|
|
| (27 intermediate revisions by 2 users not shown) |
| Line 1: |
Line 1: |
| − | =General Units= | + | =General IR astronomy units= |
| | Wavelengths in infrared astronomy are commonly expressed in microns = micrometers = µm (or um if you don't have a µ). | | Wavelengths in infrared astronomy are commonly expressed in microns = micrometers = µm (or um if you don't have a µ). |
| | | | |
| Line 13: |
Line 13: |
| | Because the unit is named for [http://en.wikipedia.org/wiki/Karl_Jansky Karl Jansky], the plural of the unit is really Janskys, not Janskies. | | Because the unit is named for [http://en.wikipedia.org/wiki/Karl_Jansky Karl Jansky], the plural of the unit is really Janskys, not Janskies. |
| | | | |
| − | ==Aside on fluxes and flux densities== | + | =Fluxes and flux densities= |
| | | | |
| − | Astronomically, it can be important to understand the difference between luminosity, flux, and flux density. In practice for this stuff, you probably don't need to know the gritty details of this until you are more familiar with the numbers and the jargon. | + | Astronomically, it can be important to understand the difference between luminosity, flux, and flux density. |
| | | | |
| − | Colloquially, flux means the rate of something through something else, such as water through a pipe, or traffic on a highway. In physics and astronomy, it means the same thing. | + | Colloquially, flux means the rate of something through something else, such as water through a pipe, or traffic on a highway. In physics and astronomy, it means basically the same thing, but it has a very specific meaning. |
| | | | |
| − | ''Flux'' is a measurement of ''energy per unit area per unit time.'' Using our analogies above, this would be the number of cars per lane per second that pass under a bridge on a highway (or grams of water through the cross-sectional area of the pipe per second). In measuring energy from celestial objects, the units of flux are Joules per second per meter squared if you like mks (meters-kilograms-seconds) units, or ergs per second per centimeter squared if you like cgs (centimeters-grams-seconds) units. | + | ''Flux'' is a measurement of ''energy per unit area per unit time.'' Using a traffic analogy, this would be the number of cars per lane per second that pass under a bridge on a highway (or grams of water through the cross-sectional area of a pipe per second). In measuring energy from celestial objects, the units of flux are Joules per second per meter squared if you like mks (meters-kilograms-seconds) units, or ergs per second per centimeter squared if you like cgs (centimeters-grams-seconds) units. |
| | | | |
| − | ''Luminosity'' is a measurement of ''energy per unit of time,'' such as Joules per second if you like mks units, or ergs per second if you like cgs units. This would be, in our analogy, the total number of cars on the highway passing under the bridge per second. (The flux of cars is the luminosity per lane.) | + | ''Luminosity'' is a measurement of ''energy per unit of time,'' such as Joules per second if you like mks units, or ergs per second if you like cgs units. This would be, in our traffic analogy, the total number of cars on the highway passing under the bridge per second. (The flux of cars is the luminosity per lane.) |
| | | | |
| − | ''Flux density'' is a measurement essentially of ''energy per unit area per unit time "per photon".'' In our analogy, this would be the number of RED cars per lane per second that pass under the bridge on the highway. In this analogy, the "per photon" is seen in the red cars. In astronomy, the "per photon" manifests itself as a "per Hz" (unit of frequency) or "per cm" (unit of wavelength). A Jansky is proportional to Watts/m^2/Hz. Recall that Watts are energy per second. So this is energy per second per square meter per Hertz. | + | ''Flux density'' is a measurement essentially of ''energy per unit area per unit time "per photon".'' In our traffic analogy, this would be the number of RED cars per lane per second that pass under the bridge on the highway. In this analogy, the "per photon" is seen in the red cars. In astronomy, the "per photon" manifests itself as a "per Hz" (unit of frequency) or "per cm" (unit of wavelength). A Jansky is proportional to Watts/m^2/Hz. Recall that Watts are energy per second. So this is energy per second per square meter per Hertz. |
| | | | |
