overview on data reduction, calibration and analysis -...

Overview on data calibration, reduction and analysis

Spectral Lines

Andrea TarchiPhoto by G. Alvito

Outline

Outline• Calibration

Everything else matters To move or not to move? Through the mist Good ol’ Jansky!



• Reduction Breaking the waves Summing up Would you buy this?



• Reduction Breaking the waves Summing up Would you buy this?

• Analysis Bright enough One moment in time Spectral presences 3-D

CalibrationEverything Nothing else matters

CalibrationEverything else matters

We observe a point source with our (radio)telescope

The source has a certain power

We replace the telescope feed with matched load (resistor)

We adjust the load temperature until the power received = source power

The temperature reached is = to the Antenna Temperature

What do we measure?

• ON the source, we have:

Tmeas,ON(α,δ,Az,ZA)= Tsrc(α,δ,Az,ZA) + Telse

• OFF the source, we have:

Tmeas,OFF(α,δ,Az,ZA)= Telse

Where Telse=Tsys=TRX+Tgr(Az,ZA)+Tcel(α,δ,t) +TCMB+Tatm(ZA)


Tsrc + Telse Telse

OFFON


(Tsrc + Telse) - (Telse)

=

ON - OFF


(TON - TOFF)

[(Tsrc + Telse) - (Telse)]/ Telse

=

(ON – OFF)/OFF


This is what is typically provided during a line observation

(TON - TOFF) / TOFF

A spectrum in Tsys units

Conversion to K (or Jy) required

Telse=off = Tsys

Estimate required

A spectrum in Tsys units (counts, so far)

Conversion from counts to K (or Jy)

required


• Theory

• Noise Diodes

• Hot & Cold Loads

• Astronomical Measurements

See also next section

Noise diodes (frequency dependence; precision in diodes meaurements affects calibration accuracy)

Astronomical sources (quite accurate; knowledge in the flux cal. Intensity influences calibration accuracy)

Tsource aka TA of the source in K can be obtained


CalibrationTo move or not to move?

CalibrationTo move …?

Position Switching

ON


Position Switching

ON OFF


Position Switching

Pros• good baselines(typically)• Iittle a priori infos required

Cons• requires to move the telescope• source cannot be too extended

Calibration… or not to move?

Frequency Switching

ON OFF

ON-OFF


Frequency Switching


Frequency Switching

Pros• does not require to move the telescope• rapid ON-OFF switching (good efficiency)


Frequency Switching

Pros• does not require to move the telescope• rapid ON-OFF switching (good efficiency)

Cons• frequency of the line has to be well known• requires time- and frequency- stable baselines

Calibration…or not to move?

Beam Switching

Pros• does not require to move the telescope

Cons• requires hardware• source cannot be too extended


Beam Switching with 2 beams (NODDING)Pros• does not require to move the telescope• ON and OFF at the same time

Cons• requires hardware• source cannot be too extended

CalibrationTo move or not to move?

Further methods

• Baseline fitting (simple but requires good baselines)

• Baseline fitting with average fit (for extended sources)

• Double position switching (to remove residual standing waves due to strong continuum)

CalibrationThrough the mist


When νobs ≥ 15 GHz, it is necessary to correct for atmospheric absorption/attenuation!

Path length through the atmosphere for the radiation from a celestial source


Tsys and AM can be determined

Tatm can be assumed ≈ to the air temperature (on ground level) or calculated through approximated relation

A number of measurements Least-square fit

τ (& T0) can be estimated


Average opacities measured at Effelsberg.

Zenith opacity applied as the default in the GBTIDL procedures for quick-look calibration of GBT data.

Warning: τ depends on the weather conditions; especially at high frequencies!


Sky-dip procedures and Water-Vapour Radiometers installed at the telescope sites and/or on the telescopes allow to derive (quasi) real-time τ estimates.

Left: Opacity at 22 GHz measured with the microwave radiometer (in the circle of the picture above) at the SRT site (Courtesy: F. Nasir, F. Buffa, G. Deiana, and collaborators)

CalibrationGood ol’ Jansky


When moving at higher or lower Elv, the dish loses sensitivity due to small-scale deformations, viz.the telescope Gain changes.


To convert from Antenna Temperature (K) to Flux Density (Jy)

Γ is typically determined though observations of know calibrators (and tabulated)

A correction factor, Cs, has to be applied if the source is not point-like


In summary, a good calibration procedure could be described by



T A[K] = counts·T cal[K]

T cal depends on freq





Atm. contributionRequires opt. depthand source Elv






Telescope GainRequires gain curve and source Elv







Flux Gain (Sensitivity)Typically tabulated



For tricks and shortcuts…wait the hands-on actvities





Flux Gain (Sensitivity)Typically tabulated

ReductionBreaking the waves


Spectrum: Well behavingSystem and source: CollaborativeObserver: Lucky


Spectrum: Well behavingSystem and source: CollaborativeObserver: Lucky

Baseline fit (and subtract) by a polynomial of order 1


Often baselines are ‘corrupted’ by ripples (instrumental and structural origin) and standing waves (mainly originating from the reflective path between the receiver feed and the reflector).

