056C), and −515 km s−1 (BM112G).
smallerthantwicethemajorandminoraxes
The motivation for this extension of our de-
of the convolving beam. In cases where
tectionlimitwasbetterestablishmentofline
6
shape for weak features. It was not used to 2.5. The Error Budget
increase the number of features.
ForeachGaussianfit,therandommeasurement
• High-velocity features (> 3.5σ) outside the errorinpositionwasestimatedasbeingthelarger
nominalrange(i.e.,Nakai, Inoue, & Miyoshi of the fitting error or the beam full-width at half-
1993)wereaccepted,ifsingle-dishstudysep- maximum (FWHM) divided by twice the peak
arately identified the Doppler components. signal-to-noiseratio(S/N). Weestimatedthesys-
In this way, we detected the 1647kms−1 tematic position error from two components: (1)
component first reported by Modjaz et al. errors that scale with difference in sky frequency
(2005) for epoch 2003.75. Extrapolat- between a given channel and the reference (i.e.,
ing from the positions of other red-shifted ν −νref), and (2) errors that scale with the dif-
Doppler components and adopting a Kep- ferenceinbasebandfrequenciesofagivenchannel
lerian rotation curve for the “maser disk,” and the reference (i.e., [ν − ν◦]− [νref − νref◦],
we confined the anticipated position of the where ν◦ and νref◦ are the band-center frequen-
1647kms−1 emission to within 1 beam cies). The maximum difference in sky frequencies
× 3 channels. Emission was detected in is ≈ 75 MHz for NGC4258; the maximum differ-
BM112M at 5σ in the line-center channel ence in baseband frequencies is < 8 MHz. Er-
and 4σ in adjacent channels. Marginal de- rors in the absolute position of the reference and
tections were also found in two adjacent calibrators, or errors in zenith propagation delay
epochs, i.e., emission at 2.4 and 3.0σ in two and baseline coordinatesgive rise to the first type
contiguous spectral channels for BM112K of systematic error. Uncertainty in station clocks
andfour2.8σ−3.3σ pointsinadjacentspec- give rise to the second type.
tral channels for BM112O. A consistency check of the high-accuracy (∼ 3
mas)maserreferencepositionofThompson, Moran, & Swenson
In addition to identifying maser emission, we (2001)canbe obtainedfromourcontinuumimag-
searched for continuum emission at all epochs ing of BM081B. In this epoch, we imaged with a
within12.5masofthelow-velocityreferenceemis- less accurate (∼ 60 mas) a priori maser reference
sion. Continuumu,v-datawereconstructedbyfre- position, which led to a substantial difference be-
quencyaveragingeachbasebandpriortoimaging. tween red- and blue-shifted position offsets, due
In the case of BG107 and all medium-sensitivity to the largefrequencydifference betweenred-and
epochs, we discarded the outer 2% of each of the blue-shifted continuum “bands” (see Table 4). If
red-orblue-shiftedbasebandsandobtainedanef- we assume that this misalignment of red- and
fective average of 1960 channels (30.6 and 61.3 blue-shifted continuum is entirely due to an inac-
MHz for BG107 and medium-sensitivity epochs, curate a priori maser reference position, we ob-
respectively). Intheotherhigh-sensitivityepochs, tain a new reference position that is offset from
we discardedthe outer 2%ofeachofthree red- or Thompson, Moran, & Swenson(2001) by 0s.001in
blue-shifted basebands and averaged 1470 chan- rightascensionand0′.′01indeclination,wellwithin
nels (23.0 MHz). Fewer channels were retained in our 1.5σ combined errors (ours plus Herrnstein’s,
these epochs, because ofextensive overlapofside- added in quadrature). We note that all channel
bands for adjacent baseband mixers. and continuum peak positions in this epoch were
Finally, we performed a separate search for corrected, post-imaging, for the lower-accuracy a
maser emission that might be associated with priori maser reference position.