| − | Now, just to further confuse things, the units of Spitzer ''mosaics'' are not just Janskys, but Janskys per area! To make the numbers easier, they are in MJy/sr, but they could also be in uJy/square arcsecond. Read on for more, including definitions and scale factors! | + | Now, just to further confuse things, the units of Spitzer and some Herschel mosaics are not just Janskys, but Janskys per area! To make the numbers easier, they are in MJy/sr, but they could also be in uJy/square arcsecond. Read on for more, including definitions and scale factors! |
| | | | |
| − | For completeness, we note here that ''magnitudes'' are proportional to ''the log of the ratio of two fluxes''. Most magnitudes with which you are most likely familiar are tied to the magnitude of Vega, so a magnitude of 0 means that the object has the same flux as Vega. There's more on this below, too. | + | For completeness, we note here that ''magnitudes'' are proportional to ''the log of the ratio of two fluxes''. Most magnitudes with which you are most likely familiar are tied to the magnitude of Vega, so a magnitude of 0 means that the object has the same flux as Vega. |
| | | | |
| − | =Units of Spitzer Images=
| + | [[Magnitudes]] has a different wiki page. |
| | | | |
| − | Optical data with which you are familiar may be in counts or photons, or possibly (like Hubble data) calibrated to be energies. That, combined with the exposure time of the image, gives you ''flux units''. Spitzer data comes in ''flux (density) per unit (pixel) area'' instead, MegaJanskys per steradian (MJy/sr). 1 MJy = <math>10^{6}</math> Jy, and a sr is a solid angle. | + | =Units of Spitzer and Herschel Images= |
| | + | |
| | + | Optical data with which you are familiar may be in counts or photons, or possibly (like Hubble data) calibrated to be energies. That, combined with the exposure time of the image, gives you ''flux units''. Spitzer data (and some Herschel data) come in ''flux (density) per unit (pixel) area'' instead, MegaJanskys per steradian (MJy/sr). 1 MJy = <math>10^{6}</math> Jy, and a sr is a solid angle. |
| | | | |
| | If you've done photometry before, and expect to do it exactly the same way again here, '''it won't work''', because '''this matters'''. | | If you've done photometry before, and expect to do it exactly the same way again here, '''it won't work''', because '''this matters'''. |
| | | | |
| − | 1 square arcsec is <math>2.3504 \times 10^{-11}</math> sr. (1 degree = 60 arcmin = 3600 arcsec.) | + | 1 square arcsec is <math>2.3504 \times 10^{-11}</math> sr. (1 degree = 60 arcmin = 3600 arcsec, and a sphere subtends 4pi steradians. |
| | | | |
| | If you want to convert the image from MJy/sr to uJy/square arcsec, multiply the image by 23.5045. The units of this number are (uJy/arcsec)/(MJy/sr). | | If you want to convert the image from MJy/sr to uJy/square arcsec, multiply the image by 23.5045. The units of this number are (uJy/arcsec)/(MJy/sr). |
| | | | |
| − | If you want to take a Spitzer image and use your previous routines on it, the most efficient way to do this is probably to take the image in MJy/sr and multiply out the "per sr" part of it so that it is instead in MJy/px. The subtlety in this step is that each Spitzer array has slightly different pixel sizes, and the mosaics that we create have different sizes yet again from the original images. You can make mosaics with whatever size pixels you want, so if you get Spitzer mosaics from more than one astronomer, or more than one Spitzer wavelength, chances are excellent that the pixels will be slightly different sizes. The information on the pixel sizes are in the [[FITS_format|FITS]] header of each image. | + | If you want to take a Spitzer or Herschel image and use your previous routines on it, the most efficient way to do this is probably to take the image in MJy/sr and multiply out the "per sr" part of it so that it is instead in MJy/px. The subtlety in this step is that each Spitzer (or Herschel) detector has different pixel sizes, and the mosaics that we create have different sizes yet again from the original images. You can make mosaics with whatever size pixels you want, so if you get Spitzer(or Herschel) mosaics from more than one astronomer, or more than one Spitzer(or Herschel) wavelength, chances are excellent that the pixels will be slightly different sizes (and for Herschel, maybe slightly different units). The information on the pixel sizes are in the [[FITS_format|FITS]] header of each image. |
| − | | |
| − | The following paragraphs are a high-level summary of what to do for any Spitzer image data you may encounter; see below for a cookbook of the process for one mosaic.
