Cosmological Measurements from Large-Separation Gravitational Lens J1004+4112

Jack Steiner

June 9 2004

Abstract

At a redshift of 1.734 with angular separation greater than 14", J1004+4112 is more than twice as large as any other gravitationally lensed quasar discovered to date (Inada et al. 2003). Observations show that the lensing object is a galaxy cluster at a redshift of roughly z=.68 (Oguri et al. 2003). By astrometrically calibrating the field, this project calculates the lensing mass from astrometric measurements through going deep on this target in I to a limiting magnitude of roughly 21, this project measures the light from the brightest lensing galaxy. This allows  constraints to be placed on the mass-to-light ratio (M/L) for the lensing object.

    Mass to light ratios serve a very important role in current cosmology. Gravitational lenses provide an especially useful means of probing this measurement by 'revealing' the gravitational potential of the lensing object. Lenses have been a popular source of study since they were first discovered by Walsh, Carswell, and Weymann (1979).

    Visible lenses are most often quasars, because of their brightness, and have been used to study such cosmological properties as the geometry of space and stellar evolution. By better understanding M/L, we are able to better understand galaxy formation, cluster formation, including evolution of M/L, dark matter and morphology. J1004+4112 is the largest known quasar lens with a maximum angular separation of 14.62", breaking the previous record of 6.97" separation held by RX J0921+4529 (Munoz et al. 2001). 
 
    This discovery is so important that its existence will provide previously unavailable means of probing dark mater halos, which have so far only been measured with weak gravitational lensing.  Though it is important to note that other unconfirmed candidates do exist for large-separation lenses, this object is the first confirmed discovery.  Its existence and properties are supportive of cold dark matter (CDM) models and is consistent with the 'standard model' of cosmology (Wambsganss 2003).  Many exciting new investigations will likely surround this object in the next several years, this study being one of the first.
   
    By measuring angular separation between lensed images and the lensing object's I magnitude, constraints can be placed on M/L. According to the group that has studied it: Oguri et al. and Inada et al. of the Sloan Digital Sky Survey (SDSS), there will be a very large dark matter mass and correspondingly high M/L in order to create such a large separation between lensed images.

    J1004+4112 was observed using the 10 inch Great Ohio Telescope (GOT) on the nights of 2004 May 16 and 2004 May 22. Conditions on the night of May 16 were not photometric; it was warm and very humid, with persistent problems including the lens of the telescope fogging up. The CCD temperature was -14^oC, and foggy weather conditions worsened from night to morning. During an effort to remove condensation from the telescope during the first exposure taken on J1004+4112, an error was encountered which stopped the exposure prematurely at 411s.  Another 5 x 600s exposures in I were taken  between 11:00 and 12:30 local time with an additional 4 x 600s darks, 7 flats in I (3 in evening sky, 4 in morning), and 22 zeros.

    On May 22, the night was much warmer than expected, only allowing the CCD to cool to -7^oC.  The high operating temperature we worked at caused problems finding objects throughout the night and guiding was problematic.  The night was mostly clear, but some thin clouds were present; it was not photometric. Fogging of the lens was not persistently a problem this night, though several inspections were necessary. Before data was taken, the telescope was re-collimated.  6 x 600s exposures in I were taken between 11:00 and 12:30 local time.  5 morning flats and 4 evening flats were taken in I with some minor fogging on the telescope lens during the morning flats.  4 x 600 s darks and 20 zeros were taken.  Clouds were observed around sunrise, but there were no noticeable signs of clouds having been present otherwise at the end of the night.
 

    Basic reductions were done in a standard way using IRAF. For both nights, the zero frames were combined, the dark frames combined, and a zero-corrected combined dark frame was made. This zero-corrected combined dark frame was scaled by exposure time and used to correct the flat frames and the shortened exposure from the first night. These frames were also zero-corrected. The rest of the object frames were corrected using only the combined dark frame. From here, all object frames were flat-field-corrected. For both nights, it was found that the morning flats fit better with the data. This is likely because the camera was dismounted between evening flats and actual data, so the alignment is off for evening flats, but correct for morning flats. In fact, a rotation is clearly visible between morning and evening flats.  It was also necessary to throw out one of morning flats from each night due to what was likely a lighting bug in the first night and an anomalous pattern in the second.

    _{3.2  Combining Images and Astrometric Calibration}

    Registration of the images was also done using IRAF routine 'xreg'.  By directly inspecting the fields, 10 objects over a large span of the field were selected as reference points for registration (see Figure 2).  IRAF routine 'xreg' was used to then register the images for both nights separately.  The images were then combined into one composite image per night.  Below is a 'zoomed-in' view of the fully composite image of J1004+4112.