jet activity in NGC4258, well downstream from Table 4 gives the magnitudes of random and
the central engine. In the most sensitive of our systematic position error. Random error domi-
high-sensitivity observations (BM112H), we box- nates the error budget for weak masers, whether
car averaged the u,v-data over four channels to they be at low- or high-velocities. For instance,
improve sensitivity and imaged a 30.72×491.52 blue-shifted masers are dominated by random
mas (512×8192 pixels, E-W×N-S) strip centered error. Systematic error dominates red-shifted
on the reference position. No emission peaks ex- masers stronger than ≈ 0.1Jy and low-velocity
ceeded a 6σ detection threshold (13mJy). masers stronger than ≈ 0.5Jy. The largest con-
7
tribution to systematic error arises from uncer- tain a relativistic LSR velocity,
tainty in the absolute position of the reference
tehmeistsyiponic,aclafuresqinugen≈cy1s0epµaarsateirornorbaectwroesesn7l5owMaHnzd, vrLSR = 1+v(rvtrotpop+∆∆vvLLSSRR)/c2.
high-velocitymasers. For agivenDoppler compo-
After velocity correction, all positions were re-
nent, the error repeats from epoch to epoch, with
referencedtov =510.0kms−1,corresponding
second-order impact (because reference emission rLSR
to the classical LSR velocity v = 509.6 km
velocitiesdifferby<4MHzamongepochs). How- cLSR
s−1. We note that in all previous NGC4258stud-
ever, a 10 µas error is comparable to upper limits
ies(e.g.,Herrnstein et al.1999),thequotedveloc-
on disk thickness and the hydrostatic scale height
ities have been classically defined and conversions
(Moran et al. 1995), with implications discussed
performed during accretion disk modeling made
in a later paper.
the analyses relativistically correct. Those con-
2.6. Relativistic Velocity Assignments versions included a general relativistic correction,
which for a black hole of mass 3.8×107M was
⊙
Velocities in the LSR reference frame, assum- ≈4kms−1 at the disk inner radius and 2 km s−1
ing the radio definition of Doppler shift, were as-
at the outer radius. We have not applied a gen-
signed to each channel. The choices of reference
eral relativistic correction to the data presented
frame and definition were made for consistency
here because the correction is model dependent,
with previous work (e.g., Herrnstein et al. 2005).
and its discussion is reservedfor a later paper.
However,the first-order(radio definition)andfull
relativistictreatmentofvelocitydiffer byasmuch 3. Results
as 4kms−1 for the most red-shifted emission. Be-
cause this is comparable in magnitude to impor- 3.1. Data Products
tant physical effects (e.g., distortion of the rota-
Maser Spectra — Spectra of low- and high-
tion curve by disk warping), we have adopted rel-
velocity masers are shown in Figures 1-4. These
ativistic velocities for purposes of disk modeling.
spectra were constructed from fitted maser spot
Both first-orderand relativistic velocities are pre-
flux densities. An averagespectrum forallepochs
sented with the fitted maser spot parameters in
isshowninFigure5. Channelswithoutdetectable
Table 5.
emission are not shown.
In order to convert classical to relativistic ve-
locities, we first reconstructed the actual sky
Maser Maps — We present the full set of Gaus-
frequency of a feature observed in the earth’s
sianfits fordetectedmaserspotsinTable 5. Note
topocentric frame at 12h UT for the date of ob-
that spots that lie in the overlap between adja-
servation. This involved removing the LSR cor-
cent basebands appear twice. Quoted position
rectionto obtainthe classicaltopocentric velocity
uncertainties are fitted random error. The true
and converting to the observed frequency accord-
random error is estimated to be the maximum
ing to the classical radio Doppler formula
of the fitted random error and the random er-
νobs vctop ror computed according to Table 4. The sky dis-
x= =1− ,
ν c tribution and related statistics of the masers are
0
shown in Figures 6-9; the position along the ma-
where ν is the observed sky frequency, ν the
obs 0 jor axis of the disk versus LSR velocity are shown
frequency in the emitter’s rest frame, v is the
ctop in Figures 10-13. We define the impact parame-
classical velocity in the topocentric frame, and c ter to be b = ±(∆x2 + ∆y2)1/2, where ∆x and
is the speed of light. We then convertedto a rela-
∆y are the east-westandnorth-southoffsets from
tivistic topocentric velocity, the emission at 510.0kms−1 (relativistic), respec-
tively, and the sign of b is taken from the sign of
v (1−x2)
rtop
= . ∆x(whichisfeasiblebecausethediskiselongated
c (1+x2)
chiefly east-west). The formal uncertainty in im-
Finally,wereintroducedtheLSRcorrectiontoob-
8
pact parameter (σ ) is given by of 10, whereas the measurement error for points
b
thatdeviatedby1σisincreasedbyafactorof1.06.
