Photometry Stellar Photometry: Implementation
• Select a detector and a suite of filters • Define a “zero point” in both brightness and in colors, based on fundamental reference stars • Measure a network of standard stars around the sky relative to the reference stars • You now have a “photometric system” • Measure your unknown stars relative to the network of standards • Correct for various influences on the data that make it depart from the ideal (for example, atmospheric absorption) • Compare the properties of the unknown stars with those of well measured ones A “Heritage” Photometer You may never use one, but a lot of the concepts are based on this type of instrument
A pupil is formed on the photomultiplier photocathode, since it can have highly non-uniform response. The wide field eyepiece allows finding the star, and the microscope lets the observer verify it is centered within the aperture. Harold Johnson’s UBVRI System Why the photometer gives accurate results:
• Allows accurate guiding • Every star measured the same way • Generally took multiple repetitions • Filters far away from a focus • Detector (photomultiplier) placed at a pupil • Detector cooled so dark current was negligible Measurements with Detector Arrays • Start with well-reduced data (as discussed under imagers) • Aperture photometry: • Measure signal within an aperture centered on the source and sky/background in an annulus around the source • Simplest method, reliable with clean data • Subject to errors if have artifacts in the image (they come through unattenuated as signal) • Can be adapted to extended sources • Point spread function (PSF) fitting • Fit an idealized image of an unresolved source to the image • Best for crowded fields • More immune to artifacts (fits tend to de-emphasize them) • Determining PSF may be difficult (it may be dependent on where a source is within the FOV, or on time of observation in a night) • More difficult to adapt to extended sources • Array measurements • Allow accurate differential measurements (e.g., through clouds) • But are subject to detector artifacts (e.g., fringing, intra pixel response)
Photometry : Terms • Magnitude system • Response of the eye is roughly logarithmic • Hipparchos: 150 BC, sorted stars into bins by apparent brightness, or magnitudes, from 1 to 6 (brightest to faintest) • Pogson, 1856, defined m1 – m2 = -2.5 log(f1/f2), where m is the apparent magnitude and f is the flux • As fainter and brighter objects came within reach, astronomers extrapolated
Procedure for Stellar Photometry
• Establishing the photometric system • Set the zero point (Johnson used six A0 stars averaged, but that was quickly forgotten and his work became the “Vega system” • Get accurate standard star measurements over the entire sky relative to the zero point defining stars
• m = apparent magnitude = -2.5 log (fstar/fzero pt. ) • Then in terms of the network of well-measured standard stars,
m=-2.5 log (fstar/fstandard) + mstandard
Procedure for Stellar Photometry - II
•Air mass corrections – have to correct for different paths through the atmosphere • Can assume plane parallel atmosphere for a crude correction sec(zenith angle) (cos cos HA cos sin sin)1 (1)
• A more accurate formula is given in the text • If the extinction is exponential: dI I , (3) ds
• Then
m (am) m (am 1) 2.5 (am 1). (4)
• However, the atmospheric effects may be more complex, like shifting the center wavelength of the spectral band (a major issue for M and Q in the infrared)
Is the system based exclusively on an instrument – the defining photometer? • If so, how do you maintain it?
One solution:
Harold Johnson maintaining the defining UBVRI photometer A Truly Great Review • Johnson, H. L. 1966, ARAA, 4, 193
• What makes this review so great? You need to read it (posted on class web site). Some Issues: What is the System, Really???? The following slides compare real Johnson with “other Johnson” Cousins came up with his own R and I bands
Barr used to sell this filter set
Another example: Stromgren uvby systems. These are all supposed to be the same!! J H K
Extending to the infrared – Johnson comes to the Lunar and Planetary Laboratory and sets up JKLM, Frank N Low adds N (OP) Q. Eric Becklin L M (CalTech grad student) adds H. These bands are pretty well determined by the atmospheric windows, but to get cheap filters people often used to buy stock ones that are not identical from one system to another. To a large extent Q this issue has been resolved at JHK by 2MASS defining a standard. The bands are also significantly influenced by atmospheric conditions (mostly water vapor). Some of these problems can be addressed with transformations – fits to the trend of magnitudes with colors, or colors vs. colors, or etc. etc.