| |
| − | | |
| − | Look in the FITS header of the mosaics for the keywords "CDELT1" and "CDELT2". These keywords are set to be the scale of the rows and columns in degrees per pixel. Using the values of these keywords, and the conversions above, you can figure out the number of square degrees per pixel, the number of square arcsec per pixel, and finally the number of steradians per pixel. Multiply the whole image in MJy/sr by the number of sr/px to get MJy/px.
| |
| − | | |
| − | If you are instead working with the individual BCDs (read this as: the individual little images that went into the big mosaic), you should look for keywords "PXSCAL1" and "PXSCAL2". NOTE that these pixels ARE NOT SQUARE, and this is more important for MIPS data. From here, you now have the same information as the "CDELT1" and "CDELT2" above, so you can follow the same procedure.
| |
| − | | |
| − | =Units of Spitzer Photometry=
| |
| − | | |
| − | ''[[Photometry|See this page]] for a '''brief''' introduction to photometry and magnitudes.''
| |
| − | | |
| − | ==Introduction==
| |
| − | | |
| − | The photometry software that people at the SSC wrote for use with Spitzer data, called APEX, produces flux densities in microJanskys. The final bandmerged catalog you can get has listed flux densities in microJanskys, as well as magnitudes.
| |
| − | | |
| − | Astronomers use magnitudes in color-color or color-magnitude plots. Astronomers use a variant on flux densities in spectral energy distribution (SED) plots.
| |
| − | | |
| − | ==Magnitudes==
| |
| − | | |
| − | A magnitude is really a flux ratio. It is defined as follows, where M's are magnitudes and F's are fluxes:
| |
| − | <math>M_1 - M_2 = 2.5 \times \log \left(\frac{F_2}{F_1}\right)</math> (eqn 1)
| |
| − | | |
| − | The magnitude system (in the optical) was defined to be referenced to Vega. In other words, Vega is defined to be zero magnitude, and you would then define magnitudes of anything else as follows:
| |
| − | <math>M = 2.5 \times \log \left(\frac{F_{\mathrm{Vega}}}{F}\right)</math> (eqn 2)
| |
| − | | |
| − | When they looked at Vega with IRAS, they discovered that it did NOT look like they expected, and in fact it has a large infrared excess! Therefore, infrared magnitudes are defined with respect to what Vega would be, if it did not have an excess.
| |
| − | | |
| − | We have published the zero points (e.g., the "Vega flux") for most of our bandpasses. They are (copied from various places on the web):
| |
| − | *IRAC 1 : 280.9 Jy
| |
| − | *IRAC 2 : 179.7 Jy
| |
| − | *IRAC 3 : 115.0 Jy
| |
| − | *IRAC 4 : 64.13 Jy
| |
| − | *MIPS 1 : 7.14 Jy
| |
| − | *MIPS 2 : 0.775 Jy
| |
| − | *MIPS 3 : 0.159 Jy
| |
| − | | |
| − | Therefore, in order to convert the uJy that apex returns into magnitudes, use the equation 2 above, substituting these so-called "zero-point fluxes" in for "Fvega." Note that the zero-point fluxes are in Janskys and the fluxes returned by APEX are in microJanskys.
| |
| − | | |
| − | You can find the zeropoints for 2MASS magnitudes on the web as well:
| |
| − | *J : 1594 Jy
| |
| − | *H : 1024 Jy
| |
| − | *K : 666.7 Jy
| |
| − | (see also [[Central wavelengths and zero points]] for more numbers.)
| |
| − | | |
| − | Note that plain magnitudes get fainter (the number gets larger) as the distance of the object increases. This happens because Vega, your reference object, stays the same while such an example object moves farther away. BUT, colors (which are differences in magnitudes) are ratios of fluxes ''of the same object'', and therefore ''independent of distance.'' This is powerful when you are studying objects whose distances you don't know, or comparing objects at a variety of distances.