Baseline fit and subtraction require a polynomial of order > 1

…but not higher than 5-7, otherwise line features can be destroyed or fake spectral lines created!


Spectrum: Reasonably well behavingSystem and source: Quite standardObserver: Still Lucky


Spectrum: Badly behavedSystem and source: OddObserver: Probably Tarchi



Remove scan!



There are a priori ways to reduce the standing waves:• Focus modulation• Double position-switching observing mode

Remove scan!




Remove scan!

• Shaping design (SRT)




Remove scan!

• Shaping design (SRT)• Off-axis feed arm (GBT)


Spikes and interferences

Our Interference-busters mobile unit

MobLab: a fully equipped mobile laboratory to seek radio interferences (Courtesy: F. Gaudiomonte, P. Bolli, F. Messina, and collaborators)

ReductionSumming up

ReductionSumming up

…..…..…..

+ many other more scans

Longer integration time gives a lower noise.

Observations are performed by obtaining several scans (on-off)In individual scans, there is no evident emssion…

…should we give up?

Individual scans

ReductionSumming up

…..…..…..


…Not yet!

Let’s try averaging all the scans

The signal to noise ratio (SNR) would increase by √N (N=number of scans)

Individual scans

ReductionSumming up

…..…..…..


…Not yet!

Let’s try averaging all the scans

The signal to noise ratio (SNR) would increase by √N (N=number of scans)

Individual scans

Sum of the scans

ReductionSumming up

…..…..…..


Individual scans

ReductionSumming up

…..…..…..


Individual scans

Smoothed (x4) sum of the scans

ReductionWould you buy this?


Gaussian or ‘normal’ distribution



68% values drawn from a normal distribution are within one standard deviation (1 sigma) away from the mean.



99.7% values drawn from a normal distribution are within three standard deviation (3 sigma) away from the mean.


3σ


3σ

5σ


Chances to publish your detection:



• SNR > 5 σ (very likely)




• SNR between 3 and 5 σ (likely)





• SNR ~ 3 σ (more difficult; the author should be very convincing and/or having an independent measurement for confirmation)





• SNR ~ 3 σ (more difficult; the author should be very convincing and/or having an independent measurement for confirmation)

• SNR < 3 σ (almost impossible)

AnalysisOne moment in time


Moments are equally defined for T (in K)


Total Intensity


Mean Velocity


Dispersion

AnalysisBright enough


Speak

Δν

vpeak

Gaussian FitLine peak fluxLine FWHM (Δν= √8ln2·σ)Line peak velocity


If the distance of the emitting source is known the isotropic luminosity of the water maser can be derived:

• kilomaser or megamaser?

• star formation or AGN nature?

In two radio galaxies, water megamasers with Liso ~ 10000 Lsun has been found!!!


Column density can be derived from the line total intensity

If the dimension of the source (or its distance from us) is known, a gas mass estimate can be obtained


The velocity of the line provides information on the gas dynamics:

Frequency shift according to the non-relativistic Doppler equation in the optical and radio convention

νobs > νrest: the emitting gas is approching us toward the l.o.s.νobs < νrest: the emitting gas is receding from us toward the l.o.s.

For extragalactic objects, recessional velocity of the galaxy does matter

Recessional velocity of the galaxy

Red-shiftedBlue-shifted NGC

4258


AnalysisSpectral presences 3D

AnalysisSpectral presences 3-D

Contour map made bya regular grid of individual pointings


3-D structure

…but…

Not truly source 3-D

Data cube


Leiden-Argentine-Bonn (LAB) HI survey. Sweeping through the data cube;Galactic center projection. Kalberla et al.; Hartmann & Burton; Arnal et al.

Useful textbooks:• J.D. Kraus”Radio Astronomy”, 1986, Cygnus-Quasar Books • K. Rohlfs & T.L. Wilson “Tools of Radio Astronomy”, 1996, Springer-Verlag

This lecture has also taken inspiration from past lectures and talks by U.Back, D. Muders, K. O’Neil, and B. Winkel.

Useful textbooks:• J.D. Kraus”Radio Astronomy”, 1986, Cygnus-Quasar Books • K. Rohlfs & T.L. Wilson “Tools of Radio Astronomy”, 1996, Springer-Verlag

This lecture has also taken inspiration from past lectures and talks by U.Back, D. Muders, K. O’Neil, and B. Winkel.

Thank you…and…Happy

overview on data reduction, calibration and analysis -...

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