These work well only when you are dealing with closely related objects, i.e., stars. Using transformations determined on stars when studying AGN at high redshift is guaranteed to get you into trouble!!!!! • Here is how a simple set of transformations might look:
(K S )2MASS KCIT (0.000 0.005)(J K)CIT (0.024 0.003)
(J H)2MASS (1.076 0.010)(J H)CIT (0.043 0.006)
(J K S )2MASS (1.056 0.006)(J K)CIT (0.013 0.005)
(H K S )2MASS (1.026 0.020)(H K)CIT (0.028 0.005) (5)
• You may find that they are based on a shockingly small number of stars well- measured in the two systems. • Trying to put Johnson’s photometry on the 2MASS system is very difficult, as an example • Transformations work pretty well in the infrared where stellar spectra are relatively simple • However, transformations are not nearly so good in the optical because of the complexity of stellar spectra there A Happier Solution • Use all-sky surveys • Near infrared: 2MASS, accurate to about 2 – 3% • Not quite as good as it seems because of ~ 2% offsets between read 1 and read 2, plus some general calibration drift over the sky (but < 2%) • BV: Tycho, accurate to better than 1% (but sometimes gets confused by stars with small separations) • These surveys are as uniform over the whole sky as the best previous standard systems were over limited regions and with very small numbers of stars.
• It used to be necessary to take photometry of widely spaced standards, including at large air mass, and solve for the instrumental zero point plus the air mass corrections. Now there is an option of tying in directly with these all sky networks. Common Terms:
• CI = color index = difference in magnitudes at two bands, e.g., CI = mB – mV, or B-V • E = color excess = the difference between observed CI and standard CI for the star • M = absolute magnitude, that is the magnitude the object would have at 10pc • m-M = distance modulus = 5 log (distance in pc) – 5 = 5 log (d/10pc)
• Mbol = bolometric magnitude = absolute magnitude integrated over all wavelengths to provide the luminosity of the object • BC = bolometric correction = the correction to the apparent magnitude at some wavelength to give the apparent bolometric magnitude Physical Photometry
• When not studying stars (and at z = 0), there are serious shortcomings in the approaches just described • Therefore, we use physical photometry, where we reduce the measurements to physical units rather than just making color and brightness comparisons • Our measurements are made through a spectral band with certain characteristics:
• We would like to characterize this band by a single wavelength. One candidate is the mean: T() d 0 . (6) T() d
• This works to first order, but we will find that some corrections are necessary Overview of Absolute Calibration • Optical/IR • Absolute calibration tied to measures of local sources relative to celestial ones (or local emitting spheres in the case of MSX) • A clever round-about devised by Harold Johnson: the solar analog method • 1 – 2%, 0.4 to 25 microns • Radio • Primary standards measured with horn antennas, which have cleaner beams and are easier to model than a paraboloid with a feed antenna. • Performance confirmed by measurements of local sources • Calibrators then tied in with other standards with conventional radio telescope • Accuracies achieved are ~ 10 – 15% (Maddalena & Johnson) • X-ray • Calibrate telescope throughput on the ground • Illumination not exactly parallel, so there is an uncertainty in telescope throughput • Celestial sources also used (e.g., Crab) but very dependent on models • ACIS: 5% 2 – 7kev, 10% 0.5 – 2 kev (Bautz) The most famous horn antenna antenna pattern for a horn antenna antenna pattern for a paraboloidal antenna with a horn feed X-Ray Calibration Facility at Marshall Space Flight Center
Optical/Infrared Absolute Calibration
Ultimate goal is about 1% for supernova dark energy experiments. • Direct calibrations One transfers a calibrated blackbody reference source to one or more members of the standard star network. Ideally, one would use the same telescope and detector system to view both, but often the required dynamic range is too large and it is necessary to make an intermediate transfer. • Indirect calibrations One can use physical arguments to estimate the calibration, such as the diameter and temperature of a source. A more sophisticated approach is to use atmospheric models for calibration stars to interpolate and extrapolate from accurate direct calibrations to other wavelengths. • Hybrids The solar analog method uses absolute measurements of the sun, assumes other G2V stars have identical spectral energy distributions, and normalizes the solar measurements to other
