2014 年 9 月 24 日

VERA ユーザーズミーティング

VERA Iriki station

位置天文観測によるミラ型変光星の周期光度関係の確立
中川 亜紀治(1), 面高 俊宏(1), 半田 利弘(1), 亀崎 達矢(1), VERA プロジェクト(2)（1）鹿児島大学大学院 理工学研究科 （2）国立天文台 水沢VLBI観測所
nakagawa@sci.kagoshima-u.ac.jp

Kagoshima
University

ミラ型変光星などの長周期変光星は太陽の 1−8 倍の質量を持ち、進化の末期に差し掛かった星である。質量放出が激しく、宇宙の化学組成の理解においても重要な天体である。この種の星には明るさと変光周期の間の比例関係が知られており、これは周期光度関係（Peirod-luminosity relation；PLR）とよばれている。大マゼラン銀河で発見されたこの関係を我々の天の川銀河独自で決めることは絶対等級決定の観点から難しく、この関係の確立を VERA プロジェクトの科学目標の一つとしている。PLR は見か
け等級と変光周期から星の距離を導出するツールとしても重要である。見かけ等級が得られた多くの変光星の年周視差を VERA で計測し、そこから正確な絶対等級 (MK) をわり出して天の川銀河での PLR の確立を目指す。年周視差の検出のためには星の周囲に分布する水メーザーを相対 VLBI により観測する。
VERA を用いたこれまでの観測から、いくつかの天体について 10％より高い精度で距離を決定することができた。例えばミラ型変光星 T Lep の年周視差は 3.06±0.04 masであり、距離 327±4 pc (Nakagawa et al. 2014) に対応する。星周メーザーの分布や運動も同時に得られている。VERA と VLBA に代表されるこれまでの位置天文 VLBI 観測から、天の川銀河のミラ型変光星に対する PLR は MK = −3.51 log P + 1.37 ± 0.07 と得られた。ここで P は変光周期である。

1. Astrometry of Mira variables

3. Recent result and discussion of T Lep

Mira variables are pulsating stars with periods of 100 to1000 days, showing rapid mass loss before ejecting their8outer layers as planetary nebula shells. Accurate distance ofthe sources helps us to understand the nature of the variables.
10Although a narrow PL relation for Miras in the Large
Magellanic Cloud (LMC) was found (figure 1), the same12
relation for the Galactic Miras has not been precisely
Feast et al. 1989
14
obtained (figures 2,3) because of large errors. Such large
3.0
2.0
2.8
2.6
2.4
2.2errors arise from the ambiguity of absolute magnitudeslog(Period) [day]suffering directly from inaccurate distances to each object.
Fig.1. PLR of Miras in LMC,
Using absolute
Feast et al. 1989.
magnitudes derived
Milky Way Galaxy
from accurate distances-12
measured with VERA,-10
we can investigate
precise PL relation in-8
the Galaxy. Once wehave calibrated the-6
van Leeuwen et al. 1997
relationbasedonthe3.0
2.0
2.2
2.8
2.4
2.6
absolute distance, welog(Period) [day]can convert theFig.3. PLR of Galactic Miras,
Fig.2. PLR of Galactic Miras,
pulsation period to theWhitelock et al. 2008.
van Leeuwen et al. 1997.
distance for many
Galactic variables.

3.1 Parallax measurement
Among the water maser spots around T Lep detected in radial velocity (VLSR) range of −32 to−23 km/s, VLSR = −29.73 km/s was continuously bright during our VLBI monitoring period. The
annual parallax was estimated to be 3.06±0.04 mas, corresponding to a distance of 327±4 pc.
Figure 6 shows parallactic motions in R.A. and Dec.
3.2 Properties of the sourceWe revealed distribution of the maser spots around T Lep together with their internal kinematics(Figure 7). Color image at the map center is obtained from VLTI infrared interferometer (leBouquin et al. 2009). Angular radii of a photosphere (2.9 mas) and a molecular layer (7.5 mas) inle Bouquin et al. (2009) can be converted to linear sizes of 0.95 AU (=204 Rsun) and 2.45 AU(=527 Rsun), respectively. From a consideration of the proper motion in Galacto-centriccoordinate, we obtained peculiar motion ofT Lep to be 69.9 km/s. Direction of thisNakagawa et al. 2014
peculiar motion projected on sky plane isalso shown.
Galacticplane

4

Relative R.A. [mas]Absolute magnitude

Apparent magnitude

LMCBest Fit Model
Observation (R.A.)