| |
| − | | |
| − | To convert magnitudes back into fluxes (e.g., if you have optical or 2MASS magnitudes and need to get fluxes), you need to invert the equation above. Recall that to invert a logarithm (base 10), you have to raise both sides to the power of 10, e.g., if log x = y then x = 10^y.
| |
| − | | |
| − | ==Spectral Energy Distributions (SEDs)==
| |
| − | | |
| − | SEDs are energy plotted against some measure of the photon -- frequency or wavelength. The reason astronomers do this is to see how much energy is produced by the object as a function of frequency or wavelength.
| |
| − | Now it's really going to get a little hairy! Steel your nerves and plunge onwards... it really all comes down to unit conversion.
| |
| − | | |
| − | The units that are used in Spitzer data are Janskys. 1 Jy = <math>10^{-23}</math> erg/s/cm^2/Hz (in cgs units rather than mks units, sorry). A Jansky is technically a unit of "flux density," represented by <math>F_{\nu}</math>. We want to plot "energy density", so one way to do this (''DON'T DO THIS TO YOUR DATA YET'') is to
| |
| − | get rid of the "per Hz", e.g., multiply the Jy by the frequency (<math>\nu</math>) of the bandpass center, or <math>\nu F_{\nu}</math>. You could just stop here, and plot <math>\nu F_{\nu}</math> vs. <math>\nu</math> to get something that is technically a spectral energy distribution. BUT, now it starts to get a little hairy, because there are some cultural influences here. Do you know off the top of your head what the frequency of the IRAC-1 band is? I don't either, but I do know its wavelength -- 3.6 microns. Astronomers coming from the longer wavelengths (mm, radio, etc.), because they think in units of frequencies, will tend to plot up <math>\nu F_{\nu}</math> against <math>\nu</math> (nu). The units of <math>F_{\nu}</math> really are Janskys. BUT, astronomers coming from the shorter wavelengths (optical, etc.), because they think in units of wavelengths, will tend to plot instead <math>\lambda F_\lambda</math> , where <math>\lambda</math> (lambda) is the wavelength of the light. This is what we want to do here (because we have been thinking of the wavelengths of the Spitzer bands but not the frequencies). The catch here is that the units of <math>F_{\lambda}</math> are NOT Janskys.
| |
| − | | |
| − | <math>\lambda \times \nu = c</math>, the speed of light. In order to convert the Janskys into units of <math>F_{\lambda}</math>, you need to take into account the differentials (ah-HA, calculus being used here!), e.g., the fact that
| |
| − | <math>\frac{dF}{d\lambda} = \frac{dF}{d\nu} \frac{d\nu}{d\lambda}</math> and <math>d\nu = \frac{c}{\lambda^2}d\lambda</math>
| |
| − | So you need to multiply the <math>F_{\nu}</math> by <math>c/\lambda^2</math> to convert it into <math>F_{\lambda}</math>. But we are not done yet! Recalling from above, the units of <math>F_{\lambda}</math> are not an energy density. You need to get another factor of <math>\lambda</math> in there to make the units work out to be energy density: calculate <math>\lambda F_{\lambda}</math> to get units of ergs/s/cm^2.
| |
| − | | |
| − | SO, IN SUMMARY: Take your <math>F_{\nu}</math> measurements that are in Jy. (Ensure they are in Jy! If they're in magnitudes, convert them to Jy first; see 'magnitude' discussion above.) Multiply by <math>10^{-23}</math> to get them into cgs units. Multiply these <math>F_{\nu}</math> values by <math>c/\lambda^2</math> to get them into <math>F_{\lambda}</math>. Multiply them by <math>\lambda</math> to get them into <math>\lambda F_\lambda</math>.
| |
| − | NB: c = 2.997924d10 cm/sec
| |
| − | | |
| − | In words, in order to analyze our data from photometry to SEDs, we need to have something that does the following:
| |
| − | | |
| − | #Reads in the flux densities from the files of photometry.
| |
| − | #Converts the Spitzer flux densities (and errors) into magnitudes (if necessary).
| |
| − | #Converts the 2MASS magnitudes (and errors) into flux densities (if necessary).
