А.М. Sobolev (Ural Federal University, Ekaterinburg, Russia) S. Deguchi, W.D. Watson, D.M. Cragg, A.B. Ostrovskii, M.A. Voronkov, E.C. Sutton, V.S. Strelnitskii, M. Gray, et al. Hong Kong, 2011 Basics of Numerical Modelling of Molecular Masers

M icrowave I=I 0 exp(-  ) A mplification by if  <0 matter S timulated amplifies background E mission of instead of obscuring it R adiation Maser effect is realized due to the pumping mechanism which reflects the balance between population transfer processes (radiative, collisional and chemical)

Why do we need to study masers? Sensitive tracers of specific objects + Tool to study kinematics (arranged and chaotic) + Tool to measure physical parameters + Tool to measure magnetic fields + Tool for direct measurement of distance + Tool to study structure of the Galaxy, etc.

Why do we need to study masers? Sensitive tracers of specific objects + Tool to study kinematics (arranged and chaotic) + Tool to measure physical parameters + Tool to measure magnetic fields + Tool for direct measurement of distance + Tool to study structure of the Galaxy, etc. + Unique phenomenon which is interesting by itself

Model construction requires INPUT elaboration of basic description which allows computation: - -definition of parameter space - -basic relations.

OSO 20m CS(2-1) Spitzer 3.6 u 2m Faulkes telescope optical image optical image RHCP - - LHCP

relevant molecular spectroscopy and collisional rate coefficients importance of spectroscopy Sobolev&Deguchi (1994a)

relevant molecular spectroscopy and collisional rate coefficients importance of collisional coefficients Dinah Cragg

conditions in and around masing region internal conditions

conditions in and around masing region internal conditions

conditions in and around masing region internal conditions

conditions in and around masing region external conditions

conditions in and around masing region external conditions Dependence of maser line ratios on the pumping dust composition Ostrovskii & Sobolev (2002)

conditions in and around masing region external conditions

geometry and size of the masing region G S Per Bartkiewicz et al. (2005) Asaki et al. (2011)

colour μm white cont.- 15 GHz grey cont. - L′ colour μm white cont. - K-band grey cont GHz G jet at different wavelengths (de Buizer et al. 2006) zoom in on the centre colour μm white cont. - L′ black – 8.5 GHz * - OH masers x – H 2 O masers + - CH 3 OH masers

BIMA spectra of methanol maser candidates in W3(OH) Sutton, Sobolev et al. (2001)Sutton

relevant molecular spectroscopy and collisional rate coefficients importance of spectroscopy Sobolev&Deguchi (1994a)

25 GHz masers in ОМС-1 (Sobolev, Wallin & Watson 1998) Watson Menten propagation of maser radiation

So, we have considered INPUT of the molecular maser numerical modeling This description is not full. Mainly because we did not consider polarization and related phenomena

Further we will consider OUTPUT of the molecular maser numerical modeling This description is also not full. We will be happy to hear suggestions on what else is expected from the models!

Images and evolution for 25 GHz maser clusters in model (Sobolev, Watson & Okorokov 2003)Watson Menten propagation of maser radiation

Time dependence of fluxes of 25 GHz maser spots and spectra in Model (Sobolev, Watson & Okorokov 2003)

Analysis of the images shows that the maser spots formed in the turbulent medium have fine structure and the brightest spots have small sizes (Sobolev, Watson & Okorokov 2003)Watson propagation of maser radiation

Change of the image with the viewing angle (Sobolev,Sutton,Watson,Ostrovskii & Shelemei 2008) Shelemei Ostrovskii

One of the basic outputs is exploration of parameter space Models of individual sources based on Cragg et al. (2001, 2004), Sutton et al.(2001) multi-transitional data on maser emission can be found in Cragg et al. (2001, 2004), Sutton et al.(2001)

One of the basic outputs is exploration of parameter space Model of generic (common) source based on (Cragg et al., 2004) extensive surveys of the 6, 23 & 107 GHz CH3OH maser emission (Cragg et al., 2004)

Analysis of the pumping mechanism Processes which control population numbers 1) Radiative Processes responsible for interaction with radiation field (i.e., emission and absorption of photons) 2) Collisional Processes responsible for interaction with particles of substance (acceleration of other particles) 3) Chemical Processes responsible for appearance/disappearance of particles in particular quantum states (chemical reactions, injection of particles, etc.) Strelnitski

Analysis of the pumping mechanism Sobolev & Deguchi (1994b)

Analysis of CH3OH maser pumping in W3(OH) Sutton et al.(2001)

Predictions: list of maser candidates

class I CH3OH maser pumping (see poster) Log Tb Log density Beaming=20, Tk= 50 K, log(Nm/dV)=10 4 regimes distinguished by 4 regimes distinguished by the set of transitions displaying the set of transitions displaying the highest brightness temperature: the highest brightness temperature: - J -1 -(J-1) 0 E series: E at 36.1, E at 84.5 GHz, etc. (SgrB2, G ) - J 0 -(J-1) 1 A+ series: A+ at 44.1, A+ at 95.2 GHz, etc. (DR21W, NGC2264, OMC-2) - J 2 -J 1 E series at about 25 GHz: OMC-1 -J -2 -(J-1) -1 E series: E at 9.9 & E line at GHz (G , W33A) Voronkov

Implementation of the modeling for future research with the new facilities Lists of maser candidate transitions for SMA (some of them are detected already) and ALMA ranges (to be published soon) It is shown that changes of the CH3OH maser images in the turbulent model are quite slow and do not prevent measurement of the distances by trigonometric parallax method using data on the 12 GHz methanol masers (Sobolev et al. 2008) Brightest maser spots have small sizes which fit demand of the space vlbi

THANKS A LOT!