Peculiarmotion

Nakagawa et al. 2014

20-2-4

2. Observation and data reduction

200

1.8

2

2.2

2.4

2.6

2.8

3

3.2

Period（Log P）

Fig.4. Period distribution of Mira variables in Feast et al. (2000)(white) and our targets (red).

2.2 VLBI observation
VERA is a Japanese VLBI project dedicated for the Galactic astrometry. We observe QSOs
adjacent to the maser sources as a position reference, and this simultaneous observation
towards two sources can be realized by a dual-beam system equipped to the VERA antennas.
We conduct 22 GHz multi epoch VLBI observations during 1‐2 years with a typicalinterval of one month.
In the data reduction, we use AIPS. Image of maser emission detected in phase-referenced
map is fitted with 2-dimensional Gaussian model to determine its position and flux density.
Motion of the maser obtained from sequential VLBI observations is considered as acombination of its linear proper motion and parallactic motion. We numerically deduce theparallax and linear proper motion.
System parameters of observations for Mira variables.
VERA
・20m aperture x 4antennas
・Array:VERA
20m
antenna×4stations
・Maximum baseline 2300km
Mizusawa・Astrometry at 22/43 GHz
・Frequency : 22GHz (rest freq. 22.235080 GHz)・Geodetic VLBI at 2/8 GHz
・Phase referencing VLBI
・Band width for maser : 16 MHz・Velocity resolution for maser : 0.42 km/s
Iriki
・Band width for reference QSO : 240 MHz・Recording rate : 1024 Mbps.
IshigakiOgasawara・Separation angle of maser and QSO : 0.3 - 2.2 °・Reduction software : AIPS software package (NRAO)
・Technique : Phase referencing mapping
Fig.5. VERA array.

-4

300

400

500

600

700

800

900

days from 2004/01/01 [day]Fig.6. Oscillation of the maser spot at
VLSR = -29.73 km/s in T Lep. Filled circles
represent the maser position obtainedby phase-referencing analysis. Solidlines indicate the best fit model of theparallactic oscillation.

(石垣)

（小笠原）

VERA

T Lep Mira 3.06±0.04(a) 368
S CrtSR2.33±0.13(b) 310*
R Aqr Mira 4.7 ±0.8 (c) 390
SY Scl Mira 0.75±0.03(d) 411
RX Boo SR
7.31±0.5 (e) 340
S CrB Mira 2.39±0.17(f) 360
U Her Mira 3.76±0.27(f) 406
RR Aql Mira 1.58±0.40(f) 394
W Hya SR
10.18±2.36(g) 361
R Cas Mira 5.67±1.95(g) 460

2.566
2.190
2.591
2.614
2.531
2.556
2.609
2.595
2.558
2.663

MK[mag]0.12 (h) -7.45±0.03
0.73 (i) -7.43±0.12-1.01(h) -7.65±0.37
2.61 (j) -8.01±0.09-1.85(k) -7.53±0.15
0.21(h) -7.90±0.15-0.27(h) -7.39±0.16
0.46(h) -8.55±0.56-3.16(h) -8.12±0.51-1.79 (l) -8.02±0.78

VLBA

3.3 Period luminosity relation
Table 2 shows parallaxes of variables
stars measured with astrometric VLBI(VERA and VLBA). Errors in absolutemagnitudes are attributed to the parallax
errors. Based on these VLBI results, we [†] Reference of the parallax; (a)Nakagawa et al 2014, (b)Nakagawa et al 2008,
obtained a period luminosity relation of (c)Kamohara et al 2010, (d)Nyu et la 2011, (e)Kamezaki et al 2012, (f)Vlemmings &Langevelde 2007, and (g)Vlemmings et al. 2003.
the Galactic Mira variables as (red line van[‡] Reference of the m_K; (h)Whitelock et al. 2000 (Fourier mean magnitude), (i)Jura &Kleinmann 1992, (j)Whitelock et al. 1994, (k)Glass & van Leeuwen 2007, and (l)Feastin Figure 8),& Whitelock 2000.
MK = −3.51 log P + 1.37 ± 0.07.
[*] For the period of S~Crt, we use 310~days, which is the double of its first overtoneperiod of 155~day.
Un-weighted least squares fitting wasadopted in this fitting. We solved for thezero point of 1.37 ± 0.07. The slope ofVERA (weighted)
VERA (unweighted)-3.51 (Whitelock et al. 2008) was fixed.
VLBI (weighted)
Whitelock et al.2008
Various fitting results are also presented
RR Aqlin the same figure.
Fig.8. Period luminosity relation derived
from astrometric VLBI. Filled symbols
represent absolute magnitudes MKthat derived from VERA observations.
Open symbols represent those fromother VLBI observations conducted byVlemmings et al. (2003) andVlemmings & van Langevelde (2007).
Square symbols are used to denotesemiregular variables. Dashed line
shows a relation reported by Whitelocketal. (2008).

