The Millimeter Regime Crystal Brogan (NRAO/NAASC) MOPRA Australia 22m LMT Mexico 50m APEX Chile 12m IRAM 30m Spain Nobeyama Japan 45m CSO Hawaii 10.4m.

The Millimeter RegimeCrystal Brogan

(NRAO/NAASC)

MOPRA Australia

22m

LMT Mexico

50m

APEX Chile 12m

IRAM 30m Spain

Nobeyama Japan

45m

CSO Hawaii 10.4m

JCMT Hawaii

15m

SMT Arizona

10m

Onsala Sweden

20m

GBT West Virginia

100m

ASTE Chile 10m

ARO 12m Arizona

The Millimeter RegimeCrystal Brogan

(NRAO/NAASC)

MOPRA Australia

22m

LMT Mexico

50m

APEX Chile 12m

IRAM 30m Spain

Nobeyama Japan

45m

CSO Hawaii 10.4m

JCMT Hawaii

15m

SMT Arizona

10m

Onsala Sweden

20m

GBT West Virginia

100m

ASTE Chile 10m

ARO 12m Arizona

Outline

• Effect of the Atmosphere at mm wavelengths

• Effective System Temperature

• Direct Method of mm calibration

• Simplified formulation of Chopper Wheel method of mm calibration

• More accurate approach

• Efficiencies and different ways of reporting temperature

• Why is mm so interesting?

Problems unique to the mm/sub-mm

• Atmospheric opacity is significant for λ<1cm: raises Tsys and attenuates source

– Varies with frequency and altitude

– Changes as a function of time mostly due to H2O

– Causes refraction which leads to pointing errors – Gain calibration must correct for these atmospheric effects

•Hardware

–Noise diodes such as those used to calibrate the temperature scale at cm wavelengths are not available at mm to submm wavelengths

•Antennas–Pointing accuracy measured as a fraction of the beam (PB ~ 1.22 /D) is more difficult to achieve–Need more stringent requirements than at cm wavelengths for: surface accuracy and optical alignment

Constituents of Atmospheric Opacity

• Due to the troposphere (lowest layer of atmosphere): h < 10 km

• Temperature decreases with altitude: clouds & convection can be significant

• Dry Constituents of the troposphere:, O2, O3, CO2, Ne, He, Ar, Kr, CH4, N2, H2

• H2O: abundance is highly variable but is < 1% in mass, mostly in the form of water vapor

• “Hydrosols” (i.e. water droplets in the form of clouds and fog) also add a considerable contribution when present

Troposphere

Stratosphere

Column Density as a Function of Altitude

Opacity as a Function of PWV (PWV=Precipitable Water Vapor)

Optical Depth as a Function of Frequency

• At 1.3cm most opacity comes from H2O vapor

• At 7mm biggest contribution from dry constituents

• At 3mm both components are significant

• “hydrosols” i.e. water droplets (not shown) can also add significantly to the opacity

43 GHz

7mm

Q band

22 GHz

1.3cm

K band

total optical depth

optical depth due to H2O vapor

optical depth due to dry air

100 GHz

3mm

MUSTANG

Effect of Atmosphere on Pointing

• Since the refractive index of the atmosphere >1, an electromagnetic wave propagating through it will be bent which translates into a pointing offset

The index of refraction

-Pointing off-sets Δθ ≈ 2.5x10-4 x tan(i) (radians)

@ elevation 45o typical offset~1’

- GBT beam at 7mm is only 15”!

atm

waterdry

T

PPn

1

The amount of refraction is strongly dependent on the elevation

In addition to receiver noise, at millimeter wavelengths the atmosphere has a significant brightness temperature:

Tsys ≈ Trx + Tsky

where Tsky =Tatm (1 – e)

so Tsys ≈ Trx +Tatm(1-e)

Sensitivity: System noise temperature

Receiver temperature

Emission from atmosphere

Before entering atmosphere the signal S= Tsource

After attenuation by atmosphere the signal becomes S=Tsource e-

(Tatm = temperature of the atmosphere ~ 270 K)