G2V stars at some wavelength where both have been measured, such as mV • Current "best" methods The calibrations in the visible are largely based upon comparisons of a standard source (carefully controlled temperature and emissivity) with a bright star, often Vega itself. Painstaking work is needed to be sure that the very different paths through the atmosphere are correctly compensated. In the infrared, there are three current approaches that yield high accuracy: 1.) Measurement of calibration spheres by the MSX satellite mission and comparing the signals with standard stars. This experiment has provided the most accurate values. 2.) Measurement of Mars relative to standard stars while a spacecraft orbiting Mars was making measurements in a similar pass band and in a geometry that allowed reconstructing the whole-disk flux from the planet. 3.) Solar analog method, comparing new very accurate space-borne measurement of the solar output with photometry of solar-type stars.
Following astronomical tradition, Vega was a very bad choice for a star to define photometric systems
It has a debris disk that contributes a strong infrared excess above the photosphere, already detected with MSX at the ~ 3% level at 10mm and rising to an order of magnitude in the far infrared
Interferometric measurements at 2mm show a small, compact disk that contributes ~ 1.2% to the total flux
Vega is a pole-on rapid rotating star with a 2000K temperature differential from pole to equator.
This joke nature has played on Harold and the rest of us accounts for some of the remaining discrepancies in absolute calibration.
Now we are nominally calibrated, but we still have to relate our measurements to the monochromatic calibration.
The issue is that we measure through filters of significant bandpass so we actually get some signal. Thus the response to sources J-band photometry of an early L-dwarf. The dashed line is with different SEDs is the spectrum of an A0V calibrator star, the dotted line is that of the L dwarf, and the solid line is the transmission different and we need to profile of the J filter. The A0 and L dwarf spectra have correct to equivalent been adjusted to give identical signals in the J band. The monochromatic fluxes. solid arrow is the mean wavelength of the filter, while the dashed arrow is the wavelength dividing the A-star signal equally within the band, while the dotted arrow divides the L dwarf signal equally. Attempts to minimize bandpass corrections
Some use alternates of 0: for example, IRAS defines
This definition reduces the corrections for warm and hot objects and increases them for cold ones. It is harmless except for causing some confusion.
A much worse approach is embodied in the isophotal wavelength. The idea is not to adjust the measured flux density, but to adjust the wavelength of measurement for every source so the measured flux density applies at that wavelength. This process is mathematically equivalent to adjusting the flux density, but has the unfortunate result that sources measured with the same photometric system all have different wavelengths assigned to the results.
Since 0 is one of the succinct ways to characterize the passband, the result borders on chaos (think of how to put the data into a sensible table!). Furthermore, real stars have absorption features, and so the definition of isophotal wavelength has to include interpolating over them to get an equivalent continuum. If the interpolation is done in different ways, one can get different isophotal wavelengths for the same measurement on the same star!
Determining the isophotal wavelength at K While we are discussing peculiar thought patterns, we have to mention “AB magnitudes”. These take the zero magnitude flux density at V and compute magnitudes at all bands relative to that flux density. Thus, they are a form of logarithmic flux density scale, with a weird scaling factor of –2.5 and a weird zero point of ~ 3630 Jy. (This type of foolishness has led to mistakes causing waste of many orbits of HST time -- due to confusion between Johnson and AB magnitudes: mK(AB)-mK(Johnson)~2, for example.)