(∆x σx)2+(∆y σy)2 1/2 Finally, we obtained offset correctionsfor individ-
σ = ,
b h ∆x2+∆y2 i ualepochs(bothhigh-andmedium-sensitivity)by
minimizing the sum of the squares of the offsets
where σ and σ are the random components of
x y from the variance-weighted averages above. Fig-
uncertaintyin eastandnorthoffsets, respectively.
ure16showstheobservedandcorrectedoffsetsfor
red-shifted emission in observation BM112H, an
ContinuumMaps—Wedetectedcontinuumemis- epochwithoneofthelargestshifts. Table7quan-
sion > 3σ in fifteen epochs and averaged decon- tifiesthecomputedshiftsforeachepoch,whichwe
volved images (with uniform weighting) to obtain applied to the data. However,we note that Table
a peak intensity of 1.1 mJy (23σ) (Figure 14). 5 contains uncorrected maser spot positions. In
Nondetection for the remaining three epochs may addition, no corrections have been computed for
be attributed to known time variability of the blue-shifted emission because it is too sparse to
source(Herrnstein et al.1998). InTable6,welist enable comparisons.
(angleintegrated)fluxdensitiesandcentroidposi-
tions. Figure15showsaplotoffluxdensityversus 4. The Sky Distribution of Maser Emis-
time. Our measurements are consistent with the sion
hypothesis that the emission traces a jet extend-
ingoutwardfromthecentralengine,alongthespin Maser emission in NGC4258 traces a thin,
axis of the accretiondisk (Herrnstein et al. 1998). slightlywarped,nearlyedge-ondisk(Miyoshi et al.
1995; Herrnstein et al. 1998, 2005). The new
3.2. Position Shifts VLBI data (Figure 6) trace this structure more
fully, due to both emission time variability (i.e.,
Visual comparison shows that the position-
development of new Doppler components) and
velocity loci for low- and red-shifted high-velocity
broader observing bandwidth (e.g., velocities
emission are offset at a few epochs by up to
above 1500kms−1). The flaring (in north off-
∼30µas from a weighted average locus computed
set range) of low-velocity maser spots at the east
from the medium-sensitivity epochs. The shifts
offset edges of the plot is an artifact and is due
do not appear to be frequency dependent. We
to the fact that the weaker spots, which have
attribute them to residual phase offsets between
lower positional accuracy, are preferentially lo-
basebands correlated in separate passes (as were
cated away from the middle of the low-velocity
low and high-velocity bands), uncertainty in the
spectrum (Figure 1). Crowding of plot symbols
postself-calibrationregistrationthatwasrequired
alsoobscurestherelativebreadthsofthedistribu-
forparticularhigh-sensitivityepochs,andunmod-
tions of maser spots with different flux densities.
eledchangesinthestructureofthereferenceemis-
Toassessthestatisticsofthedistributionofmaser
sion from epoch to epoch.
spots, we have computed perpendicular offsets of
We computed corrections for this effect as fol-
low-velocity masers from a boxcar-smoothed (30
lows. First, we constructed variance-weighted av- km s−1 width), weighted average locus of emis-
erage x and y positions for each channel from all
sion observed in the medium-sensitivity epochs.
medium-sensitivity epochs. (Weighting depended
For spots <250mJy, the distribution is Gaussian
upon random measurement error alone.) Next,
and is consistent with measurement noise (Figure
we downweighted outliers according to the em-
8, top panel). For spots > 250 mJy, the distribu-
piricalscheme belowand computednew variance-
tion exhibits significant non-Gaussian wings and
weighted averages. To downweight outlying sam-
tail (Figure 8, bottom panel), which is a result
ples, we multiplied measurementerrorsby anem-
of source structure on scales of order 10 µas. If
piricalfactorthatincreasedwithoffset: exp(∆)2,
4σ werestrictthevelocityrangeunderconsideration,
where ∆ is the offset in x or y from the weighted
the distribution of strong spots may be related
averageandσ is the unmodifiedmeasurementun-
to accretion disk thickness. The inclination and
certainty. Forinstance,themeasurementerrorfor
position angle warp of the disk combine to cre-
pointsthatdeviatedby6σ isincreasedbyafactor
ate a concavity on the near side, the bottom of
9
which is tangent to our line of sight (i.e., the disk speed (Frank, King, & Raine 2002). Note that
is seen edge-on at this point). Maser spots in the v /r =(GM/r3)1/2 =ω,whichis the slope ofthe
φ
velocity range 485-510 km s−1 lie in this part of impact parameter versus velocity curve of Fig-
the disk (Herrnstein et al. 2005, their Figure 14). ure 10 and equals 2.67× 10−10 s−1. Hence, for
Previously measured accelerations for masers in σ = 5.1 µas or 5.5×1014 cm, we obtain c = 1.5
s
this velocity range are 8-10 km s−1 yr−1, which km s−1, corresponding to a temperature of about
suggestsaradiusof3.7-4.1masandfromthewarp 600 K (about half the limit given by Moran et al.