| |
| − | #Makes color-color and color-magnitude plots for stars in our region using magnitudes. (and picks out the 'interesting' objects!)
| |
| − | #Makes SED plots for individual objects, but converting numbers first into the right units:
| |
| − | ##Creates an array of the wavelengths of each measurement, keeps a copy of the version in microns, and converts to cm.
| |
| − | ##For any real measurements, converts the microJanskys into cgs units.
| |
| − | ##For any real measurements, converts <math>F_{\nu}</math> into <math>F_{\lambda}</math> by multiplying the <math>F_{\nu}</math> values by the <math>d\nu/d\lambda</math> corresponding to the wavelength of each bandpass.
| |
| − | ##For any real measurements, multiplies <math>F_{\lambda}</math> by the lambda corresponding to the wavelength of each bandpass to get <math>\lambda F_{\lambda}</math>.
| |
| − | #For any real measurements, plots the log of the <math>\lambda F_{\lambda}</math> data points (in cgs units) against the log of the lambda data points (in microns, only because that makes it easier to read). Labels the axes (with units)! Plots the error bars on top of the data points (also converted from uJy).
| |
| − | | |
| − | | |
| − | | |
| − | ===Notes on plotting===
| |
| − | | |
| − | Why are we plotting <math>\lambda F_{\lambda}</math> vs. <math>\lambda</math> instead of <math>\nu</math>? Well, only because I think in wavelength, not frequency. I don't know off the top of my head the frequencies of the Spitzer bandpasses, but I do know their wavelengths.
| |
| − | | |
| − | Why are we plotting <math>\lambda F_{\lambda}</math> instead of <math>\nu F_{\nu}</math>? Well, only for internal consistency. Since one axis is in wavelength units, it makes sense to have the other axis also in wavelength units.
| |
| − | | |
| − | If you have gotten this far using real data, you will find (if you have done the calculations correctly) that you have numbers that are very small, like 9.77237e-12, 1.99526e-11, etc. Any time you find yourself with these kinds of numbers, you should automatically plot in log space (or log/log space), NOT linear space. You want to actually plot log(<math>\lambda F_{\lambda}</math>) vs. log(<math>\lambda</math>).
| |
| − | | |
| − | ===The next step ===
| |
| − | | |
| − | IF you are highly motivated and ready to go on to the next step... It can be useful, in the course of analysis of the Spitzer data, to pretend that the contribution from the star is a blackbody. It's not really, but it's awful close, especially in the infrared. A blackbody's flux density is given by (where T is temperature, and other constants are given below)
| |
| − | <math>B_{\lambda} = \left(\frac{2hc^2/\lambda^5}{\exp(hc/\lambda kT)-1)}\right)</math> (eqn 3)
| |
| − | but of course we want to plot <math>\lambda \times B_{\lambda}</math>:
| |
| − | <math>\lambda B_{\lambda} = \left(\frac{2hc^2/\lambda^4}{\exp(hc/\lambda kT)-1)}\right)</math> (eqn 4)
| |
| − | Values of these constants all in cgs units:
| |
| − | *h = 6.6260755d-27 erg*sec
| |
| − | *c = 2.997924d10 cm/sec
| |
| − | *k = 1.380658d-16 erg/deg
| |
| − | | |
| − | So, in summary, for the list of things to do above, add this one:
| |
| − | #For any real measurements, for any star with at least 2 fluxes, fit a model -- one ''very'' simple way to do that is to fit a blackbody to the energies derived from the three 2MASS and first 2 IRAC bands. There are two free parameters in this fit -- the temperature of the blackbody and an additive (in the log) offset related to the distance of the object. If we know the temperature of the star (via a spectral type) and the distance to the object, then we know the values for the temperature and the offset.
| |
| − | | |
| − | =Cookbook for image conversion (or calculating the number APT needs): Method One=
| |
| − | | |
| − | ==Step zero. What do you have and what do you need?==
| |
| − | You have an image in MJy/sr(/px). You have the number of degrees per pixel.
| |
| − | | |
| − | You need to convert the image to MJy(/px), a.k.a "get rid of the steradians." This is also the number that APT needs to do the conversion to MJy.