    In order to combine the two composite images and have an astrometrically calibrated field, it was necessary to fit world coordinate system (WCS) data to the composite images.  In order to do this, the United States Naval Observatory (USNO) database was used to provided a list of coordinates for objects in the field of view. By matching USNO coordinates to the stars used for registration, a fit was obtained with IRAF routine 'ccmap' for each composite field.  Fits using 'ccmap' for each night were accurate to within 0.2".

    In order to combine the two nights' composite images, registration based on WCS was required.  Using IRAF's 'wreg', the second night's composite image was registered with respect to the first night. This automatically rotated and shifted the second night's field to match the first night.  The fields were then added together to get a fully composite image without significantly sacrificing quality: a full-width-half-maximum (FWHM)  between 5 and 7 pixels was measured using 'imexamine' for stars in the combined image which is the same range measured for stars in any single frame of data. 

    Finally, in order to do photometric analysis of the field, it is necessary to have corrected for sky brightness.  To correct for this, the sky was assumed to be uniformly bright across the field.  This uniform sky background was calculated from 4 x ~10,000 pixel source free regions around J1004+4112.  This background was then subtracted from the composite image.  Below is a picture of the composite field with labels on the objects used for astrometric calibration.

    In order to do the astrometric measurements, data from other studies were used, including Digitized Sky Survey (DSS) images and data from Oguri et al. (2004) as guides for centroid-fitting. Using the IRAF process 'imcentroid,' which fits centroids within a boxed-in region, a range of centroid fits were obtained for A,B,C,and G (identified in Figure 1).   The only problem in doing this was that the proximity of A and B prevented limited the ability to isolate one from the other for centroid fitting, and also prohibited large-scales altogether for the centroid-fitting.

    One problem encountered in this was that error estimates for 'imcentroid' routine were not explained. In order to get an estimate of these errors, the centroid fits were run through the routing 'phot', described below, which has its own centering algorithm. The shifts that phot made to the 'imcentroid' fits were used as an estimate of systematic error. Total error estimates used both the systematic errors from 'phot', and treated the 'imcentroid' errors as statistical errors. Largely, the systematic errors were dominant.

    _{3.3  Photometry}

    Photometry was analyzed using the IRAF routine 'phot'. Several complications were present during this stage of reduction. One was that no photometric calibrations were performed due to weather problems, which prevented using accurately calibrated star magnitudes for this procedure. The faintness of G, the central galaxy, gave rise to several challenges because using large aperture sizes (>9 pixels in radius) leads to dominant systematic errors due to small error in background measurement.

    This combined with the closeness of the lenses to each other and the lensing galaxy required choosing small aperture values for the photometric analysis. I decided to use an aperture size of no greater than 8 pixels radially, corresponding to a statistically reasonable area of ≤~200 pixels. Within 8 pixel radial apertures, field stars were found to have more than 80% of their light. The FWHM of the images was determined to be ~6 pixels using 'imexamine'. Using this as a lower limit, and 8 as the upper limit, aperture sizes of 6, 7, and 8 were chosen for the photometric analysis.  Net errors were primarily statistical, given by 'phot' for each object.  The figure below shows the apertures used on J1004+4112.

  

Figure 3. This is an image showing the three apertures used in photometric analysis of the magnitude differences between C,G, and treating A and B together.  The scale for this image is 54" x 38".

Object	RA	DEC	Error in Position (arcsecs)	Distance from G (arcsec)	Error in Distance from G (arcsec)	Distance from G' (arcsec)	Error in Distance from G' (arcsec)
A	10 04 34.8264	+41 12 39.5642	0.441	8.626	0.782	5.618	0.441
B	10 04 35.0184	+41 12 42.9120	0.361	9.923	0.740	6.791	0.361
C	10 04 33.7992	+41 12 35.3160	1.050	9.120	1.54	10.224	1.050
G	10 04 34.1400	+41 12 43.4160	0.646	-	-	3.181	0.646
G'	10 04 34.4175	+41 12 42.7860	-	3.181	0.646	-	-

These positions give a corresponding largest angular separation of 15.717" ± 1.110" between B and C. 
    

     _{4.2 Lensing Mass}

   
    In order to apply the model that will be described in this section, some approximations and assumptions must be made. For this study, H₀=70 is assumed. The universe is approximated as flat (eq 1.) and Euclidean geometry is applied, neglecting space curvature (eq 2.). This study ignores K-correction in measured magnitudes and assumes proper distance is interchangeable with angular diameter distance and luminosity distance. However, based on the quality of data that is being analyzed and the goals of this study, these approximations are reasonable to obtain general conclusions about M/L.
 

