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

)1()sinsincoscos(cos)sec( 1 HAanglezenith

•Air mass corrections – have to correct for different paths through the atmosphere • Can assume plane parallel atmosphere for a crude correction

• A more accurate formula is given in the text • If the extinction is exponential:

• Then

• 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)

)3(, I

ds

dI

)4().1(5.2)1()( amammamm

Is the system based exclusively on an instrument – the defining photometer? • If so, how do you maintain it?

Harold Johnson

maintaining the

defining UBVRI

photometer

One solution:

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!!

H KJ

L MN

Q

Extending to the infrared – Johnson comes to the Lunar and Planetary Laboratory and sets up JKLM, Frank Low adds N (OP) Q. Eric Becklin (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 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!!!!!

)5()005.0028.0())(020.0026.1()(

)005.0013.0())(006.0056.1()(

)006.0043.0())(010.0076.1()(

)003.0024.0())(005.0000.0()(

2

2

2

2

CITMASSS

CITMASSS

CITMASS

CITCITMASSS

KHKH

KJKJ

HJHJ

KJKK

• Here is how a simple set of transformations might look:

• 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.

• 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

Common Terms:

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:

)6(.)(

)(0

dT

dT

• We would like to characterize this band by a single wavelength. One candidate is the mean:

• This works to first order, but we will find that some corrections are necessary

• 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)

Overview of Absolute Calibration

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

with different SEDs is

different and we need to

correct to equivalent

monochromatic fluxes.

J-band photometry of an early L-dwarf. The dashed line is

the spectrum of an A0V calibrator star, the dotted line is

that of the L dwarf, and the solid line is the transmission

profile of the J filter. The A0 and L dwarf spectra have

been adjusted to give identical signals in the J band. The

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

)8(085.56))(log(5.2 12 HzmWfmAB

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.

full age spread

2

2.5

3

3.5

4

4.5

1 1.2 1.4 1.6 1.8 2 2.2 2.4V-K

M_K

0-1000

1000-3500

3500-6000

6000-8000

8000-11000

sun

500

2000

4500

7000

10000

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.

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

• Focal length: 30 cm

• Field of View: 7x 7 degrees

• Detector: 4096x4096 CCD with 9mm pixels

VULCAN search Modest telescopes are fine for

this type of work.

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.

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”).

Basic instrumentation approach,

From Charbonneau et al. (2006)

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.

http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=45518

CoROT (below), MOST (right) demonstrate

that huge telescopes are not needed to

carry out critical high accuracy photometry

from space.

Use transit photometry to detect Earth-size

planets

0.95 meter aperture provides enough photons

Observe for several years to detect transit

patterns

Monitor a single large area on the sky

continuously to avoid missing transits

Use heliocentric orbit

Up to 170,000 targets at 30 min

cadence & 512 at 1 min

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

Get statistically valid

results by monitoring;

100,000 stars

• Wide Field-of-view telescope (100 sq deg)

• Large array of CCD detectors

1.4m Primary

Mirror

Focus

Mechanism (3)

Focal Plane

Radiator

Graphite Metering

Structure

95 cm Schmidt

Corrector (Fused

Silica)

Focal Plane w/ 42

Science CCD’s &

4 Fine Guidance

Sensors

Focal Plane

Electronics

SAMPLE OF LIGHT CURVES

0 1 2 3 4 5 6 7 8 9 10-0.6

-0.4

-0.2

0

0.2

Time Since 54953 MJD

Norm

. R

el. F

lux

0 5 10 15 20 250

2

4

6

8x 10

4

Frequency, Cycles Per Day

PS

D

Star Index

Fre

q., D

ay

-1

50 100 150 200 2500

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10-0.6

-0.4

-0.2

0

0.2

Time Since 54953 MJD

Nor

m. R

el. F

lux

0 5 10 15 20 250

5

10

15x 10

4

Frequency, Cycles Per Day

PS

D

Star Index

Fre

q., D

ay-1

50 100 150 200 2500

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10-2

0

2

4

6x 10

-3

Time Since 54953 MJD

No

rm. R

el. F

lux

0 5 10 15 20 250

5

10x 10

4

Frequency, Cycles Per Day

PS

D

Star Index

Fre

q.,

Day

-1

50 100 150 200 2500

5

10

15

20

Non-aligned spin axes of hot, fast-rotating stars?

SAMPLE LIGHT CURVES

0 1 2 3 4 5 6 7 8 9 10-0.4

-0.2

0

0.2

0.4

Time Since 54953 MJD

Norm

. R

el. F

lux

0 5 10 15 20 250

5

10

15x 10

4

Frequency, Cycles Per Day

PS

D

Star Index

Fre

q., D

ay

-1

50 100 150 200 2500

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10-0.06

-0.04

-0.02

0

0.02

Time Since 54953 MJD

No

rm. R

el.

Flu

x

0 5 10 15 20 250

5

10

15x 10

4

Frequency, Cycles Per Day

PS

D

Star Index

Fre

q.,

Day-1

150 200 250 300 3500

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10-0.5

0

0.5

1

1.5

Time Since 54953 MJD

Nor

m. R

el. F

lux

0 5 10 15 20 250

5

10

15x 10

4

Frequency, Cycles Per Day

PS

D

Star Index

Fre

q., D

ay-1

400 450 500 550 6000

5

10

15

20

2-day transit; dwarf orbiting a giant?

SAMPLE LIGHT CURVES

0 1 2 3 4 5 6 7 8 9 10-5

0

5

10x 10

-3

Time Since 54953 MJD

Norm

. R

el. F

lux

0 5 10 15 20 250

5

10

15x 10

4

Frequency, Cycles Per Day

PS

DStar Index

Fre

q., D

ay

-1

4400 4450 4500 4550 46000

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10-0.01

-0.005

0

0.005

0.01

Time Since 54953 MJD

Norm

. R

el.

Flu

x

0 5 10 15 20 250

2

4

6x 10

4

Frequency, Cycles Per Day

PS

D

Star Index

Fre

q., D

ay

-1

4900 4950 5000 5050 51000

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10-0.01

0

0.01

0.02

Time Since 54953 MJD

No

rm. R

el.

Flu

x

0 5 10 15 20 250

2

4

6x 10

4

Frequency, Cycles Per Day

PS

D

Star Index

Fre

q.,

Day-1

5900 5950 6000 6050 61000

5

10

15

20

BINARY WITH CIRCUMBINARY PLANET?

LOS

Planet ? Binary Star

x

Focus of ellipse

A probable secondary eclipse and planet “map” obtained in reflected light.

Another application: Stellar Ages

Meibom et al. (2009),

M35, 150 Myr old;

accurate photometry

can determine stellar

rotation

• 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

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

http://www.asteroseismology.org/

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.

CoROT power spectra of red giants,

X-axis in micro-Hz.

CoROT,

solar-like

stars