Consider the signal to noise ratio:

S / N = (Tsource e-) / Tsys = Tsource / (Tsys e)

Tsys* = Tsys e ≈ Tatm(e + Trxe

The system sensitivity (S/N) drops rapidly (exponentially) as opacity increases

Effective System Temperature

*

Atmospheric opacity, continued

Typical optical depth for 230 GHz observing at the CSO:

at zenith225 = 0.15 = 3 mm PWV, at elevation = 30o 225 = 0.3

Tsys*(DSB) = e(Tatm(1-e-) + Trec)1.35(77 + 75) ~ 200 K

assuming Tatm = 300 K

Atmosphere adds considerably to Tsys and since the opacity can change rapidly, Tsys must be measured often

Many MM/Submm receivers are double sideband, thus the effective Tsys for spectral lines (which are inherently single sideband) is doubled

Tsys*(SSB) = 2 Tsys (DSB) ~ 400 K

Direct Method of MM CalibrationTA’ is the antenna temperature of the source corrected as if it lay outside the atmosphere

rxsky

A

rxsky

rxskyrxskyA

TT

eT

TT

TTTTeT

'

)()'(

off

offon

V

VV

l

AA

TT

'

* Where ηl accounts for ohmic losses, rear spillover, and scattering and is < 1

' eTV

VVT sys

off

offonA

Inverting this equation at the observing frequency must be obtained by a tipping scan or some other means

This is the method used at the GBT

Direct Calibration of the Atmosphere eTTeTTTT CBRlspilllatmlRx

skyAsys )1()1(

Ael oo eee )sin(/

With enough measurements at different elevation, ηl and can be derived as long as reasonable numbers for the other parameters are known

Trx: Receiver temp. from observatory

Tatm ~ 260 K

Tspill: Rear spillover temperature ~300 K

Tcmb = 2.7 K

ηl accounts for ohmic losses, rear spillover, and scattering and is < 1

Tipping scan

eTT syssys *

Down side of the Direct Method

http://www.gb.nrao.edu/~rmaddale/Weather/index.htmlFor a forecast of current conditions

•Atmosphere changes too rapidly to use average values

•Tipping scans use considerable observing time ~10min each time

Probably not done often enough Assume a homogeneous, plane-parallel atmosphere though the sky is lumpyDone as a post-processing step so if something went wrong you’re out of luck

Ael oo eee )sin(/

1

Y

YTTT COLDHOT

RX

][][]/[

COLDRXHOTRX

COLDHOT

VVVV

TTVoltKelvinsg

Determining the Trx and the Temperature Scale

COLDRX

HOTRX

VV

VVY

Then

and

V

TTcold Thot

Vcold +V rx

Vhot + V rx

Treceiver

In order to measure Trx, you need to make measurements of two calibrated ‘loads’:

Tcold = 77 K liquid nitrogen load

Thot = room temperature load

and the temperature conversion factor is

• Trx is not a constant, especially for mm/submm receivers which are more difficult to tune to ideal performance.

• A significant improvement to the Tsys* measurement can be made if Trx is measured rather than assumed

• Currently the SMA and soon ALMA will use a two temperature load system for all calibration

Chopper Measurement of Tsys*

• So how do we measure Tsys* without constantly measuring Trx and the

opacity? Tsys* ≈ TrxeTatm(e

• At shorter mm λ, Tsys* is usually obtained by occasionally placing an

ambient temperature load (Thot) that has properties similar to a black body in front of the receiver.

• We want to know the effective sensitivity, not how much is due to the receiver vs. how much is due to the sky. Therefore, we can use:

offload

off

hotsys VV

VTT

*

Voff is the signal from the sky (but not on source)

Vload is the signal from the hot load

IRAM 30m chopper Blue stuff is called eccosorb

• As long as Tatm is similar to Thot, this method automatically compensates for rapid changes in mean atmospheric absorption

offloadcalcal TTVgT

])1()1([][ spilllatmlRxhotRx TeTTTT

Simplified Load Calibration Theory

Note that the load totally blocks the sky emission, which changes the calibration equations from cm result

Simplify by assuming that

ambatmspillhot TTTT i.e., all our loads are at ambient temp.

eTT amblcalThen most everything cancels out and we are left with

Let

ambhotcal TTT cal

caloffonoffon T

TTTT

)(

Recall from cm signal processing

But instead of diode we have a BB load so

*1

)( Al

A

loffonoffon T

e

T

eTTT

and

offload

hotoffonA TT

TTTT

)(*

So How Does This Help?