| |
| − | | |
| − | The things that make this hard are:
| |
| − | *The pixel size of the mosaic changes depending on wavelength and where you got the mosaic, so I can't just give you one number to work for all mosaics every time.
| |
| − | *The "pixels" in the above are kind of a funny, hidden unit and the accounting of it works in some unexpected ways, which is why it's in parentheses above (and below).
| |
| − | | |
| − | ==Step one. Find out what the size of the pixels are in your images==
| |
| − | For the IRAC-1 mosaic I created for you in July 2006, CDELT1=-0.000339 degrees per pixel, and CDELT2=0.000339 degrees per pixel. (ignore the minus sign; it has something to do with a fits convention.) You can find this out for any given mosaic by looking in the fits header.
| |
| − | | |
| − | ==Step two. Find out what the size of the pixels are in square degrees per pixel==
| |
| − | | |
| − | degrees degrees square degrees
| |
| − | 0.000339 ------- * 0.000339 ------- = 1.14921e-7 ---------------
| |
| − | pixel pixel (square) pixel
| |
| − | | |
| − | ==Step three. Find out what the conversion is between square degrees and sr.==
| |
| − | There are 60 arcminutes in a degree. There are 60 arcseconds in an arcminute.
| |
| − | | |
| − | 60 arcminutes 60 arcseconds 3600 arcseconds
| |
| − | ------------- * -------------- = ---------------
| |
| − | 1 degree 1 arcminutes 1 degree
| |
| − | | |
| − | Square it!
| |
| − | | |
| − | (1 degree)^2 = 1 square degree = (3600 arcsec)^2 = 1.296e7 square arcsec
| |
| − | | |
| − | We look up that 1 square arcsec is 2.3504x10^(-11) sr.
| |
| − | | |
| − | 1.296e7 square arcsec 2.3504e-11 sr sr
| |
| − | ------------- * ---------------- = 0.0003046118 ------------
| |
| − | square degree 1 square arcsec square degree
| |
| − | | |
| − | ==Step four. Find out what the size of the pixels are in sr.==
| |
| − | | |
| − | square degrees sr sr
| |
| − | 1.14921e-7 --------------- * 0.0003046118 ------------ = 3.500629e-11 ----
| |
| − | (square) pixel square degree px
| |
| − | | |
| − | ==Step five. Convert the units of the image.==
| |
| − | | |
| − | MJy sr MJy
| |
| − | --------- * 3.500629e-11 ---- = ---
| |
| − | sr px px
| |
| − | | |
| − | So you or APT needs to multiply this whole image by 3.500629e-11. This is what APT does with the number that you type into the "More settings" window -- it multiplies the result by the number we enter. The number that you need to enter, then is the number that we just calculated. BUT look at the units of that number. The units of the image (and consequently the photometry you get out) are then in '''MJy (MegaJanskys)'''. None of the sources will be that bright. If you want to get it in Janskys:
| |
| − | | |
| − | 1e6 Jy
| |
| − | ----
| |
| − | MJy
| |
| − | | |
| − | so then multiply the image (a.k.a. the number above) by 1e6 to get the image (e.g., the result of the photometry) into Jy (or multiply the number you get above by 1e6 before entering it into APT):
| |
| − | | |
| − | MJy 1e6 Jy Jy
| |
| − | --- * ---- = ----
| |
| − | px MJy px
| |
| − | | |
| − | For the specific example we're working through, 3.500629e-11 * 1e6 = 3.500629e-5. If you enter that number into APT, the result of its calculation will be in Jy. But, most sources will be even fainter. MOPEX returns results in MICROJANSKYS. If you want to have your results produced in microJy, there are 1e6 uJy in a Jy, and I'll let you do that one.
| |
| − | | |
| − | =Method 2: Alternative but completely equivalent and possibly more straightforward solution=
| |
| − | ==Step zero. What do you have and what do you need?==
| |
| − | You have an image in MJy/sr(/px). You have the number of degrees per pixel.
| |
| − | | |
| − | You need to convert the image to uJy(/px), a.k.a "get rid of the steradians" AND convert to microJanskys to get the numbers to still be reasonable and not very tiny or very large.