W Hya

(水沢)

(入来)

Table2: Results from VLBI astrometry
Source Type Parallax†
PLogP mK‡
[mas]
[day]
[mag]

ー940-2

ー8.560SY Scl415 2.62 Mira
WX Psc660 2.82 Mira
RU Ari354 2.55 SR
T Lep
368 2.57 Mira
BW Cam --- --- Mira
RW Lep 150 2.18 SR
BX Cam 454 2.66 MiraU Ori
368 2.57 Mira
AP Lyn450 2.65 Mira
U Lyn
434 2.64 Mira
GX Mon 527 2.72 MiraZ Pup
509 2.71 Mira
QX Pup--- --- Mira
R Cnc
362 2.56 Mira
X Hya
301 2.48 Mira
R UMa
302 2.48 Mira
S Crt
155 2.19 SR
VX UMa 215 2.33 MiraT UMa
257 2.41 Mira
RS Vir354 2.55 Mira
FV Boo340 2.53 SR
W Hya
361 2.56 Mira
RX Boo278 2.44 SR
Y Lib
276 2.44 Mira
S CrB
360 2.56 Mira
SW Lib292 2.47 Mira
FS Lib415 2.62 Mira
IRC+10374 --- --- Mira
IRC-20540 510 2.71 MiraSY Aql356 2.55 MiraSV Peg
145 2.16 SR
R Aqr
390 2.59 Mira

Fig.7. Water maser distribution in T Lep. Superpositionof VLTI infrared interferometric image and watermaser distribution obtained with VERA. Color image at
the center is an image obtained with VLTI (le Bouquin
et al. 2009). Water masers observed with VERA aredistributed at outer area of this figure. Colors of filled
circles indicate their VLSR. Color of the central star isunrelated to the color index of the maser.

0Reference

Feast, M. W. et al. 1989, MNRAS, 241, 375
Feast, M. W., & Whitelock, P. A. 2000, MNRAS, 317, 460
Glass, I. S., & van Leeuwen, F. 2007, MNRAS, 378, 1543
Jura, M., & Kleinmann, S. G. 1992, ApJS, 83, 329
Kamezaki et al. 2012, PASJ, 64, 7
Kamohara et al. 2010, A&A, 510, A69
Le Bouquinet al. 2009, A&A, 496, L1
Nakagawa, A., et al. 2008, PASJ, 60, 1013
Nakagawa, A., et al. 2014, Accepted to PASJ, arXiv:1404.4463

ー880

LogP TypeS CrBSY Scl

R Cas

R Aqr

S Crt

ー7.5

Number of sources

100P2RX Boo

T Lep

U Herー7VERAFitFeast et al. 2000
Fit120Name

Best Fit Model
Observation (Dec.)

MK140

Table1: Target Sources

Relative Dec. [mas]2.1 Source selection and single dish monitoring
Water maser emission around Mira variables are so bright andcompact thet they are good targets to observe with VLBI as a tracerof their motion.
In table 1, we show a part of our target sources. Long periodvariables including Miras and semiregular variables are presented.
Pulsation periods (P) of these sources are aslo presented. Figure 4
shows a period distribution of ~800 Mira variables in Feast et al.
(2000) and our ~80 target sources. Period average of ~80 Miras withwater maser emission is 407 day (LogP = 2.61), which is longer thanthat of 338 day (LogP = 2.53) of the sources in Feast et al. (2000).
To determine a beginning of the series VLBI observations, wemonitor >250 long period variables at Iriki station (Shintani et al.
2008). Intensity of ~10 Jy is a threshold of a successful detection inVLBI observation with VERA.

4IR interferometric imageat map center ;Le Bouquin et al. 2009

2.45

2.5

2.55

2.62.65

Log P
Nyu, D., Nakagawa, A., Matsui, M., et al. 2011, PASJ, 63, 63
Shintani, M., et al. 2008, Submitted to PASJ.
van Leeuwen, F. et al 1997, MNRAS, 287, 955
Vlemmings, W. H. T. et al 2003, A&A, 407, 213
Vlemmings, W. H. T., & van Langevelde, H. J. 2007, A&A, 472, 547
Whitelock, P., Menzies, J., Feast, M., et al. 1994, MNRAS, 267, 711
Whitelock, P., Marang, F., & Feast, M. 2000, MNRAS, 319, 728
Whitelock, P. A., Feast, M. W., & van Leeuwen, F. 2008, MNRAS, 386, 313

2.7