In case you need to use mAB to communicate with other astronomers (you will!), it is
2 1 mAB 2.5 log( f (W m Hz )) 56.085 (8) Recommendation: Use 0 or eff and correct for the bandpass effects.
Most direct correction is just to convolve a trial source SED with the system spectral and integrate the result to get a synthetic signal.
So the same for a standard star SED, normalized to the same flux density at the fiducial wavelength.
Ratio the results to get the correction. The necessary corrections go as (D/)2 and can be quite large for broad bands (shown here for N and Q, both of which have D/ ~ 0.5 but even more so for the X-ray where sometimes D/ ~ 1) Narrowband Photometry and Photometric Indices Can stellar types be determined accurately by photometry? Does the answer open up photometry approaches to other problems?
Exhibit 1: The Stromgren photometric system
A method of spectral classification of F stars through photo-electric photometry with interference filters is described. Two classification indices are determined, one measuring the strength of the Hb line, the other the Balmer discontinuity. Both indices are practically uninfluenced by interstellar reddening. -- Stromgren 1956 Example 2: Enhance the system with a narrower Hb filter (Stromgren and Crawford) Calibration and a good understanding of source behavior is critical, or the index may be indexing something else!
Equivalent width, W, vs ratio of signals Another approach: use wide color baseline. Advantage is data are readily available, disadvantage is strong reddening-dependence
However, for nearby stars (little reddening), the colors are very well behaved and can indicate the spectral type more accurately than routine spectra can. For nearby stars (inside local bubble) and V-K baseline, this can work very well. It can also work well if the reddening can be measured and corrected. For both methods, metallicity can be a problem. Here is a HR diagram for local stars age dated by chromospheric activity and compared with isochrones.
full age spread
2
0-1000
1000-3500
3500-6000 2.5 6000-8000
8000-11000
sun
500 3 2000 4500
7000
M_K 10000
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4
4.5 1 1.2 1.4 1.6 V-K 1.8 2 2.2 2.4 Here is the same thing corrected for metallicity. HR diagrams are widely used to determine star cluster membership and ages.
This figure emphasizes the importance of getting the correct metallicity in such studies (from Gaspar et al. 2009); even small differences affect the isochrones.
It is also critical to transform all the photometry to the same system.
Remember that identical doubles will lie 0.8 mag. above the single-star main sequence for the cluster.
Good isochrones from An et al. (2007), Girardi et al. (2004), Siess et al. (2000) , Marigo et al. (2008) A Small Revolution: time resolved high accuracy photometry
• Observing planet transits from the ground • The MOST satellite • CoROT • Kepler • HST and Spitzer • LSST
• Part of the search for “other earths”
TELESCOPE: • Aperture: 10 cm VULCAN search • Focal length: 30 cm Modest telescopes are fine for • Field of View: 7x 7 degrees this type of work. • Detector: 4096x4096 CCD with 9mm pixels
But networks of automated telescopes are also available, for example the Las Cumbres Observatory, http://lcogt.net/, with two 2-meter telescopes, a 1-meter, and a number of 0.4-meter telescopes being deployed. Basic instrumentation approach, From Charbonneau et al. (2006)
TopHAT is a 0.26 m diameter f /5 commercially available Baker Ritchey- Chre´tien telescope on an equatorial fork mount developed by Fornax Inc. A 1.25 degree square field of view is imaged onto a 2k X 2k Peltier-cooled, thinned CCD detector, yielding a pixel scale of 2.2”. The time for image readout and associated overheads is 25 s. Well-focused images have a typical FWHM of 2 pixels. A two-slot filter exchanger permits imaging in either V or I. In order to extend the integration times and increase the duty cycle of the observations, we broadened the point-spread function (PSF) by performing small, regular motions in right ascension and declination according to a prescribed pattern that was repeated during each 13 s integration. The resulting PSF had a FWHM of 3.5 pixels (7.7”). Here are some high- quality examples. However, comparing with the numbers for the solar system, this is indeed a large planet. A lot higher accuracy is desired,
which can be obtained by observing from space. Spitzer covers the peak of the emission of “hot Jupiters” - from 3.6 to 24 mm. Tracking the planet of Upsilon Andromedae around its orbit shows variations that indicate it has a hot and a cold face. This method has produced the first (albeit not very detailed) images of planets orbiting other stars. CoROT (below), MOST (right) demonstrate that huge telescopes are not needed to carry out critical high accuracy photometry from space.