Relating things back to measured quantities:

So all you have to do is alternate between Ton and Toff and occasionally throw in a reading of Thot (i.e. a thermometer near your hot load) and a brief observation with Tload in the beam

The poorer the weather, the more often you should observe Tload . This typically only takes a few seconds compared to ~10min for a tipping scan

*1

)( Al

A

loffonoffon T

e

T

eTTT

To first order, ambient absorber (chopper wheel) calibration corrects for atmospheric attenuation!

Millimeter-wave Calibration Formalism

1)/exp(

/),(

kTh

khTJ

Corrections we must make:

1. At millimeter wavelengths, we are no longer in the R-J part of the Planck curve, so define a Rayleigh-Jeans equivalent radiation temperature of a Planck blackbody at temperature T.

ambchopspillatm TTTT

2. Let all temperatures be different:

Linear part is in R-J limit

Once the function starts to curve, the assumption breaks down

3. Most millimeter wave receivers using SIS mixers have some response to the image sideband, even if they are nominally “single sideband”. (By comparison, HEMT amplifiers probably have negligible response to the image sideband.)• The atmosphere often has different opacity in the signal &

image sidebands• Receiver gain must be known in the signal sideband

1 si GG

Gs = signal sideband gain, Gi image sideband gain.

)exp(

)(1*

skyRxs

i

sys

TTG

G

T

fss

AR

TT

*

*

Commonly used TR* scale definition (recommended by Kutner and Ulich):

• TR* includes all telescope losses except direct source coupling of the forward beam in d

• The disadvantage is that fss is not a natural part of chopper wheel calibration and must be included as an extra factor

• TA* is quoted most often. Either convention is OK, but know which one the observatory is using

*

*

Mfss

AMB

TT

If the source angular extent is comparable to or smaller than the main beam, we can define a Main Beam Brightness Temperature as:

Main Beam Brightness Temperature

M* -- corrected main beam efficiency – can measure from observations of planets which have mm Tb ~ few hundred K

][)(

][**

PlanetTdisk

PlanetT

Bcfss

AM

2

2lnexp1)(beam

diskc disk

fss the forward spillover and scattering can be measured from observations of the Moon, if moon = diffraction region

)(

)(*

moonT

moonT

B

Afss

pA

Av A

kTS

2

pA

Alv A

kTS

2*

Conventional

TA* definition

Flux conversion factors (Jy/K)

• mm/submm photons are the most abundant photons in the spectrum of most spiral galaxies – 40% of the Milky Way Galaxy

• After the 3K cosmic background radiation, mm/submm photons carry most of the radiative energy in the Universe

• Probe of cool gas and dust

Why do we care about mm/submm?

Science at mm/submm wavelengths: dust emission

In the Rayleigh-Jeans regime, h« kT,

S= 2kT2 Wm-2 Hz-1

c2

and dust opacity,

so for optically-thin emission, flux density

S

emission is brighter at higher frequencies

Galactic star forming region NGC1333

Spitzer/IRAC image from c2d with yellow SCUBA 850 µm contours

•Dust mass

•Temperature

•Star formation efficiency

•Fragmentation

•Clustering

Jørgensen et al. 2006 and Kirk et al. 2006

Unique mm/submm access to highest z

Andrew Blain

SED of Arp 220 at z=0.02Redshifting the steep FIR dust SED peak counteracts inverse square law dimming

Increasing z redshifts peak

SED peaks at ~100 GHz for

z~10!