| |
| − | | |
| − | The things that make this hard are:
| |
| − | * The pixel size of the mosaic changes depending on wavelength and where you got the mosaic, so I can't just give you one number to work for all mosaics every time.
| |
| − | * The "pixels" in the above are kind of a funny, hidden unit and the accounting of it works in some unexpected ways.
| |
| − | | |
| − | ==Step one. Find out what the size of the pixels are in your images==
| |
| − | For the IRAC-1 mosaic I created for you in July 2006, CDELT1=-0.000339 degrees per pixel, and CDELT2=0.000339 degrees per pixel. (ignore the minus sign; it has something to do with a fits convention.) For any given mosaic, you can find out these values by looking in the fits header.
| |
| − | | |
| − | ==Step two. Convert your image from MJy/sr to uJy/square arcsec==
| |
| − | We look up that there are :
| |
| − | | |
| − | [uJy/sq. arcsec]
| |
| − | 23.5045 -----------------
| |
| − | [MJy/sr]
| |
| − | | |
| − | So the first factor to multiply the image by is 23.5045 to get it into uJy/square arcsec. If you are attempting to get the number for APT, this is the first factor to write down on a piece of scrap paper.
| |
| − | | |
| − | ==Step three. Find out what the size of the pixels are in square degrees per pixel==
| |
| − | | |
| − | degrees degrees square degrees
| |
| − | 0.000339 ------- * 0.000339 ------- = 1.14921e-7 ---------------
| |
| − | pixel pixel (square) pixel
| |
| − | | |
| − | ==Step four. Find out how many square arcsec there are in a pixel.==
| |
| − | There are 60 arcminutes in a degree. There are 60 arcseconds in an arcminute.
| |
| − | | |
| − | 60 arcminutes 60 arcseconds 3600 arcseconds
| |
| − | ------------- * -------------- = ---------------
| |
| − | 1 degree 1 arcminutes 1 degree
| |
| − | | |
| − | Square it!
| |
| − | | |
| − | (1 degree)^2 = 1 square degree = (3600 arcsec)^2 = 1.296e7 square arcsec
| |
| − | | |
| − | Convert the pixel size.
| |
| − | | |
| − | square degrees square arcsec square arcsec
| |
| − | 1.14921e-7 --------------- * 1.296e7 -------------- = 1.48938 ---------------
| |
| − | (square) pixel square degree (square) px
| |
| − | | |
| − | ==Step five. Convert the image==
| |
| − | | |
| − | uJy 1.48938 square arcsec uJy
| |
| − | ----------- * --------------- = ------
| |
| − | sq arcsec (*px) (square) px (px)
| |
| | | | |
| − | So multiply the image by another factor of 1.48938 to get it into uJy/px. (If you are trying to get the number for APT, get the factor from way up above, 23.5045, and multiply it by 1.48938 [for this example] to get the number you want to put into APT so that it can do the multiplication for you.) Note that the output of APT will then be in microJanskys.
| + | To figure out the pixel size, look in the FITS header of the mosaics for keywords corresponding to pixel size -- they are often "CDELT1" and "CDELT2", but may be "PXSCAL1" and "PXSCAL2" or something else. These keywords are set to be the scale of the rows and columns in degrees per pixel. Using the values of these keywords, and the conversions above, you can figure out the number of square degrees per pixel, the number of square arcsec per pixel, and finally the number of steradians per pixel. Multiply the whole image in MJy/sr by the number of sr/px to get MJy/px. |
General IR astronomy units
Wavelengths in infrared astronomy are commonly expressed in microns = micrometers = µm (or um if you don't have a µ).
- 5000 Å =500 nm =0.5 µm =Visible light
- ~0.9 to 5 µm =Near-infrared (~smoke particles)
- 5 µm to ~30 µm = Mid-infrared (~hair)
- 30 µm to ~350 µm = Far-infrared (~salt grain)
Brightnesses or fluxes are most likely to be given in Janskys (Jy) or mJy (milli Jy) or µJy (micro Jy). 1 Jansky = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 10^{-26}}
Watts/m^2/Hz.