http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=45518 INSTRUMENT
KEPLER: A Wide Field-of-View Photometer that Monitors 100,000 Stars for 3.5 yrs with Enough Precision to Find Earth-size Planets in the Habitable Zone Use transit photometry to detect Earth-size planets 95 cm Schmidt 0.95 meter aperture provides enough photons Corrector (Fused Observe for several years to detect transit Silica) patterns Focal Plane Monitor a single large area on the sky Radiator continuously to avoid missing transits Use heliocentric orbit Up to 170,000 targets at 30 min Graphite Metering Focal Plane cadence & 512 at 1 min Structure Electronics
Get statistically valid 1.4m Primary Focal Plane w/ 42 Mirror results by monitoring; Science CCD’s & 4 Fine Guidance 100,000 stars Sensors • Wide Field-of-view telescope (100 sq deg) Focus Mechanism (3) • Large array of CCD detectors
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200 -1 4 -0.215 Non-alignedPSD spin axes of hot, fast-rotating stars? -0.4102
Norm. Rel. Flux Rel. Norm. 5 Freq., Day Freq., -0.60 0 1 52 3 104 5 156 7 208 9 2510 0 Frequency,Time Since Cycles 54953 Per MJD Day 4 50 100 150 200 250 x 10 15 Star Index -3 x 10 106
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0 10 20 -1 -0.02 15 -0.04PSD 5 2-day transit; dwarf orbiting a giant?
10 Norm. Rel. Flux Rel. Norm. -0.065 Freq., Day Freq., 00 1 2 3 4 5 6 7 8 9 10 0 0 5 10 15 20 25 400 450 Time Since500 54953 MJD 550 600 4 Frequency, Cycles Per Day x 10 Star Index 15 1.5 10 1
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Norm. Rel. Flux Rel. Norm. 0 -0.01 5900 5950 6000 6050 6100 0 1 2 3 4 5 6 7 8 9 10 0 Star Index 0 5 Time10 Since 54953 MJD15 20 25 4 0.02x 10 Frequency, Cycles Per Day 6
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0 0 5 10 15 20 25 Frequency, Cycles Per Day BINARY WITH CIRCUMBINARY PLANET?
Binary Star Planet ? LOS
x
Focus of ellipse
A probable secondary eclipse and planet “map” obtained in reflected light.
Another application: Stellar Ages
• Solar type stars spin down as they age due to angular momentum loss in winds • Rotation rates can be measured due to effect of star spots
Meibom et al. (2009), M35, 150 Myr old; accurate photometry can determine stellar rotation figure from Mamajek & Hillenbrand 2008) Astroseismology • Stars have a number of oscillatory, or wave, modes – Pressure or p-modes, driven by internal pressure fluctuations within a star; their dynamics being determined by the local speed of sound – Gravity or g-modes driven by buoyancy – Surface gravity or f-modes, driven by surface waves – P-modes dominate in main sequence stars like the sun, but g-modes can be important in white dwarfs
P-modes Power spectrum for alpha Cen
Alpha Cen has a dominant 7-minute mode (2.4 mHz), very comparable to the 5-minute mode of the sun.
http://www.asteroseismology.org/ CoROT power spectra of red giants, X-axis in micro-Hz.
CoROT, solar-like stars