The theory of what drives maser variability

A.M. Sobolev S.Yu. Parfyonov

Ural Federal University, Ekaterinburg, Russia

Microwave I=I0 exp(-τ) Amplification by if τ <0, matter Stimulated amplifies background emission

Emission of instead of obscuring it Radiation maser effect appears due to pumping mechanism reflecting balance between population transfer processes (radiative, collisional and chemical)

- Changes of background emission (brightening-dimming, shielding, arrival, etc., e.g. OH maser with pulsar on bg Weisberg et al., 2005)

- Changes of the pumping (heating-cooling, compression, dissociation, e.g. propagation of IR radiation from dust which is heated by a source with a rapid variability, Sugiyama et al., 2008)

- Radiative transfer effects (changes of geometry: rotation, expansion, etc., e.g. numerous measurements of proper motions, radiative instabilities, e.g. Scappaticci & Watson, 1995)

Pumping mechanisms (what masers are sensitive to)

Role of source and sink of energy can play

Collisions with neutral and charged particles Radiative processes (emission and absorption of photons) Chemical processes (chemical reactions, dissociation, ionization, freezing out on the dust)

Molecule No. of transitions stellar ISM extragal.

OH >5 + + + H2O >10 + + + SiO >6 + + - CH3OH >40 - + | H2CO 1 - + + etc. (NH3, CH, HC5N, HCN, ...)

hydrogen masers cyclotron masers

Maser lines are in λ range from cm to FIR

Strongest masers are in cm range

Stellar envelopes: periodic changes and flares

- Periodic heating of dust by variable IR emission of the star - Shock waves driven by stellar pulsation - Density variations due to variability of mass loss

A.M.S. Richards (2012)

H2O maser in RS Vir

M.D. Gray et al. (2009)

Interstellar masers

Edges of HII regions (hypercompact, compact, SNR) Outflows (jets - wide angle, shocked clumps) Accretion structures (disks, rings, etc.)

Monotonic changes

Flares

Periodic changes

Velocity drifts

CH3OH:HartRAO H2O:Pushchino

H2O:Medicina

Gwinn (1994) observations

theory

TURBULENCE MacLow et al.(1994)

class I masers at 25 GHz in ОМС-1

(Johnston et al. 1995)

Watson

class I masers at 25 GHz in ОМС-1

(Sobolev,Wallin & Watson 1998)

small τ0

Ori-KL

images

Velocity correlations

class I masers at 25 GHz in ОМС-1 (model by Sobolev, Watson & Okorokov 2003)

evolution of turbulent velocity field leads to maser spot evolution: change in brightness, position and velocity, as well as merging and division of spots

class I masers at 25 GHz in ОМС-1 (model by Sobolev, Watson & Okorokov 2003)

Masers tracing outflows: variability is caused by the turbulence and shock wave propagation

Voronkov, Brooks, Sobolev et al. (2006)

«hot» spots with sizes ~ 0.001 arcsec (Menten et al.1991), surrounded by «halo» with size ~ arcsec (Sobolev et al. 2005, Harvey-Smith & Cohen 2006)

HII region edges

6.7 GHz methanol maser images in

W3(OH): slow variations in

intensity and position

(Sutton, Sobolev, Salii, Malyshev, Ostrovskii, Zinchenko 2004)

class I methanol masers are tracing star forming clumps at the edges of outflows:

slow variations in intensity and position (Strelnitskij 1982), (Sobolev & Strelnitskij 1983)

Strelnitskij Sutton

3.6 µ

Periodic, flares G9.62+0.20 maser flares (Goedhart et al. 2003) G9.62+0.20 interferometry: a time delay of one to two weeks was observed between groups of maser features. These delays can be explained by the light travel time between maser groups (Goedhart et al. 2005)

Periodic, flares G9.62+0.20 maser flares (Goedhart et al. 2003) G9.62+0.20 interferometry: a time delay of one to two weeks was observed between groups of maser features. These delays can be explained by the light travel time between maser groups (Goedhart et al. 2005)

500 a.u.

G9.62+0.20 monitoring: periodic variability is observed at 6, 12 and 107 GHz. The 12 GHz masers are the most variable with relative amplitude having a value of 2.4 (van der Walt et al. 2009)

Different classes of Methanol Masers display strong emission in different transitions:

class I – at 25 GHz, 44 GHz, 36 GHz, etc. class II – at 6 GHz, 12 GHz, 157 GHz, etc.

Cragg

Salii

class II masers: (see Sobolev etal. 2001, Cragg etal 2005)

Caswell Henkel

6, 12, 107, 156, 23, 19, 37, 38, 86, 93, etc. GHz

Ostrovskii

Ellingsen

model with n=106 cm-3 Tdust=Tgas

br ightness

Among physical parameters only the dust temperature

can react sufficiently fast to the changes of the radiation from the distant object.