Jy can be converted to magnitudes which have historically been relatively rarely used in the mid- or far-infrared.
Because the unit is named for Karl Jansky, the plural of the unit is really Janskys, not Janskies.
Fluxes and flux densities
Astronomically, it can be important to understand the difference between luminosity, flux, and flux density.
Colloquially, flux means the rate of something through something else, such as water through a pipe, or traffic on a highway. In physics and astronomy, it means basically the same thing, but it has a very specific meaning.
Flux is a measurement of energy per unit area per unit time. Using a traffic analogy, this would be the number of cars per lane per second that pass under a bridge on a highway (or grams of water through the cross-sectional area of a pipe per second). In measuring energy from celestial objects, the units of flux are Joules per second per meter squared if you like mks (meters-kilograms-seconds) units, or ergs per second per centimeter squared if you like cgs (centimeters-grams-seconds) units.
Luminosity is a measurement of energy per unit of time, such as Joules per second if you like mks units, or ergs per second if you like cgs units. This would be, in our traffic analogy, the total number of cars on the highway passing under the bridge per second. (The flux of cars is the luminosity per lane.)
Flux density is a measurement essentially of energy per unit area per unit time "per photon". In our traffic analogy, this would be the number of RED cars per lane per second that pass under the bridge on the highway. In this analogy, the "per photon" is seen in the red cars. In astronomy, the "per photon" manifests itself as a "per Hz" (unit of frequency) or "per cm" (unit of wavelength). A Jansky is proportional to Watts/m^2/Hz. Recall that Watts are energy per second. So this is energy per second per square meter per Hertz.
Now, just to further confuse things, the units of Spitzer and some Herschel mosaics are not just Janskys, but Janskys per area! To make the numbers easier, they are in MJy/sr, but they could also be in uJy/square arcsecond. Read on for more, including definitions and scale factors!
For completeness, we note here that magnitudes are proportional to the log of the ratio of two fluxes. Most magnitudes with which you are most likely familiar are tied to the magnitude of Vega, so a magnitude of 0 means that the object has the same flux as Vega.
Magnitudes has a different wiki page.
Units of Spitzer and Herschel Images
Optical data with which you are familiar may be in counts or photons, or possibly (like Hubble data) calibrated to be energies. That, combined with the exposure time of the image, gives you flux units. Spitzer data (and some Herschel data) come in flux (density) per unit (pixel) area instead, MegaJanskys per steradian (MJy/sr). 1 MJy = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 10^{6}}
Jy, and a sr is a solid angle.
If you've done photometry before, and expect to do it exactly the same way again here, it won't work, because this matters.
1 square arcsec is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 2.3504 \times 10^{-11}}
sr. (1 degree = 60 arcmin = 3600 arcsec, and a sphere subtends 4pi steradians.
If you want to convert the image from MJy/sr to uJy/square arcsec, multiply the image by 23.5045. The units of this number are (uJy/arcsec)/(MJy/sr).
If you want to take a Spitzer or Herschel image and use your previous routines on it, the most efficient way to do this is probably to take the image in MJy/sr and multiply out the "per sr" part of it so that it is instead in MJy/px. The subtlety in this step is that each Spitzer (or Herschel) detector has different pixel sizes, and the mosaics that we create have different sizes yet again from the original images. You can make mosaics with whatever size pixels you want, so if you get Spitzer(or Herschel) mosaics from more than one astronomer, or more than one Spitzer(or Herschel) wavelength, chances are excellent that the pixels will be slightly different sizes (and for Herschel, maybe slightly different units). The information on the pixel sizes are in the FITS header of each image.
To figure out the pixel size, look in the FITS header of the mosaics for keywords corresponding to pixel size -- they are often "CDELT1" and "CDELT2", but may be "PXSCAL1" and "PXSCAL2" or something else. These keywords are set to be the scale of the rows and columns in degrees per pixel. Using the values of these keywords, and the conversions above, you can figure out the number of square degrees per pixel, the number of square arcsec per pixel, and finally the number of steradians per pixel. Multiply the whole image in MJy/sr by the number of sr/px to get MJy/px.