Images Used	Mass Calculated centered at G (1013 M0)	Error  (1013 M0)	Mass Calculated centered at G'  (1013 M0)	Error  (1013 M0)
A and B	5.7203	0.6716	2.5495	0.2993
A and C	5.2570	1.0097	3.8383	0.7372
B and C	6.0478	1.1189	4.6403	0.8585
Weighted Result	5.6703	0.5674	2.9122	0.6991

 

    This project concludes that the lensing object cannot be a single lensing galaxy alone; the brightest galaxy must be part of a massive cluster.  It is only such a massive cluster that could be responsible for this wide-separation lens.  This is consistent with the discussion in Inada et al. (2003) of velocity dispersion models for large-angle lensing requiring ~600km s^-1.   This speed is consistent with a galaxy group or cluster of galaxies and not consistent with a single galaxy.  Though the model used in this study is limited in scope, the general conclusion is that M/L is large (>100).  This large M/L ratio is consistent with CDM theory and also with many of the findings of Oguri et al. (2004) and Inada et al. (2003). 

    Assuming H₀=70,  Oguri et al. (2004) identify a total cluster mass of ~1.43 x 10¹⁴ M₀ over a 30" radius.  Only some of this total mass is within the lensing region, but still constituting a significant size (~7" radius) and in the most dense portion of the cluster.  Their total mass is on the same order as the lensing mass calculated in this study, which supports this study's conclusions.  This study's measurements of angular separation and position in close agreement close with those of Oguri et al. (2004) with all objects but B falling well within 2σ.  This large error in B is likely due to problems fitting a centroid to B because of the space limitations with A close-by, and similarly A's error is larger than C and G because of spacial constraints for centroid fitting.  This study measures the largest angular separation from B to C as 15.717" ± 1.110", Oguri et al. (2004) find the largest separation from B to C to be 14.62", within 1σ of this study's results.  Below is a table comparing astrometric results for this study and Oguri et al. (2004).

Object	Oguri et al. (2004) : RA	Oguri et al.: DEC	This Study : RA	This Study : DEC	Agreement (σ)
A	10 04 34.794	+41 12 39.29	10 04 34.8264	+41 12 39.5642	1.27
B	10 04 34.910	+41 12 42.79	10 04 35.0184	+41 12 42.9120	4.49
C	10 04 33.823	+41 12 34.82	10 04 33.7992	+41 12 35.3160	0.61
D	10 04 34.056	+41 12 48.95	-	-	-
G	10 04 34.170	+41 12 43.66	10 04 34.1400	+41 12 43.4160	0.79
G'	10 04 34.418	+41 12 42.79	-	-	-

 

  The flux ratio results from Inada et al. (2003) are C/AB = 0.27 ± 0.04  and C/D = 1.84 ± 0.02.  This paper's numbers do not match these as nicely, but are still about 2σ for error range.  This study's numbers are in similarly reasonable agreement with model predictions given in Inada et al. (2003) corresponding to C/AB=0.24 and C/D=1.95.    These numbers are summarized in the table below.

Objects Compared	Inada et al. (2003) : Flux Ratio	This Study : Flux Ratio	Model from Inada et al. (2003)
C/AB	0.27	0.36±0.07	0.24
C/D	1.84	> 2.02	1.95

Though the results from this study seem to suggest either steady conditions or small scale variations between the time of the study by Inada et al. (2003) and this study, more likely the small discrepancies reflect error from photometric limitations due to the small distance scale between objects and the large PSF of the GOT.  This paper does not conclude that there are not time-variations, merely that the data from this study are not sufficient to draw significant conclusions.  It is recommended that further investigation into possible flux variation is carried out.  It is important to note that models from Oguri et al. (2004) predict a range of flux variation time intervals from as short as weeks to as long as several years.  Future studies involving a more powerful telescope may want to look at small time-intervals of weeks over the course of a year or two to look for variations in (especially A and B) flux ratios in order to constrain H₀ (Oguri et al. 2004).  In essence, the best conclusions to be drawn from the photometric analysis is a confirmation of the general results found by Inada et al. (2003); anything beyond this would be invalid.


6. Acknowledgments

    Thanks to all of my classmates for their help throughout this project including Steven Diehl, Tomomi Watanabe, Swati Gupta, Manasvita Joshi, Zach Heinen, and Justin Finke.  Thanks to Dr. Statler for being patient and keeping his door open, Rocco Samuele for his patience and help, and to Mangala Sharma for always lending a hand to any of us who needed it, and to Dan Hoy for some statistics help and encouragement.   And thanks to George Eberts for generously letting us use his home for our projects.  Thanks to Christina Barr for her editing suggestions.