Faint-end bias investigation (Eddie Schlafly)

I've been investigating correcting the faint-end bias in PS1 stellar photometry empirically over the past several days. Doug Finkbeiner has found that the bias can be seen comparing PS images to PS images with different PSF FWHM, and that this bias can be well modeled as a constant offset in flux (e.g., the following plot).

http://faun.rc.fas.harvard.edu/eschlafly/faintbias/example1.png

Motivated by this, I have fit a function of this form to every PS image overlapping the SDSS, transforming the SDSS magnitudes onto the PS system following JT's color transformations. This produces a list of flux offsets for every PS1 image. I want to use this information to remove the faint-end bias in all of the PS1 images.

Trend in bias with FWHM

There is a clear relation in the flux offset as a function of PSF FWHM, consistent with what Doug found. The relation is different for exposures in different filters and with different exposure times. Unfortunately, I haven't been able to figure out what controls the differences in these relations. Accordingly, I have just fit a quadratic for the flux offset as a function of PSF FWHM for every exposure time and filter combination. Additionally, I found that the residuals in this relation changed around MJD 55660, and so I fit separation relations before and after that date. The relevant plots describing these fits follow. The title gives the filter, exposure time, and MJD range corresponding to each plot. The 30s y band plot shows what look like two loci, but I haven't been able to figure out what controls the two loci; there is no clear split in MJD or sky background or any other parameter I have looked at.

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g240(-inf-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g52(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r240(-inf-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r36(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r40(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r40(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r60(-inf-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i32(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i45(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i45(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z20(-inf-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240(-inf-55660).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y30(55660-inf).png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y30(-inf-55660).png

Test of corrected data

I have then tested applying these relations to images drawn at random from the survey. What follows are a large number of examples of the original data, and then the data corrected according to the relations above. I think the moral is that the correction does substantially more good than harm. Nevertheless, there are clear examples where the correction fails badly.

g 113s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5251g0315o.140316.cm.50480.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5479g0079o.237418.cm.128173.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5584g0566o.285261.cm.163780.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5587g0557o.287505.cm.165634.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5614g0254o.304643.cm.176183.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5665g0270o.323460.cm.193488.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5767g0500o.368085.cm.239892.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5776g0416o.372285.cm.243824.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g113o5812g0351o.389175.cm.262313.png

g 240s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g240o5014g0017o.84016.cm.110311.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g240o5828g0212o.398809.cm.274325.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g240o5828g0222o.398819.cm.274349.png

g 43s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43o5389g0402o.191736.cm.96638.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43o5446g0275o.221000.cm.115108.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43o5480g0557o.238390.cm.128857.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43o5563g0298o.271504.cm.156357.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43o5676g0187o.329346.cm.198005.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43o5745g0346o.356720.cm.229845.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g43o5797g0141o.381642.cm.252912.png

g 52s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g52o5242g0461o.135993.cm.44982.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/g52o5276g0177o.150138.cm.61403.png

r 113s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5413g0123o.202995.cm.103038.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5440g0434o.217489.cm.112486.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5590g0591o.289723.cm.167238.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5593g0123o.291166.cm.168437.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5629g0074o.306275.cm.181382.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5761g0095o.364733.cm.236426.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5764g0097o.366395.cm.238063.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5773g0523o.370606.cm.242041.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r113o5821g0277o.393199.cm.269672.png

r 240s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r240o5014g0021o.84020.cm.110313.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r240o5828g0233o.398830.cm.274385.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r240o5828g0234o.398831.cm.274386.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r240o5828g0353o.398950.cm.274507.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r240o5828g0354o.398951.cm.274508.png

r 36s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r36o5247g0044o.137655.cm.48612.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r36o5248g0373o.138455.cm.49231.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r36o5298g0383o.156806.cm.73453.png

r 40s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r40o5502g0168o.249478.cm.135885.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r40o5767g0177o.367762.cm.239864.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r40o5860g0408o.414635.cm.308637.png

r 60s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r60o5163g0176o.105438.cm.88654.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r60o5163g0184o.105446.cm.88659.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/r60o5163g0186o.105448.cm.88660.png

i 240s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5339g0049o.171150.cm.80799.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5447g0277o.221521.cm.115317.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5504g0259o.251004.cm.137108.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5576g0471o.280585.cm.160011.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5576g0644o.280758.cm.160127.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5738g0094o.353113.cm.225669.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5777g0055o.372427.cm.243999.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5804g0087o.384586.cm.256174.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i240o5804g0518o.385017.cm.256529.png

i 32s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i32o5248g0138o.138220.cm.49100.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i32o5250g0271o.139657.cm.50250.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i32o5258g0196o.144831.cm.55640.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i32o5282g0197o.152058.cm.63203.png

i 45s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i45o5351g0157o.176929.cm.84410.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i45o5577g0393o.281273.cm.160392.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i45o5577g0468o.281348.cm.160483.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i45o5722g0116o.345929.cm.218855.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i45o5724g0179o.347078.cm.219719.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/i45o5791g0240o.378336.cm.249626.png

z 20s (weird camera testing images, but in my copy of the database anyway)

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z20c5799g0011o.382220.cm.253876.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z20c5799g0019o.382228.cm.253891.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z20c5799g0021o.382230.cm.253894.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z20c5799g0022o.382231.cm.253896.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z20c5799g0024o.382233.cm.253898.png

z 240s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5241g0210o.135249.cm.44215.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5250g0501o.139891.cm.50064.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5304g0069o.158595.cm.74014.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5322g0296o.161478.cm.76125.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5481g0035o.238522.cm.129026.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5712g0054o.342671.cm.215619.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5775g0529o.371779.cm.243286.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5799g0368o.382561.cm.254137.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z240o5854g0333o.410066.cm.305806.png

z 30s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30o5255g0359o.143120.cm.53426.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30o5255g0708o.143449.cm.53703.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30o5547g0060o.265953.cm.151473.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30o5636g0193o.311238.cm.184607.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30o5694g0088o.335318.cm.209156.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30o5814g0164o.390120.cm.263874.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30o5814g0462o.390418.cm.264048.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/z30o5863g0046o.415289.cm.310066.png

y 240s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5017g0027o.84780.cm.110333.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5257g0465o.144514.cm.55228.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5403g0196o.197245.cm.99477.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5430g0291o.211036.cm.108534.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5434g0124o.213464.cm.110158.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5669g0231o.325836.cm.195069.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5755g0508o.361274.cm.233356.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5800g0085o.382688.cm.254424.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5800g0087o.382690.cm.254435.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y240o5837g0053o.402142.cm.283056.png

y 30s

http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y30o5267g0535o.147178.cm.57349.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y30o5557g0130o.268377.cm.153126.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y30o5646g0111o.316495.cm.187830.png http://faun.rc.fas.harvard.edu/eschlafly/faintbiasfigs/y30o5701g0033o.338773.cm.212208.png