model we infer a projected range vertical offset of (1995)). This temperature is consistent with the
only 3 µas. The observed distribution of maser 400-1000K range that is believed necessary for
spotpositionoffsetsfromthemeanlocusisnearly maser action from H O (Elitzur 1992). Further-
2
Gaussian with σ = 5.1 µas (12 µas at full-width more, the inferred sound speed is comparable to
half-maximum). Because most of the maser spot the line width of individual maser Doppler com-
positions in this velocity rangeare measured with ponents seen in spectra, which is consistent with
< 3µas accuracy, we propose that this Gaussian maser saturation. We note that in our discus-
distribution largely represents a true distribution sion,wehaveassumedthatthemaserdistribution
about the local midplane of the disk (i.e., the samples the full thickness of the accretion disk,
thickness of warm molecular material.) See next rather than a surface layer, whose depth could
section for interpretation. be well below that of the physical disk. This as-
sumption is consistent with the disk models of
5. Notes on Source Structure and Evolu- Neufeld & Maloney(1995)for radiativelyefficient
tion accretion. A more detailed inspection of residuals
from models fit to maser spot distributions (e.g.,
The long-termimportance of VLBI monitoring
residualsarisingfromanantisymmetricoffsetper-
of the NGC4258 H O maser includes contribu-
2 pendiculartothediskplane,causedbyirradiation
tions to estimation of a geometric distance and
of “upper” and “lower” surfaces of the disk for
its application to high-accuracy measurement of
high-velocityred- andblue-shifted masers)is nec-
the Hubble constant. Estimation of a distance re-
essaryforfurthercomment. Wealsonotethatthe
quires additional quantification of centripetal ac-
measuredthicknessplacesalimitonthe magnetic
celerations for disk material and modeling of 3-
pressure. Themagneticfieldstrengthmustbeless
D disk structure and dynamics. These will be
than about 100 mG, which is about the current
treated in follow-on papers. However, we can
limit from the non detection of the Zeeman effect
makeseveralobservationsbasedonthetime-series
(Modjaz et al. 2005).
VLBI data alone.
Highlyred-shiftedemission.—Red-shiftedemis-
Accretion disk thickness.— In prior analy- sionatvelocities≫1460kms−1 hasbeenmapped
ses, scatter in low-velocity maser spot positions here for the first time. Emission at 1647kms−1
(north-south) have been used to estimate an up-
was first reported by Modjaz et al. (2005) in
per limit on the thickness of the underlying ac- a single-dish spectrum, while the 1566kms−1
cretion disk. Moran et al. (1995) obtained a limit
Dopplercomponentwaspreviouslyunknown. The
of ∼ 10µas by focusing on strong maser features
detectionofthese veryhighvelocityemissionsen-
toward the middle of the spectrum for a VLBI
ables the mid-line of the disk, along which the
epoch in 1994. We have combined the results
rotation curve is apparent, to be traced to about
for all 18 VLBI epochs to obtain a time-average
30% smaller radii (≈ 0.11 pc) than before. This
sample ofemission for which the width of the dis-
innermost radius is now also ≈ 20% smaller than
tribution (1σ) is 5.1µas. This may be the first
that for the low-velocity emission. Perhaps most
directly measured thickness for an accretion disk importantly, the radius of the 1647kms−1 emis-
around any black hole. In hydrostatic equilib-
sion is small enough that curvature in the disk is
rium the accretion disk is expected to have a
directly observable, which will enble more robust
Gaussian distribution of density as a function of
geometricmodelingofthe warp(cf.Miyoshi et al.
height with σ = r c /v , where r is the radius,
s φ 1995; Herrnstein et al. 1998).
v is the orbital velocity, and c is the sound
φ s Thelow-velocityemissionwasshownbyHerrnstein et al.
10