Science at mm/sub-mm wavelengths: molecular line emission

• Most of the dense ISM is H2, but H2 has no permanent dipole moment use trace molecules

Plus: many more complex molecules (e.g. N2H+, CH3OH, CH3CN, etc)

–Probe kinematics, density, temperature–Abundances, interstellar chemistry, etc…

–For an optically-thin line S ; TB (cf. dust)

List of Currently Known Interstellar MoleculesH2 HD H3+ H2D+ CH CH+ C2 CH2 C2H *C3

CH3 C2H2 C3H(lin) c-C3H *CH4 C4

c-C3H2 H2CCC(lin) C4H *C5 *C2H4 C5HH2C4(lin) *HC4H CH3C2H C6H *HC6H H2C6

*C7H CH3C4H C8H *C6H6

OH CO CO+ H2O HCO HCO+HOC+ C2O CO2 H3O+ HOCO+ H2COC3O CH2CO HCOOH H2COH+ CH3OH CH2CHOCH2CHOH CH2CHCHO HC2CHO C5O CH3CHO c-C2H4O CH3OCHO CH2OHCHO CH3COOH CH3OCH3 CH3CH2OH CH3CH2CHO(CH3)2CO HOCH2CH2OH C2H5OCH3 NH CN N2 NH2 HCN HNC N2H+ NH3 HCNH+ H2CN HCCN C3NCH2CN CH2NH HC2CN HC2NC NH2CN C3NHCH3CN CH3NC HC3NH+ *HC4N C5N CH3NH2

CH2CHCN HC5N CH3C3N CH3CH2CN HC7N CH3C5N HC9N HC11NNO HNO N2O HNCO NH2CHO SH CS SO SO+ NS SiH*SiC SiN SiO SiS HCl *NaCl*AlCl *KCl HF *AlF *CP PNH2S C2S SO2 OCS HCS+ c-SiC2

*SiCN *SiNC *NaCN *MgCN *MgNC *AlNCH2CS HNCS C3S c-SiC3 *SiH4 *SiC4

CH3SH C5S FeO

The GBT PRIMOS Project:Searching for our Molecular Origins

Hollis, Remijan, Jewell, Lovas

Many of these lines are currently unidentified!

Detection of Acetamide (CH3CONH

2):

The Largest Molecule with a Peptide Bond(Hollis et al. 2006, ApJ, 643, L25)

Detected in emission and absorption toward Sagittarius B2(N) using four A-species and four E-species rotational transitions. All transitions have energy levels less than 10 K.

This molecule is interesting because it is one of only two known interstellar molecules containing a peptide bond.

Thus it could provide a link to the polymerization of amino acids, an essential ingredient for life.

GBT at 7mm

Telescope altitude diam. No. A range (feet) (m) dishes (m2) (GHz)

GBT 2,650 100 1 1122* 80 - 115

SMA 13,600 6 8 230 220 - 690

CARMA 7,300 3.5/6/10 23 800 80 - 230IRAM PdBI 8,000 15 6 1060 80 - 345ALMA 16,400 12 50 5700 80 -

690

Comparison of GBT with mm Arrays

* Effective GBT collecting area at 3mm is ~10% compared to ~70% for others so GBT A/7 is listed

All other things being equal, the effective collecting area (A) of a telescope is good measure of its sensitivity

The Millimeter Regime

MOPRA Australia

22m

LMT Mexico

50m

APEX Chile 12m

IRAM 30m Spain

Nobeyama Japan

45m

CSO Hawaii 10.4m

JCMT Hawaii

15m

SMT Arizona

10m

Onsala Sweden

20m

GBT West Virginia

100m

ASTE Chile 10m

ARO 12m Arizona

Summary

• Effect of the Atmosphere at mm wavelengths

Attenuates source and adds noise

• Effective System Temperature

• Direct Method of mm calibration

Requires measurement of , used at GBT

• Simplified formulation of Chopper Wheel method of mm calibration

Needed to replace diode method at shorter λs

• More accurate approach

Planck, Different temperatures, Sidebands

• Efficiencies and different ways of reporting temperature

Know what scale you are using

• Why is mm so interesting?

Traces cool universe