Wei Zhu（祝伟）
I'm now an Assistant Professor in the Department of Astronomy at Tsinghua University in Beijing.
Isolated Black Hole from Astrometric Microlensing(?)
Wei Zhu (祝伟)
Tsinghua Astro Student Seminar
2022 March 4
Outline
-
Microlensing detecting dark objects
- Opportunity & challenges
-
OGLE-2011-BLG-0462
- The first dark object from astrometric microlensing?
- Summary
微引力透镜 (Gravitational microlensing)
Einstein (1936); Paczynski (1986); Mao & Paczynski (1991)
\(t_{\rm E} \sim 30{\rm days} \left(\frac{M_{\rm L}}{M_\odot}\right)^{1/2} \)
\( t_q \sim 40{\rm min} \left(\frac{q}{10^{-6}}\right)^{1/2} \left( \frac{t_{\rm E}}{30 \rm days}\right) \)
背景恒星亮度
背景恒星
”透镜“星体
\( t_{\rm E} \)
\( t_q \)
First microlensing BH candidate?
(see also Bennett+2002, Agol+2002)
OGLE-1999-BUL-32: \( t_{\rm E} = 640 \) days
\( t_{\rm E} = \frac{\theta_{\rm E}}{\mu_{\rm rel}} \approx f(M_{\rm L}, D_{\rm L}, \mu_{\rm rel}) \)
A statistical approach
Nature of microlenses
Microlensing toward the bulge:
White dwarf (WD): 17%
Neutron star (NS): 3%
Black hole (BH): 1%
(see also Gould 2000)
How can we tell BH lenses from normal lenses?
$$ M_{\rm L} \propto \frac{\theta_{\rm E}}{\pi_{\rm E}} $$
Microlensing parallax
Figures from Sahu et al. (2022, left) and Wyrzykowski et al. (2016, right)
Microlensing parallax: an observable more sensitive to mass
Image credit: Bill Saxton, NRAO/AUI/NSF
- Parallax (absolute): \( \pi \equiv \frac{\rm au}{d} \)
- Microlensing parallax: $$ \pi_{\rm E} \equiv \frac{\pi}{\theta_{\rm E}} \approx f(M_{\rm L}, D_{\rm L})$$
Parallax effect in BH event
Typical BH events have
- long timescales (\(t_{\rm E} \gtrsim 100 \) d);
- small parallaxes (\(\pi_{\rm E} \lesssim 0.05\));
- usually undetectable (Karolinski & Zhu 2020; Ma, Zhu, & Yang, 2022).
\(\theta_{\rm E}\) from Astrometric microlensing
Animations credit to: B. Scott Gaudi (see also Dominik & Sahu 2000)
Photometric
Animations credit to: B. Scott Gaudi (see also Dominik & Sahu 2000)
Photometric
Astrometric (source frame)
Astrometric (lens frame)
\( \delta_{\rm max} (u=\sqrt{2}) = \frac{\sqrt{2}}{4} \theta_{\rm E} \approx 0.35 \theta_{\rm E} \)
\(\theta_{\rm E}\) from Astrometric microlensing
Previous attempts
(see also Lu+16, Kains+17)
Previous attempts
(see also Lu+16, Kains+17)
Astrometric microlensing detecting dark object
Precise astrometry on
- Long timescale events
- Bright & isolated source star
Constraints on
- Angular Einstein radius \(\theta_{\rm E}\)
- Relative proper motion
Take-home message
Long-timescale event, OGLE-2011-BLG-0462, was caused by a dark object, probably an isolated stellar-mass black hole, based on HST astrometric microlensing and ground-based photometry.
The key difference came from photometric microlensing signal (\(\pi_{\rm E}\)), not astrometric microlensing signal (\(\theta_{\rm E}\)).
OGLE-2011-BLG-0462 (OB110462)
Light curve plot from Sahu et al. (2022)
\( A_{\rm max}=372.62 \)
\( t_{\rm E}=231.56\) days
First HST observation
Imaging (OGLE vs. HST)
2'
8"
2"
HST observations
WFC3 F606W & F814W filters.
Additional observations obtained in Lam et al.
HST astrometric analysis
- Reference frame
- Gaia frame
- Bias correction due to nearby star (~0.4 mas)
- Reconstructed PSF vs. injection-recovery exercise
- Astrometric color offset
Astrometric signal (Sahu et al.)
F606W
F814W
Angular Einstein radius \( \theta_{\rm E} = 5.18 \pm 0.51 \) mas
Astrometric signal (Lam et al.)
F606W
F814W
Angular Einstein radius \( \theta_{\rm E} = 4.0 \pm 1.1 \) mas
Astrometric microlensing
Angular Einstein radius
\( \theta_{\rm E} = 5.18 \pm 0.51 \) mas (Sahu et al.)
\( \theta_{\rm E} = 4.0 \pm 1.1 \) mas (Lam et al.)
Figure from Sahu et al. (2022)
Photometric microlensing
Microlensing parallax
\( \pi_{\rm E}=0.089 \pm0.014 \) (Sahu et al.)
\( \pi_{\rm E} = 0.13 \pm0.01 \) or \( 0.24 \pm 0.05\) (Lam et al.)
Mass determination
| Sahu et al. | Lam et al. | |
| Angular Einstein radius (mas) | 5.18+-0.51 | 4.0+-1.1 |
| Microlensing parallax | 0.089+-0.014 | 0.13+-0.01 or 0.24+-0.05 |
| Lens mass (M_sun) | 7.1+-1.3 | [1.6, 4.5] |
| Lens distance (kpc) | 1.58+-0.18 | [0.9, 1.5] |
\( M_{\rm L} = 1.2 M_\odot \left( \frac{\theta_{\rm E}}{\rm mas} \right) \left( \frac{\pi_{\rm E}}{0.1} \right)^{-1} \)
Summary
-
Microlensing detecting dark objects
- Opportunity: unique in detecting isolated dark objects
- Challenge: direct mass determination (via parallax & Einstein radius)
-
OGLE-2011-BLG-0462: The first dark object from astrometric microlensing
- HST astrometric microlensing yielding Einstein radius
- Ambiguity in microlensing parallax
Back-up slides
BH detection from astrometric microlensing
By Wei Zhu（祝伟）
BH detection from astrometric microlensing
A talk on the recent discovery of an isolated stellar-mass BH (or NS?) from the HST astrometric microlensing
