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 JCMT Hawaii 15m SMT Arizona 10m Onsala Sweden 20m GBT West Virginia 100m ASTE Chile 10m ARO 12m Arizona

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 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 T sys and attenuates source –Varies with frequency and altitude –Changes as a function of time mostly due to H 2 O –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:, O 2, O 3, CO 2, Ne, He, Ar, Kr, CH 4, N 2, H 2 H 2 O: 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 H 2 O 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 H 2 O 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) elevation 45 o typical offset~1’ - GBT beam at 7mm is only 15”! 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: T sys ≈ T rx + T sky where T sky =T atm (1 – e  ) so T sys ≈ T rx +T atm (1-e  ) Sensitivity: System noise temperature Receiver temperature Emission from atmosphere Before entering atmosphere the signal S= T source After attenuation by atmosphere the signal becomes S=T source e -  (T atm = temperature of the atmosphere ~ 270 K) Consider the signal to noise ratio: S / N = (T source e -  ) / T sys = T source / (T sys e  ) T sys * = T sys e  ≈ T atm (e   + T rx e  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 zenith   225 = 0.15 = 3 mm PWV, at elevation = 30 o   225 = 0.3 T sys *(DSB) = e  (T atm (1-e -  ) + T rec )  1.35( ) ~ 200 K assuming T atm = 300 K  Atmosphere adds considerably to T sys and since the opacity can change rapidly, T sys must be measured often Many MM/Submm receivers are double sideband, thus the effective T sys for spectral lines (which are inherently single sideband) is doubled T sys *(SSB) = 2 T sys (DSB) ~ 400 K

Direct Method of MM Calibration T A ’ is the antenna temperature of the source corrected as if it lay outside the atmosphere Where η l accounts for ohmic losses, rear spillover, and scattering and is < 1 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 With enough measurements at different elevation, η l and  can be derived as long as reasonable numbers for the other parameters are known T rx : Receiver temp. from observatory T atm ~ 260 K T spill : Rear spillover temperature ~300 K T cmb = 2.7 K η l accounts for ohmic losses, rear spillover, and scattering and is < 1 Tipping scan

Down side of the Direct Method For 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 lumpy  Done as a post-processing step so if something went wrong you’re out of luck

Determining the T rx and the Temperature Scale Then and V T T cold T hot V cold +V rx V hot + V rx  T receiver In order to measure T rx, you need to make measurements of two calibrated ‘loads’: T cold = 77 K liquid nitrogen load T hot = room temperature load and the temperature conversion factor is T rx is not a constant, especially for mm/submm receivers which are more difficult to tune to ideal performance. A significant improvement to the T sys * measurement can be made if T rx is measured rather than assumed Currently the SMA and soon ALMA will use a two temperature load system for all calibration

Chopper Measurement of T sys * So how do we measure T sys * without constantly measuring T rx and the opacity? T sys * ≈ T rx e  T atm (e   At shorter mm λ, T sys * is usually obtained by occasionally placing an ambient temperature load (T hot ) 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: V off is the signal from the sky (but not on source) V load is the signal from the hot load IRAM 30m chopper Blue stuff is called eccosorb As long as T atm is similar to T hot, this method automatically compensates for rapid changes in mean atmospheric absorption

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 i.e., all our loads are at ambient temp. Then most everything cancels out and we are left with Let Recall from cm signal processing But instead of diode we have a BB load so and

So How Does This Help? Relating things back to measured quantities: So all you have to do is alternate between T on and T off and occasionally throw in a reading of T hot (i.e. a thermometer near your hot load) and a brief observation with T load in the beam The poorer the weather, the more often you should observe T load. This typically only takes a few seconds compared to ~10min for a tipping scan To first order, ambient absorber (chopper wheel) calibration corrects for atmospheric attenuation!

Millimeter-wave Calibration Formalism 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. 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 G s = signal sideband gain, G i image sideband gain.

Commonly used T R * scale definition (recommended by Kutner and Ulich): T R * 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 T A * is quoted most often. Either convention is OK, but know which one the observatory is using

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 T b ~ few hundred K  fss the forward spillover and scattering can be measured from observations of the Moon, if  moon =  diffraction region

Conventional T A * 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  = 2kT 2   Wm -2 Hz -1 c 2 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 and Kirk et al. 2006

Unique mm/submm access to highest z Andrew Blain SED of Arp 220 at z=0.02 Redshifting 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 H 2, but H 2 has no permanent dipole moment  use trace molecules Plus: many more complex molecules (e.g. N 2 H +, CH 3 OH, CH 3 CN, etc) –Probe kinematics, density, temperature –Abundances, interstellar chemistry, etc… –For an optically-thin line S   ; T B   (cf. dust)

List of Currently Known Interstellar Molecules H 2 HD H 3 + H 2 D+ CH CH + C 2 CH 2 C 2 H *C 3 CH 3 C 2 H 2 C 3 H(lin) c-C 3 H *CH 4 C 4 c-C 3 H 2 H 2 CCC(lin) C 4 H *C 5 *C 2 H 4 C 5 H H 2 C 4 (lin) *HC 4 H CH 3 C 2 H C 6 H *HC 6 H H 2 C 6 *C 7 H CH 3 C 4 H C 8 H *C 6 H 6 OH CO CO+ H 2 O HCO HCO+ HOC+ C 2 O CO 2 H 3 O+ HOCO+ H 2 CO C 3 O CH 2 CO HCOOH H 2 COH+ CH 3 OH CH 2 CHO CH 2 CHOH CH 2 CHCHO HC 2 CHO C 5 O CH 3 CHO c-C 2 H 4 O CH 3 OCHO CH 2 OHCHO CH 3 COOH CH 3 OCH 3 CH 3 CH 2 OH CH 3 CH 2 CHO (CH 3 ) 2 CO HOCH 2 CH 2 OH C 2 H 5 OCH 3 NH CN N 2 NH 2 HCN HNC N 2 H + NH 3 HCNH + H 2 CN HCCN C 3 N CH 2 CN CH 2 NH HC 2 CN HC 2 NC NH 2 CN C 3 NH CH 3 CN CH 3 NC HC 3 NH + *HC 4 N C 5 N CH 3 NH 2 CH 2 CHCN HC 5 N CH 3 C 3 N CH 3 CH 2 CN HC 7 N CH 3 C 5 N HC 9 N HC 11 N NO HNO N2O HNCO NH2CHO SH CS SO SO+ NS SiH *SiC SiN SiO SiS HCl *NaCl *AlCl *KCl HF *AlF *CP PN H 2 S C 2 S SO 2 OCS HCS+ c-SiC 2 *SiCN *SiNC *NaCN *MgCN *MgNC *AlNC H 2 CS HNCS C 3 S c-SiC 3 *SiH 4 *SiC 4 CH 3 SH C 5 S FeO

The GBT PRIMOS Project: Searching for our Molecular Origins Hollis, Remijan, Jewell, Lovas Many of these lines are currently unidentified!

Detection of Acetamide (CH 3 CONH 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

Telescopealtitude diam. No. A range (feet) (m)dishes (m 2 ) (GHz) GBT 2, * SMA13, CARMA 7, /6/ IRAM PdBI 8, ALMA 16, 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