Models show that the changes in the dust temperature by a few %

can explain G9.62+020 variability

model with n=105 cm-3 Tdust=Tgas

Beuther et al. Protostars and Planets V

Whitworth et al. SPH modelling

Okamoto et al. (2009) Subaru observations of HD200775

T Tau binary systems with elliptical orbits

maser

Map of the outflow origin 1.3 mm color image with overlaid CH3CN line contours. Inserts (0.6”x0.6”) show 7 mm cont. emission

(Zapata et al. 2007)

Sobolev, Voronkov, Green et al. (in prep.)

Ori-S 6 GHz methanol maser

There are 2 classes of Methanol Masers: class I normally trace the shocks

class II are normally close to YSOs

class I (class I/II) class II

Tdust = Tgas

log Tb

G331.13-0.24 monitoring Methanol masers at 6 and 9 GHz

(= V645 Cyg)

V645 Cyg shows irregular variations of the optical brightness

Optical monitoring at AO UrFU

6 GHz maser monitoring at Torun

6 GHz maser monitoring at Torun

Optical monitoring at AO UrFU

6 GHz maser monitoring at Torun

Optical monitoring at AO UrFU

6 GHz maser monitoring at Torun

Optical monitoring at AO UrFU

Brightness variations of components of the V645 Cyg 6 GHz methanol maser show correlation with the brightness variations of the V645 Cyg star in the optical range (filters V and R). There is possible time lag of the optical brightness in comparison to the maser variations. It can be explained that in the course of rotation of accreting material (debris) the light points toward the maser position earlier than toward the observer.

maser

observer rotating debris

-12

-10

-8

-6

-4

-2

0

2

4

6

-46 -45.5 -45 -44.5 -44 -43.5 -43 -42.5 -42-1

0

1

2

3

4

5

6

7

-46 -45.5 -45 -44.5 -44 -43.5 -43 -42.5 -42

19.05.2009

20.05.2009

21.05.2009

22.05.2009

26.05.2009

27.05.2009

28.05.2009

29.05.2009

Variability of H2O maser in V0645 Cyg (19-29.05.2009) Red rectangles show features with pronounced variability The strongest feature at -43.8 km/s experienced dramatic change between May 26 and 27. At this moment the source was not monitored.

V645 Cyg H2O maser normally shows slow variations in intensity (~2 times a month) Characteristic times of maser relative stability are about 2 months. There is some similarity between variability pattern of the star and associated H2O maser but it is difficult to suggest numerical measure of this similarity. Nothing regular.

𝑑𝐼(𝑠, 𝜈�) 𝑑𝜏

=𝐼(𝑠, 𝜈�) + 𝐴

Γ exp −𝜈�2

1 + 𝐴Γ + 𝐼(𝑠, 𝜈�)

+ 𝜂exp −𝜈�2

Flare of saturated maser two-level uniform linear maser in steady-state

distant and small background continuum source Following (Watson & Wyld 2003) and taking into account spontaneous emission we obtain following radiative transfer equation :

𝐼 =𝑐2𝐴𝐼ℎ𝜈03Γ

, �̃� =𝑐𝑣𝐷

𝜈 − 𝜈0𝜈0

, 𝑑𝜏 =𝑐3𝑣𝐷2𝐴𝜆− 0

8𝜈03Γ𝑑𝑠, 𝜂 =

𝐴Γ𝜆+(0)𝜆−(0)

, 𝐼 0, �̃� = 𝐼0,

where vD - thermal breadth; λ+(0) and λ –(0) are sum and difference of pumping rates of upper and lower levels; ds – differential path length within the maser; I0 –intensity of background continuum source radiation; Γ – loss rate from states due to all processes other than the maser transition. The saturation degree R/ Γ is measured as I(L,0)/2 where L – the maser length.

Fixed parameters of the model: • vD = 0.5 km/s • λ-(0) = 0.009 cm-3 s-1

(consistent with the range of λ-(0) in Anderson & Watson, 1993) • λ+(0) = 0.09 cm-3 s-1

(λ+(0) / λ-(0) = 10÷100 in Watson & Wyld, 2003)

Varied parameters of the model: • Background I0 • Pump rate Γ (range of values from Anderson & Watson 1993) • Path Length of the maser

With Tbg=10 K, Γ=1 s-1 , and L= 1013 cm this model has Tb = 6.6 106 K and ∆v/∆vD= 0.28

Possible increase of brightness is LESS than 2 orders of magnitude

CHANGE OF BACKGROUND

Possible rebroadening is LESS than 2 times

CHANGE OF PUMP RATE

Possible increase of brightness is MORE than 2 orders of magnitude

Possible rebroadening

is MORE than 3 times

CHANGE OF PATH LENGTH

Possible increase of brightness

is MORE than 3 orders of magnitude

Possible rebroadening

is MORE than 3 times

There is also variability which is not related to the maser itself but appears due to changes of the maser emission on the way to observer. It is well pronounced for extragalactic sources. This phenomenon is known as scintillation. In the case of Circinus water megamaser the rapid variability is a result of quenched diffractive scintillation while the long time-scale variability is due refractive scintillation (McCallum et al., 2009).

RadioAstron project http://www.asc.rssi.ru/radioastron/index.html

W3 IRS5 H2O maser, 40 microarcsec resolution

Data on distant pulsar requires correction of the scattering theory

THANK YOU VERY MUCH!